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Microwave investigation of partial and hydrogen bonded molecular complexes

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MICROWAVE INVESTIGATION OF PARTIAL AND HYDROGEN BONDED
MOLECULAR COMPLEXES
A THESIS SUBMITTED TO THE FACULTY OF THE GRADUATE SCHOOL OF
THE UNIVERSITY OF MINNESOTA BY
Denise L. Fiacco
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
Dr. Kenneth R. Leopold. Adviser
June 2001
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C Denise L. Fiacco
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U N IV E R SIT Y OF M IN N E S O T A
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Denise L. Fiacco
and have found that it is complete and satisfactory in all respects,
and that any and all revisions required by the final
examining committee have been made.
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R..
1<L_____
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Table o f Contents
Acknowledgements. Page vii.
Introduction. Pages viii-xii.
C hapter 1. Quadrupole Coupling Constants for "SO ,: Microwave Measurements for Ar"SO; and Ab Initio Results for the "SO? Monomer. Pages 1-10.
C hapter 2. Structure. Bonding, and Dipole Moment of (CH;hN-SO’,. A Microwave
Study. Pages 1 1-40.
Appendix to Chapter 2. Pages 41-43.
C hapter 3. Dipole Moments of Partially Bound Lewis Acid-Base Adducts. Pages 44-78.
Appendix to Chapter 3. Pages 79-90.
C hapter 4. Structural Change at the Onset of Microsolvation: Rotational Spectroscopy of
HCN •• HCN-SCh. Pages 91-105.
Appendix to Chapter 4. Pages 106-116.
C hapter 5. Microwave Investigation o f Sulfuric Acid Monohydrate. Pages 117-146.
Appendix to Chapter 5. Pages 147-151.
C hapter 6 . Microwave and Ab Initio Investigation o f H:0-BF',: Spectrum. Structure, and
Internal Dynamics. Pages 152-180.
Appendix to Chapter 6 . Pages 181-210.
C hapter 7. Partially Bonded Systems as Sensitive Probes of Microsolvation: Rotational
Spectrum and Structure o f HCN- • HCN-BF?. Pages 211-236.
i
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A p p e n d ix to C h ap ter 7. Pages 237-239.
Appendix A. Unassigned Microwave Transitions Dependent of H(D):0 and H(D);SO.i.
Pages 240-245.
Appendix B. Syntheses. Pages 246-249.
I.
(CHO j 'N . Page 246.
Ii.
i5\'H ;. Page 247.
HI.
HCCCN. Page 248.
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List o f Figures
Page
Figure 1.1. A portion o f the J = 4
3 transition o f Ar-"SO-,.
4
Figure 2.1. The J = 3
2 transition o f (CH 3b l4N- 'S O , showing several
hyperfine components due to the l4N nucleus.
Figure 2.2. A portion of the J=2«-l transition of (CH-,)’, l4N-''SO', taken at an
applied electric field of 18.59 V cm.
Figure 2.3. The structure of trimethylamine-sulfur trioxide in the gas phase.
25
Figure 2.4. Stereoscopic view along x of (CH’,hN-SCh
32
Figure 2.5. Stereoscopic view along x of (CH’,):HN-SO'.
32
Figure 2.6. Stereoscopic view along x of CH-,H;N-SO-,
33
Figure 2.7. Stereoscopic view along x of H-.N-SO-,
33
Figure 3.1. The J = 2<—1 transition of CH-.CN-SO-, taken at 1.55 V cm.
48
Figure 3.2. (a) Calculated dipole moments for SO-.. BF-,. and BH-, vs. cos
( 7t-a). where a is the obtuse angle formed from the S-O. B-F. or B-H bonds
and the C-. axis of the molecule, (b) A(ij,s,(A) from BLW calculations vs.
cos(Jt-a).
Figure 3.3. (a) Induced dipole moment as a function o f S -0 bond length for
complexes of SO',, (b) Induced dipole moment as a function of B-F bond
length for complexes o f BF-„
Figure 3.4. Electron density difference plots for (a) HCN-SCh. polarization
(b) HCN-SO-,. charge transfer, (c) (CPLbN-SO?. polarization, (d) (CH-,bNSO-„ charge transfer, (e) (CH',bN-BF?. polarization. (f> (CHihN-BF;, charge
transfer.
Figure 4.1. The 7 <— 6 transition of HCI4N - HCl4N-"2SO’,.
58
Figure 4.2. Definition o f angles used to describe the structure of HCN •• HCNSO-,.
Figure 5.1. J = 2 ,;<— 1,, Transition of H: S 0 4-H;0 .
Is
Figure 5.2. 1()I<—O00 Transitions of two isotopomers o f O substituted
H;S 0 4.
Figure 5.3. Thirteen o f the nineteen fitted parameters for H^SO^H^O.
17
22
60
66
95
97
122
136
135
Figure 5.4. Parameters used to define the position o f the water unit within
the H:S 0 4-H:0 complex.
Figure 5.5. Parameters obtained from the Fitted Structure o f H: S 0 4-H;0 .
136
Figure 5.6. Structural changes within the sulfuric acid unit upon
complexation with water.
141
iii
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141
List o f Figures continued.
Figure 6.1. F = 2.5 <—1.5 component o f central J = 1 <—0 transition of
H: lhO-n BF-.
Figure 6.2. Stick spectra representing hvperfine-free linecenters for
isotopomers of H;0-BF;,
Figure 6.3. Stark spectrum of central J=l<—0 transition of H ;lf,0 - ‘ 1BF',
157
Figure 6.4. The counterpoise corrected structure o f H;0-BF-, at the
MP2 aug-YTZ level o f theory basis set.
Figure 6.5. Two-fold transition state for the H ;0 wag in H:0-BF-,.
170
15S
164
172
Figure 6 .6 . Transition state for the H ;0 wag coupled with rotation about
the B-0 bond.
Figure 6.7. Structural Parameters included in the rotational constant fits for
H:0-BF,.
Figure 7.1. Gas phase structure of HCN-BF-,.
172
214
Figure 7.2. Solid phase structure of HCN-BF-,.
215
Figure 7.3. J = 7 <■— 6 Transition of HCIJN - H C 'V !BF-,
218
Figure 7.4. Definition of aneles used to describe the structure of HCN •• HCNBF-,.
Figure 7.5. Fitted Structural Parameters o f HCN ■• FfCN-BF-,.
225
Figure 7.6. Electron difference density (EDD) map for HCN-BF-, complex.
231
Figure 7.7. Electron difference density (EDD) map for HCN •• HCN-BF;;
complex.
232
175
226
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List o f Tables
Table
Table 1.1. Assigned Transitions of Ar-~ SO;,
Page(s
5
Table 1.2. Spectroscopic Constants of Ar-'^SO;
5
Table 2.1. Observed Transitions of (CH',);UN -':SO;
18-19
Table 2.2. Observed Transitions of (C ^ b ^ N -^ S O ;
19-20
Table 2.3. Observ ed Transitions of (C H -.b^-^'SO ;
20
Table 2.4. Observed Transitions of ,?N Containing Derivatives of (CHOiN-SO’,.
Table 2.5. Spectroscopic Constants for (CH-,);,N-SO',.
21
21
Table 2.6. Comparison of(CH ’,)',N-SO', and H',N-SO',.
25
Table 2.7. Selected Solid Phase Structural Parameters for the H;.n(CH',)nN-SO-,
Systems.
Table 2. A l. Observed Transitions o H C H ^^N -S O ’, at Non-zero Electric Field.
Table 3.1. Summary o f Stark Effect Measurements.
31
41-43
49
Table 3.2. Dipole Moment Data for Selected Lewis Acid-Base Complexes.
53
Table 3.3. Structural Parameters of Lewis acid-base adducts.
54
Table 3.4. Computed Dipole Moments Using BLW-ED Approach.
55
Table 3.5. Computed Induced Dipole Moments (D) (BLW-ED).
56
Table 3.6. Charge Transfer in Lewis Acid-Base Adducts.
64
Table 3.7. Comparison of Calculated and Experimental Dipole Moments.
69
Table 3.A1. Assigned Stark Transitions for HCl?N-SOy
79-80
Table 3.A2. Assigned Stark Transitions for CH 3CN-SO 3
81-82
T able 3.A.3. Assigned StarkTransitions for HCl'N -llBF 3.
83-84
Table 3.A4. Assigned StarkTransitions for A state o f H;,I''N - 1IBF;.
85
Table 3.A5. Assigned Stark Transitions for E state o f H?I'N - IIBF;„
86
Table 3.A6. Assigned StarkTransitions for (CH 3)3I‘N -IIBF;,
87-90
Table 4.1. Spectroscopic Constants of H C N ;- HCN1-SO 3.
96
Table 4.2. Structural Parameters for HCN - HCN-SO3.
98
Table 4.3. Comparison of Structural and Electronic Properties for HCN •• HCNSO 3 and Related Complexes.
Table 4.4. Induced Dipole Components at the HF/aug-cc-pVDZ Level Using
BLW-ED.
99
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102
List o f T a b le s continued.
Table 4.A1. Observed Transitions for Istopomers of HCN-- HCN-SO3.
106-110
Table 4.A2. Stark Assignments for HCl5N-HCl5N-SO?.
111-116
Table 5.1. Additional a-type spectra for Istopomers of H ;S 0j-H ;0.
123
Table 5.2. Spectroscopic Constants for Isotopomers of H^SOi-HTD.
129-130
Table 5.3. Fitted vs. Calculated Structural Parameters for H;S 04 -H; 0 .
139
Table 5.4. Residuals of the Fitted Rotational Constants for PLSO^-I-TO.
140
Table 5.A1. Transition Frequencies for Isotopomers of PLSO^-fTO.
147-151
Table 6.1. Hyperfine-free linecenters for Isotopomers of H:0-BF;,.
159
Table 6.2. Spectroscopic Constants of Isotopomers of f-TO-BF;; from Starred 162
Transitions in Figure 6.2.
Table 6.3. Measured Effective Dipole Moments of H :0-BF’. Isotopomers.
164
Table 6.4. Fitted Spectroscopic Constants for Isotopomers of H:0-BF? from
both m assignments according to eq. (3).
Table 6.5. Minimum Energy Structures of H:0-BF;, and H :0 and BF-,
monomers
Table 6 .6 . Summary of Rotational Constant Fits for HiO-BFi.
167
Table 6.A1. Transition Frequencies for All H20-BF3 Isotopomers.
181-190
Table 6.A2. Stark Transitions for H;0-BF;, Isotopomers.
190-200
Table 6 .A3. Fit of Observed Transitions of Isotopomers of PLO-BF;, to eq.
13) of Chapter 6 .
Table 7.1. Transitions for l?N substituted isotopomers of HCN - HCN-BF;,.
200-210
219-223
Table 7.2. Spectroscopic Constants for Isotopomers of HCNr •• HCN:-BF?.
Table 73. Structural Parameters for HCN-HCN-BF;,.
223
226
169
176
Table 7.4. Structural and Electronic Properties for HCN - HCN-BF3 and
227
Related Complexes.
Table 7.5. Structural and Electronic Changes for Complexes with the General 228
Formula HCN-• HCN-Y.
Table 7.6. Results of BLW-ED calculations for HCN-BF3 and HCN-- HCN230
BF; using the 6-3 IG(2df.2pd) basis set.
Table 7.A1. Transitions for Isotopomers of HCN •• HCN-BF3 with Three
237-239
Quadupolar Nuclei.
VI
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Acknowledgements
The person who I would like to thank first is Jefferson Bjoraker who has been the most
important part of my life since the beginning o f my graduate career. He has always been
available for scientific debate, always encouraging and endlessly creative. I owe a lot of
my success to his belief and confidence in me. The second person I would like to thank is
my advisor. Ken Leopold. Ken has consistently believed in my abilities (even when I had
serious doubts) and has always treated me as a colleague more than a student. Ken has
sharpened my skills as a scientist and a researcher, and has taught me to continually
question myself as well as my results. He is a dedicated and conscientious scientist and I
am fortunate to have worked with him. I would also like to thank my co-workers,
especially Sherri Hunt, with whom I shared countless hours at the spectrometer. We
shared both good and challenging times, and matured considerably in the process. Matt
Craddock also deserves a special acknowledgement, for as co-workers and roommates,
we spent many hours in each other's company. Matt is a caring and trustworthy person
who has always been there as a listening and tolerant ear. I thank him for being a true
friend. Lastly. I would like to thank my Mom who has been as close to me over the phone
as she could have been from next door. 1 also thank my Dad for being proud o f me and
for always providing the laughter.
vii
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Introduction
A detailed understanding of molecular structure and bonding is central to almost
all aspects of chemistry. Indeed, chemical structure is one o f the earliest topics taught in
introductory chemistry courses worldwide. Beginning chemists are taught simple rules
for predicting the shapes and symmetries o f molecules, all o f which are founded within
simple valence bond theory and or the more comprehensive molecular orbital theory. [ 1]
This approach has vast utility, for most chemically bound systems, one can often readily
predict ground state geometries and bond orders by the application of several
fundamental notions. In this picture, chemical bonds can typically be described as
belonging to a distinct class, for example, electrostatic, covalent, or metallic. Another set
of compounds, which are described as "weakly bound" exhibit a type o f bonding that is
characterized by van der Waals forces. There is a unique group of compounds, however,
whose bonding interaction resists classification: in these compounds the bonding is best
described as an admixture of electrostatic, covalent, and van der Waals effects. These
systems were first described by Lewis [2] who introduced the concept o f electron pair
donor-acceptor (Lewis acid-base) complexes. Jonas et al. describe the difference between
donor-acceptor complexes and covalent bonds by their dissociation behavior, the former
dissociate into two closed shell fragments while the rupture o f a covalent bond produces
only open shell entities. [3] A second important difference with donor-acceptor (dative)
bonds is that interatomic distances are dependent on the state of aggregation. [4] Because
of their unique bonding interaction and their sensitivity to phase, these systems have been
coined "partially bound".
The structure and bonding o f numerous adducts o f the Lewis acids BF; and SO?
with bases containing nitrogen as the donor o f an electron pair have been investigated
over the past decade. [4.5] The results indicate a decreasing dative bond distance with
increasing basicity of the electron pair donor, as well as a greater degree of distortion
from planarity of the Lewis acid with shorter dative bond distances. This is perhaps not
surprising considering that a stronger Lewis base is defined as a “better" donor of an
electron pair, but what is of interest are the various contributions to the bonding
interaction. For example, what portion of the interaction is due to electrostatics and what
viii
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portion to electron pair sharing or to transfer o f an electron pair into an unoccupied
orbital on the acid? Can a set o f rules be defined that generalize the contributions to the
bonding interaction for a series of partially bonded complexes? These questions were
examined in detail by Jonas et al. in a theoretical study of a total of 18 Lewis acid-base
complexes of BH;. BF5. A1CI;„ and SO;. [3] The authors conclude that the degree of
charge transfer in Lewis-acid base complexes is not correlated to the strength of the
bonding interaction. In fact, the authors point out that '“neither the degree o f covalencv
nor the electrostatic interactions alone determine the strength o f the donor-acceptor
bond".
A related aspect o f partially bonded systems is the sensitivity of the geometry to
environment, evidenced by large changes in structure between the gas and solid phase.
The most striking example is HCN-BF-,. where the N-B bond distance contracts by
0.835A between the gas and crystalline phases. [6.7] Smaller yet significant differences
are noted in numerous partially bonded complexes and imply a hypersensitivity of the
dative bond to intermolecular interactions. Phase dependent structure necessarily implies
that intermolecular interactions in the crystal provide enough o f a perturbation on
intramolecular bonds to result in measurable structural changes. This situation is unique
to systems that have not realized the lull potential o f their bonding interaction in the gas
phase. The obvious question here concerns the physical mechanism underlying this bond
contraction.
Several authors have speculated on a cooperative effect in which the formation of
the bond increases the stabilization of the crystal via enhanced dipolar interactions. [4.8]
A h in itio
SCRF calculations have indeed reproduced the contraction o f the N'-B bond in
HCN-BF-. concomitant with a rapid rise in the dipole moment that "saturates" with a
dieletric constant o f 10. [9] Dielectric continuum models, however, begin with a fully
assembled “medium” and suffer from the lack o f molecular detail necessary to interpret
the degree of change associated with first, second, and third near neighbor interactions.
Perhaps a more interesting question is whether the entire lattice is necessary to observe
these effects or can they be initiated by x near neighbors? Furthermore, how big is x?
This question has been addressed in several theoretical studies o f higher order assemblies
ix
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of partially bonded complexes. For example. Jonas et. al. have calculated the structures
with the formula (FhN-BF^h and have demonstrated that 60% of the total bond
contraction has taken place at x = 4. [3] Using an identical approach. Cabaleiro-Lago and
Rios demonstrate that most of the contraction o f the N-B bond in HCN-BF? is accounted
for at x = 2 . [ 10]
Sharing some similarities to partial bonding, hydrogen bonding is perhaps best
described as mainly an electrostatic interaction with a small degree of covalency mixed
in. Hydrogen bonding is arguably one o f the most important non-chemical types of
bonding interactions in nature: responsible for the unique properties of water as well as
securing DNA in a double helical configuration. Hydrogen bonding occurs when a
hydrogen atom is bonded to a more electronegative atom and hence acquires a partial
positive charge. This partially positive hydrogen atom is weakly to moderately attracted
to regions of excess electron density, such as the lone pair on oxygen or nitrogen. The
strength of a hydrogen bond is on the order o f 2-10 kcal mol. which is clearly weaker
than any ordinary chemical bond, but more similar in magnitude to binding energies for
partially bonded molecules (typically on the order o f 5-50 kcaLmoi). Since Pauling's
initial prediction that hydrogen bonds in water acquire some of their bonding character
from the stronger covalent bonds in the H ;0 molecule. [11] there has been some debate
over what portion, if any. of a typical hydrogen bond is better described as covalent.
Pauling's prediction was recently confirmed, when direct evidence for covalencv in
hydrogen bonds was obtained in Compton scattering experiments on the hydrogen bonds
in ice I/,. [12] The results are in quantitative agreement with a recent density functional
model for ice b, [13] and provide the first direct experimental evidence for a significant
covalent component to hydrogen bonding.
The work described in this thesis is mainly aimed at investigating the nature o f the
these unique types of bonds; in with an emphasis on the electronic and geometrical
details of complexes that are best described as quasi- or “partially"’ bound. The electric
dipole moments of these systems are analyzed and compared in detail, as are the changes
in bonding that accompany microsolvation. The thesis opens with a measure o f the
excursion angle in A r-^SO j. a measurement that is complicated by the low isotopic
x
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abundance of 'JS in nature (x°o). This measurement provides a benchmark for other
complexes involving SO j and allows for its utility in other complexes involved a weakly
or partially bound SO? unit. The second chapter highlights the experimental study o f the
(CH.3);N-SO; complex, which is nearly fully bound in the gas phase. The structure of this
and the related NH3-SO3 complex are discussed at length and compared to crystal phase
data. The third chapter provides a comprehensive study o f the dipole moments of
partially bonded systems and uses the BLW-ED method to decompose the contributions
to the large induced moments arising from distortion, charge transfer, and polarization
effects. The calculated degree of charge transfer is compared to that determined from
experimentally measured quadrupole coupling constants. Both Chapters 4 and 7 provide
the first studies of microsolvation effects in partially bonded molecules and investigate
the change in bonding arising from the addition o f a single near neighbor to a partially
bonded complex. In Chapter 6 . the 1:1 adduct between H :0 and BF; is presented as an
example of oxygen as the donor of an electron pair. Hydrogen bonding is touched upon in
Chapters 4 and 7 but discussed in detail in Chapter 5. where the complex formed between
H;SOj and H ;0 is presented, providing an example o f the shortest gas phase hydrogen
bond measured to date.
xi
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References:
1. See for example. Ebbing. D.D. General Chemistry, Houghton Mifflin Co.: Boston.
1990.
2.
Lewis. G.N. Valence and the Structure o f Atoms and Molecules', The Chemical
Catalog Co.. Inc.: New York. 1923.
3. Jonas. V.; Frenking. G.; Reetz. M.T. J. Am. Chem. Soc. 1994. 116. 8741.
4. Leopold. K.R. In Advances in Molecular Structure Research: Hargittai. M.. Hargittai.
I.. Eds.: JAI Press: Greenwich. CT. 1996; Vol2. p. 103 and references therein.
5. Leopold. K.R.: Canagaratna. M.: Phillips. J.A. Acc. Chem. Res. 1997. 30. 57.
b. Reeve. S.W.: Bums. W.A.: Lovas. F.J.: Suenram. R.D.: Leopold, K.R. J. Phys. Chem.
1993. 9~. 10630.
7. Bums. W.A.: Leopold, K.R. J. Am. Chem. Soc. 1993. 115. 11622.
8. Oh. J.J.: LaBarge. M.S.; Matos. J.: Kampf. J.W.; Hillig. II. K.W.; Kuczkowski. R.L. J.
Am. Chem. Soc. 1991. 113. 4732.
9. Jiao. H.: Schlever. P. von R. J. Am. Chem. Soc. 1994. 116. 7429.
10. Cabaleiro-Lago. E.M.; Rios. M.A. Chem. Phys. Lett. 1998. 294. 272.
II. Pauling. L. J. Am. Chem. Soc. 1935. 57. 2680.
12. Isaacs. E.D.; Shukla. A.; Platzman. P.M. ; Hamann, D.R.; Barbiellini. B.: Tulk. C.A.
J. Phys. Chem. Solids 2000. 61. 403.
13. Hamann. D. R. Phys. Rev. B 1997. 55. 157.
XII
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Chapter 1.
Quadrupole Coupling Constants for 33S0 3 : Microwave Measurements
for Ar-33S 03 and Ab Initio Results for the 33S(>3 Monomer
D.L. Fiacco1, B. Kirchner’" W.A. Bums1-3, and K.R. Leopold' ' 1
1 Department o f Chemistry, University of Minnesota, 207 Pleasant St., SE.
Minneapolis, MN 55455.
2 Institut fur Physikalische Chemie der Universitat Basel, Klingelbergstr. 80, CH4056, Basel.
J Present Address: Department of Chemistry, Arkansas State University, P.O. Box
419 State University, AR 72467.
Reproduced with permission: Fiacco, D.L.; Kirchner, B.; Bums, W.A.; Leopold, K.R J.
Mol. Spec. 1998.191,389-391. Copyright © 1998 by Academic Press.
1
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Complexes of SO3 have been the subject o f a number of microwave spectroscopic
investigations [1-7]. Early studies involved weakly bound species with Ax [I], N; [1], and
Kr [2 ], while more recent publications have examined the "partially bonded" complexes
formed with NH3 [3] and HiO [4], Consistent with the strong Lewis acidity of SO3, the
binding partners in all cases approach the SO3 along its C3 axis, giving rise to a three-fold
symmetric arrangement of the heavy atoms within the complex.
One quantity which has been particularly difficult to determine in these systems has been the
amplitude o f the zero point angular oscillations o f the SO3 unit within the complex. In
weakly bound species with hyperfine structure, such information can often be obtained from
the observ ed reduction in quadrupole coupling constants of the complex relative to their
known values in the free monomer. In particular, if the electric field gradient at the
quadrupolar nucleus is unperturbed by the intermolecular interaction, the observed coupling
constants are given by the tensor projections o f the free-molecule values onto the inertial
axes of the complex. For a symmetric top with the coupling nucleus on-axis, this gives rise
to the well known formula
(eQq)complcx — (cQq)monomer<‘3cOS”0 - l > / 2
(I)
where the brackets denote averaging over vibrations. For symmetric species containing an
MX 3 unit, 0 is the instantaneous angle between the C3 axis of the MX3 and the equilibrium
C;, axis of the complex. Clearly, knowledge of the angular vibrational amplitudes comes in
the form of <cos20> once (eQq)comp!ex and (eQqjmononwr are known.
In this note, we address the problem of estimating the vibrational amplitude o f SO3 in the
prototypical weakly bound system Ar-S0 3 . To date, the absence of nuclear spin in the
common isotopes of sulfur (32S and WS) has precluded this possibility for any SO3containing species. Thus, we first present a microwave spectroscopic determination o f the
2
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3jS quadrupole coupling constant in Ar-3jSC>3. Moreover, since SO3 is non-polar, only a
very weak centrifugally-induced microwave spectrum can be detected [8], and the value of
the JJS coupling constant has not been determined experimentally. Thus, we also report
accurate quantum chemical calculations o f the quadrupole coupling constant in the 3jS03
monomer. The results are then combined in equation (1) to determine a value for <cos20>,
which in turn should provide a reasonable benchmark for estimating the SO3 vibrational
amplitude in other weakly bound systems as well.
Spectra were obtained using a pulsed nozzle Fourier transform microwave spectrometer [9]
the details of which have been described elsewhere [6,10]. AX-SO3 was prepared by passing
pure argon over solid polymerized SO3 at 0 °C prior to expansion through a 0.8 mm nozzle
at a stagnation pressure of 2 atm. Spectra of the 33S complex were observed in natural
abundance (0.76%) and were readily located using the known rotational constants o f the j2S
and j4S species [1]. A sample spectrum is shown in Figure 1.1.
Table 1.1 lists the transitions observed in this study. The data were readily fit to the usual
energy level expression for a symmetric rotor with a single quadrupolar nucleus [ 11], viz.,
v = 2B(J+1) - 4Dj(J+1)3 + AEquad
(2)
where B and Dj are the rotational and centrifugal distortion constants, respectively, and
AEQuad is the difference in quadrupole hyperfine energies between the upper and lower states
of the transition. The usual first order expression for EQuad [11] was sufficient to reproduce
the observed hyperfine structure to within the experimental uncertainties. The residuals from
a fit to equation 2 are also listed in Table 1.1 and the spectroscopic constants obtained are
given in Table 1.2.
3
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
To obtain an accurate quadrupole coupling constant for free SO 3, the concept of "high local
quality" [12] was applied. Briefly, a large basis set is utilized on the atom o f interest, while
neighboring atoms are treated with smaller basis sets. This idea was developed 15 years ago
GJ
s
>>
U
53
U
|
u
<
A,
11550.5
aJ I A
11551.1
11551.7
Frequency (MHz)
Figure 1.1. A portion of the J = 4 <— 3 transition of Ar-33S0 3 . This spectrum was observed
in natural abundance and is the average signal accumulated in 1200 gas pulses, with 10 free
induction decays recorded per pulse. The observed splittings in the labeled peaks are due to
the Doppler effect. The unlabeled peaks are due to ringing o f the microwave cavity, not
molecular transitions. This ringing was present in all observed spectra since the signals
recorded in this work were weak.
4
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 1.1. Assigned Transitions of Ar-33S 0 3 (a’
T il
p ti(b )
1
1
1.5
2.5
1.5
3.5
1.5
0.5
2.5
3.5
2.5
1.5
4.5
1.5
2.5
3.5
4.5
J
1
->
2
"i
2
">
2
2
j
j
j
j
3
y
F
Frequencylcd|
(Obs-Calc)d
2
2
2.5
3.5
1.5
3.5
2.5
1.5
3.5
4.5
2.5
1.5
4.5
2.5
3.5
4.5
5.5
5776.313
5776.313
5779.043
8660.053
8662.920
8662.920
8663.869
8663.869
8665.660
8666.749
11547.325
11550.712
11550.712
11551.155
11551.155
-0.001
-0.001
-0.004
0.006
-0.003
-0.004
-0.001
-0.001
0.005
0.004
-0.008
2
3
j
3
3
3
3
3
4
4
4
4
4
0 . 0 0 0
0.001
0 .0 0 0
-0.001
(a) All transitions correspond to K=0. (b) F = I + J. (c) Frequencies are accurate to 5 kHz.
(d) All frequencies in MHz.
Table 1.2. Spectroscopic Constants of Ar-33SC>3
Constant
B (MHz)
Dj (kHz)
eQq(MHz)
(a) Uncertainties are one standard error in the fit.
Value13’
1444.03544(54)
4.859(21)
-15.292(12)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
by Huber [12] and later used successfully under the name "locally dense basis sets" by
Chesnut and Moore [13] for the calculation of chemical shifts. Since that time several
groups have shown that the use of such "unbalanced" basis sets produces excellent results
[14], Detailed arguments have been given in a review [15].
A (20sl5p4d2f)/[12s9p4d2f] basis for sulfur was constructed in previous work [16] and
applied here to S 0 3 in ab initio calculations including electron correlation. The SO 3 was
held at the planar structure determined by microwave spectroscopy [8], with an OSO angle
of 120° and the S- 0 bond length held fixed at the estimated equilibrium value o f 1.4175 A.
The electric field gradient was transformed using the 3jS quadrupole moment o f -67.8 x 10'
Jl m: [17] to give the coupling constant, and the resulting value o f (eQq)m0nom« was found to
be -17.43 MHz. At the vibrationally averaged bond length o f 1.4198 A [8 ], the value
obtained was -17.14 MHz.
Previous calculations of j3S coupling constants have reproduced the experimental values for
approximately twenty molecules with an rms deviation o f about 1 MHz [16], leading us to
assume an error of similar size here. The differences between observed and calculated
values are partially due to limited quantum chemical accuracy, and partially to the neglect of
vibrational averaging. The dependence o f the coupling constant on structure is quite small,
however, as seen from the above results at re and r0.
The value of the quadrupole coupling constant for 33SC>3 obtained in this work is
significantly different from that of -24.85 MHz previously reported by Palmer [18]. The
difference can be understood by consideration of the related compound 33SC>2 and the size of
the basis sets used in similar calculations. For 33SOa, the component of the quadrupole
coupling tensor along the b-inertial axis o f the molecule is 32.72 MHz in Palmer's work
[18], 26.94 MHz with the present method [16], and 25.71 ± 0.03 MHz experimentally [19].
In this case, Palmer's basis set had a size of 67 functions while the present one has 113
6
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functions. For SO3 the sizes are even more different, with 63 functions for the correlated
level contained in Palmer's reduced basis and 133 functions applied here. The concept of
high local quality, and the specially optimized 33S basis set, further improve the present
result. A smaller part of the deviation from Palmer's work arises from the use of a slightly
different S-0 bond length o f 1.4082 A. Our calculation at this structure gives -18.20 MHz.
The experimental quadrupole coupling constant in Ar-JJS03 , when combined in equation (1)
with the theoretically derived monomer value (at r0) yields <cos:0> = 0.928(+0.037/-0.033).
This corresponds to a value of "9" = cos'l(<cos20>1') equal to 15.6° (+3.3°/-4.8°), which is
a very reasonable result. If the bending vibration is treated as harmonic, the mean squared
angular displacement from equilibrium is given as [20 ]
<(9-0e)‘>" = h‘/Ibbkb
(3)
where kb is the force constant for the bending vibration, Ibb is the moment of inertia o f the
oscillating subunit, and 9C is the equilibrium value of 9 (zero for Ar-SC>3). Since (0-0e) has
only a weak (fourth root) dependence on kb, it is common to find that in a series of
complexes with the same binding partner, the common entity exhibits a nearly constant
angular excursion amplitude. In Ar-BF3 [21], OC-BF3 [21], HCI-BF3 [22], HF-BF3 [10], and
HCN-BF3 [23], for example, the angular oscillation amplitudes of the BF3 are 15°, 13.7°,
15.7°. 13.6°, and 13.1°, respectively. That the 15.6° determined above for Ar-S 03 is so close
to these values is expected since the B rotational constants of BF3 [24] and SO3 [8,25] are
very similar (10343 ± 15 MHz and 10449.0667 ± 0.0023 MHz for “ BFs and 32S 0 3,
respectively). In light of these results, we further expect that the bending amplitude of the
SO3 moiety determined here for Ar-SC>3 should provide a reasonable estimate (to within a
few degrees) of that in other weakly bound complexes of SO3.
7
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Acknowledgement
Work at the University of Minnesota was supported by the National Science Foundation.
The theoretical investigation is part of the project 20-052264.97 of the Schweizerischer
Nationalfonds zur Forderung der Wissenschaften. We are also grateful to Prof. Hanspeter
Huber for valuable advice and discussion.
8
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References
1.
K.H. Bowen, K.R. Leopold, K.V. Chance, and W. Klemperer, J. Chem. Phys., 73,
137(1980).
2.
K.R. Leopold, K.H. Bowen, and W. Klemperer, J. Chem. Phys. 7 4 ,4211 (1981).
3.
(a) M. Canagaratna, J.A. Phillips, H. Goodfriend and K.R. Leopold J. Am. Chem.
Soc 118, 5290 (1996). (b) M. Canagaratna, M.E. Ott, and K.R. Leopold Chem.
Phys. Lett 281,63(1997).
4.
J.A. Phillips, M. Canagaratna, H. Goodfriend, and K.R. Leopold, J. Phys. Chem. 99,
501 (1995).
5.
W.A. Bums, Ph.D. Thesis, University of Minnesota, (1996).
6.
J.A. Phillips, Ph.D. Thesis, University of Minnesota (1996).
7.
M. Canagaratna, Ph.D. Thesis, University o f Minnesota (1997).
8.
V. Meyer, D.H. Sutter, and H. Dreizler, Z. Naturforsch 46a, 710( 1991).
9.
T.J. Balle and W.H. Flygare, Rev. Sci. Instrum. 52, 33 (1981).
10.
J.A. Phillips, M. Canagaratna, H. Goodfriend, A. Grushow, J. Almlof, and K.R.
Leopold, / Am. Chem. Soc. 117, 12549 (1995).
11.
W. Gordv and R.L. Cook, Microwave Molecular Spectra; John Wiley and Sons:
New York (1984).
12.
H. Huber, J. Chem. Phys. 83, 4591 (1985).
13.
D.B. Chesnut and K.D. Moore, J. Comp. Chem. 10, 648 (1989).
14.
See, for example, D.B. Chesnut and E.F.C. Byrd Chem. Phys. 213, 153 (1996), and
references therein.
15.
H. Huber. Z Naturforsch. 49a, 103 (1994).
16.
B. Kirchner, H. Huber, G. Steinebrunner, H. Dreizler, J.-U. Grabow, and I. Merke,
Z Naturforsch. 52a, 297 (1997).
17.
P. Pyykko and J. Li, Report HUKI 1-92, Helsinki (1992).
18.
M.H. Palmer, Z. Naturforsch, 47a, 203 (1992).
19.
G.R. Bird and C.H. Townes, Phys. Rev. 94, 1203 (1954).
9
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
20.
(a) M.R. Keenan, L.W. Buxton, E J. Campbell, A.C. Legon, and W.H. Flygare, J.
Chem. Phys. 74, 2133 (1981). (b) S.E. Novick, J. Mol. Spectrosc. 118, 550 (1986).
21.
(a) K.C. Janda, L.S. Bernstein, J.M. Steed, S.E. Novick, and W. Klemperer, J. Am.
Chem. Soc 100, 8074 (1978). (b) Values of 0 are calculated from the original data of
reference [21 a] using the subsequently measured value o f eQq(MBF3) = 3.002(13)
MHz: (b) H. Dreizler, Z. Naturforsch. 47a, 342 (1992). (c) K. Vormann,
Dissertation, Kiel (1991).
22.
J.M. LoBue, J.K. Rice, T.A. Blake, and S.E. Novick, J. Chem. Phys. 85, 4216
(1986).
23.
S.W. Reeve, W.A. Bums, F.J. Lovas, R.D. Suenram, and K.R. Leopold, J. Phys.
Chem. 97. 10630(1993).
24.
S.G.W. Ginn, J.K. Kenney, and J. Overend, J. Chem. Phys. 48. 1571 (1968).
25.
A. Kaldor and A.G. Maki, J. Mol. Struct. 15, 123 (1973).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Chapter 2.
Structure, Bonding, and Dipole Moment of (CH 3)3N-SC>3. A Microwave
Study
D.L. Fiacco, A. Toro\ and K.R. Leopold*
Department of Chemistry, University of Minnesota
207 Pleasant St. SE, Minneapolis, MN 55455
(a)
Present Address: Department of Chemistry, Rutgers, The State University of New
Jersey. 610 Taylor Road, Piscataway, NJ 08855-0939.
Reproduced with permission from: Fiacco, D.L: Toro, A.; Leopold, K.R. Inorg Chem.
2000,3 9 ,37-43. Copyright © 2000 American Chemical Society.
11
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A bstract
Six isotopic derivatives of the complex (CHahN-SOj have been studied in the gas phase by
microwave spectroscopy. The N-S bond length is 1.912(20) A and the NSO angle is
100.1(2)°. The dipole moment, determined from Stark effect measurements, is 7.1110(69)
D. representing an enhancement o f 6.5 D over the sum of the dipole moments of the free
monomers. Analysis of the l4N nuclear hyperfme structure indicates that about 0.6 electrons
are transferred from the nitrogen to the SO3 upon formation o f the complex. Comparison
between the gas phase structure and that previously determined for the adduct in the solid
state reveals small but significant differences, indicating that the formation o f the dative
bond is slightly less advanced in the gas. Gas phase and solid state structural data are
compared for several related amine-SCb systems.
12
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Introduction
Recently in our laboratory we have been concerned with the structure and bonding of
electron pair donor - acceptor complexes, primarily involving BF3 and SO3. [1,2] Using
microwave spectroscopy, [3-9] and in some cases X-ray diffraction, [10,11] we have
investigated a series of adducts of these acids with nitrogen, [3-6,10] oxygen, [7] and
halogen [8,9] donors. We have found that by suitable choice of the acid-base pair, the nature
o f the dative bond in the gas phase can be adjusted in a near-continuous manner between
that of a van der Waals interaction and that of a fully developed chemical bond. Moreover,
we observe that adducts whose dative linkage lies in the intermediate regime between
bonded and non-bonded interactions display extraordinary changes in structure upon
crystallization. Indeed, bond length differences as much as 0.84 A have been observed
between the gas phase and the solid state. [ 10]
.Among the systems we have investigated is the gas phase zwitterion of sulfamic acid f H3NSO 3'). [5] Prior to our work, the solid state structure of this compound had been well
characterized by X-ray and neutron diffraction techniques [12-14] but several ab initio
studies had been unable to reproduce the observed solid state structure. [15,16] In 1992,
Wong, Wiberg, and Frisch [17] applied the Self Consistent Reaction Field (SCRF) model
and showed the zwitterion undergoes significant changes in structure and bonding when
placed in a dielectric continuum. The implication was that the disparity between the
experimental and theoretical results did not arise from computational deficiency but rather,
resulted from the real influence of the crystalline environment on the nature of the
zwitterion. The structure determined from microwave spectroscopy [5a] turned out to be in
excellent agreement with the computational results and demonstrated that the N-S bond
length indeed contracts by 0.186(23) A upon crystallization.
The complex (C ^bN -S C h is another classic example o f a Lewis acid-base adduct, and its
comparison with the analogous complex o f ammonia should be of fundamental interest with
regard to the nature o f the dative bond in the gas phase. Several previous studies o f this
13
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system have been reported, including X-ray diffraction, [18] matrix isolation, [19] and
solution phase kinetic and thermochemical [20,21] measurements. However, the microwave
spectrum and gas phase structure have not been investigated. In this paper, therefore, we
present a microwave study of (CHsbN-SOj in the gas phase. In addition to elucidating the
molecular structure, aspects of electronic structure are also determined from measurement of
the molecular dipole moment and 14N nuclear hyperfme interactions. The results are
compared with those previously reported for H3N-SO3, and the observed gas-to-solid
structure changes for both compounds are discussed in the context of their known crystal
structures.
Experimental
Rotational spectra of six isotopomers o f (Cfy^N-SCb were obtained using a Balle-Flygare
type pulsed-nozzle Fourier transform microwave spectrometer, [22] the details o f which
have been described elsewhere. [8,23] Briefly, it consists of a cylindrical Fabry-Perot cavity
composed of two circular aluminum mirrors (84 cm radius of curvature) housed in a
chamber evacuated with a 20" diffusion pump. Molecules produced in a supersonic
expansion enter the cavity traveling perpendicular to its axis, and a 1.5-1.7 (is radiation
pulse creates a coherent excitation o f the molecular sample. The subsequent free induction
decay is heterodyne detected and the resulting signal digitized and Fourier transformed to
produce a frequency domain spectrum. The range o f the instrument is 3-18 GHz, with a
resolution of approximately 3 kHz.
Since trimethylamine (TMA) and SO 3 react in the bulk to form solid TMA-SO 3, a co­
injection source similar to that employed elsewhere [24-27] was utilized in this study. Argon
at a backing pressure o f approximately 2 atm was flowed over a solid sample of
polymerized SO 3 maintained at 0 °C. The resulting Ar/SC>3 mixture was pulsed at a rate of 6
Hz through a 0.8 mm diameter nozzle orifice. Pure TMA at a pressure o f approximately
0.06 atm was continuously injected into the expansion through a 0.012" I.D. stainless steel
needle. The needle was inserted into the expansion 0.2" below the nozzle orifice and was
14
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
bent at a 90° angle to achieve directed flow along the expansion axis. Nine free induction
decays of the molecular polarization, each containing 256 data points, were collected per gas
pulse, and the time domain signals were averaged over a minimum o f 270 gas pulses. An
airlock, which is employed on our system for facile removal o f the nozzle from the vacuum
chamber, was particularly important in the present study due to frequent clogging of the
needle by solid TMA-SO3.
For the determination of the molecular dipole moment, a pair o f parallel 30x40 cm
aluminum plates straddle the cavity to provide a uniform electric field which is
perpendicular to both the cavity axis and the supersonic expansion. Equal and opposite dc
voltages were applied to each plate to reduce the effect o f fringing fields. The distance
between the plates was calibrated as previously described [5b] by measuring the first order
Stark shift on the J = 4<—3, K=±3 transition of Ar-SCb, for which the dipole moment has
been previously determined (0.2676=0.0003 D). [28] Although this procedure employs a
secondary standard in favor of the more conventional OCS primary standard, the first order
Stark effect permits the measurement o f larger Stark shifts and hence a slightly more
accurate value for the inter-plate spacing. In order to eliminate possible effects due to the
accumulation of diffusion pump oil on the plate surfaces, [5b,29] calibrated plate distances
were obtained both before and after the collection of experimental data. Data were admitted
for analysis only upon agreement of the pre- and post- collection values.
Initial spectral searches were guided by an estimation of the rotational constant of TMA-SO3
obtained from the known gas phase structures o f both TMA and SO3 monomers [30,31] and
estimates of the N-S bond length in the complex. The spectral peaks due to the TMA-SO3
complex were identified by their dependence on both TMA and SO 3 as well as the
characteristic hyperfme splittings due to the l4N nucleus. Further confirmation of their
identity was obtained by the close agreement between the observed and predicted rotational
spectra for the 15N and
containing species. The l5N/32S and 14N/3jS isotopomers were
observed in natural abundance. For the 15N/34S and I5N/33S derivatives, 15N-trimethylamine
15
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
was synthesized according to literature procedures. [32] (CH3)3HI5N~Cf was prepared from
the reaction of I5NH 4C 1 (99.5 atom %, Icon Services) and paraformaldehyde (Aldrich) and
the free amine released by reaction with NaOH.
Results
The observed frequencies for the J = l«-0, 2 « -l, 3<—2, and 4<—3 transitions o f the parent
isotopomer are listed in Table 2.1. Tables 2.2-2.4 list the observed frequencies for the :,4S,
” S, and l:>N containing species. The spectra were characteristic of a semi-rigid symmetric
rotor with no evidence of internal rotation. A representative spectrum is shown in Figure
2 . 1.
Analysis of the spectra was carried out using standard methods. The frequencies for each
isotopomer were fit to the usual expression [33] for a symmetric top with one or two
quadrupolar nuclei, as appropriate, viz.
v = 2(J"+1)[B-DjkK2] - 4Dj(J"+1)3 + AEq
(1)
Here, AEq is the difference in hyperfine energies between the upper and lower states and
was adequately calculated via the usual first order treatment for the l4N and j3S containing
species. The other symbols have their usual meanings. [33] Least squares fits o f the
observed spectral frequencies were carried for each o f the isotopomers investigated, and the
fitted spectroscopic constants are given in Table 2.5. The value o f Djk in equation (1) was
found to be vanishingly small and was constrained to zero in the final fits.
16
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Z)
c
>
U%
«u
9800
9800.5
9801
9801.5
Frequency (MHz)
Figure 2.1. The J = 3 <— 2 transition of (C H sb’^N-^SOj showing several hyperfme
components due to the l4N nucleus. The total signal collection time for this spectrum was
16 s.
17
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 2.1. Observed Transitions of (CH 3>3,4N-32S0 3 a
J"
F"
K
J'
F
Frequency11(MHz)
(obs.-calc.) (MHz)
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
1
1
1
2
0
0
0
0
0
1
1
0
1
0
1
1
0
1
0
0
2
2
1
1
I
2
2
2
2
2
2
2
2
2
2
2
2
3
3
3
1
2
0
2
1
2
2
2
1
3
j
1
1
1
1
3
2
3
-0.002
-0.002
0.001
-0.004
-0.002
-0.002
-0.002
-0.002
-0.002
-0.002
1
I
0
0
0
1
1
2
2
2
2
1
0
0
3
0
I
0
I
0
J
j
3
3
3
3
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
3
2
3266.565
3267.024
3267.715
6533.431
6533.509
6533.509
6533.738
6533.892
6533.892
6533.925
6533.987
6534.121
6534.200
6534.471
6534.659
9800.336
9800.455
9800.455
9800.486
9800.731
9800.760
9800.835
9800.847
9800.869
9800.869
9800.942
9800.942
9800.942
9801.213
9801.249
9801.517
13067.242
13067.409
13067.717
13067.717
13067.756
13067.756
13067.769
2
2
2
2
2
*\
j
3
j
j
3
j
3
0
1
2
1
1
2
2
->
2
0
1
3
2
2
j
2
1
j
3
1
3
j
-*
j
I
2
2
4
J
T
j
3
2
4
3
4
4
2
4
3
2
2
2
2
4
4
3
4
4
3
5
0 .0 0 0
-0.002
-0 .0 0 0
0.003
-0 .0 0 0
-0.002
0.008
0.008
-0.002
-0.003
0.007
0.005
-0.001
-0.002
0.001
0.003
0.003
0.003
0 .0 0 0
-0.002
-0.002
-0.001
0 .0 0 0
-0.003
0.002
0.003
0 .0 0 0
0.004
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 2.1. continued.
J"
3
3
3
J
J
J
J
3
J
3
3
(a) F
F"
K
J’
F
Frequencyb (MHz)
4
4
13067.774
1
5
2
4
4
5
13067.813
4
4
3
3
13067.813
2
2
4
3
13067.861
2
4
3
3
13067.861
4
3
4
5
13067.861
2
4
4
3
13067.861
2
3
4
3
13068.042
4
4
4
j
13068.042
4
j
1
3
13068.272
J
0
4
3
13068.409
= I(N) + J. (b) Estimated uncertainty in measured frequencies
(obs.-calc.) (MHz)
-0.002
0.004
-0.004
-0.002
-0.002
-0.003
-0.002
0.002
-0.004
-0.0 0 1
0.000
is ±3 kHz.
Table 2.2. Observed Transitions of (C H s^ N -^S O j*
J"
F"
K.
2
0
1
2
2
0
0
1
1
0
1
0
0
1
1
0
2
2
3
2
1
2
3
3
1
1
1
0
0
0
1
1
0
1
2
1
1
3
2
2
j,
F
Frequency15(MHz)
(obs.-calc.) (MHz)
2
2
2
2
2
2
3
2
2
2
2
2
1
2
2
2
1
3
J
3
1
1
2
3
3
3
2
3
4
4
2
6500.595
6500.671
6500.671
6500.902
6501.054
6501.054
9751.076
6501.086
6501.153
6501.634
6501.823
9751.191
9751.191
9751.220
9751.472
9751.499
9751.574
9751.589
9751.610
9751.610
0.000
-0.001
-0.001
0.000
-0.002
-0.002
-0.001
-0.003
0.004
0.002
-0.001
0.004
0.004
-0.008
-0.003
0.005
0.003
0.000
-0.002
0.001
3
3
3
j
3
3
3
3
3
19
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 2.2. continued.
J"
F"
K
J'
F
Frequency13(MHz)
(obs.-calc.) (MHz)
2
2
2
2
2
2
3
3
->
j
1
2
2
2
2
2
2
1
0
3
3
3
3
3
3
4
3
2
2
2
2
9751.682
9751.682
9751.682
9751.958
9751.982
9752.262
0.002
0.002
0.002
0.004
-0.011
0.001
(a)
F = I(N) + J. (b) Estimated uncertainty in measured frequencies is ±3 kHz.
Table 2J . Observed Transitions of (CH3)3UN-33SQ3a
J"
F,"
F"
K
J’
F,'
F
Frequency13(MHz) (obs.-calc.) (MHz)
2
2
2
2
2
2
2
2
3.5
1.5
1.5
2.5
0.5
2.5
2.5
3.5
3.5
3.5
3.5
0.5
3.5
0.5
3.5
3.5
2.5
2.5
2.5
4.5
2.5
1.5
2.5
0.5
3.5
2.5
3.5
4.5
2.5
4.5
0.5
3.5
1.5
4.5
2.5
2.5
3.5
1.5
0
0
1
I
0
1
0
0
I
0
0
1
1
1
1
1
1
1
I
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3.5
2.5
2.5
3.5
1.5
3.5
3.5
4.5
4.5
4.5
4.5
1.5
4.5
1.5
4.5
4.5
2.5
2.5
2.5
4.5
3.5
2.5
3.5
0.5
4.5
3.5
4.5
4.5
3.5
5.5
1.5
4.5
2.5
5.5
3.5
2.5
3.5
1.5
9771.213
9775.018
9775.054
9775.105
9775.214
9775.260
9776.047
9776.130
9776.154
9776.154
9776.180
9776.220
9776.355
9776.474
9776.496
9776.517
9776.891
9776.976
9777.008
2
2
2
2
2
2
2
2
2
2
-0.001
0.006
0.000
0.002
-0.002
-0.007
-0.001
-0.001
0.004
0.009
0.002
-0.014
0.000
0.010
0.002
0.011
-0.004
-0.004
-0.011
(a) Fi=I(S)+J; F=Ft+I(N). (b) Estimated uncertainty in measured frequencies is ±3 kHz.
20
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 2.4. Observed Transitions of lsN Containing Derivatives o f (CH3)3N-SC)3ib
Isotopomer
J"
(CH 3)3I5N- 32S 0 3
0
1
2
F"
J
(CH 3)3i5N-34S03
0
1
2
3
(CH 3)3i5N- 33S 0 3
I
1
I
1
2
2
2
2
?
2
2
2
2
2
2
0.5
2.5
1.5
2.5
1.5
0.5
1.5
1.5
3.5
3.5
3.5
3.5
3.5
2.5
1.5
K
J’
0
0
0
0
1
2
3
4
3256.199
6512.390
9768.577
13024.753
0
0
0
0
1
2
3
4
3239.617
6479.234
9718.841
12958.437
-0.002
0
0
0
1
0
0
2
2
0
0
1
2
2
0
0
2
2
2
2
6495.626
6496.053
6496.053
6496.823
9742.452
9742.452
9743.438
9743.438
9743.670
9743.747
9743.965
9744.840
9744.840
9745.963
9747.365
-0.004
0.001
0.001
-0.001
0.001
0.001
0.003
0.003
0.001
-0.004
0.003
3
3
3
3
3
3
3
3
■n
J
3
3
F
Freq. (MHz) (0-C)(MHz)
0.5
3.5
2.5
3.5
2.5
1.5
2.5
1.5
4.5
3.5
4.5
4.5
3.5
2.5
1.5
0 .0 0 0
-0.003
-0.002
0.003
0 .0 0 0
0 .0 0 0
0 .0 0 0
0 .0 0 0
0 .0 0 0
-0.001
-0.004
(a) Estimated uncertainty in measured frequencies is ±3 kHz. (b) F=I(S)+J.
Table 2.5. Spectroscopic Constants for (CHsfoN-SCV
Isotopomer
B(MHz)
Dj(MHz)
eQq(l4N)(MHz)
eQq(33S)(MHz)
1633.4749(1)
-1.5303(34)
0.177(12)
(CH3)3i'vN-3:S 0 3
1628.0999(5)
0.188(13)
(CH 3)315N - 32S 0 3
-1.5352(44)
1625.2657(2)
0.215(63)
(CH 3 )314N - 34S 0 3
0.1579(77)
1619.8097(5)
(CH 3 )3 i5N - 34S 0 3
1629.3243(3)
0.18b
-1.513(15)
-19.673(25)
(CH 3)315N - 33S 0 3
1623.9087(3)
0.161(35)
-19.672(14)
tCH-ibl5N - 33SO '
(a) Uncertainties are one standard error in the least squares fits, (b) Held fixed in fit.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Three sets of Stark shifted transitions were investigated, corresponding to the J = 1 <—0 and
2
i, K = 0,±1 of the parent species. A detailed list containing 74 observed Stark-
hyperftne components at electric field strengths from 0.42 to 37.01 V/cm is included as an
Appendix to this chapter. Both parallel (AMp=0) and perpendicular (AMf= =1) components
were observed, corresponding to either a parallel or perpendicular orientation of the
oscillating microwave field with respect to the applied electric field. The low intensity as
well as the large first order Stark shifts of the K=±l components limited the applicable field
strengths to less than 10 V/cm. Greater field strengths were utilized in the examination of
the K=0 components, which are susceptible only to a much weaker second order Stark
effect, and hence smaller Stark shifts. A sample spectrum, taken at 18.59 V/cm, is shown in
Figure 2.2.
>>
VS
e
V
C
>>
u
a
u
6533
6534
Frequency (MHz)
Figure 2.2. A portion of the J=2<—1 transition of (CH3)31+N-j2S03 taken at an applied
electric field of 18.59 V/cm. Signal collection time for this spectrum was 25 s.
22
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The Stark-hyperfine energies were calculated in the intermediate field regime using a
IJ,K,I,M[,Mj,Mf> basis as previously described. [33,5b] A non-linear least squares fit of
the observed frequencies was performed with 6 , Dj, and eQq constrained to their values
determined at zero electric field. This fit yielded the ratio of the molecular dipole moment to
the effective inter-plate spacing from which the molecular dipole moment was calculated
using the AJ-SO3 calibration results. The dipole moment of the complex was determined to
be 7.1110(69)D.
Structure Analysis
The observation of a symmetric top spectrum as well as the results o f the isotopic
substitution experiments confirm the expected geometry in which the nitrogen lone pair is
directed toward the sulfur along the C3 axis of the SO3. Preliminary analysis o f the observed
rotational constants indicated an N-S distance of approximately 1.90 A, a value which is
slightly larger than the 1.844(2) A distance observed in solid TM A-SO3 [18] but
significantly shorter than the 2.9 A distance expected for a nitrogen-sulfur van der Waals
interaction. [5a] Thus, the structure analysis was performed using standard methods
appropriate for valence bonded systems. [33]
With only six rotational constants to be analyzed, a full determination o f all atomic
coordinates in the complex is not possible. However, several reasonable constraints can be
applied which allow the chemically interesting structural features o f the system to be
obtained. In particular, we note that the TMA unit does not change significantly upon
formation of the solid adduct. For example, the N-C bond length and CNC angle reported in
crystalline TMA-SO3 [18] differ from those in gas phase TMA [30] by only 0.045 A and
1.8 °, respectively. Similarly, we find an expansion o f the S-O bond length o f only 0.0148 A
between gaseous SO3 [31] and the crystalline complex. These changes are small and suggest
that the neither the structure of the TMA unit nor the S -0 bond length need be re­
determined from the present data. The dimensionality of the problem can thus be reduced to
23
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an acceptable level by constraining the structure of the TMA and the S-0 bond distance
while still retaining the N-S bond length and NSO bond angle as determinable parameters.
The nitrogen-sulfur bond length, R, and the NOS bond angle, a, were obtained from least
square fits to the observed rotational constants with the remaining bond lengths and bond
angles constrained as described above. Since the choice o f crystallographic vs. freemonomer values for the constrained parameters introduces the primary source of uncertainty
into R and oc, two fits were performed. The first employed the TMA structure and SO bond
distance observed in solid TMA-SO 3, and resulted in values o f R and a o f 1.892 A and
99.86 °. respectively. The second used the gas phase monomer values for the constrained
parameters and resulted in R and a values o f 1.932 A and 100.32°, respectively.
It is clear that regardless of the choice of the S-0 bond length or TMA structural parameters,
the fitted N-S distance and NSO angle lie between those o f a hypothetical van der Waals
complex and those observed in the crystal. Correspondingly, we expect that the remaining
structural parameters of the complex will lie between those of the free monomers and those
observed in the solid. Thus, the results o f the two fits provide a reasonable window within
which the true structural parameters of the gas phase species are likely to lie. [34] The
preferred values of R and a , therefore, are taken as the average of two fits, with the
uncertainties chosen to encompass both determinations. These results are given in Table 2.6,
and the structure of the complex is shown in Figure 2.3. Note that the rotational constants do
not depend on the torsional angle between the TMA and SO3 units and thus the relative
configuration (staggered vs. eclipsed) cannot be determined in this study.
24
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100.1
Figure 2J . The structure of trimethylamine-sulfur trioxide in the gas phase. The torsional
angle between the (CH3)3N and SO3 moieties is not determined in this work.
Table 2.6. Comparison of (CHj^N-SOs and H3N-SO 3
h 3n - s o 3
(CH 3)3N -S0 3
Parameter
Gas3
Solid6
Gasc
Solid
R(NS) (A)
1.912(20)
1.844(2)
1.957(23)
1.7714(3)d
a(NSO) (deg)
100. 1(2 )
101.8( 1)
97.6(4)
I02.5(8)d
# e'
0.58
0.36
11(D)
7.1110(69)
6.204(11)
M-md ( D)
6.50(1)
4.73(1)
9.6(6)c
(a) This work, (b) Reference 18. (c) Reference 5. (d) Reference 14. (e) Reference 35. (f) |imd
s |KcomplexHi(NR 3HJ.(S03) = p( complex )-p(NR3).
As an independent check of the above results, a Kraitchman analysis was performed [33] to
determine the N-S bond length. This method has the advantage of giving the N-S distance
directly from isotopic substitution of the nitrogen and sulfur without the need for
supplementary approximations about the position o f other atoms in the complex. Its
disadvantage is that with the present data set, the NSO angle cannot be determined.
Nevertheless, with this approach, an average value of 1.915 A is obtained for the N-S bond
distance, which is in almost exact agreement with the 1.912 A value reported in Table 2 .6 .
25
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Discussion
Molecular Structure
Table 2.6 compares the gas phase structural parameters determined above with those
previously published for the adduct in the solid state. Also included are the corresponding
values for H3N-SO3. It is apparent that the gas phase bond length o f the TMA complex
exceeds that in the solid by 0.068(22) A, which represents a modest, but nevertheless
significant contraction upon crystallization. The NSO angle displays a correspondingly
small increase between the gas phase and solid state (1.7°±0.3°). These changes are smaller
than those observed for H3N-SO3, but are in the same direction and indicate that the dative
bond is driven toward completion by the crystallization process.
The gas phase bond length in TMA-SO3 is very similar to that in gaseous H3N-SO3. That the
value appears slightly shorter and that the N SO bond angle 2.5° larger is consistent with the
increased basicity of TM A relative to ammonia. Interestingly, however, in the solid state,
the ammonia complex has a shorter bond length and larger bond angle, and it is this reversal
which largely accounts for the smaller gas-to-solid structure changes observed in TM A
adduct. Moreover, it is perhaps significant to note that the sum of ordinary covalent bond
radii for nitrogen and sulfur is 1.74 A, [36] which is very close to the N-S distance observed
in crystalline H3N-SO3. On this basis it appears that the bond in H3N-SO3 is driven virtually
to completion in the solid, while that in the T M A complex is not. This relationship between
the crystal structures and the degree of dative bond formation in these systems is discussed
in the final section of this paper.
Electronic Structure
Two aspects of the electronic structure o f the complex can be elucidated from the data
obtained in this work. The dipole moment is determined directly from the spectroscopic
measurements, as described above. Moreover, a measure o f the degree o f electron transfer
upon dative bond formation is accessible via interpretation of the 14N nuclear quadrupole
26
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coupling constants given in Table 2.5. These two features o f the system are discussed in this
section.
The dipole moment o f 7.1110(69) D determined for TMA-SO 3 in the gas phase is indicative
of significant charge rearrangement upon complexation. Indeed, for free TMA and SO 3, the
dipole moments are only 0.612(3) D [37] and 0 D, [36] respectively. Thus, the formation of
the adduct generates an induced moment o f 6.50 D. This value is given in Table 2.6, as is
the corresponding value for the NH 3 complex. It is significant to note that although the
dipole moment of ammonia (1.47149(15) D [38]) is substantially larger than that o f TMA.
the induced moment in TMA-SO 3 exceeds that in H3N-SO 3 by more than 1.7 D. Thus, it is
clear that the induced moment contains significant contributions from sources other than
electrostatic polarization. This is reasonable in light o f the increased basicity o f TMA
relative to that of NH 3 and its correspondingly greater tendency for dative bond formation.
The shorter gas phase bond length and larger NSO angle in the TMA complex further reflect
this trend.
The l4N nuclear quadrupole coupling constants in Table 2.5 are also consistent with this
picture. These constants depend on the electric field gradient at the coupling nucleus and
may be interpreted in a simple manner by the well-known method of Townes and Dailey.
[33.39] In essence, for atoms in the first row o f the periodic table, the electric field gradient
at the nucleus is dominated by the population o f valence p electrons. Thus, changes in the
coupling constant upon complexation reflect the loss o f p electron density to the acceptor.
To implement the method, the one-electron wavefunction for the dative bond between the
TMA and SO3 is written as \j/=a<|>N+|3<|>s, where <}>n is the approximately spJ hybridized
nitrogen lone-pair orbital and <f>s is the acceptor orbital on the SO3. We are careful to speak
of electron transfer "to SO3" (rather than just sulfur) because o f the delocalization o f electron
density onto the oxygens. The square of the coefficients, a and (3, represent the electron
population on the nitrogen and the SO3, respectively. Using this wavefunction, the reduction
27
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in nitrogen quadrupole coupling constant upon formation of the dative bond is given by
[5a,40,41]
[(eQqjcompiex - ( c Q cO t m a ] = ^ ^ ( e Q q i i o X 1 -O T )
(4 )
where (eQq)compiex is the l4N quadrupole coupling constant in the complex and
(e Q q )rM A
is
that of free TMA. a / represents the amount of s character in the N-C a bonds of TMA and
(eQq:io) is the quadrupole coupling constant for a single 2pz electron in atomic nitrogen.
The value o f a*2 can be obtained from the estimated CNC bond angle in the complex, y,
according to [41]
a*2 = cosy/(cosy-1)
(5)
Using y = 110.0° (intermediate between that of free TM A and solid TMA-SO3), eQqijo - 9.0 MHz, [41] and eQqiMA = -5.5024(25) MHz, [42] a value o f 1-oc2 = 0.289 is obtained.
For two electrons in the dative bond, this corresponds to a total electron transfer of 0.58 e
from the nitrogen to the SO3. This result, and the corresponding value obtained previously
for H3N-SO3, [5a] are also included in Table 2.6. Note that while it would be desirable, in
principle, to perform a complementary analysis o f the j3S quadrupole coupling constants in
Table 2.5, such a possibility is precluded by the absence o f a suitably simple orbital
description of the SO3.
The result o f the above calculations indicates that in TMA-SO3, the degree o f electron
transfer is significantly larger than that in H3N-SO3. This is a pleasing result, as it is
consistent with the increased basicity o f TMA relative to ammonia and therefore with the
trends in bond length, bond angle, and induced dipole moment noted above. It is also
satisfying in light o f previous work on with the weaker Lewis acid, SCK In TM A -SO i, [40]
where the N-S bond length is correspondingly longer than that in TMA-SO 3 (2.26±0.03 A
vs. 1.91 ±0.02 A ), quadrupole coupling data indicate only about 0.24 e transferred upon
complexation.
28
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While these comparisons are all very sensible, it should be emphasized that the form o f the
dative bond wavefunction used in the calculations, as well as the method o f Townes and
Daily itself, are extremely crude. Thus, the resulting values of the electron transfer are
approximate. Indeed, it is noteworthy that in H3N-SO3, a quantum topological analysis gives
a "charge transfer" of 0.28 electrons, [17] which appears to be, at least superficially, in
reasonable agreement with the 0.36 e value obtained experimentally. However, the analysis
also indicates [ 17] that the largest changes in charge upon complex formation take place on
the hydrogens and the oxygens, a feature which cannot be described by the simplistic dative
bond wavefunction used above. Despite these comments, however, we note that the Townes
and Dailey analysis has long provided a wealth o f chemical information from quadrupole
coupling constants [33,41] and the results obtained here, taken with an appropriate level of
caution, present a simple and consistent picture of the changes which occur upon
methyiation of H3N-SO3.
Finally, it is o f interest to return to the question of the origin of the large induced moments
in both H3N-SO3 and TMA-SO3. In our previous work on the ammonia complex, [5b] we
showed that a very simple model could be used to recover a large portion of the
experimentally determined moment. In this model, three terms contribute to the observed
moment (i) the dipole moment o f the amine moiety, taken to be that of the free amine, (ii)
the dipole moment of the pyramidally distorted SO3 moiety, calculated from an SO bond
moment of 3 D, [43] and (iii) a charge transfer component obtained from the product of the
NS bond length and the number o f electrons transferred (the latter determined from the
Townes and Dailey analysis). The value obtained for H3N-SO3 was 6.1 D, which agrees
with the experimental determination to within 2%.
As we have noted previously, [5b] the above calculation omits contributions due to
polarization. Furthermore, the use o f the N-S bond length is not necessarily correct. Thus,
the remarkable agreement with experiment may be fortuitous and it is therefore useful to
have another system with which to test the model. In the case o f TMA-SO 3, the dipole
29
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moment of the amine is 0.612 D, [37] that o f the pyramidally distorted SO3 is 1.58 D, and
the charge transfer component is 5.33 D. The sum of these values is 7.52 D, which is only
6 % higher than the experimentally determined dipole moment. The agreement is, once
again, astounding and suggests that (as in the case of H3N-SO3) a large portion o f the
induced moment arises from charge transfer between the donor and acceptor. It is interesting
to observe (Table 2.6) that the large changes in both electron transfer and dipole moment
accompany a relatively modest contraction o f the N-S bond between H3N-SO3 and
(CH 3)3N-S0 3 . Such an observation suggests that much of the charge redistribution which
occurs upon complex formation does so at very short distances.
Comparison of Crystalline TMA-SO 3 and H3N-SO 3
As noted above, the acid-base interaction in TM A-S0 3 is expected to be stronger than that
in H5N-SO 5 because of the greater basicity o f TMA. However, while the N-S bond distance
and NSO bond angle in the gas phase complexes are consistent with this notion, the solid
state structural data are not. Hargittai and Hargittai have shown that small gas-to-solid
structure differences can be meaningfully interpreted in a wide variety of systems [44] and it
is of interest to see whether the amine-S03 data presented here can be similarly understood.
Table 2.7 compares structural parameters for the series o f sulfamic acid complexes with the
general formula H3.n(CH 3)nN-S0 3 . Although in some cases, the uncertainties are large
enough to preclude a meaningful comparison between adjacent members o f the series, two
overall trends emerge. First, as the number of methyl groups increases, the N-S bond
elongates. Second, with increasing methyiation, the S-0 bond length decreases. This latter
effect is difficult to discern for the mono- and di-methylated species given the uncertainties,
but is apparent for the H3N and (CH3)3N adducts. These trends have been noted previously
[45,46] and are consistent with a weakening o f the dative interaction upon methyiation. The
NSO bond angles, unfortunately, are neither consistent nor inconsistent with this picture,
given the experimental uncertainties and range of crystallographically distinct angles.
30
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Curiously, the S-0 bond length in TMA-SO3 appears anomalous in that it is shorter than the
1.4198(2) A value observed in free SO3. [31] The reason for this is not clear. [47]
Table 2.7. Selected Solid Phase Structural Parameters for the H3.„(CH3)„N-S03 Systems
(C H 3)3N -S 03 a H (CH3)2N-S03b H2C H 3N -S 0 3c H3N -S 0 3d
1.779(8)
N-S (A)
1.844(2)
1.790(6)
1.7714(3)
S-0 (A)e
1.405(2)
1.430(5)
1.425(8)
1.442(3)
102.4(7)
N-S-0 (deg)c 101.8(1)
102.5(8)
102.1(3)
(a) Reference 18. (b) Reference 45. (c) Reference 46. (d) Reference 14. (e) Average over
crystallographically distinct values.
We have previously established [1-11] that dative bonds whose formation is incomplete in
the gas phase are strongly susceptible to the influence o f a crystalline environment.
Moreover, there is evidence, both from the calculation of lattice sums [40] and application
of SCRF methods [17,48,49] that this effect may be understood (at least to a first
approximation) in terms of the dipole moment functions for these systems. In particular,
since the dipole moments increase as the dative bond forms, the bonding advances upon
crystallization in order to lower the total intermolecular interaction energy in the solid. The
gas phase and solid state dipole moments given in Table 2.6 for H3N-SO3 illustrate the
magnitude of the change in dipole moment which can occur in these types o f systems.
To see whether the observed anomaly in the crystal structure o f the amine-SC^ complexes
could be understood in terms of this mechanism, packing plots were generated for H 3N-SO 3
[14] and TMA-SO 3 [18] from published crystallographic data. These plots, together with
similar diagrams for CH 3H 2N-SO3 [46] and (Cfy^HN-SCh are included in Figures 2.4-2.1
below. As expected, the bulkiness o f the three methyl groups in TMA-SO 3 has a large effect
on packing in the molecular solid. Individual monomer units line up uni-directionally in
one-dimensional chains, with the SO 3 end of one molecule directed toward the TMA end of
a second molecule. The oxygen-to-hydrogen distance is 3.0 A. Neighboring chains are
staggered relative to one another, with the distance between an N-S bond in one chain and
31
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Figure 2.4. Stereoscopic view along x of (CH 3)3N -S0 3 generated from data of Ref. 18.
Figure 2.5. Stereoscopic view along x of (CH 3)2HN-S0 3 generated from data o f Ref. 45.
32
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Figure 2.6. Stereoscopic view along x of CH 3H :N -S0 3 generated from data o f Ref. 46.
Figure 2.7. Stereoscopic view along x of H3N-SO 3 generated from data o f Ref. 14.
33
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
the closest methyl carbon on a neighboring chain being 4.8 A. Successive layers of TMASO3 chains fit into the grooves between the chains below ensuring tight packing.
In contrast, H3N-SO 3 crystallizes in a complex 3-dimensional network exhibiting extensive
intermolecular hydrogen bonding, with H—O distances ranging from 1.918 A to 2.404 A.
Throughout this intricate network are series of antiparallel H3N-SO 3 pairs, wherein each
nearest neighbor is related to its partner by a 180° rotation about one o f the two equivalent
principle axes of the monomer. The distance between the center of the N-S bond in one
monomer to that in its nearest anti-aligned neighbor is 3.9 A, almost a full angstrom shorter
that the equivalent distance in TMA-S 03 (s).
In view of these observations, it may be possible to rationalize the differences between
crystalline H3N-SO 3 and TMA-SO 3. Due to the bulkiness o f the methyl groups, the optimum
spatial arrangement of molecules in TMA-SO 3 produces fewer and more distant
intermolecular contacts than in the case of H 3N-SO 3. Thus, interactions between adjacent
dipoles and consequently the capacity o f near-neighbor interactions to drive the formation of
individual N-S bonds are reduced. Moreover, the differences are likely to be compounded
by the propensity for hydrogen bonding in the ammonia complex, which gives rise to
especially strong intermolecular interactions. The overall picture, then, is that in TMA-SO 3,
the unidirectionality o f the interactions, the larger intermolecular distances, and the lack of
hydrogen bonding diminish the ability o f dipolar interactions in the solid to stabilize the
charge separation associated with the advancement of the dative bond. Thus, while the N-S
bond in the ammonia complex can be driven essentially to completion, that in the TMA
adduct is not. Moreover, we may infer that in CH 3H2N-SO 3 and (C ^hH N -SC h, both the
bulkiness of the amine and the opportunities for hydrogen bonding are between those o f the
H 3N-SO 3 and (CH 3)3N-S0 3. Hence, it is perhaps not too surprising that the physical
properties listed in Table 2.7 progress as they do across the series. Close scrutiny o f the
stereoscopic projections for these crystal systems are consistent with such an idea.
34
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Conclusions
Microwave spectroscopy has been used to investigate the molecular and electronic structure
of (CH 3)3N -S0 3 in the gas phase. The N-S bond length is 1.912(20) A and the NSO angle is
100.1(2)°, indicating a dative bond which is nearly, but not entirely formed. Analysis of the
l+N nuclear hyperfine structure indicates that about 0.6 electrons are transferred from the
trimethylamine to the S 0 3 upon formation of the adduct and Stark effect measurements
reveal a gas phase dipole moment o f 7.1110(69) D. These results are consistent with
significant charge redistribution upon complex formation. The degree of charge transfer
between the donor and acceptor is nearly twice that observed in the related complex H3NS 0 3 and the induced dipole moment is 1.8 D larger. These changes are particularly
interesting in light o f the more modest difference in N-S bond lengths between the two
compounds. The trends in bond length, electron transfer, and induced moment, however, are
consistent with the greater basicity o f (CH3)3N relative to that of ammonia.
The observed N-S bond length in the gas phase is longer than that previously reported for
the crystalline adduct, and the NSO angle is larger. These differences indicate that the
crystallization of the complex drives the dative bond toward completion. Interestingly,
however, while the N-S bond length is shorter than that o f the NH 3 complex in the gas
phase, it is longer in the crystal. This anomaly can be rationalized in the context o f previous
work on medium effects in donor-acceptor systems, and by close examination o f packing
plots generated from published crystallographic data. In essence, the larger intermolecular
distances resulting from the methyl groups, as well as the lack of hydrogen bonding
interactions present in the ammonia adduct render the crystallization of TM A-S0 3 less
effective at driving the charge separation associated with the formation of the dative bond.
Acknowledgements
This work was supported by the National Science Foundation and the donors of the
Petroleum Research Fund, administered by the American Chemical Society. A.T. was
supported by a Lando-NSF-REU Summer Undergraduate Research Fellowship at the
35
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
University of Minnesota. The authors, especially D.L.F. would like to acknowledge Dr. M.
Pink for assistance in attaining and analyzing the crystallographic packing plots.
36
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
References
1.
Leopold, K.R. in Advances in Molecular Structure Research, Hargittai, M.;
Hargittai, I., Eds., JAI Press: Greenwich, CT, 1996; Vol. 2, p. 103.
2.
Leopold, K.R.; Canagaratna, M.; Phillips, J.A. Acc. Chem. Res. 1997, 30, 57.
3.
Dvorak, M.A.; Ford, R.S.; Suenram, R.D.; Lovas, F.J.; Leopold, K.R. J. Am. Chem.
Soc. 1992, 114, 108.
4.
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5.
(a) Canagaratna, M.; Phillips, J.A.; Goodfriend, H.; Leopold, K.R. J. Am. Chem.
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Lett. 1997,281,63.
6.
Bums, W.A.; Phillips, J.A.; Canagaratna, M.; Goodfriend, H.; Leopold, K.R., J.
Phys. Chem., submitted.
7.
Phillips, J.A.; Canagaratna, M.; Goodfriend, H.; Leopold, K.R. J. Phys. Chem. 1995,
99, 501.
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Phillips, J.A.; Canagaratna, M.; Goodfriend, H.; Grushow, A.; Almlof, J.; Leopold.
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Canagaratna, M.; Phillips, J.A.; Goodfriend, H.; Fiacco, D.L.; Ott, M.E.; Harms, B.;
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Bums, W.A.; Leopold, K.R. J. Am. Chem. Soc. 1993, 115, 11622.
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12.
Kanda, F.A.; King, A.J. J. Am. Chem. Soc, 1951, 73,2315.
13.
Sass, R.L. Acta Crystallogr. 1960, 13,320.
14.
Bats, J.W.; Coppens, P.; Koetzle, T.F. Acta Crystallogr. 1977, B33, 37.
15.
Douglas, J.E.; Kenyon, G.L.; Kollman, P.A. Chem. Phys. Lett. 1978,57, 553.
16.
Hickling, S.J.; Woolley, R.G. Chem. Phys. Lett. 1990, 166,43.
17.
Wong, M.W.; Wiberg, K.B.; Frisch, M.J. J. Am. Chem. Soc. 1992, 114, 523.
37
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
18.
Morris, A.J.; Kennard, C.H.L.; Hall, J.R.; Smith, G.; White, A.H. Acta Crystallogr.
1983, C39, 81.
19.
Sass, C.S.; Ault, B.S. J. Phys. Chem. 1986,90, 1547.
20.
Krueger, J.H.; Johnson, W.A. Inorg. Chem. 1968, 7, 679.
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Blandamer. M.J.; Burgess, J.; Duce, P.P. J. Inorg. Nucl. Chem. 1981,43,3103.
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Bunsenges. Phys. Chem. 1995,99, 1451.
23.
Phillips, J.A., Ph.D. Thesis, University o f Minnesota, 1996.
24.
Legon, A.C. Chem. Commun. 1996, p. 109.
25.
Gillies, C.W.; Gillies, J.Z.; Suenram, R.D.; Lovas, F.J.; Kraka, E.: Cremer, D. J. Am.
Chem. Soc. 1991, 113,2412.
26.
Gutowsky, H.S.; Chen, J.; Hajduk, P.J.; Keen, J.D.; Emilsson, T. J. Am. Chem. Soc.
1989, 111, 1901.
27.
Emilsson, T.; Klots, T.D.; Ruoff, R.S.; Gutowsky, H.S. J. Chem. Phys. 1990, 93
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28.
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29.
Coudert, L.H.; Lovas, F.J.; Suenram, R.D.; Hougen, J.T. J. Chem. Phys. 1987, 87,
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31.
(a) Kaldor, A.; Maki, A.G.; J. Mol. Struct. 1973, 15, 123. (b) Meyer, V.; Sutter,
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32.
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Clippard, P.H., Ph.D. Thesis, University o f Michigan, 1969.
33.
Gordy, W.; Cook. R.L. Microwave Molecular Spectra, Wiley: New York, 1984.
34.
It might be argued that, in view o f the similarity of the N-S bond length to that in the
solid, the fit employing the crystal phase parameters gives the more reasonable
numbers However, it is likely that the changes in monomer structure which occur as
the dative bond forms take place at short distances where the orbital overlap is most
38
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
substantial. Thus, even at the gas phase structure of the complex, the changes in the
TMA structure and SO bond length may not yet be those observed in the crystal.
Moreover, it is likely that these changes result, to some degree, from forces acting in
the crystal, in which case, again, the crystal phase parameters are not necessarily
more valid than the free monomer values.
35.
Coppens, P.; Guru Row, T.N.; Leung, P.; Stevens, E.D.; Becker, P.J.; Yang, Y.W.
Acta Crystallogr. 1979, A35, 63.
36.
Cotton, F.A.; Wilkinson, G. Advanced Inorganic Chemistry. 3rd Ed.: Interscience:
New York, 1972.
37.
Lide, D.R., Jr.; Mann. D.E. J. Chem. Phys. 1958, 28, 572.
38.
Marshall, M.D.; Muenter, J.S. J. Mol. Spectrosc. 1981, 85, 322.
39.
Townes, C.H.; Dailey, B.P. J. Chem. Phys. 1949, 17, 782.
40.
Oh. J.J.; LaBarge, M.S.; Matos, J.; Kampf, J.W.; Hillig, K.W., II; Kuczkowski, R.L.
J. Am. Chem. Soc. 1991, 113, 4732.
41.
Lucken, E.A.C. Nuclear Ouadrupole Coupling Constants: Academic Press: New
York. 1969.
42.
Rego. C.A.; Batten, R.C.; Legon, A.C. J. Chem. Phys. 1988, 89,696.
43.
Huheey, J.E.; Inorganic Chemistry, 3rd Ed.: Harper and Row: New York, 1983.
44.
(a) Hargittai, I.; Hargittai, M.; in Molecular Structure and Energetics, Liebman, J.F.;
Greenberg, A. Eds.; VCH Publishers: Deerfield Beach, 1987, Vol. 2, p.l. (b)
Hargittai, M; Hargittai, I., Phys. Chem. Miner. 1987, 14,413, and references therein.
45.
Morris, A.J.; Kennard, C.H.L.; Hall, J.R.; Smith, G. Inorganica Chemica Acta 1982,
62, 247.
46.
Morris, A.J.; Kennard, C.H.L.; Hall, J.R. Acta Crystallogr. 1983, C39, 1236.
47.
To check the possibility of a typographical error in the published SO bondlength in
solid TM A-SO3, we regenerated the structure from available crystal data and found
agreement with the value cited in Ref. 18.
48.
Jiao, H.; Schleyer, P.v.R. J. Am. Chem. Soc. 1994, 116, 7429.
39
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
49. Buhl, M.; Sternke, T.; SchJeyer, P.v.R.; Boese, R. Angew. Chem. Int. Ed. Engl.
1991,30, 1160.
40
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Appendix to Chapter 2.
Table 2. A l. Observed Transitions of (CH 3>3UN-S03 at Non-zero Electric Field.
J"
Mj" M,"
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
-1
-1
0
-1
-1
0
-1
-1
0
0
0
-1
-1
1
1
1
1
1
0
0
0
0
1
-1
0
1
1
-1
1
1
1
0
0
0
0
0
-1
0
1
1
1
1
-1
1
t
0
1
-1
0
0
1
1
1
1
1
0
0
-1
-1
-1
-1
0
0
1
-1
-1
0
1
1
0
0
-I
-1
1
1
1
1
-1
1
J'
M / M,’ K.
E (V/cm)
Freq. (MHz)
Obs-Calc (MHz)
I
1
1
1
1
1
1
1
1
1
2
0
-1
-1
-1
0
1
-1
6.24
6.24
6.24
9.27
3267.083
3266.621
3267.765
3267.160
3266.690
-0.002
-0.003
-0.001
-0.001
0.000
3267.830
3267.276
3266.778
3267.927
3266.889
-0.003
0.004
-0.001
0.002
-0.001
6533.736
-0.003
6534.440
6533.718
6533.778
6533.556
6534.205
6533.747
6534.144
-0.010
0.014
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
0
-I
-1
0
-1
-1
-1
0
-2
1
0
1
2
0
0
0
0
0
-1
1
2
0
2
0
0
-1
-2
-1
0
_2
0
1
-1
0
1
0
-1
I
-1
1
1
-1
-1
0
1
0
0
-1
0
-1
-1
0
0
I
-1
0
0
-1
1
0
0
0
0
0
9.27
0
0
0
9.27
12.36
12.36
0
0
I
12.36
15.56
0.42
1
1
I
I
1
0.42
0.42
0.42
0.42
0.42
1
1
1
1
1
0
0
0.72
0.71
0.72
37.01
37.01
6533.772
6533.925
6533.908
6534.517
6534.971
0
0
0
37.01
37.01
37.01
6534.209
6533.221
6534.052
1
I
0
0
0
37.01
37.01
30.86
30.86
30.86
6534.825
6534.425
6534.323
6533.694
0
0
30.86
30.86
0.72
0.72
6534.815
6533.482
6532.876
-0.010
-0.004
-0.002
-0.001
0.000
-0.006
-0.005
-0.002
0.004
-0.002
-0.006
-0.001
-0.005
0.004
-0.003
-0.003
0.001
-0.002
0.002
0.000
41
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 2.A 1. continued.
Vfj” M,” J ’ Mj’ M,’ K
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
2
0 -I
1
0
-1
2
2
1 0
1
I
2 -1 -I
0
-1
0
2
-1 -1
-1 -1
0
2
0
0
0
0
1
2
0
1
1 0
1
2
0
-1
0
0 -1
2
0
1
0
1 0
0
0
1
-1
-1
-1
-1
-1
0
0
0
2
2
-1
-1
-1
-1
0
6533.248
6533.082
6534.619
6534.224
-0.001
-0.004
0.001
6534.176
-0.002
24.73
24.73
6534.456
6533.614
0.003
-0.007
24.73
24.73
6534.704
6533.680
-0.005
-0.001
0
0
0
24.73
24.73
6533.412
6533.302
0.001
0.001
24.73
6533.900
0
0
0
0
24.73
18.59
6534.053
6534.064
-0.002
0.001
18.58
6533.532
-0.002
-0.002
6533.580
6534.649
-0.001
-0.001
I
0
0
18.58
18.59
18.59
6533.819
1
1
-1
0
0
0
18.58
18.59
18.58
6533.495
6534.714
6533.432
0
0
0
18.59
18.59
6533.867
-0.002
-0.002
0.000
-0.001
0.000
-0.001
0
1
18.59
18.59
1
0
18.59
18.59
15.57
2
2
2
-1
_2
-1
2
2
-1
.2
2
0
-1
-1
2
0
0
I
0
0
1
0
-I
0
0
0
1
1
0
1
2
2
2
2
0
0
1
0
2
2
1
0
0
1
-1
-1
2
2
0
2
-1
-1
-1
0
2
2
-1
-I
0
0
-1
0
0
2
-1
0
.2
1
-1
0
0
2
2
-1
2
2
2
0
-1
-1
0
0
1
0
30.86
30.86
30.86
30.86
30.86
Obs-Calc (M
6534.122
6533.391
0
0
0
-1
2
2
Freq. (MHz)
0.000
0.000
0.001
0
1
2
_2
2
E (V/cm)
1
1
0
-1
-1
0
0
30.86
24.73
6533.996
6533.783
6534.324
6533.927
6534.775
6534.028
6533.901
15.58
15.57
6534.637
15.58
15.57
15.57
6533.862
6534.407
6533.234
-0.003
0.000
-0.003
-0.001
0.005
0.005
-0.001
-0.004
0.001
-0.002
42
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 2.A1. continued.
J" Mj" M,"
1
0
0
1
0
1
1
1
1
1
1
1
J'
2
2
2
2
I
1
0
0
0
1
Mj' M,'
K
E (V/cm)
Freq. (MHz)
Obs-Calc (MHz)
6533.467
6533.835
6533.973
6533.536
6534.272
6533.879
-0.001
-0.005
-0.003
-0.002
-0.002
0
1
0
15.57
1
2
1
0
1
0
1
0
0
2
0
0
1
2
0
1
1
15.58
15.58
15.57
15.57
15.57
-0.002
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Chapter 3. Dipole Moments of Partially Bound Lewis Acid-Base Adducts
D.L. Fiacco, Y. Mo, S.W. Hunt, M.E. Otta.
A. Roberts15, and K.R. Leopold
Department o f Chemistry
University of Minnesota
207 Pleasant St., SE
Minneapolis, MN 55455
(a) Present Address: Western Wyoming Community College, PO Box 428, Rock Springs.
WY 82902-0428
(b)
Present Address: Department of Chemistry, University of California, Berkeley, CA
94720
Reproduced with permission from: Fiacco, D.L; Mo, Y.; Hunt, S.W.; Ott, M.E.; Roberts, A.:
Leopold, K.R. J. Phys. Chem. A 2001,105,484-493. Copyright © 2001 American Chemical
Society.
44
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Abstract
Stark effect measurements have been performed on six Lewis acid-base complexes
containing j 2SC>3 and llBF3. The following dipole moments have been obtained: H C i+NS 0 3 (4.4172 = 0.0031 D); C H 3C 14N -S 0 3 (6.065 ± 0.018 D); H C ,5N -B F 3 (4.1350
±
0.0073 D); H 3I5N -B F 3 (5.9027 ± 0.0093 D (A state), 5.917 ± 0.010 (E state)); (CH 3)3,5NBF 3 (6.0157 = 0.0076 D); (CH 3)3I5N-B(CH 3)3 (4.5591 ± 0.0097 D). Across a series of
complexes with a common acid the induced dipole moment increases sharply as the dative
bond shortens. Contributions to the total molecular dipole moment arising from distortion,
polarization and charge transfer have been estimated for these and a number of related
complexes using the block-localized wave function energy decomposition (BLW-ED)
analysis of Mo, Gao, and Peyerimhoff.
Mulliken and NPA population analyses are
presented, as are electron density difference maps for HCN-SO3, (CH3)3N-BF3, and
(CH 3)3N-S 03 . Theoretical values for the degree o f charge transfer are compared with
experimental estimates based on nuclear hyperfine parameters and the validity of a simple
chemical model involving charge transfer and bond moments is examined. Ab initio
calculations of the induced dipole moment of HCN-SO3 and H3N-SO3 are given as a
function of N-S bond length and compared with the experimentally observed values for a
series of SO3 complexes. The results suggest that the induced moments of the series
collectively approximate the induced dipole moment Junction for individual members of
the series. Similar results are obtained using previously published dipole moment
functions for HCN-BF3, and H3N-BF3.
45
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Introduction
Lewis acid-base complexes containing a partially formed dative bond offer some new
and interesting perspectives on molecular structure and bonding [1,2]. While the
traditional definitions o f van der Waals and covalent radii epitomize the sharp
distinction between chemical and weak physical interactions, there is a long history of
examples in the crystailographic literature [3,4] in which bond distances and bond
angles lie between those characteristic o f these normally recognized limits. A growing
number of gas phase and theoretical studies also indicate that molecular structure in this
regime is not an immutable property o f a molecule but rather, exhibits an extraordinary
dependence on phase [1,2,5,6]. Indeed, bond lengths and bond angles change
dramatically upon crystallization and there is significant theoretical evidence to support
the idea that the molecular dipole moment function, ^i(R), plays an important role in the
effect [5,7-10],
The study o f Lewis acid - base complexes is, o f course, not new. Recognized as early
as 1923 [11], such systems have been the subject of numerous structural studies [12],
and a large volume o f solution phase data, both spectroscopic [12b.c, 13] and
thermodynamic [12bcd,14], has been reported. Most closely related to the work
reported here are a number o f gas phase electron diffraction [15] and microwave [16]
studies that have investigated the structures of donor-acceptor complexes with fully,
and in some cases, partially formed dative bonds. Matrix isolation techniques have also
been applied [17], and an increasing amount of theoretical attention has been paid to
these systems in recent years [18].
The dipole moment is an important property for donor-acceptor complexes, both in the
context o f phase-dependent structure, noted above, and as a fundamental measure of
charge distribution. While solution phase measurements o f dipole moments for acidbase complexes are certainly to be found in the literature [12b,c,19], the values
obtained are. in general, subject to the effects of solvent polarization [12b]. For gas
46
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
phase species, a number o f isolated measurements now exist [5,16abdfgk, 20] though
there appear to be few, if any, systematic investigations based on modem high
resolution techniques.
In this paper we present Stark effect measurements for a series o f six Lewis acid-base
complexes in the gas phase. The dipole moments obtained are combined with literature
values for several related adducts and a number o f computational methods are used to
aid in the interpretation o f the results. From an experimental standpoint, we examine
the relationship between the dipole moment induced by complexation and the length of
the donor-acceptor bond. From a theoretical perspective, we discuss not only the
magnitude of the induced moments per se, but also the relative contributions from
polarization, charge transfer, and distortion. Further, in light of these theoretical results,
we examine the validity o f a simple chemical model o f polarity based on bond moment
and charge transfer considerations. Separate calculations o f the dipole moment
functions, |i(R), are also presented for some of the systems studied, and their
relationship with the experimentally obtained dipole moments is discussed.
Experimental Methods and Results
Spectra were recorded using a pulsed nozzle Fourier transform microwave spectrometer
[21], the details o f which have been described previously [22]. The system is equipped
with a pair o f rectangular aluminum Stark plates, which operate in a bipolar configuration
and straddle the microwave cavity to apply a uniform DC electric field to the molecular
sample. For the systems studied in this work, one or more transitions previously assigned
at zero electric field were examined at a series of field strengths. Little, if any, spectral
broadening occurred as the electric field was increased, but the intensity of the transitions
was observed to diminish. In most cases, this ultimately limited the degree to which
transitions could be shifted, but the problem was not severe enough to preclude
sufficiently accurate determination o f the dipole moments.
47
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The effective plate spacing for each experiment was determined by calibration using either
the J = 1 <- 0 transition of OCS [23] (p. = 0.71521(20) D) or the J = 4 <- 3, K = ±3
transition Ar-SOj [24] (|i = 0.2676(3) D), as described elsewhere [20], In order to
eliminate possible effects due to the accumulation of diffusion pump oil on the plate
surfaces [20.25], calibrated distances were obtained both before and after the collection of
experimental data and the data were admitted for analysis only upon agreement o f the preand post- collection values.
For complexes of SO3, which itself has no quadrupolar nuclei, measurements were made
using the ordinary l4N isotopic derivatives of the bases. For the MBF3 species, in which
hyperfme structure is also present due to the boron, l5NH3, H C I5N , and (CH3)3I:,N were
used. HCi5N was prepared by reaction of KCI5N with dry H3PO4, while 15NH3 was
produced from ,5N?L,C 1 and KOH. (CH 3)3l5N was prepared according to literature
procedures [26],
v.
>3
L.
<
Frequency (MHz)
Figure 3.1. The J = 2<—1 transition of CH 3CN-SO 3 taken at 1.55 V/cm. This spectrum
represents 44 seconds o f data collection time.
48
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A portion of the J = 2<—1 transition o f CH 3CN-SO 3 taken at 1.55 V/cm is shown in
Figure 3.1 above. Stark-shifted frequencies were analyzed using standard methods [27]
to obtain the dipole moment for each species investigated. Rotational, distortion, and
quadrupole coupling constants were in all cases constrained to their values determined
at zero electric field, and transition frequencies were generally reproduced to within the
estimated experimental uncertainties. Tables o f transition frequencies, electric field
strengths, and residuals from the least squares fits are provided as an Appendix to this
chapter. The results are summarized in Table 3.1. Values of the dipole moment, p., the
induced dipole moment, Afi,nd, and dative bond length, R, are given in Table 3.2,
together with literature values for a number of related complexes.
Table 3.1. Sum m ary of Stark Effect Measurements
Molecule3
Transitions
Range of
Examined
Electric
Fields
(V/cm)
HCN-SO,
J=l<—0, K= 0
Number of
Transitions
Fittedb
P(D)C
15.34 -73.46
41
4.4172(31)
J=2<—1. K= 0
CH-.CN-SO,
J=2<—l,K=0,
±1
0.61 -30.75
68
6.065(18)
HC'-'N-1IBF,
J=l«—0 , K. = 0
12.33 -36.88
44
4.1350(73)
H-,'5N-llBF5(A state)
J=l<—0, K = 0
6.28-43.05
34
5.9027(93)
J=l<—0, K. = 0
6.28-43.05
32
5.917(10)
J=l<—0, K=0
0.47 - 36.89
115
6.0157(76)
0.42 - 36.82
122
H,l?N-liBF3 (Estate)
(CH3)3I?N-I1BF3
J=2<—1JC=0,
±1
(CITb'-'N^BfCH^
J=l<—0, K=0
J=2«—1,
4.5591(97)“
K= 0,±1
(a) Unless otherwise indicated, the common isotopic form was observed, (b) This
number includes multiple observations o f individual transitions at several different
values of the applied electric field, (c) Uncertainties are one standard error in the least
squares fit. (d) Measured for the more intense of two observed vibrational states.
49
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Computational Methods and Results
Theoretical Background (BLW-ED Method)
Decomposition o f the calculated dipole moments is based on the block-localized wave
function approach of Mo, Gao, and Peyerimhoff [38]. This approach has demonstrated
much less basis set dependence with respect to polarization and charge transfer energies
than other decomposition procedures and is expected to yield reliable results for the
complexes of interest here. For a monomer or dimer, the dipole moment is defined as
p. = <¥ | er in ')
( 1)
where 4' denotes the wave function of the monomer or dimer. Generally, the dipole
moment of a dimer, fi(AB), is not simply the sum o f the dipole moments of two
monomers (|i( A) and p(B) for A and B, respectively), and the variation
A^tind = ItfAB) - (I (A) - p (B)
originates
(2)
primarily from distortion, polarization and charge-transfer effects. For weakly
bound systems, vibrational averaging over large amplitude zero point motions can also
contribute. To discriminate between the distortion, polarization, and charge transfer
components computationally, the dipole moment o f the dimer at its equilibrium
configuration is assumed to evolve in a successive way. First, the two monomers
approach each other to form the dimer with their individual electron densities frozen
(State 1). The wave function for State 1 can thus be represented as:
^
1)A b =
A(4'0a4'°b)
(3)
where 4/A° and 4, b° are the optimal wave functions for the distorted monomers A and B,
respectively and A is an antisymmetrizing operator. The dipole moment o f State 1 is
nearly equal to the sum o f (i°(A) and (l°(B), viz.,
50
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[i° (A ) + [i° (B)
^ , n AB = ( ' t , < , , A B | e r | ' F <1)AB> =
(4)
where p° (A) and (i° (B) are the dipole moments o f isolated A and B at their distorted
geometries within the complex. Second, the electron densities in A and B are allowed
to relax in response to the electric field o f the interacting partner (State 2). The blocklocalized wave function (BLW) method is employed here, in which the optimal wave
function in the absence o f charge transfer is derived for the intermediate diabatic state.
The wave function for State 2 can be written as:
4 '<2,Ab
where
(5)
= A ( ' F a M 'b )
or ¥ b is a successive product of localized molecular orbitals on monomers A
and B, respectively. While the orbitals on A or B are restrained to be orthogonal as in the
usual molecular orbital theory, the orbitals on A are non-orthogonal to the orbitals on B.
Like State 1. the dipole moment o f State 2 is approximately equal to the sum o f
and
(I blvv
(A)
(B):
M-u , a b - M-b l w
where
(J-b l w
| ! blw
(AB) = ( ^
(A) and
| ! Bl w
‘U l
er
I H ^ ’a b )
=
H blw
(A) +
(I b l w
(B)
(6 )
(B) are defined as
IIblw(A) = <'FA|e r |4 'A>
(7)
Ublw(B) = <H'B|e r |4 'B>
(8 )
The difference between |IBlw(A) or Hblw(B) and (i°(A) or |i°(B) demonstrates the effect
of polarization on the individual monomers. Moreover, the energy variation between
State 1 and State 2 is the polarization energy.
51
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Finally, electrons in the dimeric complex are permitted to flow freely and we reach the
final state 'Fab, where all molecular orbitals are delocalized over the entire system. The
comparison between
|1 i 2>a b
and the final calculated moment,
|I h f(A B ) ,
yields the charge-
transfer component to the dipole moment, and the energy variation between the states
' F i 2 )a b
and
' F ab
can be defined as the charge-transfer stabilization energy.
BLW Results
Calculations were performed for the systems represented in Table 3.2 using the BLW
program and Gaussian 98 [40]. The results are summarized in Tables 3.3, 3.4, and 3.5.
Table 3.3 gives bimolecular complex geometries optimized at the HF/6-3lG(d) level and
compares with experimental data, where available. Agreement with experiment is seen to
be reasonable, with the possible exception of CH 3CN-BF 3, for which the calculated bond
length is about 0.50 A too long. Electron correlation and basis set superposition are
expected to be important for this system and likely account for the discrepancy.
However, BLW calculations at higher levels o f theory are not, at present, possible and
thus, the above level o f calculation was used to maintain uniformity throughout. The
HF/6-31G(d) calculations, however, are seen to reproduce the essential variations in
structural parameters across the series o f complexes considered and should therefore be
adequate for making rough quantitative assessments of the terms contributing to the
overall molecular dipole moments.
Results of the BLW calculations are given in Tables 3.4 and 3.5. Table 3.4 gives the
dipole moments o f the acid and bases at the distorted complex geometry, |i°(X) (X = A
or B), and in the presence o f the second monomer using the BLW wave function,
|i B L w ( X ) .
The intermediate dipole moments for the complex, (Iblw(AB), are also
reported as are those obtained from a full optimization at the HF level. For the free
base, the calculated moments at the equilibrium geometry, |i°eq(X), are also included
and are compared with the experimental values, (i(B). The dipole moments o f the free
Lewis acids are zero by symmetry and are not included. For the bases, the dipole
52
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moments calculated at the HF/6-31G(d) level o f theory/basis set
are seen to be
systematically somewhat high but again, since our concern is not in the absolute values
of the dipole contributions but rather in the relative contributions to the induced moment,
these discrepancies are not problematic. Table 3.5 gives the differences, A|i<i1St = fi°(X) M°eq(X), Afipoi = (Iblw(X) - (I°(X), and A(icr = P hf(AB) - |IBlw(AB), as well as the total
induced moments determined both theoretically and experimentally. The observed and
calculated induced moments are seen to agree to within a few tenths o f a Debye.
Table 3.2. Dipole M oment Data for Selected Lewis Acid-Base Complexes
Species
1KD)
Ref.'
Ap<„d(D)b
R(A)C
N 2-S 0 3
0.46( 1)
24
0.46
2.9e
h c n -so 3
4.4172(31)
f
1.433
2.577(6)
32
c h 3c n - s o 3
6.065(18)
f
2.147
2.466(16)
32
h 3n - s o 3
6.204(11)
20
4.733
1.957(23)
33
(CH 3)3N -S 0 3
7.1110(69)
16k
6.499
1.912(20)
16k
H 3N -S 03g
9.6(6)
34
8.1
1.7714(3)
35
HCN-BF 3
4.1350(73)
f
1.150
2.473(29)
36
h 3n - b f 3
5.9027(93)
f
4.431
1.673(10)
I6i
(CH 3)3N-BF 3
6.0157(76)
f
5.404
1.636(4)
16c
h 3n - b h 3
5.216(17)
I6f
3.745
1.6576(16)
I6 f
(CH 3)3N-BH 3
4.84(10)
16b
4.23
1.638(10)
16b
f
3.947
1.698(10)
I6e,37
(CH 3)3N-B(CH 3)3 4.5591(97)
Ref.d
(a) Reference for dipole moment data, (b) Calculated using the following
moments for the basic moiety: N 2 (0 D); HCN (2.9846(15) D, Reference
[28]); CH3CN (3.9185(20) D, Reference [29]); NH3 (1.47149(15) D.
Reference [30]); (CH3)3N (0.612 D, Reference [31]). (c) Dative bond length
(B-N or S-N)- (d) Reference for structural data, (e) Estimated from van der
Waals radii, (f) This work, (g) Solid state values.
53
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Table 3.3. Structural Parameters o f Lewis acid-base adducts.a
Species
R xy (A )
R xy (A )
0 b(donor)
a c(acceptor)
a c(acceptor)
Expt.
Theor.
Theor.
Expt.
Theor.
N ;-S 0 3
d
3.058
180.0
d
90.3
H C N -S O 3
2.577(6)
2.704
180.0
91.8(4)
91.5
C H 3C N -S O 3
2.466(16)
2.620
180.0
92.0(7)
92.0
H 3 N -S O 3
1.957(23)
1.951
109.7
97.6(4)
97.5
(C H 3)3N - - S 0 3
1.912(20)
1.898
108.7
100. 1(2 )
99.4
H C N -B F 3
2.473(29)
2.601
180.0
d
92.4
C H 3CN - BF3e
2.011(7)
2.506
180.0
95.6(6)
93.4
H 3 N -B F 3
1.673(10)
1.693
110.6
d
103.6
(C H 3)3N - - B F 3
1.636(4)
1.679
109.1
106.4(3)
105.0
H3N--BH3
1.6576(16)
1.689
110.9
104.69(11)
104.3
(C H 3)3N --B H 3
1.638(10)
1.677
109.3
105.32(16)
105.2
H3N - B ( C H })3
d
1.739
111.1
d
103.9
(C H 3)3N -B (C H 3)3
1.698(10)
1.825
110.5
108.0(15)
106.5
(a) Unless otherwise noted, experimental data are from references given in Table 2.
(b) Angle formed by the acceptor atom (B or S), the nitrogen atom, and the first
atom of the base bonded to nitrogen, (c) NBF or NSO angle, (d) Not determined
experimentally, (e) Reference [39].
54
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Table 3.4. Computed Dipole Moments Using BLW-ED Approach."
Species
Lewis Base (B)
Lewis Acid
(A)
M-exp
(J-BLW |Jhf
(AB)
(AB)
(J-BLW
(J°
M-blw
(B)
(B)
(B)
(A)
(A)
0 .0
0 .0
0 .0
0.28
0 .0
0 .1 1
0.41
0.46
HCN—SO 3
2.985
3.21
3.21
3.79
0 .2 2
0.55
4.35
4.57
CH 3 C N - S O 3
3.919
4.04
4.03
4.83
0.30
0.71
5.55
5.87
h 3n - s o
1.472
1.92
1.79
2 .6 8
1.09
2.14
4.80
6 .8 8
(CH 3 )3 N - S 0 3
0.61
0.74
0.94
2.83
1.35
2.67
5.49
7.86
HCN—BF 3
2.985
3.21
3.21
3.61
0.31
0.50
4.11
4.22
CH 3 C N - B F 3
3.919
4.04
4.04
4.61
0.42
0 .6 6
5.27
5.42
H 3N - B F 3
1.472
1.92
1.85
2.75
1.85
2.52
5.17
6.17
(CH3)3 N -B F 3
0.61
0.74
0.96
2.57
2.05
2.81
5.24
6 .1 1
H3N - B H 3
1.472
1.92
1.87
2.71
0.79
1.75
4.52
5.57
(CH 3 )3 N -B H 3
0.61
0.74
0.95
2.39
0.84
1.83
4.30
5.21
H 3 N - B ( C H 3)3
1.472
1.92
1 .8 8
2.63
0.34
1 .2 2
3.92
4.80
(CH 3 )3N-B(CH3)3
0.61
0.74
1.04
2.28
0.39
1.28
3.65
4.60
(B)b
N r-S O j
3
(a) See text for discussion of symbols, (b) References to experimenta dipole moments
are given in Table 2.
55
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Table 3.5. Computed Induced Dipole Moments (D) (BLW-ED).
Species
Afidist
Apdut
Ajlpoi
(B)
(A)
(B)
(A)
N r-S O j
0 .0
0 .0
0.28
H C N -S O 3
0 .0
0 .2 2
CH 3 C N - S O 3
0 .0
A|ijnd
Ajijnd
(AB)
(Theor)a
(Expt)
b
0 .1 1
0.05
0.44
0.46
0.58
0.33
0 .2 2
1.35
1.43
0.30
0.80
0.41
0.32
1.83
2.15
-0.13
1.09
0.89
1.05
2.08
4.98
4.73
0 .2 0
1.35
1.89
1.32
2.37
6.13
6.50
H C N -B F 3
0 .0
0.31
0.40
0.19
0 .1 1
1.01
1.15
CH 3 CN - B F 3
0 .0
0.42
0.57
0.24
0.15
1.38
c
-0.07
1.85
0.90
0.67
1 .0 0
4.35
4.43
(CH 3 )3 N—BF 3
0 .2 2
2.05
1.61
0.76
0.87
5.51
5.40
H3N - B H
0.05
0.79
0.84
0.96
1.05
3.69
3.75
(CH 3 )3 N --B H 3
0 .2 1
0.84
1.44
0.99
0.91
4.39
4.23
H3N •■••B(CH3 ) 3
-0.04
0.34
0.75
0 .8 8
0 .8 8
2.81
c
(CH 3 )3 N --B (C H 3 ) 3
0.30
0.39
1.24
0.89
0.95
3.77
3.95
H3N - S O 3
(CH 3 )3 N-■•■■SO3
H3N - B F
3
3
AHpoi Ajicr
(a) Total of all calculated contributions to A(j.in<j. (b) Calculated by subtraction of the dipole
moment of the free base from the total complex dipole moment, (c) Not determined
experimentally.
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Bond Moments
Calculations were also carried out with the intent of evaluating the bond moment
approximation for SO 3 , BF3 , and BH 3 . Thus, dipole moments were calculated for each of
these species at a series o f pyramidally distorted structures. All calculations were done
using Gaussian 98 [40] with a 6-3lG(2df) basis set at the MP2 level o f theory. The
calculated bond lengths at the planar configuration were 1.4353, 1.3091, and 1.1929 A, for
SO 3 , BF 3 , and BH 3 , respectively. These results compare favorably with the experimental
values of 1.4198(2) A [41], 1.3102(12) A [42], and 1.19001(1) A [43], indicating the
suitability of the chosen basis set and level o f theory.
The calculated dipole moments are plotted in Fig. 3.2a against cos(Tt-a), where a is the
obtuse angle between the S-O, B-F, or B-H bonds and the C 3 axis o f the molecule. In all
cases, a near-linear relationship is observed across the full range o f relevant angles, from
which values of the S-O, B-F, and B-H bond moments can be determined. The values
obtained are 2.32 D for the S-O bonds in SO 3 , 2.45 D for the B-F bonds in BF 3 , and 0.97
D for the B-H bonds in BH 3 . The B-F bond moment o f 2.45 D is in essentially exact
agreement with that calculated from the 8° distorted structure given by Jurgens and
Almlof [44], The 2.32 D value for SO 3 is somewhat less than the 3.0 D value we have
used previously [16k,33], but is probably more reliable.
57
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3.0
2.5
2.0
♦ BF3
■ S03
a BH3
1.5
1.0
0.5
0.0
0.00
0.20
0.10
0.30
0.40
2.5
2.0
1.5
■ S 03 com plexes
♦ BF3 com plexes
1. 0
0.5
0.0
0.00
0.05
0.10
0.15
0.20
0.25
0.30
Figure 3.2. (a) Calculated dipole moments for SO 3, BF 3, and BH3 vs. cos (Jt-a), where a
is the obtuse angle formed from the S-O, B-F, or B-H bonds and the C 3 axis o f the
molecule, (b) A(J<jls[(A) from BLW calculations vs. cos(n-a).
58
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Induced Dipole Moments as a Function of Dative Bond Length
Finally, calculations of the full dipole moment function, |l(R), were carried out for H3NSO3 and HCN-SO3 using Gaussian 98 [40]. For H3N-SO3, both the 6-31G(2df) and aug-
cc-pVTZ basis sets were used at the MP2 level. The choice of level o f theory and basis set
was made by carrying out geometry optimizations at a number o f levels of theory
employing several basis sets. Optimization using the 6-3 lG(2df) basis set yielded the best
agreement with the experimentally determined moment, while overestimating the N-S
bond distance by about 0.07 A. Optimizing with the larger aug-cc-pVTZ basis set gave
better agreement with the experimental bond distance (to within -0.05 A) but
overestimated the dipole moment by 4%. In order to calculate p(R), the N-S bond distance
was fixed and partial optimizations were carried out at 0.05 A intervals to obtain the
molecular dipole moment. The induced moment at each N-S distance was obtained by
subtraction of the NH3 moment calculated at the corresponding level of theory/basis set.
The results are plotted for both basis sets as the smooth curves in Figure 3.3a.
For HCN-SO3, a similar procedure was carried out in order to select the appropriate level
of theory and basis set. Calculations o f p(R) were carried out at the both the HF and MP2
levels employing the 6-31 G(2df) and cc-pVDZ basis sets, respectively. The N-S bond
distance at the HF/6-31G(2df) level of theory/basis set was in closer agreement with the
experimental value, while the dipole moment was 0.12 D too large. At the MP2/cc-pVDZ
level, the dipole moment was almost in exact agreement with that determined
experimentally, however, the N-S distance was overestimated by 0.20A. Again, the dipole
moment was calculated with the N-S bond distance constrained at 0.05A intervals, and the
induced moments were calculated by subtracting out the dipole moment o f HCN obtained
at the corresponding level of theory/basis set The results are also plotted in Figure 3.3a.
59
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7
H jN -S O j
6
MP2/aug-cc-pVTZ
MP2/6-31G(2df)
4
3
HCN-SOj
2
0
2.4
2.0
1.8
1.6
2.6
2.8
3.0
R(S-N) (A)
(a)
7 ----------------------------------------------------------
6
5
H jN - B F j
4
MP2/d95v-T-+(2d 1f,2p)
3
HCN-BFj
^
MP2/d95v-r-t-(2d 1f.2p)
0
1.5
1 .7
1 .9
21
23
25
2 7
2 9
3 .1
R(B-N) (A)
(b)
Figure 3.3. (a) Induced dipole moment as a function o f S -0 bond length for complexes
o f SO;,. The smooth curves are calculated and the discrete points are experimental data
from Table 2. The bond length for N 2-SO 3 is estimated from van der Waals radii and is
shown with an error bar o f ±0.05 A (b) Induced dipole moment as a function o f B-F bond
length for complexes of BF3. The smooth curves were generated from calculation o f
Reference 18c and the experimental data are from Table 3.2.
60
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Discussion
Experimental Results and BLW Decomposition
The set of complexes listed in Table 3.2 spans a wide range of dative bond distances, and
represent the full range from weak intermolecular interactions to genuine chemical bonds.
N;-S 03 , for example, is a van der Waals complex, while (ChfjbN-BFj and (CH 3)3N-SC>3
are stable chemical species. Moreover, as we have noted previously [1,2,32,39], and as
seen again in Table 3.3, the bond angle at the acceptor atom for these systems correlates
well with the donor-acceptor bond distance: Longer interaction distances are associated
with negligible distortion o f the planar acid, while the shortest bond lengths are
accompanied by near-tetrahedral geometries at the acceptor site. The systems may thus be
regarded as points along the progression from van der Waals to chemical bonding. The
induced moments are more useful than the dipole moments themselves for indicating
changes in charge distribution throughout this progression, as they facilitate comparison
between systems containing bases with different values of p(B). Note that zero point
averaging is not a significant issue for the purposes of comparison between these
complexes, as it contributes only a small amount to the total induced dipole moments.
For example, in HCN-SO 3, the projective reduction o f | i H c n along the symmetry axis of
the complex, Phcn( 1-cosy), is just 0.03 D. Similar numbers are obtained for the other
systems studied.
The most striking feature of the data is the sharp rise in induced dipole moment as the
length of the dative bond decreases. For example, in the series o f SO 3 complexes with
N;, HCN, CH 3CN, H3N, and (CH 3)3N, the induced moments rise from 0.46 D to 6.499
D as the N-S distance decreases from 2.9 A to 1.912 A. Likewise, in the BF3 series, the
observed values of A|iind vary from 1.150 D to 5.404 D as R(BN) decreases from 2.473
A to 1.636 A. These observations are consistent with the notion that a shorter bond
distance is accompanied by more polarization, more charge transfer, and a larger
component o f the S -0 and B-F bond moments along the symmetry axis of the complex.
61
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The BLW results presented in Tables 3.4 and 3.5 provide an approximate decomposition
of the observed moments into these constituent parts. As shown in Table 3.5, the distortion
o f the base in all cases contributes little to the overall induced moment, whereas distortion
o f the acid contributes significantly. Moreover, it is evident that for the same base, the
contribution from distortion of the acid is larger for the BF3 complexes than for the SO 3
complexes, in accordance with the greater tendency towards a tetrahedral configuration at
the boron (c.f. Table 3). Indeed, plots of A(J<iiSt( A) from Table 3.5 vs. cos(rt-a), shown in
Figure 3.2b. resemble those of Figure 3.2a, maintaining a constant slope over the entire
range of angles concerned. This indicates that A(ldlSi(A) is reasonably regarded as arising
from the reorientation of the polar S -0 or B-F bonds in the acid. The bond moments
obtained are 2.77 D and 2.62 D for the S -0 and B-F bonds in SO 3 and BF 3 , respectively,
which are similar to, though slightly larger than the 2.32 D and 2.45 D values reported
above. The values derived from Figure 3.2a, however, are more reliable, as the level of
theory and basis set were chosen to yield the closest agreement with the experimentally
determined bond distances.
As discussed in the Theoretical Background section above, polarization is separated from
charge transfer effects in the BLW-ED approach by the construction o f an “intermediate”
wave function (eqn. (5)) where the electron density o f the respective fragments remains
localized but is allowed to distort in response to the electric field of the nearby fragment.
Table 3.5 demonstrates that the polarization component contributes significantly to the
total induced moment for both the acid and base portion o f the complex. For the acid, the
polarization component increases as the length of the donor-acceptor bond decreases. This
is a reasonable result, since a shortening of the dative bond is accompanied by an increase
angular distortion and therefore by a larger component o f the B-F, B-H, or S-0 bond
polarizabilities along the primary axis of the complex. It is also consistent with the
distance dependence o f multipole-induced dipole interactions [45]. The polarization
component of the basic portion is not necessarily subject to the same type o f correlation
62
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with structure as the bases have differing polarizabilities. However, for the bases
represented in Table 3.5, a similar trend is indeed observed.
Finally, in Table 3.5. the charge transfer component of the induced moment reveals the
contribution arising from the physical transfer o f electron density from the donor to the
acceptor portion of the adduct. This is indicated by the difference between the dipole
moment of the intermediate localized diabatic state and that obtained utilizing the final
HF wave function. For the SO 3 complexes, the charge transfer component o f Apind clearly
increases with decreasing bond length throughout the series. This, too, is a sensible result.
For the BF 3 series, the trend is similar except that the charge transfer component
increases up to 1.0 D for H 3 N-BF 3 and apparently then decreases to 0.87 D for the
(CHsbN adduct. This ordering is preserved for the NH 3 and (C fy ^N complexes o f BH 3 .
For the two adducts of (CH 3 )3 B, Ap<rr increases slightly from N H 3 to (C fy ^ N but the
calculated bond distance also rises from 1.739A in NH 3-B(CH 3)3 to 1.825A in (C fybN B(CH 3 )3 . Thus, unlike the complexes o f SO 3 , the calculations indicate that for the H 3 N
and (CH 3)3N complexes o f all three boron acids studied, the shorter bond length is
associated with the smaller value o f A|icr- Such a reversal seems, at first, anomalous in
light o f the greater basicity of (C fy ^ N relative to NH 3 . However, the calculated
differences in A|icT are small and may not be computationally significant. Moreover,
even if real, whether they result from true differences in charge transfer or from
differences in charge distribution within the resulting complexes cannot be inferred from
the induced moments alone.
Charge Transfer
In order to provide a more quantitative comparison o f the degree of charge transfer in the
systems considered here, Mulliken and NPA population analyses was carried out for both
the BLW and HF wave functions. While charges assigned in this fashion are inherently
arbitrary, the approach remains useful for a comparison between similar complexes. Due to
the localized nature of the BLW wave function, the charge transfer contribution to the total
63
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density is identically zero, thus the magnitude o f the charge transfer is equal to the excess
charge on the acid portion of the complex at the HF level. Table 3.6 summarizes the results.
For the complexes o f SO 3 both the Mulliken and NPA populations indicate an increase in
charge transfer with a decrease in bond length. For the complexes o f BF 3 , on the other hand,
the Mulliken analysis indicates a rise in charge transfer up to the NH 3 complex, followed by
a small decrease for the (C fybN adduct. However, while this apparent reversal is
reminiscent of that noted above for Ajicr, it is not reproduced by the NPA analysis, which
indicates essentially the same degree of charge transfer in H3 N-BF 3 and (CH 3 bN-BF 3 .
Similar results are obtained for H 3 N-B(CH 3 )3 and (CH 3 )3 N-B(CH 3 )3 , but H 3 N-BH 3 and
(CHjbN-BHs appear to have the same degree of charge transfer regardless of the method of
population analysis used.
Table 3.6. Charge Transfer in Lewis Acid-Base Adducts.
Base....Acid
charge transferred
charge transferred
charge transferred
(Mulliken)
(NPA)
(Hyperfme Structure)
0.0062
0.0019
N r —SO’,
0.027
0.010
0.13a
HCN-SO-s
0.036
0.16a
0.015
CH^CN- -SCh
0.27
0.21
0.36b
H;N-—SOi
0.31
0.58°
0.26
(CH 3hN-—SO 3
0.015
0.0078
HCN—BF’,
0.020
0.012
CH 3CN—BF3
0.22
0.12
0.26d
H3N-BF-,
0.20
0.41e
0.12
(O T K N --B F,
0.26
0.13
H ^N -B H i
0.26
0.41'
0.13
(CHO 1N—BH3
0.18
0.11
H,N--B(CH,)3
0.14
0.12
0.40c
(CH3hN--B(CH3b
(a) Reference [32], (b) Reference [33]. (c) Reference [16k]. (d) Calculated from data
reference [46]. (e) Reference [47]. (f) Calculated from data o f reference [48].
64
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The increase in charge transfer observed across the SO 3 series is consistent with the
increasing basicity o f the electron pair donors that accompanies the decreasing bond length.
On the other hand, while HCN-BF 3 , CH 3 CN-BF 3 , and H 3 N-BF 3 behave in a similarly
orderly fashion, the results for the H 3 N and (CITjkN complexes of the boron acids are
ambiguous. The Mulliken population analysis has been widely criticized, especially for its
basis set dependence [49], and the counterintuitive results obtained for these bases should be
viewed with caution. Indeed, in light of the NPA analyses, it seems more likely that the
differences in charge transfer between the H3 N and ( C t ^ N adducts o f these boron acids
are too small to discern.
In order to provide a pictorial representation of the changes in the charge density
accompanying both charge transfer and polarization, electron density difference plots were
generated for HCN-SO 3 , (CfyhN-SC^ and (CH 3 )3 N-BF 3 and are shown in Figure 3.4. From
the Figure, it is clear that there is almost no charge transfer in the HCN-SO 3 complex, while
polarization tends to move the charge density outward toward the SO 3 oxygens on the acid
portion and away from the SO 3 on the HCN. For the two (CHs^N complexes, the effect of
polarization is to distort the charge density away from the nitrogen atomic center into the
bonding region while at the same time increasing the density in the region o f the carbon
atoms. The polarization o f SO 3 and BF 3 can be seen as arising largely from orbital
rehybridization on the oxygens or fluorines. The effect o f charge transfer is a further
migration o f charge density from the region near the N position to that o f the Lewis acid,
with a concomitant increase in charge density on the oxygens or fluorines along the S -0
or B-F bond axes, respectively. These results are similar to previous calculations o f the
charge density o f N H 3 -SO 3 [7,38]. The significant involvement o f charge density on the
methyl groups of trimethylamine carbons is also consistent with experimental evidence
from (e.2 e) spectroscopy, which indicates significant delocaiization o f the "lone pair"
orbital on the carbons [50],
65
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M
IP fes
H
e.
"
f.
Figure 3.4. Electron density difference plots for (a) HCN-SO 3 , polarization (b) HCNSO 3 . charge transfer, (c) (C ^bN -S C h, polarization, (d) (CT^bN-SCb, charge transfer,
(e) (CH 3)3N-BF 3, polarization, (f) (CH 3)3N-BF 3 charge transfer. Heavy lines indicate
increase in charge density. Dashed lines indicate decrease in charge density. The contour
level is 0.005 e/au\
66
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It is also of interest to examine the question o f charge transfer from an experimental
standpoint. Estimates of charge transfer can be made from analysis o f nuclear quadrupole
coupling constants [27,51], with the standard approach being that first given by Townes and
Dailey [52]. A number of results derived from analysis o f the 14N coupling constants, are
available for the complexes examined in this work and are also given in Table 3.6. In
obtaining these values, the one-electron wave function for the dative bond is assumed to
have the simple form ¥ = a<f>D + p<j)A, where <f>o and <t>A are the donor and acceptor orbitals,
respectively. A value of 2J32, interpreted as the "charge transfer", is derived from quadrupole
coupling constants subject to the usual assumptions of the Townes and Dailey method and
to neglect of overlap between <j>Dand <t)A. As applied to donor-acceptor complexes, this
approach also assumes that any change in the quadrupole coupling constant from its free
monomer value can be attributed to transfer o f charge from the basic portion of the adduct to
the acid. The values obtained are thus very approximate and probably represent upper limits
to the true electron transfer.
The experimentally derived values in Table 3.6 may be compared with the results o f the
Mulliken and NPA population analyses. Such a comparison is complicated, of course, by the
fact that neither approach yields the “correct” electron transfer value. Indeed, superficially, it
appears from the Table that the degree o f charge transfer obtained from a Townes and
Dailey analysis is overestimated [53], but in light o f the substantially different nature of
these estimates, it is unclear how well the experimental values are expected to agree with
those derived from population analyses. Nonetheless, despite these complications, the trend
toward increasing electron transfer at shorter bond distances is reproduced in the SO 3 series.
In the case of the boron containing adducts, there is insufficient experimental data to
establish a trend. However, it is interesting to note that the charge transfer derived from
hyperfme structure appears significantly larger in (CHsbN-BFj
than in H 3 N-BF 3 , in
contrast with the theoretical results described above.
67
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Implications for a Simplistic Chemical Viewpoint
In two previous studies, we presented a simple model that appeared to predict the observed
dipole moments of H 3 N-SO 3 [33] and (CH 3 )3 N-SC>3 [16k] to within only a few percent. The
model is based on elementary ideas of bond moments and charge transfer, and takes the
following form:
(I = |i(B) + 3pMxsin(a-90) + neR
(9)
Here, |i(B) is the dipole moment of the free base, p Mx is the bond moment o f an S -0 or BF bond (obtained from Figure 2a), n = 2(3: , and R is the N-S or N-B bond distance.
According to equation 9, the dipole moment of the complex arises mainly from that o f the
base, that of the distorted acid, and that resulting from the transfer o f n electrons across
the distance of the donor-acceptor bond.
Although equation 9 appeared to be successful in our previous work, we noted that the
neR term is a grossly oversimplified expression of the charge transfer component and that
mutual polarization of the interacting moieties is neglected. Moreover, the validity o f the
bond moment approximation, inherent in the second term o f equation 9, is not
guaranteed. Thus, it is of interest to ascertain whether similar results can be achieved for
other systems as well, or whether the apparent success for H 3 N-SO 3 and (CH 3 )3 N-S 0 3 is
fortuitous. Table 3.7 presents the results o f equation 9 for the complexes investigated in
this work for which all the necessary experimental data are available. The results for
H 3 N -SO 3 and (CH 3 )3 N -S 0 3 differ slightly from those reported in our previous work due
to the use o f the improved S -0 bond moment determined above. Remarkably, all the
observed dipole moments are predicted to within about 10%.
Some insight into the apparent success o f this model can be gained from the
computational results present above. From Figure 3.2a, it is clear that the B-F and S-0
68
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bond moments are well defined and thus, the second term in equation 9 reasonably
corresponds to the Ap^s, term calculated in the BLW method. In addition, values of
Table 3.7. Comparison of Calculated and Experimental Dipole Moments
Complex
n
(J-e x p
HCN-SO 3
0.13
CH 3 C N -SO 3
U C a lc ( D ) a
% Difference15
4.4172(31)
4.82
-9%
0.16
6.065(18)
6.06
0%
H 3 N-SO 3
0.36
6.204(11)
5.79
7%
(CH 3 )3N -S0 3
0.58
7.1110(69)
7.17
- 1%
H 3 N-BF 3
0.26c
5.9027(93)
5.30
10%
(CH 3 )3 N -BF 3
0.41
6.0157(76)
5.92
2%
(CH 3 )3N-BH 3
0.40d
4.84(10)d
4.53
6%
(a) Calculated from equation 9. (b)
[46]. (d) Reference [48].
(D)
1 0 0 ( |I e x p
- McaicV H e x p -
(c )
Calculated from Reference
A|i<ils,(B) given in Table 3.5 are small, so that the neglect o f structural distortion of the
base, implied by equation 9, also appears valid. However, it is clear from the BLW
results that electronic polarization of both the acid and base give rise to substantial
contributions to the dipole moment of the complex. Thus, neglect o f polarization is a
significant omission from the simple model and it seems likely that the neR term
overestimates the charge transfer component by an amount that approximately
compensates for this neglect. Indeed, values o f neR calculated from hyperfine structure
run some 1.6 to 7.3 times larger than the corresponding A|i<rr values obtained from the
BLW method, with the larger ratios occurring for the more weakly bound systems. Such
a situation is consistent with the notion that the Townes and Dailey analysis provides an
upper limit to the charge transfer, and that the polarization contribution to eQq is most
significant when charge transfer is not the major contributor. Differences in charge
distribution may also play a significant role. In any case, a scenario involving
cancellation o f terms is consistent with the observation that the calculated dipole
69
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moments are neither systematically high nor systematically low. In addition, the percent
accuracy quoted in Table 3.7 may artificially glorify the quality of the calculation, as the
dipole moments themselves are large and a substantial residual is still a relatively small
percentage of the total moment.
The success of this model demonstrates the arbitrariness of partitioning charge transfer
and polarization effects in systems where both contribute significantly to the bonding
interaction. In the Townes and Dailey model, it is common to summarize all the changes
in electron density at a particular nucleus into a single parameter, which is referred to as
"charge transfer”. However, this parameter not only describes real charge transfer but
charge migration due to distortion of the electron density produced by the local electric
field. Thus the terms "charge transfer” and polarization lose their clarity, and the
distinction between the two coactive effects becomes uncertain. The BLW-ED approach
allows for a solution to this problem by the construction of the intermediate diabatic state,
an unphysical state where the electron density is forced to remain localized but is allowed
to diston in the presence of the nearby electric field. Physical charge transfer is thus
partitioned from polarization and obtained only in the final step where the restriction of
localization is relaxed and charge is allowed to delocalize and become associated with
molecular orbitals on the nearby fragment. This offers a definition o f charge transfer, one
that effectively separates out polarization, which in the end may or may not turn out to be
the most reliable method. For the purposes here, the approach has provided considerable
insight into the electronic changes that accompany the formation o f the dative bond and
contribute to the measured dipole moments in these systems.
Radial Dependence of the Induced Moment
A final question arising from the observed induced dipole moments involves not their
magnitude per se, but rather their variation with bond length. As noted in the Introduction,
the sensitivity of partially bonded systems to a local environment appears to be closely
related to an increasing dipole moment function at shorter dative bond distances. The
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experimental determination of |i(R), however, is in general nontrivial, and indeed while
large structure changes upon crystallization are well documented experimentally, support
for a "dipolar enhancement" mechanism is largely theoretical [5,7-10]. We have noted,
however, that A|iind increases as bond length decreases across a series o f complexes with a
common base. Therefore, a natural question concerns the possibility that the dipole
moments of a series contain information about the radial dependence o f Aii^.. Such an
idea, while not rigorously justifiable, would be akin to the widely used structure
correlation method for determining reaction paths from crystallographic data [4],
The results shown in Figure 3.3a address this question for complexes o f SO 3 . Similar
calculations of A|ijnd(R) have been carried out previously for HCN-BF 3 [18c] and H 3 NBF 3 [ 16i. 1Sc] and the results are reproduced in Figure 3.3b. For both sets of systems, the
theoretical curves for the HCN and NH 3 complexes are seen to be similar, though exact
agreement is neither observed nor expected. Equally important is that for both sets of
systems, while the number of experimental points is small, a rough correspondence
between the experimental values and the theoretical results is suggested. In other words,
values of Apmd for a set of different complexes of SO 3 at their zero point geometries
roughly indicates the value to be found for HCN-SO 3 and H3 N-SO 3 at bond lengths far
from equilibrium. A similar situation is suggested for complexes BF 3 , though fewer
experimental points are available.
While the above result is not rigorously guaranteed, it is reasonable in the following sense:
In a previous paper, we used a series o f BF3 complexes with nitrogen donors to test the
validity of the structure correlation method for determining reaction paths [18c]. We found
that the relationship between bond length, R, and the NBF bond angle, a , across a series
of complexes was in reasonable agreement with that calculated theoretically for a single
complex across the full range of relevant B-N distances. Thus, the evolution of molecular
structure is similar among members of the series as bond formation proceeds. This is a
chemically sensible idea and is the essence of the structure correlation method. If one
71
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subscribes to this general viewpoint, then, it is a relatively small extrapolation to suppose
that changes in charge distribution that occur upon formation of the dative bond similarly
follow a common, generalized pathway. Changes arising from electrostatic polarization
will, of course, depend on the polarizabilities and multipole moments of the particular
base, and do not necessarily vary smoothly across a series. However, for the complexes
investigated here, such effects apparently do not obscure the correlation. Indeed if general,
such a method might prove useful for estimating dipole moment functions for systems of
this kind. In effect, the large dynamic range associated with the bonding across a series of
related complexes allows the radial dependence of the induced moment to be probed
without the usual need for vibrational excitation along the bond coordinate.
Conclusions
Dipole moments have been measured for a series o f Lewis acid-base complexes in the
gas phase. The results have been analyzed, together with literature values for a number
o f closely related systems, to elucidate the changes in polarity that occur across the full
range between van der Waals interactions and chemical bonds. The induced dipole
moments for the adducts studied are large and increase sharply as the length o f the
donor-acceptor bond decreases. Moreover, decomposition o f the dipole moments using
a block localized wave function scheme indicates that polarization o f the acid and base,
charge transfer, and geometrical distortion o f the acid all contribute significantly to the
overall dipole moment of the complexes. Geometrical distortion o f the base, on the
other hand, contributes negligibly. The contributions to the total dipole moment arising
from polarization, charge transfer, and distortion each individually exhibit a general
increase as the donor-acceptor bond length decreases, though a few small anomalies
may exist.
Charge transfer, as determined theoretically by population analyses and experimentally
from nuclear hyperfme structure, also generally increases for the systems studied as the
donor-acceptor bond shortens. A possible exception involves the H 3N and (CHjfrN
72
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adducts of BF3, BH 3, and (CHsbB. Comparison between experimental and theoretical
values is difficult, as the two measures are defined in substantially different ways.
Nonetheless, the experimentally derived estimates are systematically larger than those
obtained from population analysis. A simple model involving bond moments and
experimental charge transfer values appears to predict the measured dipole moments
reasonably well, but the success likely arises from an accidental cancellation involving
an overestimate o f charge transfer and neglect of polarization.
Finally, calculations o f the induced dipole moment as a function o f bond length have
been presented for several o f the systems studied. The results are compared with
experimental values for a series of complexes of different dative bond lengths. We find
that for the systems investigated here, the induced moments of the series roughly
approximate the induced dipole moment function for individual members of the series.
Thus, a group o f complexes taken as a whole, contains approximate information about
the radial dependence o f A(i,nd, much like crystallographic and gas phase structure
correlations contain information about reaction pathways.
Acknowledgements
This work was supported by the National Science Foundation (CHE-9730844) and the
Donors of the Petroleum Research Fund, administered by the American Chemical Society.
A.R. was supported by and NSF REU grant at the University of Minnesota and support for
the computational work was obtained from the Minnesota Supercomputer Institute. We
are especially grateful to Prof. Jiaii Gao for valuable input and to Dr. Deborah Hankinson
for providing us with the numerical data used to regenerate Fig. 3.3b.
73
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References
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Cabaleiro-Lago, E.M.; Rios, M.A. Chem. Phys. Lett. 1998, 294, 272. (e) Iglesias, E.;
Sordo, T.L.; Sordo, J.A. Chem. Phys. Lett. 1996, 248, 179. (f) Skancke A.; Skancke, P.N.
J. Phys. Chem. 1996, 100, 15079. (g) Ford, T.A.; Steele, D. J. Phys. Chem. 1996, 100,
19336. (h) Branchadell, V.; Sbai, A.; Oliva, A. J. Phys. Chem. 1995, 99, 6472.
(i)
Glendening, E.D.; Streitwieser, A .J. Chem. Phys. 1994, 100,2900.
19. (a) Laugengayer, A.W.; Sears, D.S. J. Am. Chem. Soc. 1945, 67, 164. (b) McClellan,
Tables o f Experimental Dipole Moments, Freeman; San Francisco, 1963.
20. Canagaratna, M.; Ott, M.E.; Leopold, K.R. Chem. Phys. Lett. 1997,281, 63.
75
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
21. Balle, T.J.; Flygare, W.H. Rev. Sci. Instrum. 1981, 52, 33.
22. (a) Phillips, J.A.; Canagaratna, M.; Goodfriend, H.; Grushow, A.; Almlof, J. J. Am.
Chem. Soc. 1995, 117, 12549. (b) Phillips, J. Ph.D. Thesis, University of Minnesota,
1996.
23. Muenter, J.S. J. Chem. Phys. 1968,48,4544.
24. Bowen, K.H.; Leopold, K.R.; Chance, K.V.; Klemperer, W. J. Chem. Phys. 1980, 73,
137.
25. Coudert, L.H.; Lovas, F.J.; Suenram, R.D.; Hougen, J.T. J. Chem. Phys. 1987, 87, 6290.
26. (a) Organic Synthesis. 2nd. Ed:. Wiley: New York 1964; Collect. Vol. I. (b) Clippard, P.H.
Ph.D. Thesis, University of Michigan, 1969.
27. Gordy, W.; Cook. R.L. Microwave Molecular Spectra. Wiley: New York. 1984.
28. Maki, A.G.; J. Phys. Chem. Ref. Data 1974, 3,221.
29. Beers, Y.; Russell, T.W. IEEE Trans. Inst. Meas. 1966. IM-15, 380.
30. Marshall. M.D.; Muenter, J.S. J. Mol. Spectrosc. 1981, 85, 322.
31. Lide. D.R.; Mann, D.E. J. Chem. Phys. 1958,28. 572
32. Bums, W.A.; Phillips, J.A.; Canagaratna, M.; Goodfriend, H.; Leopold, K.R. J. Phys.
Chem. A 1999. 103, 7445.
33. Canagaratna, M.; Phillips, J.A.: Goodfriend, H.; Leopold, K.R. J. Am. Chem. Soc. 1996,
118. 5290.
34. Coppens, P.: Guru Row, T.N.; Leung, P. Stevens, E.D.; Becker, P.J.; Yang, Y.W. Acta
Cryst. 1979, A35, 63.
35. Bats, J.W.; Coppens, P.; Koetzle, T.F. Acta Cryst. 1977, B33, 37.
36. Reeve, S.W.; Bums, W.A.; Lovas, F.J.; Suenram, R.D.; Leopold, K.R. J. Phys. Chem.
1993,97, 10630.
37. Lide, D.R., Jr.; Taft, R.W., Jr.; Love, P. J. Chem. Phys. 1959,31, 561.
38. Mo, Y.; Gao, J.; Peyerimhoff, S.D. J. Chem. Phys. 2000, 112, 5530.
39. Dvorak, M.A.; Ford, R.S.; Suenram, R.D.; Lovas, F.J.; Leopold, K.R. J. Am. Chem. Soc.
1992, 114, 108.
76
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
40. Frisch, M.J.; Trucks, G.W.; Schlegel, H.B.; Scuseria, G.E.; Robb. M.A.; Cheeseman,
J.R.; Zakrzewski, V.G.; Montgomery, J.A., Jr.,; Stratmann, R.E.; Burant, J.C.; Dapprich,
S.; Millam, J.M.; Daniels, A.D.; Kudin, K.N.; Strain, M.C.; Farkas, O.; Tomasi, J.;
Barone. V.; Cossi, M.; Cammi, R.; Mennucci, B.; Pomelli, C.; Adamo, C.; Clifford, S.;
Ochterski, J.; Petersson, G.A.; Ayala, P.Y.; Cui, Q.; Morokuma, K.; Malick, D.K.;
Rabuck, A.D.; Raghavachari, K.; Foresman, J.B.; Cioslowski, J.; Ortiz, J.V.; Baboul,
A.G.; Stefanov, B.B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Gomperts, R.;
Martin. R.L.; Fox, D.J.; Keith, T.; Al-Laham, M.A.; Peng, C.Y.; Nanayakkara. A.;
Challacombe. M.; Gill, P.M.W.; Johnson, B.; Chen, W.; Wong, M. W.; Andres, J.L.;
Gonzalez, C.; Head-Gordon, M.; Replogle, E.S. and Pople, J.A. Gaussian 98, Revision
A.9, Gaussian, Inc., Pittsburgh PA, 1998.
41. (a) Meyer, V.; Sutter, D.H.; Dreizler, H. Z Naturforsch. A 1991.46, 710. (b) Kaldor, A.;
Maki, A.G. J. Mol. Spectrosc. 1973,15,123.
42. (a) Brown, C.W.; Overend, J. Can. J. Phys. 1968,46, 977.
43. Kawaguchi, K. J. Chem. Phys. 1992,96, 3411.
44. Jurgens, R.; Almlof, J. Chem. Phys. Lett. 1991, 176,263.
45. Curiously, the calculated values of A|ipoi(A) given in Table 5 exhibit a strikingly linear
dependence on cos(a) for both the SO 3 and BF 3 series of adducts. While a dependence on
cos(a) is certainly to be expected, the variability of dipole and higher order multiple
moments of the bases across the series render this linearity interesting but of no obvious
fundamental significance.
46. Legon, A.C.; Warner, H.E. J. Chem. Soc. Chem. Commun. 1991, p. 1397.
47. Fiacco, D.L.; Hunt, S.W.; Leopold, K.R. 54th Symposium on Molecular Spectroscopy.
Columbus, OH, 1999, Abstract WF12.
48. Kasten, W.; Dreizler, H.; Kuczkowski, R.L. Z. Naturforsch 1985,40a, 1262.
49. See, for example, Bachrach, S.M. in Reviews in Computational Chemistry, Lipkowitz,
K.B.; Boyd, D.B. Editors, Vol. 5. VCH: New York, 1994.
50. McMillan, K.; Coplan, M.A.; Moore, J.H.; Tossell, J.A. J. Phys. Chem. 1990, 94, 8648.
77
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
51. Lucken, E.A.C., Nuclear Quadrupole Coupling Constants, Academic Press: London,
1969.
52. Townes, C.H.; Dailey, B.P. J. Chem. Phys. 1949,17, 782.
53. It is interesting to note that the inclusion o f even modest overlap integrals in the
calculation of 2(32 significantly reduces the value obtained. Hunt, S.W.; Leopold, K.R.,
manuscript in preparation.
78
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Appendix to Chapter 3.
Table 3.A1. Assigned Stark Transitions for HC15N-SQ 3 .
J" Mj" Mi" J' Mj' Mi' K E(V/cm) Frequency (MHz) Obs-Calc (MHz)
0
0
0
1 0
1 0
0
0
0
1 0
1 0
0
0
1 I 1
1 0
0
0
0
1 -1
1 0
0
0
0
1 -1
1 0
0
0
1 I 1
0 0
0
0
-1 1 0
-1 0
0
0
0
1 0
1 0
0
0
0
1 -1
1 0
0
0
1 1 1
0 0
0
0
1 1 I
1 0
0
0
0
1
0 0
0
0
-1
0
-1 0
0
0
-1
-1
1 0
0
0
0
-1
0 0
0
0
-1
0
0
0
0
0
-1
0
0
0
0
0
-1
0
0
0
I
1
1
1
1
1
I
I
1
1
0
1 0
0
0
0
1 0
1 0
0
0
-1 1 -1 -1 0
0
0
0
1 0
1 0
0
0
0
1 0
1 0
0
0
-1 1 -1 -1 0
0
0
-1 1 -1
0
0
-1 1 -1 -1 0
0
0
0
1 0
1 0
0
0
0
1 0
1 0
0
0
-1 1 -1 -1 0
0
0
-1 1 -1 -1 0
0
0
-1 1 -1 -1 0
-1 -1 0
0
1 0
-1
1 0
-1
0 0
-1 -1 0
1 0
15.34
15.34
15.34
15.34
15.34
3789.697
3789.697
3789.652
3791.472
3791.472
-0.002
-0.002
0.001
-0.001
-0.001
15.34
15.35
15.44
3788.500
3789.698
3789.697
3791.471
-0.002
-0 .0 0 1
-0.003
-0.003
-0.002
0.002
15.43
15.42
15.42
15.44
15.42
24.78
24.76
24.76
24.76
24.61
24.62
24.61
24.68
24.62
30.79
30.80
36.93
36.92
43.02
43.04
43.03
49.14
49.13
49.13
55.22
3788.501
3789.654
3788.503
3789.696
3791.646
3788.674
3789.763
3789.896
3791.638
3788.676
3789.762
3789.891
0.000
-0.004
0.002
-0.007
-0.003
-0.002
-0.002
-0.001
-0.002
-0.005
3789.893
3789.866
3790.076
3790.315
3789.993
3790.140
3790.140
3790.603
3790.951
3790.315
-0.001
-0.002
-0.006
-0.003
-0.001
3790.313
3790.508
79
-0 .0 0 1
-0.003
-0.003
-0.003
0.000
0.001
0.001
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 3.A1. continued.
J" Mj" M," J' Mj' Mi' K E(V/cm) Frequency (MHz) Obs-Calc (MHz)
0
0
-1 1 -1 -1 0
61.33
3790.724
0
0
1 -1 -1 0
67.39
3790.968
0
0
-1 1 -1 -1 0
73.46
3791.229
1 -1
-1 2 -1 -1 0
24.67
7578.885
1 -1
2 -2
0 0
24.68
7577.585
1 -1
0 2 0
-I 0
24.67
7578.701
1 -I
0 2 -I
0 0
24.65
7579.994
1 -1
0 2 -2
1 0
24.66
7580.668
1 -1
1 2 -1
1 0
24.68
7577.744
0.000
0.007
0.008
0.000
-0.010
0.001
0.001
0.000
0.000
1 0
-1 2 0
-1 0
24.68
7577.484
0.001
1 0
-1 2 -1
0 0
24.67
7578.774
-0.002
I
0
-1 2 -2
1 0
24.68
7579.454
0.003
1 -1
-1 2 0
-1 0
24.65
7577.612
-0.002
I -1
-1 2 -2
1 0
24.64
7579.581
-0.001
1 -1
0 2 -I
I 0
24.66
7580.707
1 -1
1 2 0
1 0
24.65
7577.705
1 0
-1 2 -1
1 0
24.64
7579.490
1 0
1 2 1
1 0
24.73
7578.756
0.000
0.000
0.000
0.003
1
1
0 2 2
0 0
24.73
7578.667
-0.005
1
1
0 2 1
1 0
24.67
7579.976
0.005
1
1
1 2 2
1 0
24.73
7578.848
0.001
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 3.A2. Assigned Stark Transitions for CH3CN-SQ3
J" Mj" Ml" J’ Mj' Mi' K E(V/cm)
1 0
1 2 0
1 1
0.61
-1 2 -1 0 1
1 0
0.61
1 0
0 2 0
0 1
0.62
1 I
1 2 1 1 1
0.62
1 0
0 2 -I
1 1
0.62
2
0
1
-1
0 -I 1
1.55
2
1 0
0
1
I 1
1.55
2
1 0
0
0
0 1
1.55
2
1 1
0
0
I 0
1.55
1 1
0 2 1 0 0
1.55
1 1
1 0
1 2 1
1.55
1
I 2 1 0 0
1.55
1
-1 2 0 -1 0
1.55
1 -1
0 2 0 -I 0
1.55
I -I
-I 2 -I -I 0
1.55
2
1 -1
1
-1
1 0
1.55
2
_2 1 0
1 -1
0
1.55
2
2
1
I
0 0
6.15
I -1
1 2 0
6.15
1 0
I 1
1 2 2
I 0
6.15
1 -1
0 2 -1
I 0
6.15
1 -1
0 2 -1
1 0
6.15
1 -1
I
1
1 -1
1 -1
1 -1
1
1 -1
1 -1
1
I -I
1 1
-1
2 .2
0
0
2 0
2 -1
-1 0
2 -I
2 -I
-1 0
-1
-I
-1
1
-I
1
0
2
0
2 _2
2 -2
2 .2
-1 2 -1
-I 2 -2
0 2 -1
0
-I
I
0
1
0
-I
-I
1
0
0
0
0
0
0
0
0
0
0
6.15
6.15
6.15
6.15
6.15
6.15
6.15
6.15
6.15
6.15
6.15
6.15
Frequency (MHz)
Obs-Calc (MHz)
4063.091
4063.554
4063.711
0.000
-0.004
-0.001
4064.044
4064.044
-0.001
4062.942
4063.026
4063.834
4065.077
4063.351
4063.428
-0.001
0.001
0.002
-0.001
-0.002
4062.318
4062.318
4063.351
4063.428
4062.489
4065.077
4062.305
0.001
4062.486
4063.435
4065.075
4065.075
4062.332
4063.351
4063.423
4063.446
4063.446
4062.485
4062.305
4062.486
4063.343
4063.418
4063.435
4065.075
0.000
0.000
0.001
-0.002
0.000
-0.002
-0.001
0.001
-0.001
-0.001
-0.001
- 0.00 1
0.001
0.004
0.000
0.002
0.002
-0.002
0.001
-0.001
0.002
0.000
-0.001
-0.001
81
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 3.A2. continued.
J" Mj" M," J' Mj’ M,' K E(V/cm)
1 -1
1 2 .2 1 0
6.15
2
1 1
1
1 1 0
6.15
2
2 -1 0
1 0
1
6.15
1 1
0 2 1 0 0
6.15
1 0
-1 2 0 -1 1
6.15
1 0
1 2 0
1 1
6.15
1 -1
1 2 -I
1 0
6.15
1 1
1 2 2 0 0
6.15
2
0
1 0
0 0 I
6.15
2
1 1
1
1 1 0
12.30
2
2
1 0
1
-1 0
12.30
2
1 1
0
1 0 0
12.30
1
0
1
0
1 -1
1
1
1
0
1 -1
-1 2 0
1 2 0
1 2 -1
1
1 -1
4063.497
4063.404
4063.340
0.000
0.002
0.004
12.30
-I
0
-1
0
1
0
0
0
0
1
12.30
12.30
12.30
18.45
18.45
4063.955
4062.369
4063.340
-0.0 0 1
0.001
-0.001
0.000
- 0.001
0.004
-1 2 -1
0 2 2
I 0
0 0
-I 0
1 0
-1 0
1 0
-1 0
0 1
-1 0
-1 0
2 -2
1 0
1 2 2
0 2 0
-1 2 _2
1 2 0
I 2 -I
1 2 2
-1 2 -1
1 2 1
0 2 0
1
0.001
0 .0 0 1
4063.073
4062.508
4062.369
0
1 -1
4062.332
4063.889
12.30
12.30
12.30
1
1
-0.001
0.001
0.004
I t
1 0
0 0
0 1
0 0
0
1
4063.423
4063.351
4062.992
4063.016
4062.500
-0.003
1
1 -I
- 0.002
0.002
0.000
0.004
4063.060
1
0
4062.485
4063.446
12.30
1 -1
1
Obs-Calc (MHz)
I
0 2 0
-1 2 -1
-1 2 -1
1 -1
Frequency (MHz)
2
1
I 0
1 -1
1 0
1 -1
1 1
0 2 -I
-1 2 -1
0 2 0
1 -1
0
-1
12.30
4063.404
4063.497
0.002
4063.342
4063.175
0.001
-0.005
18.45
4062.511
0.002
18.45
18.45
18.45
18.45
24.60
24.60
24.60
24.60
30.75
4062.438
4063.588
4063.588
4063.342
0.004
4062.475
4063.715
4064.213
0.002
0.003
0.000
4063.715
4065.121
0.003
-0.001
30.75
4065.121
-0.001
0.000
0.002
0.002
0.001
82
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 3.A3. Assigned StarkTransitions for HC15N-n BF3 .
J" Mj" M," J’ M / M,' K E(V/cm)
1.5
1.5
1.5
0.5
0.5
1
1
1
1
1
0.5
1 0.5
1 -1.5
0 0.5
1 0.5
0.5
0.5
0.5
-1.5
-1.5
1.5
1.5
1.5
0.5
0.5
0.5
0.5
0.5
-1.5
-1.5
1.5
1.5
1.5
0.5
0.5
1
1
1
1
I
1
1
1
1
1
I
1
1
I
1
1
1
1
1
1
I
0
0.5
0.5
-1.5
1.5
1.5
1.5
0.5
0.5
1
1
1
1
1
1
1
1
0
0.5 1 1 -1.5 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-1.5
1.5
0.5
-1.5
0.5
0.5
0.5
-1.5
0
0.5
0.5
-1.5
1.5
0.5
-1.5
0.5
0
0.5
1 0.5
1 -1.5
0 0.5
1 0.5
0
-1
-1
1
-1
0
1
1
0
1
1
-1
-1
1
-1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1 -1.5 0
1.5
1 -1.5
0 0.5
1 0.5
1 -1.5
0 0.5
I 0.5
-1
0
0
0
0
0
0
0
12.45
12.45
12.45
12.45
12.45
12.45
12.33
12.33
12.45
12.33
18.45
18.45
18.45
Frequency (MHz)
Obs-Calc (MHz)
4056.137
0.000
4056.115
4056.137
4056.137
-0.009
0.001
0.001
-0.009
4056.115
4056.137
0.001
4055.565
4056.216
-0.003
-0.003
0.001
-0.003
-0.004
4056.188
4056.216
-0.003
-0.004
18.45
18.45
18.45
18.45
18.45
18.45
18.45
24.98
4056.216
4056.188
4056.216
4055.630
4055.630
4056.216
4055.630
-0.004
-0.003
-0.004
24.98
24.98
24.98
24.98
4056.285
4055.730
4056.359
4056.285
4055.730
4055.730
24.98
24.98
24.98
30.81
30.81
30.81
30.81
30.81
30.81
4055.565
4055.565
4056.137
4056.359
4055.722
4056.502
4056.396
4055.822
4056.502
4056.396
4055.822
-0.002
-0.002
-0.004
-0.002
0.007
-0.004
0.006
0.007
-0.004
0.006
0.006
-0.002
-0.003
-0.0 0 1
-0.002
-0.003
-0.001
-0.002
83
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 3.A3, continued.
J" Mj" M," J’ Mj' M,' K E(V/cm)
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Frequency (MHz)
Obs-Calc (MHz)
0
30.81
30.81
36.88
36.88
36.88
4055.822
4055.822
4056.693
4056.528
4055.950
0.5 0
0.5 0
36.88
36.88
4056.693
4056.528
-0.002
-0.002
-0.003
0.003
0.005
-0.003
0.003
0.5 i 1 -1.5 0
0.5 1 -1 1.5 0
-1.5 1 1 -1.5 0
36.88
36.88
36.88
4055.950
4055.950
4055.950
0.005
0.005
0.005
0.5
-1.5
1.5
1.5
1.5
0.5
0.5
1 -1
1 1
1 0
1 1
1 1
1 0
1 1
1.5
-1.5
0.5
0.5
-1.5
0
0
0
0
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 3.A4. Assigned Stark Transitions for A state of H3 1 SN-UBF3.
J" Mj" M," J’ Mj' M,' K E(V/cm) Frequency (MHz)
Obs-Calc (MHz)
6.28
9097.958
0.000
0
1.5 1 1 0.5 0
1.5 1 0 1.5 0
6.28
9098.247
-0.002
0
0
0.5 1 -1
1.5 0
6.28
9097.722
-0.004
0
0
1.5 1 1 0.5 0
6.28
9097.989
-0.006
0
0
1.5 1 0
1.5 0
6.28
9098.284
-0.012
0
0
0.5 1 0
0.5 0
6.28
9098.009
0.002
0
0
0.5 1 -1
1.5 0
6.28
9097.757
-0.005
0
0 -0.5 1 0 -0.5 0
6.28
9098.263
-0.008
0
0
1.5 1 1
1.5 0
6.28
9097.978
-0.001
0
0
1.5 1 1 0.5 0
6.28
9098.049
-0.006
0
0
1.5 1 0
1.5 0
6.28
9098.368
-0.010
0
0
0.5 1 0
0.5 0
6.28
9098.082
-0.006
0
0
0.5 1 -I
1.5 0
6.28
9097.816
-0.001
0
0
-0.5 1 -1 0.5 0
6.28
9098.316
-0.004
0
0
1.5 1 1
1.5 0
6.28
9098.020
-0.002
0
0
1.5 i
1 0.5 0
6.28
9098.131
0.000
0
0
0.5 1 0
0.5 0
6.28
9098.200
-0.001
0
0
0.5 1 -1
1.5 0
6.28
9097.890
0.001
0
0
-0.5 1 -1 0.5 0
6.28
9098.391
-0.001
0
0
1.5 1 1
1.5 0
6.28
9098.076
-0.006
0
0
1.5 1 1 0.5 0
6.28
9098.226
0.002
0
0
1.5 1 0
1.5 0
6.28
9098.658
-0.004
0
0
0.5 1 0
0.5 0
6.28
9098.339
0.002
0
0
0.5 1 -1
1.5 0
6.28
9097.972
-0.005
0
0
1.5 1 1
1.5 0
6.28
9098.153
-0.007
0
0
1.5 1 1 0.5 0
6.28
9098.329
-0.001
0
0
0.5 1 0
0.5 0
6.28
9098.676
0.008
0
0
0.5 1 -1
1.5 0
6.28
9098.081
0.002
0
0
-0.5 1 -1 0.5 0
6.28
9098.477
0.003
0
0
1.5 I
1.5 0
6.28
9098.258
0.003
0
0
1.5 1 1 0.5 0
6.28
9098.446
-0.002
0
0
-0.5 1 1 -1.5 0
6.28
9098.199
0.005
0
0
-0.5 1 -1 0.5 0
6.28
9098.607
0.004
0
0
6.28
9098.362
-0.002
0
0
0
I
1.5 1 I
1.5 0
85
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 3.A5. Assigned Stark Transitions for E state o f H3 l5N-n BF3 .
J" Mj" M," J’ Mj' M,' K EfWcm)
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1.5
1.5
0.5
1.5
1.5
0.5
-0.5
1.5
1.5
1.5
0.5
0.5
-0.5
1.5
1.5
0.5
-0.5
1.5
1.5
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1.5
0.5
0.5
-0.5
1.5
1.5
0.5
1
1
1
1
1
1
1
-0.5
0 1.5
0 1.5
0 0.5
0 -0.5
0 1.5
1 0.5 0
6.28
1.5
1.5
0.5
1.5
1.5
-0.5
1.5
0.5
1.5
6.28
6.28
12.39
12.39
12.39
12.39
12.39
0
-1
1
0
-1
0
0
0
0
0
0
0
I
0
1
0
0
0
0 0.5 0
-1 1.5 0
-1 0.5 0
1
1
-1
-1
1
1
0
0
-1
-1
1
1
1.5
0.5
1.5
0.5
1.5
0.5
0
1.5
0.5
1.5
0.5
1.5
0.5
0
0
0
0
0
0
0
0
0
0
0
1.5 0
1 -1 0.5 0
1 1 1.5 0
1 1 0.5 0
1 -1 1.5 0
1 -1 0.5 0
1 1 1.5 0
-1
18.55
18.55
18.55
18.55
18.55
18.55
24.68
24.68
24.68
24.68
30.87
30.87
30.87
30.87
30.87
30.87
37.02
37.02
37.02
37.02
43.05
43.05
43.05
43.05
Frequency (MHz)
Obs-Calc (MHz)
9097.885
9098.172
9097.650
9097.920
9098.229
-0.002
9097.682
9098.203
9097.910
9097.979
9098.316
9098.012
9097.737
9098.246
9097.956
9098.064
9097.811
9098.316
9098.012
9098.161
9098.589
9098.271
9097.905
9098.435
9098.093
9098.258
9098.009
9098.396
9098.195
-0.010
-0.002
-0.005
-0.001
-0.005
-0.002
0.002
-0.005
0.004
-0.006
-0.006
-0.008
0.004
0.002
-0.005
-0.010
0.000
0.006
-0.008
0.002
0.001
0.000
0.003
-0.003
0.002
-0.011
0.010
9098.385
9098.128
9098.534
0.005
6.000
-0.004
9098.305
0.010
86
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 3.A6. Assigned StarkTransitions for (CH 3 )3 ISN-UBF3 .
J" Mj" M," J’ Mj' M,' K E(V/cm) Frequency (MHz)
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1.5
0.5
-0.5
1.5
0.5
1
I
1
1
1
1.5
0 0.5
-I 0.5
0 1.5
0 0.5
-0.5
0.5
-0.5
-0.5
-0.5
1
1
1
1
1
0
0
0
0
3.08
3.08
3.08
6.21
0
6.21
-1 0.5 0
6.21
I
0
1
-1
6.21
0
-0.5 0
-0.5 0
6.21
-1.5 0
0.5 0
6.21
6.21
0
-1.5 1 0 -1.5 0
0 -1.5 1 -1 -0.5 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1.5
0.5
-0.5
0.5
-0.5
-0.5
-0.5
-1.5
-1.5
I -I
1 -1 -1.5
1 -I 1.5
1 0 -1.5
1 I -0.5
1 0 1.5
1
0
1
1
1 0
1
0
1 0
-1.5
-0.5
-0.5
-0.5
0.5
1
1
1
1
1
1
1
1
2
1.5
0 0.5
-1 0.5
1 -0.5
0 -0.5
1 -1.5
-1 0.5
0 -1.5
-1 -1.5
2 _2 -0.5
2 -1 1.5
2 -2 0.5
2 1 -1.5
2 0 1.5
2
2
2
2
2
0
6.21
3503.442
3503.276
3503.142
3503.473
3503.311
0.002
3503.169
3503.446
3503.446
3503.311
3503.169
0.003
-0.010
-0.010
0.003
0.003
0.000
0
0
0
0
12.51
12.51
12.51
3503.473
3503.300
3503.610
3503.443
3503.547
12.51
3503.547
0
0
0
0
0
12.51
12.51
12.51
12.51
0.47
0.47
0.47
0.47
0.47
0.47
3503.443
3503.257
3503.547
3503.610
7006.579
0.47
0.47
0.47
0.47
0.47
7006.467
7006.306
7006.538
7006.579
0
0
0
0
1
-2 0.5 0
2 -1.5 0
0.5 1
0 -1.5 1
0 -0.5 1
0
1 -1 -1.5 2 -I -1.5 0
6.21
18.52
Obs-Calc (M
7006.746
7006.764
7006.467
7006.306
7006.662
7006.538
7006.825
0.001
0.000
0.000
0.003
0.001
-0.007
0.001
0.004
0.004
0.001
0.004
0.004
-0.007
-0.003
0.000
0.004
0.003
0.006
0.009
0.003
0.006
0.000
-0.001
-0.003
-0.002
87
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 3.A6. continued.
J" M j” Ml" J' Mj' M r K E(V/cm) Frequency (MHz)
0.5 2 1
0.5 2 0
0.5 2 -1
-0.5 2 0
1.5 2 0
-1.5 2 0
-1.5 2 _2
-1.5
-0.5
0.5
-0.5
1.5
-0.5
0
0
0
0
0
0
18.52
18.52
18.52
18.52
18.52
18.52
1.5 0
18.52
18.52
18.52
18.52
18.52
18.52
1 -0.5 2 -1
1.5
1.5
-0.5
0.5
-0.5
1.5
Qbs-Calc (MHz)
7006.713
7006.591
7006.570
7006.450
7006.450
7006.835
7006.644
-0.006
-0.007
0.008
-0.011
-0.013
0.006
-0.002
7006.713
7006.825
7006.713
7006.644
7006.570
-0.006
-0.002
-0.005
-0.005
0.008
18.52
18.52
18.52
18.52
18.52
18.52
7006.713
7006.450
7006.835
7006.713
7006.624
7006.624
0
0
0
0
0
18.52
18.52
18.52
18.52
18.52
7006.713
7006.835
7006.644
7006.450
7006.713
-0.006
-0.012
0.006
-0.006
-0.005
-0.005
-0.006
0.006
-0.002
0.000
-0.006
1 -0.5 2 -1 0.5 0
18.52
18.52
7006.570
7006.713
18.52
18.52
18.52
7006.752
7006.752
7006.713
7006.713
7006.789
7006.873
7006.873
7006.785
-1
-I
-1
0
0
1
1
1
-1
-1
-I
-1
1.5 2 1
-1.5 2 -1
-0.5 2 -1
0.5 2 1
0.5 2 -I
0
0
0
0
0
0
-0.5 2 0 0.5 0
1 -1.5 2 0 0.5 0
1 -0.5 2 0 1.5 0
1 1.5 2 2 1.5 0
-1 -1.5 2 _2 -1.5 0
0
-1
-1
-1
0
1
0.5 2 0
1.5 2 0
1.5 2 .2
-0.5 2 -1
-0.5 2 1
1.5
0 -1.5
0 1.5
0 -1.5
2
2
2
2
0
2
2
2
2
2
1
-1
-1
1
I
1.5
0.5
1.5
-1.5
-0.5
-1.5
-0.5
1.5
-0.5
-1.5
1 0.5 0
0 -1.5 1
1.5 1
0 -0.5 1
0 0.5 1
1 -1.5 0
1 -0.5 0
-1 0.5 0
-1 1.5 0
0
-1 -1.5 2 -2 0.5 0
-1
0.5 2 -1
1.5 0
18.52
24.68
24.68
24.68
24.68
24.68
24.68
7006.732
7006.785
88
0.008
-0.005
-0.011
-0.011
-0.003
-0.003
-0.002
0.006
0.006
-0.006
0.000
-0.006
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 3.A6. continued.
J” Mj" M,” J’ Mj' Mr K E(V/cm) Frequency (MHz)
-1.5 2 1 -1.5
0 0.5 2 1 0.5
1 -1.5 2 1 -0.5
1 -0.5 2 2 -0.5
1 -0.5 2 1 0.5
1 0.5 2 2 0.5
1 0.5 2 1 1.5
1 1.5 2 2 1.5
-1 -1.5 2 _2 -1.5
-1 -0.5 2 -1 -1.5
-1 -0.5 2 .1 -0.5
-1 0.5 2 -1 -0.5
-1 0.5 2 _2 0.5
-1 1.5 2 -I 0.5
0 -0.5 2 -1 -0.5
0
1.5 2 -1
0
0
0
24.68
24.68
24.68
0
0
0
0
0
0
24.68
24.68
24.68
24.68
24.68
24.68
0
0
24.68
24.68
24.68
0
0
0
0
0
0
0
1
1.5
1 -0.5 2 1 -1.5
1 1.5 2 2 -0.5
0 -0.5 2 0 -0.5
-1 -1.5 2 _2 -0.5 0
-1 -0.5 2 -1 -0.5 0
0
0.5
-I 1.5
0 -1.5
0 1.5
1 -1.5
1 -0.5
-1
1
1
1
1
2
2
2
2
2
1 -1.5 0
1 -0.5 0
0 -1.5 0
1.5 0
-1 0.5 0
2 -1 1.5 0
0.5 2 1 0.5 0
1.5 2 2 0.5 0
-1.5 2 1 -0.5 0
-0.5 2 2 -0.5 0
1.5 2 2 1.5 0
0
I
-1 -1.5 2 -2 -1.5 0
-1 -0.5 2 -2 -0.5 0
-1 0.5 2 _2 0.5 0
24.68
24.68
24.68
24.68
24.68
24.68
24.68
30.77
30.77
30.77
30.77
30.77
30.77
30.77
30.77
30.77
30.77
30.77
30.77
30.77
30.77
30.77
30.77
7006.346
7006.346
7006.873
7006.587
7006.660
7006.660
7006.838
7006.660
7006.660
Obs-Calc (MHz)
0.000
0.009
0.006
-0.001
0.006
0.002
-0.006
-0.005
-0.005
7006.838
7006.660
-0.006
0.002
7006.660
7006.587
0.006
-0.001
0.006
0.009
7006.873
7006.346
7006.346
7006.785
7006.732
7006.732
7006.768
7006.853
7006.898
7006.963
7006.214
7006.214
7006.962
7006.898
0.000
-0.006
0.000
-0.005
-0.003
0.005
0.002
-0.003
-0.002
-0.002
-0.004
0.002
7006.853
0.005
7006.768
7006.962
7006.643
7006.709
7006.709
7006.709
-0.003
-0.004
7006.643
89
0.003
0.003
-0.003
-0.003
-0.004
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 3.A6. continued.
J" Mj" M i" J'
1 -I 1.5 2
1 0 -1.5 2
1 0 1.5 2
1 -1 -0.5 2
1 -1 -0.5 2
1 -1 1.5 2
1
1
i
I
1
1
1
1
1
1
I -1
1 -1
Mj' M,’ K E(V/cm) Frequency (MHz)
-I
0
0
-1
-2
1
-1.5 2 -1
0.5 2 2
0.5 2 1
-1.5 2 1
1.5 2 2
-1.5 2 .2
1.5 2 -1
0.5 0
-1.5 1
1.5 1
-0.5 0
0.5 0
-0.5 0
0.5 0
-0.5
0.5
-0.5
1.5
0
0
0
0
-1.5 0
0.5 0
30.77
30.77
30.77
36.89
36.89
36.89
36.89
36.89
36.89
7006.962
7006.962
7006.962
7006.988
7006.780
7007.094
7007.094
36.89
36.89
7006.780
7006.988
7007.094
7006.766
36.89
36.89
7006.766
7007.094
Obs-Calc (MHz)
-0.004
0.003
0.003
0.007
-0.010
0.003
0.003
-0.010
0.007
0.003
-0.003
-0.003
0.003
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Chapter 4. Structural Change at the Onset o f Microsolvation: Rotational Spectroscopy
ofH C N -HCN-SOj
D.L. Fiacco, S.W. Hunt, and K..R. Leopold
Department o f Chemistry
University of Minnesota
207 Pleasant St.. SE
Minneapolis, MN 55455
Reproduced with permission from: Fiacco, D.L; Mo. Y.; Hunt, S.W.; Leopold, K.R. J. Phys.
Chem. A 2000,104, 8323-8327. Copyright © 2000 American Chemical Society.
91
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Abstract
The structure and dipole moment o f HCN—HCN-SO 3 have been determined by rotational
spectroscopy. The N-S bond distance is 2.470(20) A, which is 0.107(21) A shorter than that
in HCN-SO 3. In contrast, the N—H distance, 2.213(29) A, is the same to within
experimental uncertainty as that in (HCN)2. The dipole moment of HCisN -H C | 3N-3:S03 is
8.640(19) D. representing an enhancement of 1.238(19) D over the sum of the dipole
moments of HCN and HCN-SO3. The results indicate significant changes in the HCN-SO3
subunit upon interaction with a single HCN "solvent" molecule, with relatively little change
in the HCN-HCN interaction. The hypersensitivity of the HCN-SO 3 moiety to the presence
of an additional HCN arises because the dative bond is partially formed, and we suggest that
partially bound systems may offer sensitive probes of microsolvation.
92
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Introduction
The effect of solvent on molecular energetics and reactivity is a subject o f immense
importance in chemistry [I]. For this reason, in recent years much experimental and
computational effort has been expended on the elucidation o f the role o f solvent in
molecular systems [2]. Cluster science provides a microscopic view of molecules in their
early phases o f aggregation [3-8] and can thus offer a detailed picture of the early stages of
solvation. In this vein, the study o f microsolvated species constitutes an important bridge
between molecular clusters and solution phase chemistry.
In recent years, we have been concerned with a class o f molecules that are best described as
"partially bound" [9,10]. In general, these have been Lewis acid-base adducts in which the
constituent moieties are chosen to produce a dative linkage that is intermediate between a
van der Waals interaction and a fully formed chemical bond. We have shown that such
systems undergo enormous changes in structure upon crystallization and are thus
extraordinarily sensitive to the presence o f near neighbors. It is reasonable to speculate,
therefore, that partially bonded molecules may offer sensitive probes of microsolvation. The
purpose of this study is to ascertain whether a single "solvent" molecule can produce a
measurable effect on the structure and bonding of such systems.
In a previous paper [11], we reported the microwave spectrum and structure o f the complex
HCN-SO3 (I), shown below.
o
The 2.577(6) A bond length is slightly shorter than the 2.9 A distance expected for a van der
Waals interaction, but is significantly longer than the sum o f ordinary covalent bond radii
for nitrogen and sulfur (1.74 A). Correspondingly, the SO3 unit is distorted (but only
93
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minimally) from its normally planar configuration. The system can thus be regarded as
containing a nitrogen-sulfur bond in its early stages o f formation and as such represents a
viable candidate for testing the effect of microsolvation.
In this Letter, we report the rotational spectrum of H C N —HCN-SO3, which represents an
HCN-SO3 adduct microsolvated by a single H C N unit. The structure and dipole moment of
the complex are determined and indeed demonstrate a significant, quantifiable effect of the
additional HCN on the nature of the HCN-SO3 moiety. The results are considered in the
general context of medium effects in partially bonded systems.
Experimental
Rotational spectra were observed using a pulsed nozzle Fourier transform microwave
spectrometer [12,13] equipped with aluminum Stark plates [14] for the determination of
dipole moments. To produce the complex, a molecular injection source similar to previously
reported designs [15-19] was used to inject HCN into an expansion of SO3 seeded in argon.
Approximately 2 atm of argon were passed over a polymerized sample o f SO3 and expanded
through a 0.8 mm orifice. A mixture o f 32% HCN in Ar was flowed through a 0.016" I.D.
stainless steel needle into the early stages o f the expansion at a backing pressure o f 125 torr.
Spectra of eight isotopic derivatives were recorded, with ^S-containing species observed in
natural abundance. Isotopic substitution on the HCN moieties was accomplished using
enriched samples. DCN was prepared by reaction o f K.CN with dry D3PO4 while HCI5N
was prepared by reacting 99 atom % K C I5N (Icon Services) with dry H3PO4.
Results and Analysis
The observed spectra were characteristic o f a symmetric tops and only levels with K = 0 and
-3 were observed, consistent with Bose-Einstein statistics for equivalent splinless oxygens.
Tables of experimental data are lengthy and are provided as an Appendix to this chapter. A
sample spectrum is shown in Figure 4.1. With the exception of the doubly substituted l5N
derivative, all spectra exhibit the expected 14N nuclear hyperfine structure, which was
readily fit using standard methods for one or two nuclei, as appropriate [20]. Assignment of
the nuclear quadrupole coupling constants to the inner and outer nitrogens was determined
from the singly substituted l5N derivatives. Deuterium hyperfine structure was not well
resolved, and when present, broadened the observed transitions but did not preclude the
94
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determination of the nitrogen quadrupole coupling constants. Spectroscopic constants are
given in Table 4.1.
5726
5726.5
5727
5727.5
Frequency (MHz)
Figure 4.1. The 7 <—6 transition of HCI4N -H C I4N-32S03 . This spectrum is the average of
data taken in -400 gas pulses over a period of -60 seconds. The broad feature at the right is
ringing of the microwave cavity, not a molecular transition.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 4.1. Spectroscopic Constants of HCN2—HCNi-SCV
Isotopomer
B(MHz)
Dj(Hz)
Djk(1cHz ) eQq(Ni)
eQq(N:)c p(D)
HCl4N-HC14N-3:S0 3 409.05358(16)
61.9(17) 5.191(13) -3.882(15) -4.053(15)
HCl4N-HCl5N-3:S0 3 409.05958(16)
62.0d
(e)
HCl5N-HCl4N-3:S0 3 401.750(1)
55(12)
(e)
HCi5N-HC,sN-3:S 0 3 401.76559(28)
55(4)
5.020(40)
HCi5N-HC15N-34S0 3 398.8989(35)
63(39)
(e)
DCl4N-HC,4N-3:S 0 3 393.67411(7)
62.0d
(e)
-3.853(35) -4.060(34)
HCl4N-DCl4N-3:S0 3 406.93065(8)
53.87(50) (e)
-3.866(34) -4.042(41)
-4.051(9)
-3.885(16)
8.640(19)
DC14N-DCuN-32S 0 3 391.79521(6)
-3.871(24) -4.053(29)
62.0
(e)
(a) Uncertainties are one standard error in the least squares fit. (b) Inner nitrogen, (c) Outer
nitrogen, (d) Held constant in fit.
(e) This constant was not determined because only K= 0 lines were observed.
The dipole moment of HCI5N—HCi5N-j 2S 03 was measured by observing the Stark effect on
the J=6 <—5, 7<—6 , and 8<—7, K=0 transitions. The distance between the Stark electrodes was
calibrated using the first order Stark effect on the J = 4<-3, K = ±3 transition o f Ar-S03
[21], as also described previously [14]. Only moderate electric field strengths (up to 127.6
V/cm) were applied, as the intensity o f the observed components diminished with increased
voltage. Transitions were observed mainly in the perpendicular (AMj=±l) configuration and
were readily fit to within experimental uncertainties using the usual second order Stark
formula [20]. A table o f transition frequencies at various electric fields is included as an
Appendix to this chapter and the resulting dipole moment is given in Table 4.1.
The important structural parameters of the complex are defined in Figure 4.2. As in the case
o f HCN-SO3, we account for the possibility of large amplitude vibration o f the H C N and
SO3 subunits by including the angles x, Yi and 72 in the analysis. Since the complex is a
symmetric top, <x>=<7i>- <7>>=0. For HCN-SO3, we argued that yefr = cos"l<cos:7>12 =
8.3 = 4.6° and that Xefr= cos'‘<cos2x >1/2 = 7.8 ± 7.8° [11].
96
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a
r
O
N—
H
0
0
Figure 4.2. Definition of angles used to describe the structure o f HCN-HCN-SO 3. yi and y2
give the instantaneous deviations o f HCNi and HCN 2 from the equilibrium C 3 axis o f the
complex, x is the analogous angle for the C 3 axis o f the SO 3. a measures the distortion of
the SO3 unit from planarity and is equal to the NSO angle at the equilibrium geometry o f the
complex. R is the N-S distance and r is the length o f the HCN—HCN hydrogen bond.
Several methods of fitting the structure were investigated, all of which resulted in essentially
the same values for the relevant structural parameters. As in the case of HCN-SO3, the H-C,
C=N, and S-0 bond distances were fixed to those in free HCN [22] and SO3 [23],
respectively. The NSO angle, which at equilibrium is equivalent to a, was expected to differ
from 90° but preliminary fits confirmed the expectation that a and x were highly correlated
thus not independently determinable from the rotational constants. Moreover, preliminary
fits revealed a strong correlation of both a and x with R. Consequently, a was estimated to
be
92.2(6)° using Rn-s - 2.47 A and the bond length - bond angle relationship
Rn-s[A ]
= (1.621 A) - (0.449 A)log(9cos2a)
( 1)
which has been previously established for nitrogen - SO3 adducts [11]. Equation 1 was
found to accurately reproduce the NSO bond angles (a) for SO 3 complexes across a wide
range of bond lengths and is expected to be reliable here. The quoted uncertainty o f 0.6° is
the rms deviation in predicted bond angles among the complexes used to derive equation
(1). The value of x was taken to be 7.8° ± 7.8°, which guarantees its value not to exceed the
15.6° value obtained for the more weakly bound complex AX-SO3 [24], For
a Kraitchman
analysis of the hydrogen and nitrogen coordinates gave 9.4°, though for Yi, a similar analysis
failed since the inner nitrogen lies within 0.1 A o f the center o f mass o f the complex. For
97
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this reason, the value of y2 (9.4°) was utilized as a conservative upper limit for Yi , which
seems reasonable since the N-S bond is likely to be stronger than the N—H hydrogen bond
and since the inner HCN is constrained by binding partners on both ends.
The "preferred" structural parameters of the complex were obtained from a series of least
squares fits in which R and r were varied with y> fixed at 9.4° and yi, a , and x constrained to
values representing the maximum and minimum values implied by their uncertainties above
(0° and 9.4° for Yi; 91.6° and 92.8° for a; 0° and 15.6° for %)• The resulting ranges of values
for R and r were small and the average value for each parameter is reported in Table 4.2.
The uncertainties given encompass the full set of values obtained in the fits. These
uncertainteis are small, indicating that those parameters which are not well determined from
the rotational constants have little effect on the determination o f the important structural
features of the system. This situation is typical o f partially bound complexes [9-11],
Table 4.2. Structural Parameters for HCN—HCN-SO3
Parameter1
RfN-S)
r(N :-H )
a(NSO)b
Y:c
Value
2.470(20) A
2.213(29) A
92.2(6)°
9.4°
(a) Numbering of the nitrogens is according to the formula HCN2—HCN 1-SO 3.
(b) Estimated value. See text for discussion.
(c) Determined from double-substitution Kraitchman analysis.
Finally, it should be noted that in addition to the procedures described above, a broader
series of least squares fits were performed in order to test the stability of the resulting
parameters to changes in the method o f solving the structure. In these fits, different
combinations of parameters were freed. The results were essentially the same as those in
Table 4.2, but were found to be somewhat sensitive to initial estimates used in the least
squares routine. With the constraints described above, however, this sensitivity was
removed and thus the values given in Table 4.2 were deemed the most reliable.
98
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Discussion
The spectroscopic and structural parameters determined above can be used to examine the
effect of microsolvation on H C N —HCN-SO3. To do so, Table 4.3 compares the structural
and electronic properties of the system with those of several closely related species. The N-S
bond in HCN-SO3 is seen to contract by 0.107(21) A upon addition of the extra H CN unit,
which is probably the most striking result of this work. The N—H distance, on the other
hand, differs from that in (H C N ): [25] by only 0.017(29) A, which represents essentially no
change within the experimental uncertainty. Thus, while the nitrogen-sulfur interaction is
significantly affected by the presence of the remote HCN, the H CN —HCN interaction is
relatively unaltered by the SO3. The values of y> in H C N :—HCN1-SO3 (9.4°) and yi in
H C N |—HCN: (13.7°) suggest a slight alignment of the terminal HCN in the trimer, but are
nevertheless consistent with an H C N -H C N interaction which is not too different from that
in (HCN):.
Table 4.3. Comparison of Structural and Electronic Properties for HCN—HCN-SO3
and Related Complexes.
HCNrSCV
HCN2-H CN,-S03b
R(N|-S) = 2.577(6) A
a(NSO) = 91.8(4)°
y, = 8.3(4.6)°
p = 4.4172(31) D c
R(N,-S) = 2.470(20) A
cx(NSO) = 92.2(6)°
r(N :-H ) = 2.213(29)
y2 = 9.4°
eQq(N,) = -3.882(15) MHz
eQq(N:) = -4.053 (15) MHz
|i = 8.640(19) D
HCN, HCN2C
HCN, HCN2 HCN3d
eQq(N|)= -3.9779(49) MHz
r(N |-H ) = 2.230 A
rfN ,-H ) = 2.17 A
r(N: - H ) = 2.18 A
y,
= 12.6°
yi = 13.7°
y: = 9.0°
72 = 6oe
Y3 = 8.6°
eQq(N,) = -4.097(20) MHz
eQq(N,) = -4.049(2) MHz
eQq(N2) = -4.251(2) MHz
eQq(N2) = -4.440(19) MHz
eQq(N3) = -4.375(1) MHz
u = 10.6(11 D
u = 6.552135) D
(a) Ref. [11], (b) This work, (c) Ref. [25]. (d) Ref. [26]. (e) Assumed value o f Ref. [26].
99
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The nitrogen quadrupole coupling constants are consistent with this picture. The value of
eQq(N;) in HCN;—HCN 1-SO 3, for example, is nearly identical to eQq(Ni) in HCNf-HCN;,
indicating that the hydrogen bonds in the two complexes are similar. However, eQq(N 1) in
HCN;—HCN 1-SO3 is significantly less than any of the nitrogen coupling constants observed
in (HCN);, (HCN)3, or HCN-SO 3. Particularly noteworthy is the reduction in magnitude of
eQq(N,) in HCN;-HCN,-S0 3 (-3.882(15) MHz) relative to that in HCN-SO3 (-3.978(5)
MHz). The change is in the direction opposing that expected to accompany a decreased
vibrational amplitude and seems likely to reflect actual electronic rearrangement at the inner
nitrogen [27],
Both the structure and nuclear quadrupole coupling constants of the complex are consistent
with an advancement of the dative interaction upon addition of the extra HCN. It is well
established that crystallization of partially bonded systems drives their dative bonds toward
completion [9,10] and such an effect, therefore, is not unexpected. Its magnitude, however,
is somewhat dramatic. As a comparison, several complexes with the general formula
HCN-HCN-Y
(Y=HF, HC1, HCF3, and CO;) have also been investigated [28], and
shrinkage of the N-Y bonds relative to those o f HCN-Y were found to be in the range
0.04 to 0.06 A. These values, while significant, are still somewhat less than the 0 .11 A
observed here for HCN—HCN-SO 3. Undoubtedly, the ability o f SO3 to expand its octet
and form true donor-acceptor complexes produces a heightened sensitivity o f the HCNSO3 fragment to near neighbor interactions. Interestingly, contractions o f the HCN—HCN
hydrogen bond lengths in the HCN—HCN—Y systems (relative to HCN—HCN) are
somewhat larger than those o f H CN-HCN-SO 3 , falling in the range 0.004 - 0.07 A. A
similar range of values is observed for the X -H distances in the series X—HCN—HCN
(X=OC, N2, H 3N, H ;0) [29].
A previous Self Consistent Reaction Field calculation for HCN-SO3 indicates a 0.22 A
contraction of the N-S bond accompanied by a 2.2° widening of the NSO bond angle in a
medium described by a bulk dielectric constant of 78.5 [30]. Although a single HCN by no
means constitutes a bulk environment, we can draw some analogy between the electric field
of the remote HCN and the reaction field produced by polarization of a dielectric medium
surrounding a single molecule of HCN-SO 3. The substantial contraction of the N-S bond
100
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brought about by a single molecule o f HCN demonstrates that a significant portion of the
response to environment is brought about by the addition o f a single molecular
“microsolvent”. Being small and therefore inexpensive, partially bonded molecules thus
offer promising "test” systems for quantum mechanical solvation models.
The dipole moment of H C N —HCN-SO3 is 8.640(19) D, which represents an
enhancement of 1.238(19) D relative to H CN + HCN-SO3. This value is large, but its
magnitude is reasonable in the following sense: The dipole moment o f (H C N ): is
6.552(35) D [25d], which is 0.58 D larger than that of two HCN monomers [31]. Thus,
the HCN—HCN interaction in the trimer should contribute about this much to the induced
moment. On the other hand, recent ab initio calculations o f (i(R) for HCN-SO3 [32] give
a value of djivdR = -3.0 D/A at R = 2.47 A (the bond length observed in H C N —HCNSO 3.) .An increase o f 0.33 D in the HCN-SO3 moiety, therefore, should accompany the
observed 0 .11 A contraction of the N-S bond. The sum o f these values (0.58 D + 0.33 D)
gives an induced moment of 0.91 D for H C N —HCN-SO3. This result falls about 27%
short of the observed value, but the agreement is probably as good as can be expected
from a crude additivity model. The calculation further suggests that a significant portion
of the induced moment in the trimer arises from advancement o f the N-S bond.
In this light, it is also o f interest to explore a more complete decomposition of the
observed dipole moment. While the quadrupole coupling constants in HCNi-SCb and
H C N y HCN1-SO3 are indicative o f electronic rearrangement at N |, the induced moment
of the complex certainly arises from an admixture o f monomer distortion, charge transfer,
and polarization terms. In order to separate these contributions, calculations were carried
out for HCN-SO3 and H C N —HCN-SO3 at the HF/aug-cc-pVDZ level o f theory/basis set
using the block-localized wave function energy decomposition scheme (BLW-ED)
developed by Mo, Gao, and Peyerimhoff [33]. The results are given in Table 4.4. From
the table, it is apparent that for H C N -H C N -S O 3 at this level o f theory/basis set, the
polarization contribution to the induced moment (A(ip0i) is 6.65 times greater than that of
the charge transfer component (Apcr), while for HCN-SO3, the ratio is 7.44. The
difference between these numbers is too small to interpret, but it seems clear that the
major contribution to the induced dipole moment in both adducts arises from electronic
polarization of the respective fragments, and not from charge transfer [34] (i.e., about
101
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seven times more of a contribution from polarization than from charge transfer). In
addition, taking the observed induced moments for both complexes, less the calculated
contributions from monomer distortion, and using RfN-S) as a crude approximation to
the distance for electron transfer,
the calculated ratios o f Afip0i /A|Ict yield electron
transfer values of 0.012 e and 0.020 e for HCN-SO 3 and HCN—HCN-SO 3, respectively.
Interestingly, these estimates are about an order o f magnitude smaller than those obtained
from a simple Townes and Dailey type analysis of the quadrupole coupling constants.
Nevertheless, while the absolute magnitude o f the electron transfer is imprecise, an
Table 4.4. Induced Dipole Components at the HF/aug-cc-pVDZ Level Using BLWED*
Hhf
^M-poi
A|icT
a iw s o
3)
H C N -H C N -S O 3
HCN-SO3
8.88
1.13
0.17
0.23
4.5
0.908
0.122
0.183
0
A)kiist(HCN)
A |W H C N - H C N )
(i(exp.)
0.05
8.640(19)b
4.4172(31)°
(a) All values in Debye. A ^ i and Apcr are the contributions to the induced dipole
moment (Afij„d) due to polarization and charge transfer, respectively, as defined in
reference [33], A|i<iiSt is the contribution due to distortion o f the indicated moiety, (b) This
work, (c) Reference [32].
increase upon addition of a single HCN unit appears discernible. The relation between
charge transfer and induced moments in partially bound Lewis acid-base adducts will be
discussed in a future publication [32].
In conclusion, the results presented above indicate that the HCN-HCN interaction in
HCN—HCN-SO 3 is largely unaltered from that in (HCN)i, but the HCN-SO 3 interaction
is driven measurably in the direction o f bond formation. Thus, in the "solvent-solute
interaction" studied here, weak closed-shell interactions remain weak but incipient
chemistry' is promoted by even the slightest degree o f solvation. It is interesting to
102
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comment that the binding energy of (HCN): is 4.2 kcal/mol [35] while that of HCN-SO3 is
7.1 kcal/mol [34], Although these results were obtained at different levels o f calculation, it is
unlikely that the true values are widely disparate. Thus, the separation between inter- and
intramolecular energetics is not sharp, as is normal for valence bonded systems. Such a
situation should be general for partially bound complexes, making them sensitive probes of
their local environment.
Acknowledgements
This work was supported by the National Science Foundation, the Donors of the Petroleum
Research Fund, administered by the American Chemical Society, and the University of
Minnesota Supercomputer Institute. We are grateful to Professor J. Gao and Dr. Y. Mo for
their help with the BLW-ED calculations.
103
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References
1.
See, for example, Solvent Effects and Chemical Reactivity, Tapia, 0 .; Bertran, J.,
Eds. KJuwen Dordrecht, 1996 and references therein.
2.
See, for example, (a) Tomasi, J.; Perisco, M. Chem. Rev. 1994, 94, 2027. (b)
Cramer. C.J.; Truhlar, D.G. Chem. Rev. 1999,99,2160, and references therein.
3.
Zwier, T.S. Annu. Rev. Phys. Chem. 1996, 47, 205.
4.
Lisy. J.M. in Structures and Dynamics o f Clusters, Kondow, T.; Kaya, K; Terasaki,
A. Ed., Universal Academic Press: Tokyo, 1996, p. 95.
5.
Dessent, C.E.H.; Kim, J; Johnson, M.A. Acc. Chem. Res. 1998, 31, 527.
6.
Chemical Reactions in Clusters, Bernstein, E.R., Ed. Oxford: New York, 1996.
7.
Lineberger, W.C.; Nadal, M.E.; Kleiber, P.D J. Chem. Phys. 1996, 105, 504.
8.
Leopold, K.R.; Fraser, G.T.; Novick, S.E.; Klemperer, W. Chem. Rev. 1994, 94.
1807.
9.
Leopold, K.R. in Advances in Molecular Structure Research, Hargittai, M.;
Hargittai. I. Eds., JAI Press: Greenwich CT, 1996, Vol. 2, p. 103 and references
therein.
10.
Leopold, K.R.; Canagaratna, M.; Phillips, J.A. Acc. Chem. Res. 1997, 30, 57 and
references therein.
11.
Bums, W.A.; Phillips, J.A. Canagaratna, M.; Goodfriend. H.: Leopold, K.R. J. Phys.
Chem. A 1999, 103, 7445.
12.
Balle, T.J.; Flygare, W.H. Rev. Sci. Instrum. 1981, 52, 33.
13.
(a) Phillips, J.A.; Canagaratna, M.; Goodfriend, H.; Grushow, A.; Almlof, J.;
Leopold, K.R. J. Am. Chem. Soc, 1995, 117, 12549. (b) Phillips, J.A.; Ph.D. Thesis,
University of Minnesota, 1996.
14.
Canagaratna, M.; Ott, M.E.; Leopold, K.R. Chem. Phys. Lett. 1997,281, 63.
15.
Legon, A.C.; Wallwork, A.L.; Rego, C.A.J. Chem. Phys. 1990, 92, 6397.
16.
Gillies, C.W.; Gillies, J.Z.; Suenram, R.D.; Lovas, F.J.; Kraka, E.; Cremer, D. J. Am.
Chem. Soc. 1991, 113, 2412.
17.
Gutowsky, H.S.; Chen, J.; Hajduk, PJ.; Keen, J.D.; Emilsson, T., J. Am. Chem. Soc.
1989, 111, 1901.
18.
Emilsson, T.; Klots, T.D.; Ruoff, R.S.; Gutowsky, H.S. J. Chem. Phys. 1990, 93
6971.
104
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19.
Canagaratna, M.; Phillips. J.A.; Goodfriend, H.; Leopold, K.R., J. Am. Chem. Soc.
1996, 118, 5290.
20.
Townes, C.H.; Schawlow, A.L. Microwave Spectroscopy, Dover: New York, 1975.
21.
Bowen, K.H.; Leopold, K.R.; Chance, K.V.; Klemperer, W. J. Chem. Phys. 1980.
73, 137.
22.
Winnewisser, G.; Maki, A.G.; Johnson, D.R. J. Mol. Spectrosc. 1971, 39, 149.
23.
(a) Kaldor, A.; Maki, A.G. J. Mol. Struct. 1973, 15, 123. (b) Meyer, V.; Sutter, D.H.;
Dreizler, H. Z. Naturforsch 1991, 46a, 710.
24.
Fiacco, D.L.; Kirchner, B.; Bums, W.A.; Leopold, K.R. J. Mol. Spectrosc. 1998,
191.389.
25.
(a) Legon, A.C.; Millen, D.J.; Mjoberg, P.J. Chem. Phys. Lett. 1977, 47, 589. (b)
Buxton. L.W.; Campbell, EJ.; Flygare, W.H. Chem. Phys. 1981, 56, 399. (c)
Brown, R.D.: Godfrey, P.D.; Winkler, D.A. J. Mol. Spectrosc. 1981, 89, 352. (d)
Campbell, E.J.: Kukolich, S.G. Chem. Phys. 1983.76,225.
26.
Ruoff, R.S.; Emilsson, T.; Klots, T.D.; Chuang, C.: Gutowsky, H.S. J. Chem. Phys.
1988, 89, 138.
27.
A direct effect due to the field from the neighboring HCN unit seems unlikely in
light of the quadrupole coupling constants in (HCNb-
28.
Ruoff, R.S.; Emilsson, T.; Chuang, C.; Klots, T.D.; Gutowsky. H.S. J. Chem. Phys.
1989, 90, 4069.
29.
Ruoff, R.S.; Emilsson, T.; Chuang, C.; Klots, T.D.; Gutowsky, H.S. J. Chem. Phys.
1990,93, 6363.
30.
Jiao, H.; Schleyer, P.v.R., private communication.
31.
Maki, A.G. J. Phys. Chem. Ref. Data 1974, 3, 221.
32.
Fiacco, D.L.; Hunt, S.W.; Mo, Y.; Ott, M.E.; Roberts, A.; Leopold, K.R.,
manuscript in preparation.
33.
Mo, Y.; Gao, G.; Peyerimhoff, S.D. J. Chem. Phys. 2000, 112, 5530.
34.
Jonas et al. have discussed the importance o f both charge transfer andelectrostatic
interactions to the binding in Lewis acid-base complexes. See Jonas, V.; Frenking,
G.; Reetz, M.T. J. Am. Chem. Soc. 1994, 116, 8741.
35.
Kofranek, M„ Karpfen, A„ Lischka, H. Chemical Physics 1987, 113, 53.
36.
Mo, Y.; Gao, J., private communication.
105
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Appendix to Chapter 4.
Table 4.A1. Observed Transitions for Istopomers of HCN—HCN-SO3.
HC14N-HC i4N-32SQ3
J"
J
J
3
3
j■>
j
j
j
■"*
j
j
3
4
4
4
F,"
2
2
2
j
4
2
3
4
J
4
4
4
3
J
J■y
4
4
4
4
4
4
5
J
4
4
4
4
4
4
5
5
2
3
4
4
3
0
0
0
0
3273.431
3272.156
4
4
4
4
3
•>
4
4
4
4
3
4
5
4
5
2
j
j
4
4
4
5
4
5
5
5
6
3
4
3
J-v
4
4
4
4
5
4
4
5
0
0
4
4
4
4
5
5
6
3
0
0
5
5
5
5
5
5
5
5
5
5
5
4
4
4
5
4
5
5
6
6
5
5
6
5
6
5
5
6
5
6
6
4
5
5
6
5
6
7
6
6
6
6
6
6
6
6
6
6
6
7
6
6
6
5
5
5
3
1
2
2
2
5
5
5
5
3272.240
F,’
3
4
5
5
5
5
0
J'
5
5
5
6
6
5
5
4
4
5
5
K.
3
F'
2
F"
5
6
6
5
6
7
3
4
4
5
5
5
5
5
Frequency (MHz) Obs-Calc (MHz)
3272.503
3270.712
3272.352
3271.496
3272.411
0
0
0
0
0
0
0
0
0
0
0
0
6
6
7
4
4
0
0
0
-0.003
-0.001
-0.002
0.006
0.000
-0.002
-0.001
-0.002
3272.503
0.000
3270.845
3272.382
3272.471
-0.003
-0.001
-0.002
4090.410
4091.684
0.000
0.000
4090.361
4088.849
4090.477
-0.003
-0.002
4090.477
-0.003
-0.001
4089.473
4090.506
4091.856
4090.567
4090.484
0.000
0.001
0.001
0.000
0.000
-0.001
0
0
4090.545
4908.531
4909.851
5
0
4910.435
5
5
6
6
6
7
7
0
0
0
0
0
0
0
0
4908.619
4906.971
0.000
0.000
7
4908.575
4907.482
4908.594
4908.637
4907.031
4908.575
0.002
0.001
0.006
0.000
-0.001
0.005
0.002
0.000
0.001
106
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 4.A 1. continued.
HC14N-HC u N-32SQ3 continued.
J"
F"
J'
F
F,"
F,'
5
4
4
3
6
5
5
4
4
6
5
5
5
5
4
6
6
5
5
5
5
6
6
6
5
6
7
6
5
6
5
5
6
7
6
6
5
6
7
7
6
6
5
6
7
7
6
8
6
7
5
5
6
6
6
6
7
7
5
6
6
7
7
7
6
6
6
7
7
5
6
6
6
6
7
6
7
7
7
6
6
7
7
7
6
7
7
6
8
6
6
7
7
7
8
7
6
7
7
8
8
6
7
7
7
8
8
6
7
7
8
8
9
6
7
5
5
6
6
6
7
5
7
6
6
6
7
7
6
7
8
7
6
6
7
7
8
7
6
7
7
8
8
6
7
7
8
8
9
7
6
8
7
5
6
7
6
7
7
6
8
7
7
7
6
8
8
7
6
7
7
8
8
7
7
7
8
8
8
7
8
7
8
9
8
7
7
8
9
8
8
7
8
9
8
9
10
K
3
3
j
3
3
3
3
3
0
0
0
0
0
0
0
0
0
0
0
3
3
3
3
3
3
0
0
0
0
0
0
0
0
Frequency (MHz) Obs-Calc (MHz)
4908.345
-0.002
4907.995
-0.002
4907.866
-0.003
4907.527
0.001
4908.282
-0.002
4907.830
0.001
4907.927
0.001
4908.234
-0.002
5726.607
0.004
5726.688
0.002
5725.062
0.001
5726.656
0.000
5726.656
0.000
5725.505
0.001
5726.669
0.004
5726.706
0.006
5725.113
0.002
5726.656
0.002
5726.688
-0.001
5725.966
0.001
5726.175
0.003
5726.175
0.005
5725.903
0.002
5725.940
-0.002
5726.148
-0.003
6544.689
-0.011
6544.689
0.004
6544.739
-0.006
6544.727
0.003
6544.727
0.003
6544.727
-0.003
6544.761
0.003
6544.739
-0.010
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 4.A1. continued.
h c
J"
4
4
4
4
4
4
4
5
5
5
5
5
5
6
6
6
6
6
6
7
7
7
7
7
7
I4n - d
c
F,”
5
5
5
4
4
j
3
6
6
5
5
4
4
7
7
6
6
5
5
7
7
7
6
6
6
I4n -32s o 3
F"
6
5
4
5
4
3
6
5
6
4
3
4
7
6
7
5
5
4
8
7
6
7
6
5
J'
5
5
5
5
5
5
5
6
6
6
6
6
6
7
7
7
7
7
7
8
8
8
8
8
8
F,'
6
6
6
5
5
4
4
7
7
6
6
5
5
8
8
7
7
6
6
8
8
8
7
7
7
F
7
6
5
6
5
4
3
7
6
7
5
4
5
8
7
8
6
6
5
9
8
7
8
7
6
K.
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Frequency (MHz) Obs-Calc (MHz)
4069.321
0.000
4069.254
-0.005
4069.283
0.003
4069.342
0.001
4069.260
0.006
-0.004
4069.135
0.007
4069.192
4883.107
0.001
4883.127
0.006
4883.170
0.003
4883.149
-0.002
4883.066
0.005
4883.030
-0.002
5696.943
-0.001
5696.959
0.004
5696.992
0.002
-0.004
5696.972
5696.891
-0.002
5696.919
0.005
6510.809
0.002
6510.769
-0.005
6510.796
0.001
6510.769
-0.005
6510.726
-0.009
6510.742
-0.008
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 4.A L continued.
d c
J"
4
4
4
4
5
5
5
5
5
5
6
6
6
6
6
6
7
7
7
7
7
d c
J"
5
5
5
5
4
4
4
4
4
4
4
5
6
6
6
6
14n - h
c
F,"
5
5
5
4
6
6
5
5
4
4
7
7
6
6
5
5
8
7
7
6
6
I4n - d
c
F,"
6
6
5
5
5
5
4
4
j
3
3
4
7
7
6
6
14n -32s o 3
F”
6
5
4
5
6
5
6
4
j
4
7
6
7
5
5
4
9
8
7
6
5
J'
5
5
5
5
6
6
6
6
6
6
7
7
7
7
7
7
8
8
8
8
8
F,'
6
6
6
5
7
7
6
6
5
5
8
8
7
7
6
6
9
8
8
7
7
F
7
6
5
6
7
6
7
5
4
5
8
7
8
6
6
5
10
9
8
7
6
K.
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Frequency (MHz) Obs-Calc (MHz)
-0.006
3936.745
-0.001
3936.686
0.004
3936.712
3936.774
0.003
4724.017
-0.002
0.006
4724.040
0.002
4724.082
-0.002
4724.062
4723.974
0.001
7423.938
-0.005
5511.341
0.000
5511.357
0.005
5511.389
0.001
5511.371
-0.002
5511.288
-0.001
0.004
5511.314
6298.681
0.002
6298.694
0.005
6298.655
0.000
6298.611
-0.004
-0.004
6298.626
F,'
7
7
6
7
7
7
5
5
4
4
4
5
8
8
7
7
F
7
6
7
5
7
5
6
5
5
4
3
5
8
7
8
6
K
Frequency (MHz) Obs-Calc (MHz)
4701.569
-0.005
4701.490
0.001
4701.534
-0.001
4701.516
-0.003
3917.954
-0.006
0.005
3917.926
-0.002
3917.982
3917.896
0.000
0.003
3917.896
0.000
3917.779
3917.826
0.000
4701.398
-0.005
5485.037
0.001
0.001
5485.049
0.004
5485.087
5485.071
0.003
14^<-32S 0 3
F"
6
5
6
4
6
4
5
4
4
3
2
4
7
6
7
5
J'
6
6
6
6
5
5
5
5
5
5
5
7
7
7
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
109
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 4.A1. continued.
H C l4N -H ClsN-32SQ 3
J”
F”
J’
F’
7
6
5
6
6
7
6
6
6
7
6
7
7
7
6
7
7
7
6
8
K
0
0
0
0
0
Frequency (MHz)
h c , 5n - h c l4\ - 32s o 3
J"
J'
F
F"
4
5
6
5
5
5
6
6
5
6
6
7
7
6
5
6
7
6
6
7
7
6
7
7
6
7
7
8
K
0
0
0
0
0
0
0
Frequency (MHz)
4820.927
4820.948
4820.969
5624.405
5624.416
5623.063
5624.435
H C isN -H C I5N-32S 0 3
J" J’ K.
Frequency (MHz)
4 5 0
4017.626
5 6 0
4821.138
5 6 3
4820.597
6 7 0
5624.639
6 7 3
5624.009
7 8 0
6428.139
7 8 3
6427.413
H C 1SN-HC 15n - 34s o 3
J" J’ K
Frequency (MHz)
5 6 0
6 7 0
4786.731
5584.500
5726.730
5728.387
5726.746
5725.333
5726.765
Obs-Calc (MHz)
0.001
0.000
-0.004
0.001
0.003
Obs-Calc (MHz)
0.005
-0.003
0.003
0.003
-0.007
0.000
0.001
Obs-Calc (MHz)
-0.002
-0.001
0.000
-0.003
0.000
0.004
0.000
Obs-Calc (MHz)
-0.002
0.002
no
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 4.A2. Stark Assignments for HC,5 N-HC 1 5 N-S0 3 .
J"
Mj"
5
5
5
5
5
5
5
5
5
5
5
5
5
I
5
3
“t
j
J'
Mj'
6
5
6
2
6
6
6
2
6
4
3
j*>
1
6
2
0
6
1
6
5
4
6
6
6
2
6
5
3
2
6
2
5
5
5
5
5
5
4
3
j
6
6
6
6
5
4
3
2
6
2
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
4
j
j
6
6
6
6
5
4
6
2
2
6
3
2
6
1
5
5
5
5
6
1
6
1
0
6
1
0
6
0
5
5
4
3
6
6
6
6
6
2
6
5
4
3
6
0
6
1
4
3
6
2
6
5
4
3
0
6
1
1
6
0
6
E (V/cm
15.45
15.45
18.43
18.43
18.43
18.43
18.43
18.43
24.72
24.75
24.75
24.75
30.83
30.83
30.83
30.83
30.83
36.96
36.96
36.96
36.96
36.96
36.96
36.96
36.96
36.96
36.96
43.13
43.13
43.13
43.13
43.13
49.24
49.24
49.24
49.24
49.24
Frequency (MHz)
4821.185
4821.118
4821.161
4821.126
4821.148
4821.110
4821.110
4821.126
4821.185
4821.138
4821.096
4821.127
4821.211
4821.144
4821.033
4821.173
4821.117
4821.240
4821.149
4821.083
4821.256
4821.045
4821.150
4821.069
4821.045
4821.061
4821.240
4821.284
4821.154
4821.062
4821.007
4821.018
4821.157
4821.033
4820.969
4820.969
4821.046
Obs-Calc (MHz)
0 .0 0 2
-0 . 0 0 2
-0.004
0 .0 0 1
-0 . 0 0 1
-0.005
-0 . 0 0 2
0 .0 0 1
0.000
-0.006
0.000
0.000
-0 . 0 0 1
-0 . 0 0 2
-0 . 0 0 1
0.006
-0.004
-0.004
-0 . 0 0 1
0.000
0.007
0 .0 0 2
-0.004
-0.003
0.000
0 .0 0 2
-0.004
0 .0 0 2
0.000
-0 . 0 0 1
-0 . 0 0 2
0.007
-0 . 0 0 2
-0.007
0.000
-0.003
0 .0 0 1
111
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(/I Ui (_/i t/> L/i l/l l/l l/l l/l l/l l/l l/l l/l l/l l/l Wi l/i l/l l/l
Table 4.A 2. continued.
Mj”
J’
M j’ E (V/cm )
4
3
2
1
4
2
3
4
2
4
2
4
2
4
2
4
2
4
2
3
5
6
6
6
6
6
6
6
4
2
6
6
4
2
6
6
6
6
6
6
6
6
6
6
6
4
2
6
4
3
2
1
0
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
5
4
3
2
5
1
4
5
1
5
I
5
1
5
I
5
1
5
1
5
I
7
5
3
7
5
4
3
7
5
1
2
1
6
7
5
2
7
6
2
1
2
I
55.31
55.31
55.32
55.32
61.58
61.58
61.58
67.74
67.74
73.73
73.73
79.95
79.95
86.04
86.04
92.24
92.24
98.36
98.36
104.42
104.42
18.52
18.52
18.52
24.74
24.74
24.74
24.74
30.87
30.87
30.87
30.87
30.87
36.98
36.98
36.98
36.98
36.98
36.98
Frequency (M Hz)
Obs-Calc (M Hz)
4821.166
4821.011
4820.917
4820.900
4821.170
4821.183
4820.981
4821.176
4821.194
4821.185
4821.201
4821.192
4821.217
4821.201
4821.229
4821.211
4821.232
4821.219
4821.249
4821.239
4821.262
5624.656
5624.638
5624.623
5624.667
5624.639
5624.622
5624.611
5624.684
5624.628
5624.645
5624.589
5624.608
5624.706
5624.655
5624.617
5624.631
5624.574
5624.595
0 .0 0 1
-0.003
-0.008
0.004
-0 . 0 0 1
0 .0 0 0
-0.004
-0 . 0 0 2
0 .0 0 2
0 .0 0 0
-0 . 0 0 1
-0 . 0 0 1
0.004
-0 . 0 0 1
0.004
-0 . 0 0 1
-0.006
-0.003
-0.003
0.007
-0.005
-0 . 0 0 2
0.003
-0 . 0 0 2
-0.005
0.008
0.003
-0 . 0 0 1
-0.005
0 .0 0 2
0.006
-0.005
0.007
-0.005
-0.004
0 .0 0 1
-0.008
0 .0 0 0
-0 . 0 0 2
112
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 4 .A2. continued.
J”
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
Mj”
1
5
3
4
2
2
1
1
5
4
3
2
2
0
6
5
2
1
1
5
4
3
j
2
5
4
3
2
5
4
j
3
2
5
4
3
2
5
4
J’
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
Mj’ E (V/cm) Frequency (MHz)
36.98
5624.608
0
6
43.21
5624.663
4
5624.574
43.21
5624.609
43.22
5
2
5624.609
43.22
1
43.21
5624.635
2
43.22
5624.546
1
43.21
5624.580
49.31
6
5624.672
49.31
5
5624.600
4
49.31
5624.559
49.31
5624.530
3
49.31
1
5624.631
5624.559
0
49.31
7
55.37
5624.798
6
55.37
5624.680
2
55.37
5624.592
2
55.37
5624.485
55.37
1
5624.545
61.60
5624.686
6
5624.580
5
61.60
4
5624.507
61.60
2
61.60
5624.763
1
61.60
5624.632
6
67.62
5624.696
5624.564
5
67.62
4
5624.475
67.62
1
67.62
5624.635
6
74.00
5624.708
5624.557
5
74.00
4
5624.443
74.00
2
74.00
5624.823
5624.632
1
74.00
79.91
5624.723
6
79.92
5624.541
5
4
79.92
5624.431
5624.633
1
79.92
86.15
5624.737
6
5624.524
86.15
5
Obs-Calc (MHz)
0.003
-0.002
0.000
-0.002
0.002
-0.004
-0.004
-0.001
-0.001
-0.002
0.005
0.003
-0.007
0.006
0.001
-0.001
0.007
-0.006
0.002
-0.005
-0.001
0.002
-0.002
-0.004
-0.005
-0.005
-0.002
-0.001
-0.005
0.003
-0.002
0.003
-0.003
-0.002
0.001
0.001
-0.001
-0.002
0.000
113
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 4.A2. continued.
J”
Mj”
J’
6
3
6
2
6
1
6
6
5
4
6
2
6
6
5
4
6
2
6
6
5
4
6
2
6
6
5
4
6
2
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
8
2
8
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
6
8
2
8
1
8
7
5
•y
j
8
2
8
6
8
4
8
2
8
1
8
6
8
4
4
8
1
8
8
8
8
1
8
0
8
/
8
6
8
5
4
3
8
8
8
M j’ E (V/cm
86.15
4
86.15
I
86.15
0
6
92.25
92.26
5
1
92.26
6
98.47
98.47
5
98.47
1
6
104.73
5
104.73
104.73
1
110.70
6
110.70
5
110.70
1
18.69
8
18.69
3
7
24.59
24.59
3
24.59
0
30.76
8
30.76
6
4
30.76
30.76
3
7
37.04
37.04
5
37.04
3
2
37.04
7
42.98
42.98
5
42.98
3
2
42.98
0
42.98
42.98
1
49.24
8
49.24
7
49.24
6
49.24
5
49.24
4
Frequency (MHz)
Obs-Calc (M H z)
5624.371
5624.637
5624.449
5624.746
5624.509
5624.634
5624.763
5624.486
5624.629
5624.786
5624.465
5624.627
5624.800
5624.446
5624.626
6428.158
6428.122
6428.149
6428.112
6428.131
6428.166
6428.132
6428.114
6428.101
6428.151
6428.113
6428.090
6428.090
6428.157
6428.108
6428.196
6428.070
6428.108
6428.082
6428.219
6428.161
6428.120
6428.098
6428.068
-0.004
0.005
0 .0 0 1
-0.007
0.003
0.003
-0.006
-0 . 0 0 2
-0 . 0 0 1
0 .0 0 1
-0.003
-0 . 0 0 2
-0 . 0 0 2
-0 . 0 0 1
-0 . 0 0 1
0 .0 1 2
0 .0 0 0
0.008
-0 . 0 0 2
0.009
-0 . 0 0 1
0.004
0.007
-0 . 0 0 2
0 .0 0 0
0.005
0 .0 0 1
0 .0 0 1
0 .0 0 0
0.009
-0.005
-0.004
0.008
-0 . 0 0 1
0 .0 0 0
-0.004
-0 . 0 0 1
0 .0 1 0
0 .0 0 2
114
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 4.A 2. continued.
J”
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
M j”
J’
2
8
3
0
8
1
i/
1
5
3
1
2
7
7
7
7
7
7
7
7!
7
7
7
7
7
7
M j’ E (V/cm
7
8
8
6
8
7
5
4
8
6
8
2
8
0
8
6
8
5
3
I
7
5
4
8
6
8
5
1
8
2
1
8
0
0
8
1
7
8
8
6
8
7
5
3
8
6
8
2
8
5
3
1
8
0
7
8
8
6
8
7
8
6
8
8
4
3
1
8
2
49.24
49.24
55.43
55.43
55.43
55.43
55.43
55.43
61.52
61.52
61.52
61.52
61.52
61.52
67.71
67.71
67.71
67.71
67.71
67.71
73.77
73.77
73.77
73.77
73.77
73.77
80.06
80.06
80.06
80.06
7
8
8
6
8
7
5
4
3
8
6
8
6
8
5
4
7
5
4
8
6
8 6 .0 1
8
8 6 .0 1
6
8
5
7
5
4
8
6
8
6
8
5
7
5
8
6
8
8 6 .0 1
8 6 .0 1
92.36
92.36
92.36
98.34
98.34
Frequency (M Hz)
Obs-Calc (MHz)
6428.055
6428.068
6428.242
6428.171
6428.119
6428.074
6428.031
6428.049
6428.180
6428.111
6428.063
6428.009
6428.059
6428.040
6428.293
6428.192
6428.108
6428.012
6427.985
6428.049
6428.334
6428.205
6428.106
6427.985
6427.956
6427.956
6428.357
6428.215
6428.099
6428.011
6427.927
6428.241
6428.091
6428.002
6428.244
6428.094
6427.981
6428.264
6428.082
-0 . 0 0 1
0 .0 0 1
0 .0 0 0
-0 . 0 0 2
0 .0 0 2
-0 . 0 0 2
-0.004
0 .0 0 0
-0 . 0 0 2
-0.003
0 .0 0 0
-0.003
-0.005
0 .0 1 0
-0.003
0 .0 0 0
-0 . 0 0 2
0.005
-0 . 0 0 1
-0 . 0 0 1
0.008
0 .0 0 2
0 .0 0 1
0 .0 0 2
-0.003
-0.003
-0.003
-0 . 0 0 1
-0 . 0 0 1
-0.003
-0 . 0 0 2
0.013
-0.004
0.007
0 .0 0 1
0.005
0.007
0.006
-0 . 0 0 1
115
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 4 .A2. continued.
J"
7
7
7
7
7
7
7
7
7
7
7
Mj"
4
5
4
5
5
5
2
5
2
5
2
J'
8
8
8
8
8
8
8
8
8
8
8
Mj'
5
6
5
6
6
6
1
6
1
6
1
E (V/cm)
98.34
104.73
104.73
110.64
116.89
128.99
128.99
135.31
135.31
141.43
141.43
Frequency (MHz)
6427.952
6428.080
6427.926
6428.072
6428.063
6428.042
6428.055
6428.035
6428.049
6248.029
6428.041
Obs-Calc (MHz)
-0.001
0.003
-0.003
0.002
0.000
-0.006
-0.003
-0.004
-0.001
-0.001
-0.002
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Chapter S. Microwave Investigation of Sulfuric Acid Monohydrate
D.L. Fiacco, S.W. Hunt and K..R. Leopold
University of Minnesota, Mpls. MN
117
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Abstract
A-type rotational spectra for 18 isotopomers o f H 2SO4 -H 2O have been measured by
microwave spectroscopy. With 18 B and 18 C rotational constants available for the fitting
the geometry of the complex, 19 structural parameters have been determined. The results
indicate a short, strong hydrogen bond (O -H distance of 1.645(5)A) between one of the
H 2SO 4 hydrogen atoms and the oxygen on water. The water unit also acts as the donor o f
a hydrogen bond in a weaker secondary interaction with an S = 0 on H2SO4. In all regards,
the structure of the complex is in excellent agreement with theory. The spectra for a
number of the isotopic species show evidence o f internal dynamics. Possible motions
giving rise to the spectral splittings are discussed in detail.
118
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Introduction
It is commonly accepted that sulfuric acid/water aerosols play a vital role in the
formation of polar stratospheric clouds which are thought to catalyze the depletion of
polar ozone. [1] Sulfuric acid/water aerosols have been implicated in heterogeneous
reactions with hydrogen chloride and chlorine nitrate and have demonstrated significantly
high uptake o f nitric acid at temperatures at or near the frost point. [2,3] Numerous
theoretical [4] and experimental [5] studies have been aimed at investigating the
nucleation of sulfuric acid and water vapor. Due to the strong tendency o f H2SO4 to form
hydrates, accurate nucleation rates for aerosols involving sulfuric acid have been
notoriously difficult to predict. [6 , 7-11] The gas phase hydration o f sulfuric acid is thus
o f immense interest with respect to elucidating the mechanism for the formation of
sulfuric acid aerosol.
While numerous computational [8-10] and kinetic [5] studies o f the gas phase
hydrates of sulfuric acid have been carried out, only one reported experimental
investigation aimed at determining the spectroscopic properties o f H2SO4 hydrates has
been reported. [12] Several recent theoretical studies o f FTSCUd-TOln were conducted
with a focus on the transition between the neutral and ionic forms for n=0-7.[8-l0] A
number of groups independently conclude that the hydrates o f sulfuric acid remain in
their neutral form with less than 3 water molecules, while for n>3 the two forms coexist
with an energetic preference for the ion-pair. [8-10] While proton transfer is energetically
prohibited for n<3, the H2SO 4 unit demonstrates a strong ability to donate a proton and
the resulting hydrogen bonding interactions are strong and direct. For example, in the
theoretical structure for the monohydrate, the water unit accepts a proton from sulfuric
acid forming a short hydrogen bond o f -1.63A. [10] The H 2O unit acts as both an
acceptor and a donor in its interaction with H2SO4, and a secondary weak interaction is
predicted between one of the hydrogen atoms on water and a nearby S = 0 oxygen.
The study o f sulfuric acid monohydrate is of fundamental significance for a
number of reasons. It is o f course the primary product of sulfuric acid hydration, and
hence may contribute to the rate of aerosol particle formation under appropriate
conditions. The structure of the complex exhibits a strong direct hydrogen bond, offering
119
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a molecular level probe o f the gas phase interaction between a strong acid and a single
molecule o f water. It is also the simplest hydrate o f sulfuric acid and will likely provide a
benchmark for future studies of larger hydrates. Although numerous theoretical structure
calculations exist, a definitive gas phase investigation of the H2SO4-H2O complex has not
been carried out. Accordingly, in this paper, we report the microwave spectrum and
structure of the 1:1 complex H2SO4-H2O.
Experimental Section
Rotational spectra were recorded using a Balle-Flygare Fourier transform
microwave spectrometer, the details o f which have been described previously. [13]
H2SO4-H2O was produced in situ via the reaction between H2O and SO3 using a co­
injection source similar to that reported in previous studies o f reactive species. [14] In
this study, the SO j was introduced through the pulsed valve by passing Ar over solid SO3
at a backing pressure of ~3atm. The H 2<D(g) was added by passing Ar gas over a reservoir
of liquid water at a backing pressure of 0.165 atm through a 0.012in. I.D. needle. Ideal
conditions for the production o f H2SO4-H2O were obtained by clipping the needle to a
length of 0 . 11” and ensuring its central position in the "mixing region” o f the co-injection
source. Mixed isotopomers were formed by adding D2O and H2O to the reservoir in
proportions that optimized the signal under investigation.
Rotational transitions o f H2SO4-H2O and its isotopomers were initially identified
by their strong correlation with the intensity o f the l0( <—Ooo transition o f H2SO4, HDSO4,
or D2SO4, as well as the nearly symmetric triplet pattern observed for the a-type J = 2<— 1
rotational transition. This pattern is consistent with the near equivalent K=±l splitting
about the central K=0 transition predicted for a near prolate rotor. The attainment and
assignment o f spectra o f mixed isotopic species was complicated by source conditions,
and constant checking on the loi *—Ooo transitions of HDSO4, D2SO4, and H2SO4 was
necessary in order to ascertain the chemical dependence o f each transition. In addition, as
the B and C rotational constants are similar for several mixed isotopomers, the a-type
spectra were overlapping, initially precluding unique spectral assignments for each o f the
observed a-type spectral patterns. To overcome this obstacle, the dependence o f each
120
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transition on the ratio of H2O/D 2O in the liquid reservoir was tested on several
independent occasions to aid in obtaining a unique assignment for each isotopic species.
Subsequent confirmation of these assignments came from the ability to predict and
observe transitions for a number o f isotopomers based on refined structural parameters.
As an additional check of the assignments of each transition to an isotopomer of
H;0 -H:S 0 4 , the Ar carrier gas was replaced with an 80%Ne/20%He mixture. The
intensity of the assigned transitions decreased significantly with the use o f Ne/He yet
remained observable, ensuring the lack o f dependence on Ar. The spectra o f all i80
containing species were obtained by the addition of l8O H ; (95 atom%. Icon Services) to
the liquid reservoir, while the spectrum o f the j4S substituted H2SO4-H2O species was
observed in natural isotopic abundance.
A large number of additional unassigned transitions that are inconsistent with
rigid rotor predictions for H2SO4-H2O or its isotopomers were observed in this study.
These transitions displayed a chemical dependence on SO3 and either H2O, H2O/D2O, or
D :0. As a large number of species are formed under the experimental conditions detailed
above, the large number of additional lines observed was not deemed troubling. The
chemical dependencies o f a number o f the unassigned lines was extensively investigated
and documented such that future studies may reveal the chemical nature of the species
giving rise to the rotational transitions. The frequencies and intensities o f the additional
transitions are tabulated in Appendix A of this thesis.
Results
A-type rotational spectra for 18 isotopomers o f H2SO4-H2O were obtained in this
study. For the isotopomers containing HOD in the water portion o f the molecule, only
species with the deuterium in the position closest to the S= 0 oxygen o f HfDhSCU were
observed. A representative spectrum showing the Jkpk o - 2 i2<—In transition o f the parent
isotopomer is shown in Figure 5.1. The isotopic assignments and transition frequencies
are shown in Table 5.A1, which appears in the Appendix to this chapter.
121
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>
i>
w-
<
7533.0
7533.5
7534.0
Frequency (MHz)
7534.5
Figure 5.1. J = 2,: <— 1,, Transition o f H 2SOa-H:0 . where A and B states are apparent.
Total data collection time of -39s.
The a-type spectra of four H2SO4-H2O isotopomers reveal attributes that are
consistent with internal motion(s) within the complex, the nature o f which is discussed
below. Specifically, the parent H2SO4-H2O, the fully deuterated D2SO4-D2O isotopomer,
one l80 containing istopomer, and one mixed H/D isotopomer (likely HDSO4-H2O with
D in the hydrogen-bond) all exhibit a second “a-type” spectrum with a “triplet” K=0
pattern that repeats in the J=l<—0, 2«—1, and 3<—2 rotational transitions. For all
isotopomers, the central transition is the most intense and the outer two K=0 transitions
are separated from the central transition by nearly equal amounts. The ratio o f the
distance between the upper and central transitions to the distance between the central and
lower transition is nearly a constant -0.9. Table 5.1 gives the frequencies and relative
intensities of these additional transitions. As can be seen from the Table, the position of
122
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T able 5.1. Additional a-type spectra for Istopomers o f H 2 SO 4 -H 2 O.*
H 2 O-H 2 SO 4
v(MHz)
3631.183
3638.606
3645.238
7261.196
7275.971
D 2 O-D 2 SO 4
7289.272
10888.869
10910.856
10930.901
14513.042
H218 0 -H 2 S 0 4
v(MHz)
3617.124
3626.342
3634.854
H 2 O-HDSO 4
v(M Hz)
3619.938
3627.989
3635.376
3609.851
7180.203
7233.104
7238.840
7251.435
7199.883
7218.558
10717.224
10767.542
10796.700
7268.531
10846.808
7238.853
7254.839
7269.669
7269.681
10855.606
10855.612
v(MHz)
3590.637
3590.662
3600.561
10874.026
10899.835
14542.025
14568.926
10879.379
10901.736
All isotopic assignments are tentative. See text for discussion.
these additional “internal motion” components is shifted on the order o f 200-300 MHz
from the J=2<—1 “normal” a-type spectrum for the corresponding isotopomer. The
perturbed transitions are distant enough from the “normal” spectra o f each species as to
not interfere with the facile assignment o f the transitions obeying rigid rotor a-type
selection rules. Thus, the presence o f these additional spectral transitions did not prohibit
a fit o f the “normal” a-type spectra o f the isotopic species involved and were neglected in
the subsequent fit o f the obtained rotational constants to the structural parameters.
In addition to the anomalous triplet o f lines, the a-type transitions for all
isotopomers containing only hydrogen were observed as doublets with a splitting on the
order o f 50-l00kH z that increases as n (J+ l). These are labeled states A and B in Table
5.A1 with State B at a lower frequency than State A. This doubling was not observed in
the anom alous triplet state transitions. The accurate intensity ratio o f these two states was
not carefully measured, however, in all cases except for the parent H2SO4-H2O species,
the state labeled by “B” was ~3 to 6 times more intense than the state labeled by “A” . For
the parent isotopomer, the intensity ratio for each o f the com ponents varied, but were on
123
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
the order of 1:10 to 1:16 for A:B respectively. The nature o f the possible motion giving
rise to these two states will be discussed in greater detail below.
As the calculated structure for H2O-H2SO4 [10] predicts a significant dipole
component along the c-inertial axis, extensive searches for c-type transitions were carried
out for the parent and fully deuterated isotopomers. These searches were guided using the
numerous calculated H2SO4-H2O structures [8-10] as an estimate o f the A rotational
constant, the magnitude o f which could not be obtained from a fit o f the a-type spectra.
Numerous transitions were observed which were dependent on both H2O and SO3 for the
parent and D 2O and SO3 for the fully deuterated species that did not fit to predictions
based on a rigid rotor Hamiltonian. Among the myriad o f observed lines, a distinct
congested pattern of intense transitions spanning an 80 MHz region was initially
observed with H 2O in the liquid reservoir. The transitions demonstrated a dependence on
both SO3 and H2O, and subsequent replacement of the Ar carrier gas with Ne/He
confirmed their independence of Ar. Within the 80MHz span containing the H 2O (and
SO3) dependent transitions, nearly an identical spectral pattern was duplicated twice with
a decreased intensity for the pattern towards lower frequency.
Upon replacement of the H2O with D2O, a similar pattern was observed -~450
MHz lower in frequency. For the D 2O dependent species, only one congested pattern was
observed which was similar but not an exact match to that observed with H2O injected
into the expansion. The intensity o f the transitions correlated with that o f the assigned atype spectra for both the H2SO4-H2O and D2SO4-D2O isotopomers. This correlation,
however, does not confirm their assignment as belonging to the H2SO4-H2O complex as
the patterns are not in agreement with either c- or b-type spectral predictions. These
transitions as well as a number of others that exhibited a similar response to experimental
conditions remain unassigned, and are tabulated in Appendix A o f this thesis.
l80 Substitution
From Table 5.A1, it is evident that the spectral assignments include two
18
independent isotopomers containing an O in an S=0 position. This was a somewhat
surprising result in light of the proposed mechanism for the reaction between H 2O and
124
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
SO3. The mechanism for the formation o f H2SO4 from SO3 and H 20 in the gas phase is
thought to involve two water molecules and proceed through a cyclic (HiO^-SC^
intermediate. [15] This proposed mechanism is in agreement with experimentally
measured rate constants for the loss o f SO3 in the reaction to produce H2SO4, which
reveal a second order dependence on the H2O vapor concentration as well as a strong
negative temperature dependence. [16] The formation of H2SO4 from SO3 and two
molecules of H2O may occur via two different reactions:
SO3 + (H20)2 —> H2SO4 + H 20
( 1)
H2O-SO3 + H 20
(2)
H2SO4 + h 2o
Reaction (1) is predicted to proceed without a barrier, while reaction 2 is hindered by a
small barrier of ~5kcal/mol. [15] However, from a consideration o f the relative stabilities
of H2O-SO 3 vs. (H20 )2, (~ 8kcaI/mol vs. ~4kca.l/mol [15]) it is suggested that the reaction
likely proceeds with the initial formation o f H2O-SO3, and the subsequent addition of a
second molecule o f water, as in reaction (2). [16] The first addition o f a molecule of
water thus leads to the formation of a fourth S-0 bond, while the second water molecule
concertedly transfers a proton to form the H2SO4 product.
Following either mechanism (1) or (2), the formation of H2SO4 from SO3 and
H :'80 would presumably result in an l80 substitution in an S-O single bond, with its
attached hydrogen remaining. The data collected for the H2SO4-H2O complex revealed a
Io
larger number of isotopomers containing
O than predicted, and the isotope shifts were
consistent with l80 terminating an S=0 bond in the sulfuric acid portion o f the complex.
In order to confirm the existence of two
IQ
O containing isotopomers o f H2SO4 monomer,
the isotope shift of the loi<—Ooo transition o f the isotopomer with l80 in the S=0 bond
was predicted from the experimentally determined structural parameters o f H2SO4. [17]
From these predictions, the transitions were readily located and are presented in Figure
5.2. In addition, the frequency of the loi<—Ooo transition o f the 34S partner to each
125
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992?T8 9929.0—9929.2
Figure 5.2. 101<—
9929.4—9929:6—9929.8 ' 9939.3--- 994fr0----- 9940.5------ 9941.0----- 9941.5
Frequency (MHz)
18
Transitions o f two isotopomers of O substituted H-,S04.
isotopomer was also observed to ensure that these transitions were properly assigned. The
observation of the 1oi<—Ooo transition of both 34S isotopomers confirmed that these lines
were due to H2SO4 and were consistent with the isotopic assignments.
This result implies that either the formation of H :S 0 4 from SO3 and H2O involves
more than two water molecules or there are unique experimental conditions in this study
that result in isotopic scrambling. Although the latter is indeed factual, since the
particular conditions in a co-injection source are not well understood, recent calculations
have suggested that as many as four water molecules may be involved in the overall
conversion of SO3 and H2O to H2SO4. [18] This reaction proceeds with the formation of
the ionic intermediate (HSCVXHsCT) which is stabilized by the presence o f the two
additional water molecules. This reaction approaches the condensed phase hydration of
SO3 to H2SO4, which likewise proceeds through the formation of the (HSO4 -H3O’ )
contact ion pair. [19] Whatever the exact mechanism responsible for the production of
H2SO4. the isotopic scrambling necessary to produce an isotopomer o f H2SO4 with 180 in
the S = 0 bond is seemingly plausible under conditions in which there is excess water
available.
Theoretical calculations suggest that proton transfer from H2SO4 to H2O occurs
with the addition of just three water molecules, again resulting in the formation o f an ion
pair. This ion pair can subsequently be protonated at an alternate oxygen site, leaving the
126
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Jg
O label in an S = 0 bond. Under the current experimental conditions, there is the
potential for a variety o f surface reactions on the sides o f the nozzle orifice and/or needle.
Whether under these conditions the reaction proceeds through the formation o f gas phase
sulfuric acid that undergoes a number o f proton transfer events, or through the immediate
production of a solvated ion pair remains unclear.
Spectral Analysis
For all 18 isotopomers measured, the a-type spectra were fit to Watson’s
Hamiltonian for a distortable asymmetric rotor [20], viz.,
H = [(B + C)/2 - AjJ 2]J 2 + [A - (B + C)/2 - AjkJ 2 - AKJ Z2]J Z2 +
[(B - C ) / 2 - 25jJ 2](Jx2 - J y2) - 5k[J z2(J x2 - J>2) + (J*2 - J>2)Jz2] + HjJ6
(1)
where A, B, and C are the rotational constants and Aj, Ajk, A<, 8j, 5k, and Hj are
centrifugal distortion constants. For each isotopomer, the data were insufficient to fit all
of the rotational and distortion constants in (1). Specifically, in the absence of b- or ctype spectra the data were insufficient to fit the A rotational constant. Initially, the value
of the A rotational constant was held fixed at a constant value o f 4500 MHz for all 18
isotopomers. This approach resulted in larger than normal residuals for a number of
isotopic species. In order to lessen this discrepancy and obtain an improved guess for the
A rotational constant for each isotopic species, the A constant was allowed to float in a
series of fits for each isotopomer. In the final fit for each isotopic species, the A constant
was fixed at the value obtained, resulting in much decreased residuals and improved
values for the B and C rotational constants. The values o f B and C obtained were not
significantly affected by the choice o f A.
In addition, as only a maximum of seven transitions were assigned for each
isotopomer, the inclusion of all six centrifugal distortion constants in the fit o f the
transition frequencies was unnecessary. For this reason, Ak, 5j, 8 k, and Hj were held fixed
to zero in each of the fits to (1) while Aj, and Ajk were freed. The choice to fix or free
each parameter was made by testing the sensitivity o f each distortion constant to the
127
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available data. When the data were sufficient to provide a unique solution to (1) for the
tested constant, that particular constant was allowed to float in the final fit. For the
parameters that could not be determined from the data, the magnitude o f the fixed values
was chosen so as to reduce the disparity between the observed and calculated transition
frequencies. The B and C rotational constants were not significantly altered by the choice
o f these parameters. The choice to fix Ak., 8j. 8 k. and Hj to zero coincides with a complex
that is not easily distorted with additional angular momentum. Table 5.2 summarizes the
obtained rotational and distortion constants for each of the 18 isotopomers measured.
For the spectra that were split into two “states”, two separate fits were carried out
for each state. The obtained spectroscopic constants for each state are given in Table 5.2,
labeled as A and B according to intensity as discussed above. For all isotopomers
containing deuterium, the hyperfme structure was not adequately resolved to elucidate the
respective components of the quadrupole coupling constants. In order to obtain the
linecenter for each observed transition that demonstrated a hyperfme pattern, a weighted
average approach was applied, in which the contribution from each resolved hyperfme
component was weighted by its measured arbitrary intensity. The uncertainty in this
average was taken into account by considering the measurement error for each
component. This was propagated in the subsequent fit to Eq. (1), where weaker and less
well resolved transitions were assigned a larger error. In some cases, this approach
resulted in a larger than usual disparity between the observed and calculated linecenters,
however, these errors remain within the estimated error for each transition. From Table
5.2, it is evident that this difference did not affect the obtained rotational constants, which
maintain essentially the same degree o f uncertainty as is reported for isotopomers lacking
hyperfme structure.
128
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T a b le 5.2 . S pectro sco p ic C o n sta n ts fo r Iso to p o m ers o f JTSO-x-fTO.
' \
B(MHz)
__
A state 1899.1253(8)
B state 1899.1131(8)
/
V
I
B(MHz)
\
__
A state 1894.8643(8)
B state 1894.8532(8)
J
V\
B(MHz)
'Is'
A state 1798.2664(8)
B state 1798.2589(8)
/
\
C(MHz)
Dj(kHz) DjK.(kHz)
1878.2435(8) 0.94(4)
1878.2221(8) 0.88(4)
C(MHz)
Dj(kHz) Djk( kHz)
1874.243(1) 0.83(5)
1874.2238(8) 0.86(4)
C(MHz)
13.0(4)
12.4(4)
*
12.5(4)
Dj(kHz) Djk( kHz)
1779.5662(8) 0.85(4)
1779.5493(8) 0.85(4)
12.3(4)
11.9(4)
I
B(MHz)
'ly
\
A state 1782.3686(9)
B state 1782.3752(9)
____Is
V\
"is'
1
\
18— \\ 1
'u r
\
A state 1792.9347(8)
B state 1792.9117(8)
B(MHz)
'18'
\ _. )8
v
B(MHz)
A state 1787.0015(8)
B state 1786.9700(8)
\
B(MHz)
A state 1758.277(1)
B state 1758.2798(8)
/
^8I
9 ___ /
\
b
R _ ^
C(MHz)
Dj(kHz) Djk( kHz)
1747.5183(9) 0.86(7)
1747.4815(9) 0.90(7)
C(MHz)
10( 1)
11( 1 )
Dj(kHz) DiK(kHz)
1765.0065(8) 0.86(4) 10.1(4)
1765.0069(8) 0.92(4) 9.6(4)
C(MHz)
Dj(kHz) DjK(kHz)
1769.942(1)
1769.9498(8)
*
C(MHz)
Dj(kHz) DjK(kHz)
*
1.01(4) 8.9(4)
1734.3217(8) 0.70(5)
1734.3004(8) 0.75(4)
11.7(4)
11.7(4)
B(MHz)
C(MHz)
Dj(kHz) DjK(kHz)
1738.950(2)
1724.871(2)
0 .8 ( 1)
11( 1)
B(MHz)
C(MHz)
Dj(kHz)
D jk OcH z )
1814.473(2)
1800.650(1)
1.27(7)
10.3(6)
\
A
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 5.2 continued.
R ___ /
O'
B(MHz)
C(MHz)
Dj(kHz) DjK(kHz)
1853.738(2)
1835.856(2)
0.32(7) 7.5(7)
B(MHz)
C(MHz)
Dj(kHz) DjK(kHz)
1846.015(1)
1824.795(1)
0.49(6)
B(MHz)
C(MHz)
Dj(kHz) DjK(kHz)
1768.390(1)
1748.501(1)
0.84(8)
B(MHz)
C(MHz)
Dj(kHz) DjK<kHz)
1884.100(1)
1862.155(1)
0.79(7)
B(MHz)
C(MHz)
Dj(kHz) DjK(kHz)
1859.519(1)
1840.540(1)
0.72(6)
B(MHz)
C(MHz)
Dj(kHz) DjK(kHz)
1753.289(1)
1736.260(1)
0.95(8)
B(MHz)
C(MHz)
Dj(kHz) DjK(kHz)
1830.144(2)
1813.281(1)
0.87(7)
B(MHz)
C(MHz)
Dj(kHz) Djk<kHz)
1870.617(1)
1849.075(1)
1.06(7)
B(MHz)
C(MHz)
Dj(kHz) DjK(kHz)
1780.986(1)
1762.475(1)
0.85(5)
b
'
D
1
R
V
*
1
D
/
T
D
i
I*
14.7(5)
10. 1(8 )
11.8 (6 )
V
'
-0
/
\
\
11.9(5)
I
D'
-D
___ /
>2
'
\
*D
\
•s .
____
II
\.
^
\
12.3(8)
12.6 (6 )
"
\
un
i
a2
11.7(6)
6
IK -o
\
/
A
11.7(5)
1
\
130
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Internal Motion
As discussed above, the evidence for internal dynamics in the H2SO4-H2O
complex emerges from spectral patterns that cannot be fit to Eqn. (1). A brief summary of
the observations is as follows:
(1) For all isotopomers containing only hydrogen in both the H2O and H2SO 4 portions o f
the complex, the a-type spectrum in each rotational transition is split into a “doublet".
The magnitude o f the splitting is on the order of ~10-30kHz in the J = 1«—0 and increases
with rotational transition as n(J+l) where J is the rotational level of the lower state. The
intensity ratio of the doublets is dependent on isotopomer. For all isotopomers containing
IS
O the ratio is 1:3 to 1:6 for the A state vs. the B state, while for the parent species the
intensity ratio is as different as 1:16, as determined from relative peak height. It is unclear
whether this splitting is also present for isotopomers containing HDSO4 and D2SO4 since
the splitting is on the same order as the hyperfme structure and may appear to be
hyperfine components. In addition, the spectra for mixed (i.e., those containing HDSO4
and D2SO4 with H2O) were relatively weak, hence the less intense component may not
have been observable.
(2) Four isotopomers o f H2SO4-H2O, all o f which correlate with species exhibiting the
most intense “normal” a-type spectra (H2SO4-H2O, D2SO4-D2O, presumably HDSO4H2O, and one dependent on l8OH 2, presumably H2S04 -H 2I80 by intensity arguments)
display a second “a-type” spectrum ~200-300MHz away, where there are 3 Ka=0
transitions in the J=l<—0, 2<-I, and 3<-2 rotational transitions.
Before speculating on the relevant internal motions contributing to these
observations, it is crucial to understand that the data obtained is likely insufficient to form
a complete picture regarding the nature o f the internal motion in the H2SO4-H2O
complex. As microwave spectroscopy is not a broad scan technique, vital spectral
information may have not been accessed due to the unavoidable neglect o f large spectral
regions while searching for transitions o f the H2O-H2SO4 complex and its isotopomers.
Additional limitations arise from the finite range o f the spectrometer, spectral resolution,
S/N. and hyperfine structure. The latter three factors were particularly problematic for
131
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mixed isotopic species, where only relatively weak signals with a diminished
reproducibility were obtained. Furthermore, for the case o f isotopomers containing D^O
bonded to an isotopomer of H2SO 4, the doubling observed in the case of the H 2O may
have been misinterpreted or obscured due to hyperfine structure.
With these shortcomings in mind, it is nevertheless instructive to discuss the
observations outlined above. As at least one o f the motions appears to affect only those
isotopomers with either H2O or D 2O in the hydrogen bond, it seems reasonable to
speculate that the motion likely involves the H(D)20 portion o f the complex. Numerous
microwave and FIR studies involving complexes containing a hydrogen bonded water
unit support this conjecture. [21] From the findings above, with the occurrence o f a total
of 5 K = 0 lines for at least four isotopic species, more than one motion need be invoked
to interpret the obtained spectral patterns.
The motion often responsible for the small splittings as observed in Table 5.A1
involves an interchange of the two hydrogen or deuterium atoms on the water unit. In
nearly all respects, the doublets appear to be due to a tunneling motion that exchanges the
two equivalent water hydrogens through a rotation about the water C 2 axis, and the
splitting is on the same order with that observed for a number o f water containing
complexes involving a proton interchange motion. [21c, 22] In H2SO4-H2O, this motion
would involve cleavage of the weak secondary interaction between the water hydrogen
and the S= 0 oxygen and is therefore expected to be hindered to some degree by an
intermediate to a high barrier. The result is to split each torsional level into a doublet,
with one symmetric and one antisymmetric tunneling state. Since the total wavefiinction
must be antisymmetric with respect to exchange of equivalent nuclei, the symmetric
tunneling state must pair with an antisymmetric spin function, and the antisymmetric
tunneling state must pair with a symmetric spin function. For H2O, with two equivalent
fermions, there are three symmetric and one antisymmetric spin states, thus the
antisymmetric tunneling state is predicted to have a statistical weight of three, while the
symmetric state has a statistical weight o f one. The spectra are predicted to appear as
doublets with a 1:3 intensity ratio in the case o f proton interchange. In the case o f HOD,
132
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rotation about the C 2 axis would result in a new conformer, and not an isoenergetic
configuration. Thus, evidence that the motion involves exchange o f equivalent
protons/deuterons is the absence o f spectral splitting for species containing HOD bound
to an isotopomer o f H2SO4. While the second state also appears absent for isotopomers
containing D2O, it is likely that the splitting decreases sufficiently to be unresolved from
the hyperfme structure.
From the intensity ratios of the observed doublets, a definitive assignment to a
tunneling motion cannot be made, as the intensity ratios o f the components are not 1:3.
This variation in intensity may be the result of a competing perturbation (a nearby state
that is populated and effectively adds intensity to one o f the components), or may reflect
that these states are not due to proton/deuteron tunneling. Alternative interpretations
include population o f an excited vibrational state or the indication o f nearly isoenergetic
conformers having nearly equivalent B and C rotational constants. Both of these
possibilities fail to explain the absence o f spectral splitting as in observation ( 1) for
species containing deuterium. As it is possible that spectral information is lacking for
these species due to reduced relative intensities and congested hyperfme patterns, no
conclusion can be drawn from this observation. The most reasonable scenario for an
explanation o f observation ( 1) appears to be a proton interchange tunneling motion.
Although the above scenario provides a reasonable explanation for observation
( 1). it provides little insight into the presence o f the additional states observed in the case
of four isotopomers o f H2SO4-H2O as described in observation (2). From the geometry o f
the H2SO4-H2O complex, a second low barrier motion that would result in an isoenergetic
configuration and not a new conformer is not immediately apparent. Upon closer
inspection, a coupled motion involving rotation about the weak secondary hydrogen bond
combined with a rotation o f the water unit about 0 5 -0 1 (see Figure 5.3 for atom labels)
is a second pathway to the original molecular conformation. A similar coupling of the
rotation about the 0 - 0 bond with a water wag has been implicated in phenol-H 20 [23]
and C2H4-H2O [22b]. This motion appears energetically feasible as the secondary
interaction between the water unit and the S=0 bond can be preserved through a
133
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bifurcated intermediate similar to that involved in the geared donor acceptor
interconversion in water dimer. [24] In order that this motion proceed with a low barrier,
the strong hydrogen bond between 0 5 and HI must remain intact throughout the motion.
Therefore, the motion cannot exchange the lone pairs on the acceptor oxygen. The
calculated barrier to this coupled motion in phenol-HiO is 14.69cm'1, with the hydrogen
bond remaining intact throughout the motion. [23]
For H2SO4-H2O, the barrier to proton interchange is expected to be somewhat
higher as the water unit acts as both a donor and acceptor. In the absence of similar
calculations for the H2SO 4-H 2O system, it is not possible to provide an estimate o f the
barrier height to proton interchange via the coupled rotation discussed above. It is also
not possible to assign the observed spectral patterns without a comprehensive treatment
of the combined effect of both tunneling and internal rotation pathways discussed. As
discussed above, the lack o f spectral assignments for these additional states does not
preclude a determination o f the structure o f the H2SO4-H2O complex as they are distant
enough from the "normal” a-type spectra as to not interfere with their assignment. It is
hoped that this work will stimulate future theoretical studies that will address the internal
dynamics in this atmospherically important complex.
Structure Determination
A preliminary analysis o f the rotational constants yielded a structure similar to
previous DFT calculations. [10] The complex forms a distorted six membered ring in
which the water unit acts as both a proton acceptor and a proton donor in its interaction
with H2SO4. The main structural features are highlighted in Figure 5.3 below. In the
primary interaction, the H2SO4 portion of the complex donates a proton to the water unit
to form a short, direct hydrogen bond with an O-H distance on the order o f 1,6 A and an
O -H -O angle of ~ 165°. A distance o f -2.2A is predicted for the weaker secondary
interaction between a hydrogen on the water unit and an S = 0 oxygen in H2SO4.
134
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H2
v
Figure 5.3. Thirteen of the nineteen fitted parameters for H:S 0 4-H:0 including atom
labels used in text. See Figure 5.4 for a description of the additional structural
parameters.
The large number of parameters necessary to uniquely define its geometry
complicates a determination of the structure o f the H2SO4-H2O complex. It is common
procedure in fitting rotational constants to constrain the internal coordinates of each
monomeric unit to the structural parameters reported for the free monomer. This
approach relies on the accepted notion that in weakly bound complexes, the geometries o f
each monomer unit are undistorted as a result o f complexation. As the calculated
structure o f the H2SO4-H2O complex reveals a strong interaction between the two units,
this assumption appears invalid, as considerable structural changes occur in both the
H2SO4 and the H2O units within the complex. Because the H2SO4 moments of inertia
contribute largely to the moment o f inertia of the complex, this situation is exacerbated in
the case o f H2SO4-H2O.
In particular, according to the calculated structure of H2O-H2SO4 [10], for the
H2SO4 portion o f the complex, the C2 symmetry o f the monomer is broken by a 0.03A
lengthening o f the O -H distance accompanied by a similar contraction o f the S -0 bond
involved in the hydrogen-bonding interaction. Likewise, the S= 0 distance is predicted to
increase by 0.03A as a result of the secondary interaction with a water proton, while the
O l-S -0 3 angle widens by -1.5° in response to the primary hydrogen-bonding interaction.
135
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While these changes are not enormous, the validity o f constraining the geometry o f the
H2SO4 portion of the complex is called into suspect. For the water portion o f the
complex, a widening of the H-O-H angle by nearly 2° from its monomer value is
predicted, clearly demonstrating the lack of legitimacy in fixing the geometry o f the
water unit to that observed for HiO monomer. For these reasons, the monomer
geometries were not constrained in the rotational constant fit. As every atom in the
complex with the exception o f the outer water hydrogen has been isotopically substituted
at least once, there are 36 rotational constants available for fitting the structure o f the
complex.
The structure fit included 24 adjustable parameters, which were necessary to
describe the geometry of the H2SO4-H2O complex. A subset o f the structural parameters
is indicated in Figures 5.3 and 5.4.
Tz
Figure 5.4. Parameters used to define the position o f the water unit within the H;S 0 4H:0 complex.
Figures 5.3 and 5.4 demonstrate the complexity of determining the geometry of
the H2SO4-H 2O complex. The position of the HiO unit with respect to H2SO4 is
determined by defining the distance between 01 and 0 5 as shown in Figure 5.3. The
water oxygen is then allowed to migrate off o f the 01-S=03 plane by an angle labeled a .
not shown in the Figure. a=0 corresponds to the water oxygen lying in the 01-S -03
plane. The symmetry o f the water unit is broken by allowing the two 0-H bond lengths in
the water unit to differ. The position o f the water unit is therefore determined by locating
136
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the central axis with respect to the O l-S -03 plane through two angles labeled by 8 and y
as shown in Figure 5.4. 8 and y = 0 correspond to the line designating the height o f the
triangle formed between 0 5, H3, and H4 coinciding with the z axis in Figure5.4, which is
parallel to the O l-S -03 plane. Two angles are therefore needed to locate the position of
the water hydrogens; the H-O-H angle and an angle labeled 0 in Figure 5.3. For a
symmetric water molecule, 0 would equal Vi o f the H-O-H bond angle. Since the two OH bond lengths are treated independently, 0 is necessary to define the projection o f Ros-m
onto an imaginary line dividing the H :0 plane (the C 2 axis when both 0-H bond lengths
are identical). For the sulfuric acid portion o f the complex, the angular excursion o f HI
about the S-01 bond axis is depicted by (3 and the free hydrogen is allowed to rotate
about the S-02 axis through an angle 0 . |3 = 0 corresponds to H 1 located in the 0 1-S-03
plane while 0 = 0 corresponds to H2 lying in the 02-S -03 plane. Both are indicated in
Figure 5.3.
A non-linear least squares fit o f the rotational constants to the 24 parameters using
both State A and State B values was carried out. As discussed above, it is unclear which
o f these states is positively the lower energy state, thus two separate fits of the data were
carried out and an average was taken in order to determine the “final” value o f each fit
parameter. In the process of fitting the rotational constants to the geometric parameters,
the sensitivity of the data to each parameter was carefully tested. From this process, it
was concluded that five of the structural parameters could not be uniquely determined
from the measured rotational constants.
These five parameters are as follows: (1) S-01-H I, the angle between the sulfur,
0 1 . and H I; (2) S-02-H2; the same angle except involving the free H2SO4 hydrogen; (3)
03-S -04. the angle between the two S=0 bonds; (4) R0 2 -H2, the 0-H bond distance for
the free H2SO4 hydrogen, and (5) HOH, the water angle. Appropriate values for the fixed
parameters were determined from a comparison o f the theoretical structure o f H 2SO 4H 2O with that of the free monomers, H 2SO4 and H 2O, respectively. [17] As the geometry
around the free H 2SO 4 hydrogen appears to remain essentially unchanged upon
complexation with HiO, S-02-H2 was fixed at its free H2SO4 monomer value of 108.5°
while R02 -H2 was fixed at 0.95A. Although the value for this bond length in free H2SO 4 is
137
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0.97(1 )A, the value of 0.95A minimized chi-squared and hence was used in all
subsequent fits. Likewise, the angle between the two S=0 bonds is not predicted to
change from its value in H2SO4 monomer and was fixed at 123.3°, its value in free
H2SO4. This magnitude of this value was also tested in order to insure the minimization
of chi squared.
As both the H2O and the S - O l-H l angles are expected to shift from their free
monomer values, the appropriate values were obtained from a chi squared minimization.
In the minimization process, the H2O angle was allowed to vary between 106 and 107°,
while the S-01-H I angle was allowed to vary between 108.5 and 109.0°. The range for
the water angle was chosen by considering the large distortion o f this angle predicted by
theoretical calculations o f the H2SO4-H2O complex. As a verification of the chosen range,
values closer to the water angle in free H2O were tested and indeed resulted in much
larger residuals. The optimal values based on a chi squared minimization were 107° and
108.6° for the H-O-H and S -O l-H l angle, respectively.
The values for all 19 freed parameters utilizing rotational constants from State A,
State B, and an average of the two are given in Table 5.3 along with the values at the
B3LYP/D95** level of theory/basis set. [10] The error bars are representative o f the
deviations in the fit values on account o f the variation o f the H2O and S-O l-H I angles.
Table 5.4 gives the rotational constants utilized in the structure fit for both State A and B
as well as the averaged residuals for each o f the 36 constants. As is indicated in the table,
the largest residual is 0.559MHz, demonstrating the excellent quality o f the rotational
constant fit. The correlation matrix indicates that all o f the 19 fitted structural parameters
are indeed independent. The fitted structure o f the H2SO4-H 2O complex is depicted in
Figure 5.5, where the resultant distances and angles for both hydrogen bonding
interactions are indicated. In an attempt to highlight only the most noteworthy structural
features, all other fit structural parameters are reported in Table 5.3 and are not repeated
in Figure 5.5.
138
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T able 5.3. Fitted vs. Calculated Structural Parameters for H2SO4-H2O.
State A
State B
Average Calculated3
Rs-Ol
1.5663(8)
1.5686(9)
1.567(1)
1.603
R01-05
(1)
Y
2.668(9)
-163.4(4)
-13.6(4)
100.3(4)
15.2(3)
38.8(4)
-11.4(5)
2.666(9)
-163.3(4)
-13.8(4)
100.2(4)
15.5(3)
38.6(4)
-11.3(5)
2.67(1)
-163.4(5)
-13.7(5)
100.2(6)
15.3(4)
38.7(6)
-11.4(8)
2.64
-164.977
-20.339
99.93
17.937
**
**
R-S-03
1.4656(9)
1.4619(9)
1.464(1)
1.467
Roi -hi
1.04(1)
1.04(1)
1.04(1)
1.009
Rs-o:
1.578(3)
1.578(3)
1.578(3)
1.636
p
S-01-05
a
5
1.409(3)
1.411(3)
1.459
1.410(4)
106.67(4) 106.75(4) 106.71(6) 109.122
101.8(2)
101.8(2) 101.78(2)
102.654
106.8(3)
106.6(3)
106.7(4)
107.519
104.58(7) 104.84(6) 104.71(9) 104.518
0.98(1)
0.98(1)
0.974
0.98(1)
ro?-H3
0.98(1)
0.98(1)
0.98(1)
0.967
f05-H4
**
55.6(9)
55.5(9)
0
56(1)
a.) Ref. [10]. **not determinable from calculated structure.
Rs-04
O l-S -03
01-S -02
01-S -04
02-S -03
139
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T able 5 .4 . Residuals o f the Fitted Rotational Constants for H2SO4-H2O.
State A
State A
State B
State B
B (MHz) Error (MHz) B (MHz) Error (MHz) C (MHz) Error (MHz) C (MHz) Error (MHz)
1899.125
1894.864
1798.266
1792.395
i 758.277
1787.002
1782.369
1738.950
1780.986
1753.289
1814.473
1830.144
1884.100
1859.519
1870.617
1846.015
1853.738
1768.390
-0.223
0.092
-0.245
0.177
0.165
0.155
-0.093
0.035
0.183
-0.035
0.429
0.029
-0.100
-0.077
0.035
-0.031
0.554
-0.089
1899.113
1894.853
1798.259
1792.912
1758.280
1786.970
1782.375
1738.950
1780.986
1753.289
1814.473
1830.144
1884.100
1859.519
1870.617
1846.015
1853.738
1768.390
-0.234
0.071
-0.255
0.182
0 .1 1 1
0.160
-0.085
0.038
0.183
-0.042
0.431
0.028
-0.099
-0.077
0.042
-0.032
0.559
-0.090
1878.244
1874.243
1779.566
1765.007
1734.322
1769.942
1747.518
1724.871
1762.475
1736.260
1800.650
1813.281
1862.155
1840.540
1849.075
1824.795
1835.857
1748.501
-0.118
0.186
-0.198
0.047
0.014
0.171
0.075
-0.108
0.127
0.048
0.121
-0.092
0.026
-0.012
-0.166
-0.002
0.180
-0.190
1878.222
1874.224
1779.549
1765.007
1734.300
1769.950
1747.492
1724.871
1762.475
1736.260
1800.650
1813.281
1862.155
1840.540
1849.075
1824.795
1835.857
1748.501
-0.145
0.147
-0.223
0.053
0.021
0.115
0.084
-0.108
0.126
0.049
0.121
-0.091
0.024
-0.015
-0.167
-0 . 0 0 1
0.176
-0.188
The changes in the H1SO4 unit o f the complex due to the complexation with water are
highlighted in Figure 5.6. From the Figure, it is evident that the changes in bond lengths
and angles in the H2SO 4 portion of the complex are indeed significant and in agreement
with that predicted by theory [8-10]. As expected, the largest changes in the H2SO4
structure occur in the region in close proximity to the hydrogen bonded water molecule.
The changes are all in the direction that is sensible based on chemical intuition; for
example, the length of the 0 1 -HI bond increases while the 03-S-01 angle decreases.
Additionally, the S=0 bond involved in the weak secondary hydrogen bonding
interaction with H3 lengthens slightly as one of the lone pairs on the oxygen is attracted
to the partially positive H3 center.
140
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
w
Figure 5.5. Parameters obtained from the Fitted Structure of H;S 0 4-H:0 .
1.9(5)'
*0.07(1 )A r
V
Figure 5.6. Structural changes within the sulfuric acid unit upon complexation with water
as (value in H:S 0 4-H20-value in H;,S04 monomer).
Discussion
The experimentally determined structure o f H2SO4-H2O is in reasonable
agreement with that calculated by Re et al. [10]. The two H2SO4 hydrogens optimize in a
trans configuration, consistent with the lower energy from o f sulfuric acid. The H 20
positions itself as to form a distorted, non-planar six-membered ring with one half o f the
H2SO4 molecule. In doing so, the H2O unit acts as both a hydrogen bond acceptor and
141
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
donor, forming one strong hydrogen bond and a weaker secondary interaction with an
S=0 oxygen. The primary interaction, in which H2SO4 donates a proton to H2O, is
characterized by a strong, direct hydrogen bond with a short 1.645(5)A O -H distance
(2.663A 0 - 0 distance) and a 165.2(4)° O -H -O bond angle. The weaker, indirect
secondary interaction between the H 2O proton and an S= 0 oxygen is indicated by a much
longer 0 -H distance of 2.05(1 )A. This interaction, while weak, appears to provide some
stability for the complex, as is indicated by the lack of deuterium substitution at the free
water hydrogen position in the HO D containing species. The preference for deuterium
substitution in a weak hydrogen bonding interaction has been observed in several
complexes involving water and is thought to arise from the reduction in zero point energy
associated with substitution by a heavier isotope. [22a, 25]
The 05-H1 hydrogen bond distance observed for the H2SO4-H 2O marks the
shortest gas phase hydrogen bond length for a complex involving water, with a value
0.1 A shorter than that in HF-H 2O [26] and 0.134(33)A shorter than that in HNO 3-H 2O
[22a], The short hydrogen bond distance obtained implies a very strong interaction
between H2SO 4 and H2O, and the large 0.07(1 )A lengthening of the O l-H I bond distance
marks the onset of a proton transfer event. The H2SO4-H 2O complex can thus be regarded
as an intimation of the earliest conception o f an ion-pair, as is present in bulk phase
H; 0 /H 2S04 systems. [19] Upon the addition of a second water molecule, a further
lengthening o f the O l-H l bond by an additional 0.03A and a shortening of the hydrogen
bond distance by 0.127A is predicted. [10] The same calculations suggest that as the
number of H2O molecules reaches 3, the coexistence o f neutral and ion-pair clusters with
a small energetic preference for the proton transferred species. [8-10] For this reason,
further high resolution spectroscopic studies o f higher order hydrates of sulfuric acid
would be of immense interest with regards to gas phase proton transfer.
Finally, it is interesting to comment on the stability o f the monohydrate o f sulfuric
acid relative to free H2SO4 and H2O. A binding energy o f ~10kcal/mol is predicted from
DFT calculations [10] which is consistent with the short hydrogen bond distance and near
linear bond angle obtained in this study. The large stabilization energy is significant in
the role that these small clusters play in the formation o f new atmospheric particles.
142
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Conclusions
The microwave spectrum and structure of H2SO4-H2O have been obtained via
pulsed-nozzle Fourier transform microwave spectroscopy using a co-injection molecular
source. The following conclusions can be drawn from this study:
1. The structure obtained is in close agreement with DFT calculations. [8-10] The water
unit acts as both a proton acceptor and a weak donor in its interaction with H 2SO4,
forming a distorted six membered ring with half of the H2SO4 molecule. There is a short
( 1.645(5)A), direct hydrogen bond in which one o f the acidic protons on H2SO4 donates a
proton to the H :0 oxygen. A weaker secondary interaction is formed between a water
hydrogen and an S = 0 oxygen on H2SO4. Upon the addition of HOD. the stabilization
provided by this secondary interaction is exemplified by the preference for deuterium
substitution in the bonded position. There is a significant lengthening of the sulfuric acid
O-H bond (0.07( 1)A) (Figure 5.6) involved in the strong interaction with HiO, indicative
of the earliest stages of a proton transfer event.
2 . Two isotopomers of 180 substituted H2SO4 are formed in the cold jet, one o f which has
the isotopic label in the S-O-H bond and the other in an S = 0 bond. This implies that
either there are unique conditions in the supersonic jet, or that the mechanism for the
production of sulfuric acid from gaseous H2O and SO3 likely involves more than two
water molecules.
3. The water unit in the H2SO4-H2O complex demonstrates complex internal dynamics
that are not adequately described from the spectroscopic evidence. For several isotopic
species there are as many as 5 K=0 a-type transitions, indicating that there are likely at
least two motions occurring simultaneously. Speculating from the structure o f the
complex, there are two motions that appear to conserve the geometry o f the complex. The
first is a rotation about the water Cz axis which necessarily breaks the weak secondary
interaction between a water hydrogen and the S= 0 oxygen, and is thus predicted to
143
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
possess a high barrier. The second candidate involves a geared motion where the water
unit simultaneously rotates about the 0 1 -0 5 axis and about the weak secondary hydrogen
bond. This motion is likely more facile as it allows conservation of the weak secondary
interaction through a bifurcated intermediate similar to that proposed for proton exchange
in water dim er and higher order water clusters. [27]
A cknow ledgem ents. This work was supported by the National Science Foundation, the
Petroleum Research Fund, and the University of Minnesota through the Doctoral
Dissertation Program. We would also like to thank Drs. Arstila. Re. and Morokuma for
providing us with the Cartesian coordinates corresponding to their calculated H :S 0 ^-H :0
geometries.
144
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References:
1. Marlin. S.T.: Salcedo. D.: M olina. L.T.: Molina. M.J. J. Phys. Chem. B. 1997. 101.
5307.
2. Beichert. P.: Schrems. 0 . J. Phys. Chem. A. 1998. 102. 10540.
3. Hanson. D.R.: Ravishankara. A.R. J. Phys. Chem. 1994. 98. 5728.
4. Kusaka. [.: Wang. Z.-G.: Seinfeld. J.H. J.Chem. Phys. 1998. 108.
6829 andreferences
within.
5. Viisanen. Y.: Kulmala. M.; Laaksonen. A. J. Chem. Phys. 1997. 107. 920 and
references within.
6
. Russell. L.M.: Pandis. S.N.: Seinfeld. J.H. J. Geophys. Res. 1994. 99. 25607.
7. Hanson. D.R.: Eisele. F. J. Phys. Chem. A. 2000. 104. 1715.
8
. Arstila. H.; Laasonen. K.; Laaksonen. A. J. Chem. Phys. 1998. 108. 1031.
9. Bandy. A.R.: lanni. J.C. J. Phys. Chem. A. 1998. 102. 6533.
10. Re. S.: Osamura. Y.: M orokuma. K. J. Phys. Chem. A. 1999. 103. 5353.
1 1. Get references 8-10 out of Hanson. Eisele paper.
12. Givan. A.: Larsen. L.A.; Loewenschuss. A.: Nielsen. C.J. J. Chem. Soc.. Faraday
Trans. 1998. 94. 827.
13. (a) Phillips. J.A.; Canagaratna. M.: Goodfriend.
H.; Grushow. A.:
Almlof. J.:
Leopold. K.R. J. Am. Chem. Soc. 1995. 117. 12549. (b) Phillips. J.A. Ph.D. Thesis.
University o f Minnesota, 1996.
14. (a) Legon. A.C.: Wallwork. A.L.; Rego. C.A. J. Chem. Phys. 1990. 92. 6397. (b)
Lovas. F.J.: Suenram. R.D.: Fraser. G.T.: Gillies. C.W.: Zozom. J. J. Chem. Phys. 1988.
88. 722. <c) Gutowsky. H.S.; Chen. J.: Hajduk. P.J.; Keen. J.D.: Emilsson. T. J. Am.
Chem. Soc. 1989. 111. 1901. (d) Emilsson. T.: Klots. T.D.: Ruoff. R.S.: Gutowsky. H.S.
J. Chem. Phys. 1990. 93. 6971.
15. Morokuma. K.: Muguruma. C.J. Am. Chem. Soc. 1994. 116. 10316.
16. Jayne. J.T.: Poschl. U.: Chen. Y.; Dai, D.; M olina. L.T.: Worsnop. D.R.: Kolb. C.E.:
Molina. M.J. J. Phys. Chem. A. 1997. 101. 10000.
17. Kuczkowski. R.L.: Suenram. R.D.: Lovas. F.J. J. Am. Chem. Soc. 1981. 103. 2561.
145
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
18. Larson. L.J.: Kuno, M.: Tao, F.-M. J. Chem. Phys. 2000. 112. 8830.
19. Meijer. E.J.: Sprik. M. J. Phys. Chem. A. 1998. 102. 2893.
20. Gordy. W.; Cook. R.L. Microwave Molecular Spectra: John Wiley and Sons: New
York. 1984.
21. (a) Tubergen. M.J.: Andrews. A.M.: Kuczkowski, R.L. J. Phys. Chem. 1993. 97. 7451
(hi Block. P.A.: Marshall. M.D.; Pederson. L.G.. Miller. R.E. J.Chem. Phys. 1992. 96.
7321. ic) Zolandz. D.: Yaron. D.: Peterson. K.I.: Klemperer. W. J. Chem. Phys. 1992. 97.
2861. (d) Gerhards. M.: Schmitt. M.: Kleinermanns. K.: Stahl. W. J. Chem. Phys. 1996.
104. 967. (e) Peterson. K.I.: Suenram. R.D.: Lovas. F.J. J. Chem. Phys. 1995. 102. 7807.
(f) Gutowsky. H.S.: Emilsson. T.: Arunan. E. J. Chem. Phys. 1993. 99. 4883.
22. See for example: (a) Canagaratna. M.: Phillips. J.A.: Ott. M.E.: Leopold. K.R. J.
Pins. Chem. A. 1998. 102. 1489. (b) Andrews. A.M.: Kuczkowski. R.L. J. Chem. Phys.
1993. 9,V. 791.
23. Schiitz. M.: Biirgi. T.: Leutwvler. S.: Fischer. T. J. Chem. Phys. 1993. 9<S\ 3763.
24. ia .) Dyke. T.R. J. Chem. Phys. 1977, 66. 492. (b.) Zwart. E.: ter Meulen. J. J.: Meerts.
W.L.: Coudert. L.H. J. Mol. Spec. 1991. 147. 21. (c.) Fraser. G.T.: Lovas. F.J.: Seunram.
R.D.: Karyakin. E.N.; Grushow. A.: Bums. W.A.: Leopold. K.R. J. Mol. Spec. 1997. 181.
n y
25. See for example: Leung, H.O.: Marshall. M.D.: Suenram. R.D.: Lovas. F.J. J. Chem.
Pins. 1989. 90. 700.
26. Bevan. J.W .; Kisiel. Z.; Legon. A.C.: Millen. D.J.: Rogers. S.C. Proc. R. Soc. London
1980. A J72. 441.
27. Brown. M.G.: Keutsch. F.N.: Saykally. R. J. J. Chem. Phys. 1998. 109. 9645 and
references within.
146
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
T a b le 5.A 1. T ra n sitio n F req u e n cies fo r Iso to p o m ers o f H ;S 0 4 - H : 0 .
Transition State A (MHz)
3777.364
Oixr Ini
'
/
^
\
V
I
' - 3 4
\
\
X
1
’*■ N
\.
\
-0 . 0 0 1
7533.701
0 .0 0 0
101-—
02
7554.605
0.001
7554.539
0.001
1io-2,,
7575.538
0.001
7575.484
0.001
—1 2 -3 ,4
11300.540
0.001
11300.435
0 .0 0 0
- o:-3o3
11331.591
0 .0 0 0
11331.496
0 .0 0 0
-11-012
11363.184
0 .0 0 0
11363.107
0 .0 0 0
obs-calc
•Jc
State B (MHz)
3769.071
obs-calc
-0.003
1!1"—12
*
*
7517.448
0.001
101-—
02
7538.085
-0.001
7538.025
-0.001
I io-2,,
7558.760
0.001
7558.708
0.002
—12-3,3
11276.162
0.002
11276.056
0.000
2»;-3,,j
11306.825
-0.003
11306.737
0.002
2|,-3,;
11338.026
0.001
11337.943
-0.001
obs-calc
0.002
State B (MHz)
3577.804
obs-calc
-0.001
1,1-2,;
7136.890
0.001
7136.832
0 .0 0 0
101-—
02
7155.554
-0.001
7155.509
0 .0 0 0
lm - 2 ,,
7174.290
0.001
7174.252
0.001
2,;-3u
10705.231
-0.001
10705.147
0 .0 0 0
—02-3(13
10733.087
0.002
10733.011
0 .0 0 0
2„-3,;
10761.332
-0.001
10761.275
0 .0 0 0
obs-calc
-0.004
State B (MHz)
3529.863
obs-calc
Transition State A (MHz)
3529.879
0<xr b n
s1818
x
1
\.
obs-calc
-0.001
7533.773
Transition State A (MHz)
3577.831
0()o~ 1oi
'i s -
State B (MHz)
3777.331
111-2|;
Transition State A (MHz)
*
0(X)- 101
N _
obs-calc
-0.001
0 .0 0 0
11 ,-2,2
7024.857
0.001
7024.774
-0.001
1oi-2 i)2
7059.460
0.003
7059.413
0 .0 0 0
I io*2i i
7094.555
-0.001
7094.544
0.001
2 1 2 -3 1 3
10537.051
-0.001
10536.928
0.001
2o;-3(,3
10588.408
-0.001
10588.336
0 .0 0 0
2,,-3,;
10641.602
0.001
10641.576
0.001
1
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 5.A1 continued.
Transition State A (MHz)
*
Ooo-loi
18 -
i
-
1ST
-
I
D
u
-
Dn
J
D
-
===J
"&
0.001
7087.865
0.000
1oi*2o2
7115.673
0.001
7115.624
-0.001
1 io-2i i
7143.743
0.000
7143.674
0.000
212*313
10631.665
0.001
10631.628
0.000
2 o2-3o3
10672.997
-0 .0 0 1
10672.925
0.000
2, i-3 i2
10715.448
0.000
10715.342
0.000
obs-calc
State B (MHz)
obs-calc
♦
4c
3556.917
0.001
*
4t
7096.754
0.003
1oi-2 o2
7113.787
-0.001
7113.740
-0.001
I io-2i i
7130.874
7130.789
-0.003
2,2-3,3
*
-0.004
*
10645.023
-0.002
2 o2'3o3
10670.455
0.000
10670.385
0.000
2,,-3,2
10696.219
0.003
10696.087
0.002
Transition State A (MHz)
-
3557.916
-0.001
1l|-2l2
-
obs-calc
7087.885
Ooo-loi
18
State B (MHz)
*
1 ,,-2 ,2
Transition State A (MHz)
f
obs-calc
obs-calc
State B (MHz)
Ooo-loi
3492.588
-0.007
3492.577
obs-calc
0.000
1,1*2,2
6961.175
0.003
6961.111
0.001
101-2o2
0.003
6985.004
0.000
I ,o-2,,
6985.045
*
4c
7009.068
-0.001
2|2-3,3
10441.632
-0.002
10441.537
-0.001
2 o2-3o3
10477.190
0.000
10477.129
0.000
2,,-3,2
10513.498
0.000
10513.476
0.001
Transition
Frequency
obs-calc
Ooo-loi
3463.805
-0.012
1 11 - 2 1 2
6913.494
0.000
loi-2o2
6927.575
0.005
1 ,0 -2 ,1
6941.655
0.004
2,2-3,3
10370.165
0.000
2 o2-3q3
10391.193
0.000
2 ,,-3 ,2
10412.399
-0.002
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
T ab le 5.A1 co n tin u ed .
Transition
Ooo-loi
Frequency (MHz)
3615.127
obs-calc
0.009
I
1,,-2,2
7216.327
-0.014
"C
lot-—
02
7230.155
-0.006
I io-211
7244.005
0.017
2,2-3,3
10824.418
0.010
2o:-3o3
2 ,,-3,2
10845.054
0.001
10865.875
-0.002
Transition
Ooo-lo,
Frequency (MHz)
*
obs-calc
*
In-2,:
7361.290
-0.006
10I-2o2
7379.096
0.010
1,0-2,1
2,2-3,3
7396.998
-0.002
11041.926
0.005
2o:-3 o3
11068.377
-0.004
2,,-3,2
11095.373
0.003
Transition
obs-calc
-0.002
-
p
D
-
■
’
I
D
D
^
-
Ooo-lo,
Frequency (MHz)
3670.806
I
1,1-2,2
7320.327
0.001
<
1o, - 2 o2
7341.490
0.001
1,o-21 ,
7362.763
-0.001
2,2-3,3
10980.388
0.000
2 o: - 3 o3
11011.918
0.000
2,,-3,2
11044.046
0.001
Transition
Ooo-lo,
Frequency (MHz)
3516.891
obs-calc
0.003
11,-212
7013.836
0.011
1o, - 2 o2
7033.657
-0.008
1,o-2,,
7053.609
0.005
2,2-3,3
10520.626
-0.005
2o2-3o3
10550.233
0.012
2,,-3,2
10580.298
-0.001
D
D
-
D
0
- ___
[
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 5.A1 continued.
Transition Frequency (MHz) obs-calc(MHz)
-
-
D
1
-
Ooo-loi
3 7 4 6 .2 5 0
-0 .00 1
li.-2 ,;
7 4 7 0 .4 8 8
-0 .0 0 3
I oi - 2 o2
7 4 9 2 .3 7 4
0 .0 0 4
1 io- 2 ii
7 5 1 4 .3 8 0
-0.001
2 ,2-3,3
1 1 2 0 5 .6 1 9
0.001
2 o2 -3 o3
1 1 2 3 8 .2 2 1
-0.001
2,1-3,2
1 1 2 7 1 .4 5 3
0 .0 0 0
Transition Frequency (MHz) obs-calc(MHz)
D
'
I
V
Ooo-loi
3 7 0 0 .0 4 2
-0 .0 1 5
111-2,2
7 3 8 1 .0 6 7
-0 .0 0 3
101-2o2
7 4 0 0 .0 1 6
0 .0 0 4
1 io-2, 1
7 4 1 9 .0 3 3
0 .0 0 5
2 , 2 - 3 ,3
1 1 0 7 1 .5 1 1
0 .0 0 2
2 o2 -3 o3
1 1 0 9 9 .7 6 3
0 .0 0 0
2 , i- 3 |2
1 1 1 2 8 .4 4 5
-0.001
Transition Frequency (MHz) obs-calc(MHz)
D
£>
I
/
D
Ooo-lo,
3 4 8 9 .5 6 5
0 .0 2 0
l„ -2 ,2
6 9 6 1 .9 8 2
-0 .0 0 7
101- 2o2
6 9 7 8 .9 9 0
-0 .0 0 9
1 ,o-2| 1
6 9 9 6 .0 5 9
0 .0 1 3
2 ,2-3,3
1 0 4 4 2 .8 8 7
0 .0 0 3
2 o2 - 3 o3
1 0 4 6 8 .2 7 7
0 .0 0 4
2 ,,-3 ,2
1 0 4 9 3 .9 6 8
- 0 .0 0 2
Transition Frequency (MHz) obs-calc(MHz);
D
J
Ooo-lo,
3 6 4 3 .4 1 3
-0 .0 0 9
1,1-2,2
7 2 6 9 .9 1 1
0 .0 0 2
1o, - 2 o2
7 2 8 6 .7 5 6
0 .0 0 3
1 io-2,,
7 3 0 3 .6 3 2
-0 .0 0 3
2 , 2 - 3 ,3
1 0 9 0 4 .7 6 7
-0 .00 1
2 o2 -3 o3
1 0 9 2 9 .9 0 1
0 .0 0 0
2 , , - 3 ,2
1 0 9 5 5 .3 5 6
0 .0 0 0
D
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 5.A1 continued.
-
:
I
IX
Ooo-loi
3719.689
0.001
h i-2i2
7417.765
0.004
O
1
orto
j
Transition Frequency (MHz) obs-calc(MHz)
7439.237
-0.002
1 io-211
7460.844
-0.002
2,2-3,3
11126.507
-0.001
2 o:*3 o3
11158.519
0.001
2,,-3,2
11191.137
0 .0 0 1
Transition Frequency (MHz) obs-calc(MHz)
.
/
V
Ooo-loi
3543.460
0.002
l||*2l2
7068.337
-0.002
I o i- 2 o2
7086.815
-0 .0 0 1
1 io-2, i
7105.361
0 .0 0 1
2,2-313
10602.408
0 .0 0 0
2 o2*3o3
10629.975
0 .0 0 0
2| 1-3,2
10657.939
0 .0 0 0
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Chapter 6.
Microwave and Ab Initio Investigation of H2O-BF3: Spectrum,
Structure and Internal Dynamics
D.L. Fiacco, S.W. Hunt, K. Higgins, M.E. Ott and K..R. Leopold
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Abstract
The binary complex formed between BF3 and HiO has been investigated by microwave
spectroscopy. The spectra for 10 isotopomers of H2O-BF3 have been measured and the
Stark effect has been applied to investigate the dipole moment o f H : 160 - n BF 3, H 2I80 11BF 3. HDI60 - mBF3. In forming the complex, the oxygen acts as a donor o f an electron
pair to the electron deficient boron atom. Ab initio calculations at the MP2/aug-VTZ level
of theory/basis set give a B- 0 bond distance o f 1.825A, which is near agreement with the
experimentally determined value o f 1.87(4)A. The spectra are complicated by internal
motion of the water unit. The details, including barrier heights are reported along with a
detailed discussion of the possible internal dynamics as evidenced by the spectra.
153
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Introduction
Over the past 10 years, we have been intensely investigating what we have coined
"partially bonded” molecular complexes, mainly involving the Lewis acids BF3 and SO3
with nitrogen containing donors. [1-7] These partially bonded complexes have revealed
novel chemistry, in that in all cases the gas phase interaction is less complete than in the
corresponding bulk phase adduct. In the most extreme case, the dative bond distance
differs by 0.84A between the gas and solid phase.[3,8] We have also investigated the
changes in molecular structure exhibited by partially bonded complexes at the onset o f
microsolvation, and have demonstrated that complexes o f this type are extraordinarily
sensitive to near neighbor interactions. [9] While all o f this work has established the
dynamic range o f bonding interactions for adducts with nitrogen donors, relatively little
effort has been utilized on other able donors o f electron density. For this reason, we are
interested in Lewis acid base adducts in which oxygen serves as an electron pair donor in
the formation o f a dative bond. The simplest o f Lewis bases involving oxygen is certainly
H ;0 . The gas phase structure o f H2O-SO3 was determined by microwave spectroscopy,
yielding a dative bond length o f 2.432A, which lies intermediate to the covalent and van
der Waals limits. [10] To date, there have been no experimental gas phase studies o f the
related 1:1 complex between HjO and BF 3 , and only one a b initio study can be found in
the recent literature. [ 1 1 ]
The H 2 O-BF 3 complex has a long and interesting history. The stable complex was
first isolated in 1933, [12] and low temperature 'H and l9F NM R in acetone had
confirmed its existence as a donor-acceptor complex with the oxygen donating a lone pair
to boron in 1967. [13] However, a definitive X-ray structure o f the 1:1 adduct was not
reported until 1981. [14] The crystal structure reveals that H 2 O-BF 3 is extensively
hydrogen bonded in the solid phase, forming open ring-like assemblies, in which one
H 2 O-BF 3 unit interacts with two near neighbors through O-H— F interactions. The B -0
bond length in H 2 0 -BF 3 (s) is 1.532A, which is nearly equal to the sum o f covalent radii
for oxygen and boron, and the BF3 unit is distorted from planarity by -16.8°, indicating
significant electronic rearrangement. The water unit is also distorted from its free
monomer structure with O-H bond lengths o f 1.1 and 0.7A, respectively, and an H-O-H
bond angle o f 107°. The B-F bonds lengthen by -0 .0 7 A from that in the free monomer,
154
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which undoubtedly arises from a combination o f the change in coordination at the boron
center and the intermolecular hydrogen bonding interactions discussed above.
In the context of partially bonded molecular complexes in which oxygen acts as
the donor of an electron pair, we report the microwave spectrum, dipole measurements,
and an approximate gas phase structure o f H 2 O-BF 3 , formed via expansion o f BF 3 and
FTO in a supersonic jet. The spectra are consistent with a symmetric top, indicating an
averaged coincidence between the C 3 V axis o f the BF 3 unit and the bond axis as well as
free internal rotation of the HiO unit about the B -0 dative bond. Both the J=l<—0 and
J=2<—1 transitions have been obtained for 10 isotopic species and reveal evidence of
complex internal dynamics likely associated with the FTO unit. The spectral patterns.
Stark effect, and quadrupole coupling constants will be presented along with detailed ab
initio calculations aimed at elucidating the internal dynamics and ground state structural
parameters for H 2 O -B F 3 .
Experim ental
Spectra were recorded using a Balle-Flygare type pulsed-nozzle Fourier transform
microwave spectrometer, the details o f which have been presented elsewhere.[15] Initial
spectral searches were guided by utilizing the sum o f van der Waals radii for boron and
oxygen and the 1.532A B -0 distance in H20 -BF 3(s) as limiting values. H2O-BF 3 was
produced in situ via the reaction between HiO and BF3 using a co-injection source similar
to that reported in previous studies o f reactive species. [16-19] In this study, 2% BF 3 in
Ar was introduced through the pulsed valve at a backing pressure o f 2 atm while H20 (g)
was added by passing Ar gas over a reservoir o f liquid water at a backing pressure of
0.165 atm. The water entered the expansion 0.23” downstream o f the nozzle orifice
through a 0.012in. I.D. needle. D 2O-BF 3 was prepared by replacing the H2O in the liquid
reservoir with 99.9% D 2O, while HOD-BF 3 was formed by adding a 50/50 mixture of
D2O and H 2O. For the production o f H iI80 -BF 3, the H2I60 was replaced with H 2180 (95
atom%. Icon Services). Spectra were initially identified as belonging to the H2O-BF 3
complex from their dependence on H^O as well as the observed 1'B /10B (I = 1.5/1 = 3)
155
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hyperfme patterns. Isotopically substituted species were readily located from predicted
isotope shifts.
For the determination of the molecular dipole moment, a pair of parallel 30x40 cm
aluminum plates were inserted which straddle the cavity to provide a uniform electric field
which is perpendicular to both the cavity axis and the supersonic expansion. Equal and
opposite dc voltages were applied to each plate to reduce the effect o f fringing fields. The
distance between the plates was calibrated by measuring the second order Stark shift of
OCS. [20] In order to eliminate possible effects due to the accumulation of diffusion pump
oil on the plate surfaces, [21 ,22 ] calibrated plate distances were obtained both before and
after the collection of experimental data. Data were admitted for analysis only upon
agreement of the pre- and post- collection values.
Results
The spectra of 10 isotopomers of H 2O-BF 3 in the J=l<—0 and 2<—1 rotational
transitions were recorded in this study. The J=3<—2 rotational transition falls outside the
range of the spectrometer, prohibiting further exploration. As the spectral features vary
for the H ;I60 -BF 3, D:0 -BF 3, H 2I80 -BF 3, and HOD-BF 3, each will be discussed
separately below. The discussion will focus on the more intense n B spectral pattern in
each case, however the hyperfme-free linecenters yield an identical pattern for the l0B
isotopomer. The spectra in all cases were consistent with a symmetric top, in accordance
with a vibrationally averaged C 3V structure similar to that observed for HF-BF 3, HX-SO 3,
(where X= Cl, Br, or F) and H2O-SO 3. [23,24,10] The transition frequencies and isotopic
assignments are provided in Table 6.A1 in the Appendix to this chapter and a
representative spectrum o f the parent isotopomer is shown in Figure 6.1. As the spin
statistics on water forbid complete cooling to the J=0 level for H2O and D 2O. we
anticipated the appearance o f two K=0 lines corresponding to the m=0 and m=±l internal
rotor levels. For all but the parent (H 2I60 -BF 3) isotopomer, two K=0 lines were observed
in both the J=l<—0 and 2<—1 rotational transitions while for the parent form, three K=0
transitions were observed. The fitted hyperfme transitions for each isotopomer are
reported in Table 6.A1, while Table 6.1 reports the hyperfine-free linecenters. Stick
156
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spectra representative o f the hyperfme free linecenters of all ten isotopomers are
highlighted in Figure 6.2. The K-assignments are unambiguous from the hyperfme
structure and the resulting eQq values are constant across all isotopic species studied,
indicating that all spectra arise from the same molecular species. From the Figure, it is
apparent that each isotopomer of H:0-BF3 reveals a unique spectral pattern. Each will be
summarized briefly below and discussed in more detail in the sections to follow.
Si
u.
8907
8907.5
8908
8908.5
Frequency (MHz)
Figure 6.1. F = 2.5 <—1.5 component of central J = I <— 0 transition o f H :160 - n BF;,.
Total collection time of ~32 s.
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Figure 6.2. Stick spectra representing hyperfine-free linecenters for isotopomers o f HiOBF:, reported in Table 6.2. Solid lines indicate K=0 while dashed lines indicate K=l.
# Observed only for 1‘B isotopomer. * Used in fit to eq. (3). See text for further discussion.
158
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Table 6.1. Hyperfine-free linecenters for Isotopomers o f H;Q-BF
H;16Q-“ BF,
J"
eQq B (MHz) =
2.345(7)
0
0
0
H;!"0-'°BF-.
eQq B (MHz) =
4.848(9)
J"
J'
J'
K
Freq (MHz) D:l60 - lQBF,cont. J"
K.
Freq (MHz)
0
0
0
8890.093(3) __________
8907.852(3) HDI6 0 -"B F 1
1
K
0
16758.200(7)
Freq (MHz)
0
1
0
1
17780.523(4) 2.325(12)
17766.337(6)_________________
17815.511(5) HD‘6 0 - iqBF-,
J"
0
1
17258.900(4)
17258.117(4)
Freq (MHz)
17815.401(5) eQq B (MHz)
0
0
8634.409(3)
0
17887.831(5) 4.830(21)
17842.761(4)
17904.711(4) H;l8 0 - UBF,
1
I
J"
0
17268.629(5)
17267.855(6)
Freq (MHz)
K
8944.145(3) eQq B (MHz)
Freq (MHz) eQq B (MHz)
0 8895362(3) 2.327(9)
0 8912.832(3)
0 8948.554(3)
0 17791.046(2)
1 17776.074(3)
0
0
0
0
0
0
I
0
1
1
0
1
1
17896.649(4) H2 l8 0 - IQBF-,
1 17852.988(5) eQq B (MHz)
1 17913.126(7) 4.813(14)
D ^O -"B F ,
J"
J’ K.
eQq B (MHz) =
2.293(8)
0
0
0
0
0
D ^O - 10BF-,
eQq B (MHz) =
4.745(15)
1
J"
K.
8537.533(3)
8593.479(3)
17074.886(5)
17074.787(4)
17185.585(4)
17187.161(5)
17054.564(5)
17029.666(6)
Freq (MHz)
0
0
0
0
8543.363(3)
8597.542(3)
Freq (MHz)
0
17086.543(4)
8372.952(3)
8375.937(4)
16745.695(4)
0
1
1
17086.452(4)
17193.844(4)
17202.959(4)
1 16743.938(4)
0 16751.634(4)____________
1 16748.376(4) HD 180-"B F,
J"
K
17041.123(5)
17068.876(5)
Freq (MHz)
1 16801.917(5) eQq B (MHz)
0
0
8292.476(3)
0
1
K
0
0
1
16584.782(4)
J"
J’ K
0
1
1
0 8377.895(3) __________
0 8380.854(3) HD 18O-l0BF
2
2
2
0 16755.575(4) eQq B (MHz):
1 16753.817(4) 4.777(22)
0 16761.451(8)
0
0
1
1
0 17825.471(5)
1 17825.367(4)____________
0
1
K
8629.544(3)
Freq (MHz) 2.319(14)
1
1
1
1
J"
0
I
1
16584.119(5)
Freq (MHz)
8298.204(3)
16596.243(5)
16595.579(5)
159
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h . ' 6o - ' ° " b f -.
For H2160-B F 3, a total of three K=0 lines were observed in the J=l<—0 and 2<—1
rotational transitions, as reported in Table 6.1 and shown in Figure 6.2. The assignments
to K=0 and K=1 transitions were made from a fit o f the boron hyperfme and the
linecenter frequency for each transition according to:
v = linecenter + AWq
( I)
The relative intensities of the K=0 transitions are approximately 10:9.5:1.2 from lowest to
highest frequency. The splitting between the central K=0 line and the lowest frequency
K=0 transition is 17.76MHz while the spacing between the central and upper transition is
36.29MHz in the J=l<—0. In addition to the three K=0 transitions, four K=1 lines were
observed in the J=2<—1 rotational level, two lying below the central K=0 transition and
two appearing at higher frequency. These are indicated as dashed lines in Figure 6.2. The
hyperfme assignments are provided in Table 6.A1 and the fitted hyperfine-free linecenter
frequencies and B quadrupole coupling constants are provided in Table 6.1. As an
estimation of the rotational constant for the H2I60 -"B F 3 isotopomer, the starred K=0
transition and the nearest K=1 partner in the J=2<—1 were fit to the following expression
for a vibrationally averaged symmetric top with one quadrupolar nucleus:
v = 2(J + 1)«(B + C)/2) - DjkK; )- 4Dj(J + 1)3 + AWQ
(2)
where B and C are rotational constants, Dj and Djk are distortion constants and AWq is
the difference in hyperfme energies between the upper and lower states. The fitted
spectroscopic constants are given in Table 6.2. The choice to utilize these particular
transitions to approximate the rotational constant will be discussed in further detail
below. Briefly, this pair of transitions appeared as a common feature in the spectra o f all
10 isotopomers, and was regarded as the best approximation o f the ground state rotational
constants in the absence o f an exact expression to fit the numerous additional spectral
transitions.
H D I6I80 - 1q 11BF t
In the case of all four HDO-BF3 isotopomers, extensive spectral searching
revealed only one K=0 transition in the J=l<—0 and one K=0 and its K=1 partner in the
160
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J=2<—1, as shown in Figure 6.2. The deuterium hyperfme structure was not well resolved
and attempts to fit both boron and deuterium quadrupole coupling constants were
unsuccessful. This is not surprising in light o f the fluorine hyperfme structure arising
from spin-spin interactions that is always present in BFj complexes. The center
frequencies were readily fit to (2). The boron hyperfme assignments are provided in
Table 6.A1. while the hyperfine-free linecenters are reported in Table 6.1. Spectroscopic
constants and boron quadrupole coupling constants are given in Table 6.2.
D-.Q-10' 'BF-i
For D 2 O-BF 3 , two K=0 transitions were observed in both the J=l<—0 and J=2<—1
and identified from the boron hyperfme structure. The splitting between these two
transitions is ~3.0MHz in the J=l<—0, which is substantially reduced from the protonated
isotopomer. The relative intensity o f the two K=0 transitions is 4:1 in favor o f the lower
frequency transition. Three K=1 transitions were observed in the J=2<—1 for D20 - n BF3,
two of which straddle the lower K=0 line while the third is -~50MHz higher in frequency
than the upper K=0 transition. The intensities o f the K=1 transitions decrease toward
higher frequency, and the uppermost K=1 transition was too weak to observe in the case
of l0B. The hyperfme structure arising from the two deuterium atoms was not well
resolved and hence was neglected in the fit of the boron hyperfme structure. The
hyperfme assignments are provided in Table 6.A1. The linecenter frequencies o f each of
the transitions are listed in Table 6.1, where each K=0 and K=1 transition was fit
separately according to (1) and the boron quadrupole coupling constants are reported in
Table 6.3. The pair o f transitions exhibiting a similar values o f Dj as measured for the
HOD-BF 3 spectrum is marked with a star in Figure 6.2, the spectroscopic constants
determined from a fit o f these transitions to (2) are reported in Table 6.2.
FFI8Q -'°-"BF t
From Figure 6.2, it is evident that the spectral pattern o f H2I80-BF3 differs
significantly from that o f H2I60-BF3. While three K=0 transitions were observed in
H ;160-BF3, for its H2180-B F 3 analogue, only two K=0 transitions were observed in both
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the J=l<—0 and J=2<—1 rotational transitions, despite extensive spectral searching. The
two transitions are split by 54.18MHz in the J=l<—0 transition and the relative intensities
of the two K=0 transitions are approximately 1.6:1 in favor of the lower frequency
transition. In the J=2<—1, four K=1 components were observed, three o f which appear
lower in frequency than the lower K=0 transition, while the fourth is located 1.58MHz
above the upper K=0 line. The K=l transitions appear to decrease in intensity with
increasing distance from a K=0 transition. The linecenters were fit according to (1) for
both boron isotopes. The fitted hyperfine transitions are reported in Table 6.A1, the
hvperfme-free linecenters are provided in Table 6.1, and the quadrupole coupling
constants are summarized in Table 6.1. The set of transitions with a similar Dj to that
observed in HDO-BF 3 is indicated with a star in Figure 6.2. The spectroscopic constants
obtained from a fit of the starred transitions to (2) are indicated in Table 6.2. Note that in
all cases, the values of Dj are small and relatively consistent among isotopomers,
reflecting the symmetric top character o f spectra chosen. Interestingly, the values o f D
jk .
appear to increase with isotopic substitution, which is opposite to that expected based on
the heavier mass.
Table 6.2. Spectroscopic Constants of Isotopomers of H 2O-BF 3 from Starred Transitions
in Figure 6.2.
Species
(B+C)/2 (MHz) eQq B (MHz) Dj(MHz)
Djk (MHz )
H; lt’0 -" B F 3
4453.936(2)
2.359(11)
0.0070(2)
0.030(2)
H ;lbO - 10BF 3
4456.428(2)
4.893(21)
0.0073(3)
0.028(2)
D: ’(,0-'liBF3
4186.491(2)
2.289(13)
0.0084(3)
0.440(2)
D: ' 6O -l0BF 3
4188.963(2)
4.735(20)
0.0085(3)
0.441(2)
H :l80 - ‘‘BF 3
4268.777(2)
2.347(12)
0.0067(3)
0.026(1)
H ;I80 - ioB F 3
4271.692(2)
4.864(19)
0.0070(3)
0.023(1)
HDlftO -llBF 3 4314.782(2)
2.312(12)
0.0069(3)
0.197(1)
HDl6O - 10BF 3 4317.215(2)
4.826(19)
0.0071(3)
0.194(1)
h d I8o - “ b f 3 4146.250(2)
2.317(12)
0.0067(3)
0.167(1)
H D i80 -'° B F 3 4149.114(2)
4.770(20)
0.0067(3)
0.166(2)
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Stark Effect
In order to aid in the assignment o f the observed spectra and to measure the
molecular dipole moment, Stark effect measurements were carried out on several K=0
transitions of H ;l6180-B F 3, and H D 160-B F 3.
Several sets of Stark shifted transitions were investigated, corresponding to the
J=l<—0 K=0 transitions of H2I6' 180 -"B F 3 and the J=l<—0 and J=2<—1 K=0 transitions of
HDlf>0 - n BF3. Both parallel (AMf=0) and perpendicular (AMf= ±1) components were
observ ed, corresponding to either a parallel or perpendicular orientation of the oscillating
microwave field with respect to the applied electric field. The Stark-hyperfme energies were
calculated in the intermediate field regime using a | J,K,I,Mi,Mj,Mp> basis as previously
described.[6 ] A non-linear least squares fit o f the observed frequencies was performed with
B (or the linecenter frequency/2) and eQq constrained to their values determined at zero
electric field. This fit yielded the ratio of the molecular dipole moment to the effective interpiate spacing from which the molecular dipole moment was calculated using the OCS
calibration results. The fitted transitions are reported in Table 6.A2 while the dipole
moment obtained for each o f the isotopic species is given in Table 6.3. A sample
spectrum for the H :lbO-' ‘BF3 isotopomer, recorded at 43.15 V/cm. is shown in Figure 6.3.
163
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jlW
8907.3
8907.7
8908.1
‘ i
1
8908.5
Frequency (MHz)
Figure 6.3. Stark spectrum of central J= 1<—0 transition of H2l60 - n BF3 recorded at 43.15
V/cm.
Isotopomer
Transition
M-etT (D)
H ;lftO -llBF 3
J—1i—0 K=0, central line (a)
3.898(6)
H; iX0 - n BF 3
J= 1<—0 K=0 . highest frequency transition
J= 1<—0 K=0, lower transition
1.910(11)
3.834(15)
J—1<—0 K=0. upper transition
HDlbO -"B F 3 J=l<—0 K=0
4.281(19)
4.071(4)
J=2<-1 K=0
4.316(13)
(a) See Figure 6.2.
Stark spectra were initially recorded for all three K=0 transitions in the J=l<—0..
For the lowest K=0 transition, the Stark effect was extremely rapid with large spectral
splittings at low electric field strengths, inconsistent with the expected second-order Stark
effect for a K=0 transition. The observed spectral shifts could not be fit to the
intermediate field Stark expression for a symmetric rotor with one quadrupolar nucleus
164
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and hence were neglected in the analysis o f the molecular dipole moment. Both of the
remaining two K=0 transitions revealed the usual second-order Stark pattern for a
complex with one quadrupolar nuclei. However, as indicated in Table 6.3, the dipole
moments obtained for the two states differ by -1.9D , with a value o f 3.898(6) D for the
central state and a value of 1.91(1) D for the upper state.
H->ISQ-' ‘BF-,
Similar measurements as discussed above for H i^O - 1'BFj were carried out for the
heavier H2l80 - n BF3 analogue. Spectral assignments are reported in Table 6.A2 and the
dipole moments obtained for each of the two K=0 transitions are given in Table 6.3. In
this case, both moments are of similar magnitude, the lower K=0 transition yielding a
moment of 3.834(15)D, and the upper K=0 transition giving 4.28(2)D. The 3.834(15)D
value is in reasonable agreement with the 3.898(6)D moment obtained from the central
K=0 transition of H2l60 - n BF3.
HDlhO- 11BF.
Stark measurements were carried out on the single K=0 transition in both the
J—1<—0 and J=2<—1 rotational levels. Spectral assignments are reported in Table 6.A2.
Attempts to fit both rotational levels together resulted in larger than usual errors in the
assigned transitions, thus each rotational transition was treated separately, resulting in the
two dipole moments reported in Table 6.3. The dipole moment obtained in the J=2<—I is
somewhat larger than that in the J=l<—0 rotational transition. The possible reasons for
this discrepancy will be discussed at greater length below.
Internal Motion
The complexity of the spectra for all isotopomers containing H20 or D20 is
suggestive of internal dynamics that likely involve primarily the water portion o f the
molecule. The inconsistent spectral patterns observed for the H2I60 and H2I80 containing
isotopomers suggests some involvement o f the oxygen atom in the internal dynamics.
The decrease in spectral splitting upon deuteration is evidence for proton/deuteron
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interchange. Due to the incomplete cooling to the J=0 level for H20 and D20 . we
expected to obtain two K=0 lines for each H20 and D20 containing isotopomer. which in
the free rotor limit correspond to the m=0 and m=±l free internal rotor levels. In the case
of a symmetric top exhibiting free internal rotation, the transitions can be fit according to
[25]:
v = 2(J + 1)«(B + C)/2) - DjkK 2 - DJrnm 2 - DJKmKrn - H j^ n r K 2 )
- 4 D j( J + 1 )3 + AWQ
(3)
where the Dxxx and Hxxx terms are centrifugal distortion constants and the internal rotor
state is specified by m. For m=0, this equation collapses to (1), while for m =±l, the ±K
transitions symmetrically straddle the central K=0. m=±l line. Although none of the
observed spectral patterns appear to fit to eq. (3), it was utilized in an attempt to fit a
subset of the observed H2I60 -BF 3 transitions, these are indicated with an asterisk in
Figure 6.2. Due to the presence o f the additional K=0 component and the additional K=l
components in the J=2«—I transition, the assignment o f the selected K=0 transitions to
m=0 and m=±l is not unambiguous. For this reason, the subset o f transitions was fit with
both assignments. The assignments along with the residuals are provided in Table 6.A3 in
the Appendix to this chapter, while the fitted spectroscopic constants are reported in
Table 6.4. The same procedure was carried out for H2I80 -BF3 and for D20 -BF 3. The
results of the each of the fits are also provided in Tables 6 .A3 and 6.7.
From Table 6.4, it is clear that eq. (3) fails to adequately describe the internal
dynamics in the H20 -BF 3 complex. The magnitude o f several o f the fitted distortion
constants are too large to retain any physical significance, suggesting that the data can be
fit only because o f the large number o f parameters in (3). From this perspective, it is clear
that the internal motion in the H 20-B F 3 complex is more complicated than a single free
internal rotation of the water unit. The observation o f more than 2 K=0 lines in the
J=l<—0 spectrum of the parent species and the discrepancy between the H2I60 and H2I80
containing isotopomers signals a complicated combination o f internal motions likely
involving the entire water portion o f the complex.
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T able 6.4. Fitted Spectroscopic Constants for Isotopomers of H2O-BF3 from both m
assignments according to eq. (3)._________________________________________________
m=0 (B^C)/2
Species
H: lftO -llBFi
lower4445.019(3)
eQq B
D]
P |K
2.337(8)-0.0140(3)
Dim
Diicm
3.546(2) -27.092(5)
HIKm
Dum
7.744(3) -0.023( 1)-0.0331(9)
upper4472.110(2) 2.337(8)0.0191(2) -4.220(2) 27.092(3) -9.553(1) -1.787(2) 0.0331(4)
H ;l'’0 - " )BFi lower 4447.654(3) 4.84(1) -0.0134(3) 3.7462(9)-26.661(5) 7.517(1 > -0.345(2)-0.0326(8)
upper4474.315(1) 4.84(1) 0.0191(2) -4.119(2) 26.661(1) -9.6142(7)-1.752(2) 0.0325*
D ^ O - 'BF,
lower4186.491(2)
2.292(9)0.0084(2 )
0.440(1) -1.499(2 )
upper 4187.991(2) 2.292(9)0.0104(3) 0.814(1) 1.499(1)
D : ;'’0 - ll'BF;
H ;lxO -llBF-.
6.6927(8) -6.319(2) -0.002*
-7.2474(8)-7.621(2) 0.002*
lower4 188.965(1) 4.74(1) 0.0089(3) 0.440(1)
-1.484(2) 6.692(3)
-6.319*
-0.002*
upper4190.449(1) 4.74(1) 0.0109(2) 0.821(2)
1.484(1) -7.248(2)
-7.621*
0.002*
lower4268.782(1)
2.330(9)0.0076(2)
5.080(2) -28.071(4)
19.6868(9) 14.213(2)-0.0496(6)
upper4296.864(2) 2.328(9)0.0572(3) -0.394(2) 28.072(3) 5.6401(9) 6.059(2) 0.0497(4)
H; 1!,O -l0BF,
lower4271.704(1) 4.81(1) 0.0084(2) 4.417(2) -27.167(2) 20.2298(8)13.534(21-0.0429(3)
____________ upper4298.874(2) 4.81(1) 0.0516(2) -2.279(1) 27.177(2) -3.4694(9)10.165(2)0.0440(3)
* = fix e d
The elucidation of the precise motion responsible for the observed spectral
abnormalities is by no means a simple process. With several pathways available for
proton interchange, the exact solution to the problem is unclear and would involve a full
analysis of the allowed motions and their respective symmetries. An analysis o f this type
has been carried out for the structural similar methylamine molecule, which has taken
many years o f theoretical and experimental investigation. [26-29] This type of analysis,
while possible in the case of H2O-BF3, would require additional spectral information that
falls outside o f the range o f our current experimental setup. We therefore focus only on
the limited information we have been able to obtain, and use this to speculate on the type
of internal dynamics that appear feasible.
The intermolecular bond formed between H2O and BF 3 involves the donation o f a
lone pair on the oxygen o f the water unit to the incomplete octet on the boron atom o f the
BF3 unit. Only one recent ab initio calculation of the H 2O-BF 3 structure has been
reported in the literature. [11] In order to provide a more accurate estimation o f the
structure o f the complex, a series o f geometry opitimizations at the MP2 level o f theory
167
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using the VDZ, aug-VDZ and aug-VTZ were carried out using MOLPRO. [30] Table 6.5
summarizes the results o f these calculations, where both the counterpoise corrected and
non-corrected structural parameters are reported. In all cases, the counterpoise correction
results in a longer B- 0 bond distance and a slightly contracted B-F bond length. At the
aug-VTZ basis set, the O -B -F bond angle appears to be less sensitive to BSSE, while for
the two smaller basis sets, this angle contracts slightly in the counterpoise corrected
structure. For all three basis sets, in the minimum energy configuration, the water unit
lies almost exactly above a BF2 portion o f the BF3 unit, in a configuration eclipsing the
two water hydrogens with two o f the fluorine atoms on BF3. The water protons are tilted
toward the BF3 moiety, and the BF3 unit is distorted from planarity by -10°. For the H :0
and BF', monomers, the structural parameters are in the best agreement with experiment
at the aug-VTZ basis set. The binding energy is therefore deemed most reliable at this
level of theory/basis set. A value of 7.953 kcal/mol is consistent with a complex that is
partially bound and susceptible to large amplitude motion. The counterpoise corrected
geometry o f H; 0 -BF 3 with the aug-VTZ basis set is shown in Figure 6.4.
168
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Table 6. 5 . Minimum Energy Structures o f H2O-BF3 and H ;Q and BF3 monomers
H2O-BF3
VDZ
Parameter
RBO
RBF1
RBF2
RBF3
ROH1
ROH2
AOBF1
AOBF2
AOBF3
AX2
1.2*AOH
DF1
DF2
DF3
Binding energy (kcal/mol)
no CP
1.8325
1.3653
1.3508
1.3654
0.9709
0.9709
98.81
101.78
98.85
115.73
52.27
60.14
180.72
301.27
-14.140
RBF3
1.3283
ROH
AOH
0.9649
101.9
aug-VDZ
aug-■VTZ
no CP
CP
no CP
CP
2.2905 1.7763 1.8888 1.7873
1.3393 1.3788 1.3727 1.3556
1.3337 1.3630 1.3591 1.3416
1.3393 1.3789 1.3727 1.3558
0.9661 0.9709 0.9702 0.9663
0.9661 0.9709 0.9702 0.9663
99.64
99.74
93.89
98.31
95.20
102.35 100.47 102.19
99.67
93.89
98.31
99.82
133.04 119.52 120.27 121.98
52.91
51.58
53.15
53.35
59.84
60.09
59.67
60.87
180.00 180.53 180.00 181.25
-59.84 300.95 -59.67 301.59
-5.573 -10.870 -6.784 -9.332
b f3
1.3377
1.3170
h 2o
0.9659
0.9614
103.87
104.11
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CP
1.8250
1.3529
1.3396
1.3529
0.9658
0.9658
99.32
101.56
99.32
122.26
53.24
59.67
180.00
-59.67
-7.593
Figure 6.4. The counterpoise corrected structure of H2O-BF3 at the MP2/aug-VTZ level
of theory/basis set.
As the spectra of all the HiO-BF} isotopomers are consistent with a vibrationallv
averaged symmetric top. it is of interest to calculate the barrier to internal rotation of the
H:0 unit about the B -0 bond. In the minimum energy configuration shown in Figure 6.4.
the hydrogens on the water unit are eclipsed with two of the fluorine atoms on BF;. In
order to estimate the internal rotation barrier, the complex was fixed in a staggered
conformation, in which neither hydrogen atom on the water unit is aligned with a fluorine
atom on BF3. At the counterpoise corrected MP2/aug-VTZ level of theory/basis set, the
energy of the staggered configuration is 0.1 kcal/mol higher than the eclipsed
configuration, providing an estimate o f the barrier to rotation about the B -0 bond. This
small barrier for rotation about the B -0 bond is consistent with the observation of free
internal rotation of the water unit about the intermolecular axis.
As mentioned above, because of the decrease in the spectral splitting upon
deuteration of the water species, the motion giving rise to the spectral patterns likely
involves the exchange of the protons/deuterons on the water unit. This exchange can be
accomplished in several ways. The simplest to visualize is a rotation of the water about
its C; axis. Since the water portion is bound to BF3 via donation o f an oxygen lone pair,
rotation about the water C: would necessarily disrupt the bonding interaction. Preliminary
calculations at the non-counterpoise corrected MP2/aug-VTZ level o f theory/basis set
resulted in a barrier height of 28.92 kcal/mol for this motion. The calculation o f this
barrier is complicated by the unreasonable B-O-H angle o f 66 ° encountered when the
170
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water unit is fixed at the transition state. It is likely that this motion is coupled to a bendback motion of the water unit, similar to that discussed below for the water wagging
motion. No further calculations were carried out to test the existence of a two-fold
transition state for this motion, as it is clear that the motion is a high barrier process.
Nevertheless, even with such a significant barrier, both sides o f the potential can be
accessed through hydrogen/deuterium tunneling. The tunneling motion is predicted to
split each of the spectral transitions into a doublet with an intensity ratio of 3:1 for the
interchange of two hydrogen atoms (fermions) and 2:1 for the interchange of two
deuterium atoms. It is clear from the spectrum that tunneling through the barrier to
rotation about the CN does not adequately describe the internal motion in H2O-BF3, but as
a possible pathway to proton interchange, it is likely to contribute to the complexity of
the spectra.
A second motion that would lead to an isoenergetic configuration is an H ;0
inversion where the two hydrogen atoms conceitedly move to the opposite side of the
molecule, similar to the ammonia type inversion in methylamine. [28] This motion would
appear to affect the intermolecular B -0 interaction by exchange o f a free and bound
oxygen lone pair and hence is expected to proceed with a high barrier. The hydrogen
atoms would terminate in a different orientation with respect to the BF3 portion of the
molecule, however, with nearly free internal rotation about the B -0 bond, equivalence is
regained. This motion would appear to involve some movement o f the heavy oxygen
atom, and hence be affected by isotopic substitution at the oxygen position. With a high
barrier to the inversion motion, tunneling through the barrier would result in the splitting
of each rotational transition into a pair o f tunneling doublets, similar in effect to rotation
about the water C; axis. In order to ascertain the barrier height involved in the wagging
motion of the FTO unit, the energy was calculated for the geometry shown in Figure 6.5
below, where the tilt angle of the HaO unit is zero.
171
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2 .2 0 9 A
Figure 6.5. Two-fold transition state for the FTO wag in FTO-BFa.
The barrier height for this motion, where the water unit is allowed to wag without
rotation is 1.60kcal/mol or 560.46cm'1. which is not energetically surmountable in the
cold temperatures of the molecular beam. Nevertheless, the hydrogen atoms can tunnel to
through the barrier, giving rise to spectral splitting that are consistent with internal
motion. While the transition state in Figure 6.5 at first seemed a natural transition state
for the wagging motion, it turns out that a lower energy transition state can be found if
the restriction on the rotation of the water unit is removed. In this transition state, the wag
motion is accompanied by rotation o f the H ;0 about the B-0 bond axis, allowing one o f
the water hydrogens to line up with a BF 3 fluorine atom. This transition state is shown in
Figure 6 .6 .
22.82
2 .2 0 7 A
Figure 6 .6 . Transition state for the HiO wag coupled with rotation about the B -0 bond.
The barrier height to the combined wag-rotation motion is 1.58 kcal/mol or 552.47cm'1,
which is '- 8 cm ' 1 lower in energy than the wagging motion in the absence o f rotation. In
Figures 6.5 and 6.6 above, the wagging motion is accompanied by a lengthening o f the B-
172
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O bond of nearly 0.4A, and a barrier which is approximately 1/5 of the complex binding
energy, both of which are consistent with a weakening o f the B -0 bonding interaction.
The transition state in Figure 6.6 is also appropriate for describing the rotation of
the water unit about an OH bond. It was initially presumed that in the transition state
associated with this motion, one of the B-O-H angles would remain fixed while the 'free'
hydrogen was positioned in the F-B-O-H plane. However, the barrier height for this
■pure' water motion was calculated to lie 0.18 kcal/mol higher in energy than the
transition state shown in Figure 6 .6 . This, coupled to the observation o f the lower barrier
to the wag when allowed to couple to the rotation o f the water unit, suggests that it is
necessary to consider more complex motions than just simple internal rotations o f the
water unit. This is consistent with the inability to fit the spectral transitions to energy
expressions involving single, uncoupled motions o f the water unit. The coupling between
the H ;0 inversion and the internal rotation is consistent with that observed in
methvlamine, providing an explanation for the difficulty involved in fitting the spectra to
an appropriate energy expression. The numerous motions that are possible suggest an
energy diagram with a number of nearby and potentially near-degenerate states.
The possibility o f a large number of nearby states is supported by the near first
order Stark effect obtained for the lowest frequency K=0 line o f H :I60 -BF 3. If two
energy levels lie very close together, the electric field energy can no longer be considered
a small perturbation. In the limit o f degenerate states, the Stark effect will depend linearly
on the field, as in the first order Stark effect for K>0. If the energy o f any o f the involved
states and the molecular dipole moment were precisely known, the energy gap between
the two states could be determined from an analysis o f the Stark spectrum. However,
since the energy level diagram is unknown, the Stark effect for this transition could not
lend itself to analysis. The fact that we observe this special effect supports the notion that
there are several nearby energy levels, consistent with the picture o f complex internal
dynamics involving the water portion o f the molecule. Indeed, the variability in effective
dipole moments provides more evidence for this situation. Clearly, there are Stark matrix
elements connecting nearby levels which would not ordinarily be present in the usual
analysis.
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O f additional interest in the Stark spectrum is the inability to fit the two rotational
transitions o f H D l60 - n BF3 to a single dipole moment. The reason for this is unclear, as
the spectra of all HDO-BF3 isotopomers appear to conform to a rigid-rotor energy
expression. Nevertheless, it is evident that the molecule is undergoing a complex
combination o f internal motions, which are perhaps somewhat dependent on rotational
state. For example, in the case o f methylamine, the coupling between inversion and
internal rotation leads to a strong dependence o f the magnitude o f the inversion doubling
on rotational quantum number. [26] For H2O-BF3, as discussed above, more than one
internal motion need be invoked to provide an interpretation for the spectral patterns, and
the two motions are likely similarly coupled. In this regard, it is perhaps not unreasonable
to imagine that the internal motions couple more strongly with increased angular
momentum.
Structure Analysis
In the absence o f an exact energy expression to fit the spectra for H2O-BF 3, the
determination of the ground state rotational constants for the isotopomers most affected
by internal motion is complicated by the numerous additional transitions. As discussed
above and shown in Figure 6.2, a set of transitions with a similar appearance to the
spectrum of HDlbl 80 -BF 3 was observed for each isotopomer. For each isotopic species,
this set of transitions was the most intense and when tracked in an electric field yielded
reasonable and consistent values for the molecular dipole moment which were also in
reasonable accord with the theoretical value. These sets were therefore selected in the
hope to provide a reasonable approximation to the ground state rotational constant for
each isotopomer. The chosen transitions are indicated with a star in Figure 6.2. the
hvperfine assignments are provided in Table 6.A4, and the spectroscopic constants from a
fit to eq. 2 are reported in Table 6.2. From this set of rotational constants, the least
reliable are undoubtedly those obtained from the H2I6 I80 -BF 3 species as the
corresponding spectra are the most markedly affected by the internal motion. In order to
eliminate additional uncertainty in the fitted structural parameters, these isotopomers
were excluded from the rotational constant fit.
174
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The coordinate system utilized in the analysis o f the structure o f of H2O-BF 3 is
shown in Figure 6.7, where the structural parameters included in the fit are labeled
accordingly. In the Figure, RB-o is the B -0 bond length, a is the O-B-F angle at x - 0 , (3 is
the angle between the B -0 bond and the plane containing the water bisector, and x is the
angle between the C 3Vaxis of the BF3 unit and the B -0 axis, x provides a measure o f the
amplitude o f the zero point angular oscillations of the BF3 unit within the complex.
Neglecting the isotopomers containing an H2O unit, only six rotational constants are
available for analysis. For this reason, a complete determination of all atomic coordinates
in the complex was not possible.
B -0
I
F
F
Figure 6.7. Structural Parameters included in the rotational constant fits for H2O-BF3.
From a comparison of the crystal phase structural parameters o f H2O-BF3 to the gas
phase parameters of BF3 monomer, the BF bond lengths change by - 0 . 0 7 A while the F-B-F
bond angle decreases by - 8°. The H-O-H angle in the water unit widens to 107°, while one
of
the O-H bonds lengthens to 1.1 A and the other contracts to 0 .7 A . These changes are large
and result both from the formation o f the B- 0 dative bond as well as from hydrogen
bonding interactions between near neighbors in the crystal. The absence o f near neighbor
interactions in the gas phase supports the assumption that the geometry o f the monomer
units in the gas phase complex will approximate their respective monomer geometries.
Indeed, the very facile internal motion o f the water unit is also consistent with a fairly weak
interaction, as is the binding energy o f Table 6.5. This assumption has proven valid in the
175
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case of weakly bonded complexes, but is suspect when the intermolecular interaction lies in
the intermediate regime between the van der Waals and covalent limits. In this case, it is
necessary to perform the structural fit using the gas and solid phase monomer geometries as
limiting cases.
Therefore, the structural fit o f the parameters indicated in Figure 6.7 was carried out
fixing the monomer units at their respective gas phase geometries and their geometries in
H:0-B F 3(s). The values obtained for both a and x were particularly sensitive to the
magnitude of the B-F bond length. When set to its value in the crystalline phase, a widens to
112°. which is deemed unreasonable due to its equivalence to the solid phase value. For this
reason, a set of fits was carried out where the B-F bond length was increased from its gas
phase value in units of 0 .0 2 A until a > 10 6 .3 °. which is the value of the N-B-F bond angle
in (CH 3)3N-BF3. This value was chosen as a limiting value as it represents the distortion of
the initially planar BF3 unit in the case of a near covalent gas phase bonding interaction. In
other partially bonded systems involving BF3 and S 0 3, there is a strong correlation between
the degree of bond formation (which depends on the strength of the donating ability or
basicity of the Lewis base) and the distortion of the Lewis acid. [31] As H30 is presumably
a weaker Lewis base than (CH3)3N. the bonding interaction in H :0-BF 3 is not likely as
strong, hence a smaller distortion o f the BF3 unit is expected. The results of the rotational
constant fits are summarized in Table 6.6 below.
R b. f (A)\H -0-H (°)
1.3102
1.33
1.35
105
106
R b-o(A) 1.875
a(°) 104.22
R b-o(A) 1.874
a(°) 104.57
P O 100.35
P(°) 100.35
X(°) 8.89
R b-o(A) 1.864
X(°) 8.93
R b-o(A) 1.864
a(°) 105.02
a(°) 105.38
P(°) 100.25
P(°) 100.25
X(°) 5.37
R b-o (A) 1.849
a(°) 106.5
X(°) 5.41
P(°) 100.11
X O 2.30
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The effect of the various B-F bond lengths on x is clear from Table 6 .6 . It appears as
if the lengthening of the B-F bond reduces the amplitude of the angular oscillation o f the
BF3 unit while increasing the O-B-F bond angle and decreasing the B-0 bond length. In
addition to the sensitivity of the structure to the B-F bond length, the values for (5, the angle
between the H:0 plane and the B -0 bond axis are in gross disagreement with theory. From
Table 6.5, the values o f this angle (AX2 in the Table) are all nearly 120°, consistent with the
alignment of the water lone pair with the boron atom. The fitted structure gives a value of
~ 100c. which is unreasonable as it places the lone pair in an unfavorable position for bond
formation. Attempts to fix this angle to values that are in closer agreement with theory
resulted in an unreasonable B-0 bond distance and had a large impact on the magnitude of
the O-B-F bond angle. The inability to fit the bond angles, especially involving the water
unit is not surprising in light of the internal dynamics of the H:0 -BF3 complex. Clearly,
even in its lowest vibrational state, the structure is not well-defined as there is no one
potential well that is deep enough to trap a particular configuration. Nevertheless, the
average value for Rb-o ( 1 .8 7 (4 )A ) is in quite reasonable agreement with that in the
equilibrium structure predicted from theory (Table 6 .5 ) and we report this value as an
estimate to the B-0 bond distance in H:0 -BF 3(g). In comparison to the solid phase bond
distance of 1 .532A , there is clearly a contraction of the dative bond on the order of - 0 .3 A
upon crystallization. In addition, the O-B-F angle at this level of theory is -1 0 0 ° , which
widens by nearly 7° in the crystalline phase. The observation of large gas-solid structure
changes as well as a bond length that is intermediate to the sum o f covalent radii and van der
Waals radii for oxygen and boron classify H2O-BF 3 as a partially bonded complex.
As mentioned in the Introduction, H;0 -BF 3 crystallizes in an open ring-like structure
with extensive intermolecular hydrogen bonding interactions. [14] Each of the hydrogen
atoms on the water unit is hydrogen bonded to a fluorine atom on a neighboring H2O-BF3
unit with one short H— F distance o f 1.6A and two longer H— F distances of 2.0 and 2.3A.
respectively. The monomer units are orientated such that the most favorable hydrogen
bonding interactions are attained. It is evident from the difference in the monomer structure
between the gas and the crystalline phases that these intermolecular interactions act as a
177
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sufficient perturbation on intramolecular bonding to contract the dative bond. This
contraction is intrinsically tied to the observation of partial bonding in the gas phase, as it is
only in the regime where the lattice energy is comparable to the complex binding energy
that the formation of the lattice induces the formation of the donor-acceptor bond.
Conclusions
1. The spectra of all isotopomers o f fTO-BFj are complicated by internal motions. The
spectra could not be fit to a single energy expression that could account for the observed
patterns. Attempts to fit a subset o f the rotational constants to geometric parameters were
not entirely successful, which is to be expected in the regime where large amplitude
motions blur the definition of molecular structure. Nevertheless, the value determined for
the B- 0 bond distance from a series of least squares fits is 1.87(4)A, which is in near
agreement with that obtained from a series of ab initio calculations. This value is -0.3A
shorter than that observed for H:0 -BF 3(s), consistent with partial bonding in the gas
phase.
2. Ab initio calculations provide a determination of geometry o f the H2O-BF 3 complex
(Figure 6.4) in which the B -0 bond is 1 .8 2 5 A and the BF3 unit is slightly distorted from
planarity. The plane of the water unit makes an angle o f - 1 2 0 ° with the B -0 bond axis, in
a favorable configuration for donation o f a lone pair from the oxygen to boron atom. The
internal rotation o f the water unit has been examined in detail and two transition states
have been identified. The more energetically favorable transition state involves a
wagging motion of the water unit which is coupled with rotation about the B -0 bond
axis, which is also appropriate for describing the rotation o f the water unit about an OH
bond. The barrier to this coupled motion is 1.58 kcal/mol.
3. The dipole moment of several isotopomers has been measured and in most cases is
-3.9D. The Stark effect data are again consistent with multiple low-lying states and
complex internal motion of the water subunit.
178
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27. Ohashi, N.; Hougen, J.T. J. Mol. Spec. 1987,121,474.
28. Ohashi, N.; Tsunekawa, S.; Takagi, K.; Hougen, J.T. J. Mol. Spec. 1989,137, 33.
29. Oda, M.: Ohashi, N.; Hougen, J.T. J. Mol. Spec. 1990,142, 57.
30. MOLPRO is a package of ab initio programs written by H.-J. Wemer and P. J.
Knowles, with contributions from J. Almlof, R. D. Amos, M. J. O. Deegan, S. T. Elbert.
C. Hampel, W. Meyer, K. Peterson, R. Pitzer, A. J. Stone, P. R. Taylor, R. Lindh M. E.
Mura, and T. Thorsteinsson.
31. Hankinson, D.J.; Almlof, J.; Leopold, K.R. J. Phys. Chem. 1996,100,6904.
180
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Appendix to Chapter 6.
Table 6.A1. Transition Frequencies for All H20-BF3 Isotopomers.
HDI6Q -UBF 3
J”
F"
1.5
0
1
1.5
1.5
2.5
1
0.5
0
0
1
I
I
1
1
1
1
1
1
1
1
1.5
2.5
1.5
0.5
1.5
0.5
2.5
2.5
0.5
2.5
1.5
K
J’
F’
Freq (MHz)
obs-calc (MHz)
0
1
0.5
8628.960
-0.003
0
I
2.5
8629.429
8630.011
0
1
1
2
1
2
1
2
1
2
1
2
1
2
0
2
0
2
0
1.5
3.5
1.5
2.5
2.5
17257.978
17257.828
17258.547
0 .0 0 1
0 .0 0 2
0 .0 0 2
0 .0 0 2
1.5
17258.258
17258.348
-0 . 0 1 0
-0.008
-0 . 0 0 1
0.5
2.5
0.5
17257.551
17258.848
17258.898
0.015
-0 . 0 0 2
-0 . 0 0 2
2
1.5
17259.006
-0 . 0 1 0
0
2
2.5
17259.428
0
2
0
2
0
2
1.5
3.5
1.5
17259.498
17258.848
17258.438
-0.003
0.017
K.
J'
F
Freq (MHz)
obs-calc (MHz)
8633.828
8634.169
8635.134
17268.527
-0 . 0 0 2
17268.441
0.019
3
4
17268.283
17269.376
-0 . 0 0 1
-0 . 0 0 2
0.003
h d ,6o - ,0BF3
r
F"
0
J
0
1
2
0
J
0
1
4
0
1
3
0
2
0
2
0
2
0
2
0
2
2
17267.698
0
2
1
17268.376
0
2
3
5
0
i
J
4
5
4
0 .0 0 1
0.000
0 .0 0 1
i
3
j
4
i
j
i
2
i
2
i
4
1
2
i
2
1
2
1
i
4
1
2
4
17269.585
17267.558
17267.137
17268.004
i
2
1
2
3
17267.753
-0 . 0 0 2
i
2
1
2
2
17267.473
0 .0 1 1
i
i
-0 . 0 1 2
0.000
-0.005
-0.003
-0.004
-0.015
0 .0 1 1
181
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 6.A 1. continued.
01
X
o
00
HD160 - iqBF3 continued.
J”
J'
K
F”
2
4
1
1
2
1
j
1
J"
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
F’
3
2
Freq (MHz)
17267.927
17268.111
obs-calc (MHz)
0.003
-0.003
F’
0.5
2.5
1.5
1.5
3.5
2.5
0.5
1.5
2.5
1.5
0.5
3.5
2.5
1.5
2.5
Freq (MHz)
8291.895
8292.363
8292.938
16584.314
16584.730
16584.730
16584.780
16584.899
16585.314
16585.378
16583.546
16583.976
16584.274
16584.350
16584.542
obs-calc (MHz)
-0.001
0.003
-0.002
-0.004
-0.002
-0.002
-0.002
0.001
0.002
0.016
0.007
-0.002
0.006
-0.001
-0.016
bf3
F”
1.5
1.5
1.5
1.5
2.5
1.5
0.5
2.5
2.5
0.5
0.5
2.5
2.5
1.5
1.5
1C
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
J’
1
1
1
2
2
2
•>
•>
2
2
2
2
2
2
h d I8o - icb f 3
J"
0
0
0
1
1
t
1
1
1
1
I
1
1
F"
J
3
j
*
j■
j•>
4
4
2
4
j
K
J'
F
Freq (MHz)
obs-calc (MHz)
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
2
2
3
4
2
8298.920
8297.968
8297.629
16595.904
16595.992
16596.052
16596.136
16596.970
16594.867
16595.201
16595.285
16595.468
16596.191
-0.001
0.003
-0.002
0.003
-0.005
0.014
-0.004
-0.023
-0.016
0.011
-0.004
-0.012
-0.002
2
2
2
2
2
2
2
“t
j
1
4
5
4
1
2
5
j
4
182
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 6.A1. continued.
D2l60- llBF3_________
J"
0
0
0
1
I
1
1
1
1
1
!
1
I
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
F”
1.5
1.5
1.5
1.5
1.5
2.5
0.5
2.5
0.5
0.5
2.5
1.5
1.5
1.5
1.5
1.5
0.5
2.5
2.5
1.5
0.5
1.5
1.5
1.5
2.5
2.5
0.5
0.5
0.5
2.5
2.5
1.5
1.5
K
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
1
1
1
1
1
0
0
0
0
0
1
1
1
1
1
1
J’
1
1
1
2
2
2
2
2
2
2
■)
2
2
1
1
1
2
-I
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
F
0.5
2.5
1.5
1.5
2.5
3.5
0.5
2.5
0.5
1.5
3.5
2.5
1.5
0.5
2.5
1.5
1.5
3.5
2.5
1.5
0.5
2.5
1.5
2.5
3.5
2.5
0.5
0.5
1.5
3.5
2.5
1.5
2.5
Freq (MHz)
8372.375
8372.838
8373.414
16745.245
16745.642
16745.642
16745.695
16746.216
16743.374
16743.660
16743.798
16744.368
16744.154
8375.363
8375.824
8376.395
16748.096
16748.224
16748.517
16748.608
16747.806
16748.815
16751.171
16751.582
16751.582
16752.156
16751.645
16801.347
16801.634
16801.775
16802.046
16802.161
16802.356
obs-calc (M
-0.004
0.001
0.004
0.009
-0.003
-0.003
0.001
-0.003
0.009
0.009
-0.001
-0.004
-0.013
-0.001
0.002
-0.001
0.007
-0.013
-0.006
0.003
0.004
0.005
-0.004
-0.003
-0.003
-0.002
0.011
0.003
0.003
-0.003
-0.019
0.015
0.005
183
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 6.A1. continued.
D216O-l0BF3 continued.
J" F"
J'
K
0
0
0
1
1
1
1
1
I
1
I
1
1
1
1
0
0
0
1
1
1
1
1
1
1
I
1
3
3
3
3
2
3
4
2
4
2
2
4
3
3
3
3
3
3
3
2
4
3
2
4
4
4
3
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
I
1
1
1
1
H2,60 - n BF3
J" F"
K.
0 1.5
0
0 1.5
0
0
0 1.5
0
1 1.5
1 1.5
0
F
2
1
5
3
4
4
Freq (MHz)
8377.321
8377.664
8378.606
16755.246
16755.331
16755.390
16755.476
16753.123
16753.542
16753.722
16755.927
16756.299
16754.345
16754.428
16754.664
8380.281
8380.615
8381.571
16761.108
16761.209
16761.356
16760.531
16757.494
16757.897
16758.264
16758.350
16758.827
obs-calc (MHz)
-0.005
0.006
-0.001
0.010
0.000
0.018
0.003
-0.003
0.013
0.003
-0.014
-0.022
-0.014
0.001
0.004
-0.004
-0.002
0.005
-0.004
0.002
0.007
-0.005
-0.014
-0.015
-0.003
0.015
0.017
J’
1
1
I
2
2
F
0.5
2.5
1.5
1.5
2.5
Freq (MHz)
8889.507
8889.980
8890.559
17780.056
17780.470
obs-calc (MHz)
0.000
0.004
-0.003
0.002
-0.003
1
1
I
2
2
2
2
2
2
2
-)
2
2
2
2
1
I
1
2
2
i
2
2
2
2
4
3
3
1
4
5
1
5
3
2
4
j
4
2
T
4
3
3
1
5
2
184
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 6.A 1. continued.
H2160-"BF3 continued.
J" F"
K
J’
2
1 2.5
0
2
1 2.5
0
2
1 0.5
0
2
1 1.5
0
2
I 0.5
0
2
1 0.5
1
2
1 0.5
1
2
I 2.5
1
2
1 2.5
1
2
1 1.5
1
0
0
0
1
1
1
I
I
1
I
1
1
I
1
0
0
0
1
1
1
1
I
1
1
1
1
1.5
1.5
1.5
1.5
2.5
0.5
0.5
2.5
1.5
1.5
2.5
1.5
2.5
0.5
1.5
1.5
1.5
1.5
1.5
1.5
1.5
2.5
2.5
0.5
0.5
0.5
2.5
0
0
0
1
1
1
1
1
I
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
2
2
2
2
2
2
i
2
2
2
2
2
1
I
1
2
2
2
2
2
2
2
2
2
F
3.5
2.5
1.5
0.5
0.5
0.5
1.5
3.5
2.5
2.5
0.5
2.5
1.5
2.5
3.5
0.5
1.5
2.5
1.5
2.5
3.5
1.5
2.5
1.5
0.5
0.5
2.5
1.5
0.5
1.5
2.5
3.5
2.5
1.5
0.5
1.5
3.5
Freq (MHz)
17780.470
17781.052
17781.111
17779.475
17780.526
17765.746
17766.065
17766.189
17766.494
17766.761
8907.262
8907.735
8908.326
17815.846
17815.255
17814.826
17815.086
17815.550
17815.641
17815.457
17815.457
17815.041
17816.055
17816.118
17814.458
8943.555
8944.032
8944.613
17886.770
17887.371
17887.776
17887.776
17888.364
17888.428
17842.178
17842.456
17842.626
obs-calc (MHz)
-0.003
-0.007
0.002
0.007
0.003
-0.005
0.021
-0.006
0.006
-0.020
-0.004
0.000
0.005
0.002
-0.003
0.012
-0.022
-0.001
0.006
-0.004
-0.004
-0.001
0.008
0.021
0.002
-0.004
0.004
-0.001
-0.006
0.009
-0.005
-0.005
-0.003
0.011
0.003
-0.012
0.008
185
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 6.A1. continued.
H;16Q-n BF3 continued.
J" F"
K
J’
2
1 2.5
I
2
1 1.5
1
2
1 1.5
1
2
1 0.5
1
2
I 0.5
1
2
I 2.5
1
I
1
1
2.5
1.5
1.5
1
1
1
H2I6Q-I0BF3
K
J" F"
0
0
0
J
I
3
4
4
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
1
1
j
j
•>
i
J
■>
J
->
4
j
j
j
3
j
■"i
J
j
1
3
1
4
1
2
1
4
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
1
2
J’
1
1
1
2
2
2
2
2
2
2
2
2
2
2
2
2
I
1
1
2
2
2
2
2
2
F
2.5
1.5
2.5
0.5
1.5
3.5
2.5
1.5
2.5
F’
T
4
J•*
j
4
5
2
4
1
2
3
1
2
5
3
4
2
4
3
3
2
4
5
I
5
Freq (MHz)
17842.900
17843.012
17843.200
17904.149
17904.416
17904.565
17904.852
17904.941
17905.149
obs-calc (MHz)
-0.012
0.017
-0.005
0.024
-0.002
-0.003
-0.010
-0.004
-0.006
Freq (MHz)
8894.777
8895.121
8896.092
17790.696
17791.805
17790.938
17791.422
17790.837
17790.815
17790.112
17792.015
17775.365
17775.674
17775.789
17776.619
17776.719
8912.244
8912.591
8913.565
17825.122
17824.533
17825.266
17825.370
17824.658
17825.064
obs-calc (MHz)
-0.004
0.001
0.001
-0.004
-0.003
-0.004
0.002
-0.001
0.018
0.001
0.006
-0.003
-0.006
0.009
-0.010
0.021
-0.007
0.001
0.006
-0.003
-0.003
0.003
0.003
-0.003
-0.009
186
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 6.A1. continued.
H216O -l0BF3 continued.
J" F"
K
J'
2
1
1
3
2
i
:
1
2
1
1
3
0
0
0
1
1
1
1
1
1
1
1
I
1
1
1
1
1
3
3
3
3
3
4
:
4
2
2
4
3
3
2
4
2
3
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
H2,80 - n BF3
J" F"
K
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1.5
1.5
1.5
1.5
2.5
1.5
0.5
2.5
0.5
0.5
0.5
2.5
1.5
2.5
0
0
0
0
0
0
0
0
0
1
1
1
1
I
F
Freq (MHz)
obs-calc (MHz)
3
3
4
2
5
3
4
3
5
3
4
17825.920
17825.266
17826.005
8947.981
8948.319
8949.266
17896.319
17896.435
17896.551
17897.028
17897.392
17852.281
17852.584
17852.708
17853.534
17853.604
17852.888
17912.826
17913.030
17913.756
-0.001
-0.001
0.014
0.008
0.007
-0.016
0.016
-0.007
0.005
0.005
-0.019
-0.001
-0.009
0.014
-0.008
-0.007
0.001
-0.006
0.004
0.007
J'
F
Freq (MHz)
obs-calc (MHz)
1
1
0.5
2.5
1.5
1.5
3.5
2.5
0.5
2.5
1.5
0.5
1.5
3.5
0.5
1.5
8536.942
8537.416
8538.008
17074.419
17074.830
17074.830
17074.893
17075.417
17075.485
17074.211
17074.508
17074.644
17074.725
17074.725
187
-0.009
-0.001
0.010
-0.002
-0.006
-0.006
0.007
-0.001
0.017
0.006
0.012
-0.002
-0.004
-0.004
I
1
1
2
2
2
->
2
2
2
2
*>
2
2
2
2
1
2
2
2
2
2
2
2
2
2
2
2
4
3
j
4
5
2
4
1
2
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 6.A1. continued.
H2l80-" B F 3 continued.
J" F"
K
J’
2
1 2.5
1
2
1 1.5
1
2
1 1.5
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1.5
1.5
1.5
1.5
2.5
1.5
0.5
2.5
2.5
0.5
0.5
2.5
2.5
1.5
1.5
0.5
2.5
1.5
1.5
0.5
0.5
2.5
2.5
1.5
1.5
0
0
0
0
0
0
0
0
0
0
I
1
I
1
1
1
1
1
1
1
1
1
1
1
1
H218Q-10BF3
J” F"
K
0
0
0
1
1
1
3
3
J
J
2
j
0
0
0
0
0
0
1
1
1
2
2
2
2
2
2
2
*>
2
2
2
2
2
2
2
2
2
2
2
2
2
2
J’
1
1
1
2
2
2
F'
Freq (MHz)
obs-calc (MHz)
2.5
1.5
2.5
0.5
2.5
1.5
1.5
3.5
2.5
0.5
1.5
2.5
1.5
0.5
3.5
2.5
1.5
2.5
0.5
3.5
1.5
2.5
0.5
1.5
3.5
2.5
1.5
2.5
17074.934
17075.017
17075.225
8592.901
8593.365
8593.937
17185.123
17185.531
17185.531
17185.593
17185.711
17186.106
17186.170
17186.596
17187.020
17187.315
17187.380
17187.602
17029.087
17029.522
17029.901
17030.101
17053.976
17054.279
17054.428
17054.704
17054.795
17055.008
-0.002
-0.003
-0.002
0.004
0.003
-0.007
0.003
-0.004
-0.004
0.008
0.009
-0.011
0.003
0.017
0.001
0.005
-0.013
0.001
-0.006
0.006
0.006
-0.009
-0.001
0.004
0.003
-0.003
0.002
-0.006
F
2
Freq (MHz)
obs-calc (MHz)
-0.007
-0.001
0.003
-0.014
0.000
-0.002
4
3
3
1
4
8542.778
8543.121
8544.093
17086.185
17086.296
17086.335
188
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 6.A 1. continued.
H218O -10BF3 continued.
p..
J"
J'
K
2
1
4
0
1
1
0
2
0
->
2
0
1
1
2
4
1
4
1
1
1
1
2
2
2
I
4
I
j
1
1
1
j
1
2
2
2
1
2
3
0
1
i
0
0
0
j
0
I
j
0
1
1
3
0
2
1
■>
j
0
2
1
i
1
**
j
0
0
2
2
I
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
4
0
i
0
2
2
4
2
0
i
1
4
4
1
j
1
j
■>
j
1
2
2
2
2
2
1
2
T
2
1
1
2
2
4
1
*)
1
1
2
2
4
1
1
1
4
4
1
1
j
1
2
2
2
2
2
2
2
F
5
2
4
3
1
2
5
4
2
3
4
2
4
3
2
3
1
4
5
2
4
1
2
5
4
2
3
4
1
2
5
3
4
1
5
4
2
Freq (MHz)
obs-calc (MHz)
17086.439
17086.911
17087.308
17087.507
17085.739
17086.066
17086.157
17086.586
17086.703
17087.011
17087.085
8596.968
8597.306
8598.255
17192.924
17193.503
17193.605
17193.635
17193.744
17194.207
17194.588
17202.270
17202.572
17202.668
17203.094
17203.217
17203.501
17203.577
17040.398
17040.723
17040.826
17041.041
17041.287
17068.172
17068.592
17069.015
17069.141
-0.001
-0.003
0.009
0.008
-0.012
0.005
-0.003
-0.004
-0.007
0.009
0.014
0.004
0.005
-0.009
0.008
0.003
0.008
-0.003
0.003
-0.009
-0.013
0.012
0.005
0.001
-0.003
0.000
-0.009
-0.001
-0.024
-0.008
-0.005
0.018
0.027
-0.002
0.009
0.002
0.007
189
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 6.A1. continued.
H2180 - lftBF3 continued.
J" F”
J'
K
2
1
3
1
•
y
2
1
j
1
2
1
3
1
F
Freq (MHz)
obs-calc (MHz)
3
4
2
17069.413
17069.480
17041.367
-0.013
-0.015
-0.014
Table 6.A2. Stark Transitions for H1O-BF 3 Isotopomers.
J=l<—0 H2l60-BF5, central K=Q transition
Mj" M," Mj' M,'
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-0.5
1.5
1.5
1.5
1.5
-0.5
1.5
1.5
1.5
1.5
1.5
-0.5
1.5
1.5
1.5
1.5
-0.5
1.5
1.5
1.5
1.5
1.5
-0.5
1.5
1.5
1.5
1 -1.5
1 1.5
1 0.5
1 -0.5
-1
1
0
1
1
1
-1
1
1
1
1
-1
1
0
0
1
1
1
1
0
1
1
1.5
-1.5
1.5
1.5
0.5
-0.5
1.5
-1.5
1.5
0.5
-0.5
1.5
-1.5
1.5
0.5
1.5
0.5
-0.5
-1.5
0.5
1.5
0.5
E(V/cm)
Freq (MHz)
18.62
18.62
18.62
18.62
18.62
21.70
21.69
21.70
21.70
21.70
21.70
24.84
24.84
24.84
24.81
24.84
31.00
31.00
31.00
31.00
31.00
31.00
37.21
37.21
37.21
37.21
8907.801
8907.774
8907.785
8908.358
8907.311
8907.823
8908.408
8907.783
8907.805
8908.377
8907.331
8907.849
8907.799
8907.824
8908.395
8907.348
8907.393
8908.483
8907.912
8907.835
8907.877
8908.426
8907.451
8907.997
8907.876
8907.936
obs-calc (M
0.002
0.002
-0.004
-0.003
-0.006
0.001
-0.001
-0.001
-0.002
0.002
-0.003
0.000
0.000
-0.004
0.004
-0.006
-0.007
-0.018
-0.001
0.001
-0.001
-0.004
-0.004
0.004
0.000
0.000
190
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 6.A2 . continued.
J—1-^—0 H2l60-BF3, central K=0 transition continued.
Mj" M," Mj' M,'
E(V/cm)
Freq (MHz)
obs-calc (MHz)
1.5 1
-0.5 1
1.5 0
1.5 0
1.5 1
1.5 1
1.5 1
-0.5 1
1.5 0
1.5 0
1.5 1
1.5 1
1.5 1
-0.5 1
1.5 0
1.5 1
1.5 1
37.21
43.42
43.42
43.42
43.42
43.42
43.42
49.64
49.64
49.64
49.64
49.64
49.64
55.84
55.84
55.84
55.84
8908.469
8907.515
8908.667
8908.091
8907.928
8908.007
8908.534
8907.581
8908.796
8908.208
8907.988
8908.079
8908.616
8907.665
8908.327
8908.054
8908.165
-0.009
-0.002
-0.015
0.003
0.001
0.004
-0.003
-0.006
-0.003
0.010
0.003
0.002
0.009
0.001
0.007
0.003
0.006
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-0.5
-1.5
1.5
0.5
1.5
0.5
-0.5
-1.5
1.5
0.5
1.5
0.5
-0.5
-1.5
0.5
1.5
0.5
J=l«-0 H; ' 60-B F 3, highest frequency K=0 transition
Mj"
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
M," Mj' M,'
-0.5
1.5
1.5
1.5
1.5
1.5
1.5
-0.5
1.5
1.5
1.5
1.5
1.5
1.5
-0.5
1.5
1.5
1
0
0
1
1
1
-1
1
0
0
1
1
1
-1
1
0
0
-1.5
1.5
0.5
1.5
0.5
-0.5
1.5
-1.5
1.5
0.5
1.5
0.5
-0.5
1.5
-1.5
1.5
0.5
E(V/cm)
18.59
18.59
18.59
18.59
18.59
18.59
18.59
21.75
21.75
21.75
21.75
21.75
21.75
21.75
24.80
24.80
24.80
Freq (MHz)
8944.049
8944.637
8944.049
8944.033
8944.049
8944.612
8943.566
8944.054
8944.642
8944.054
8944.031
8944.054
8944.606
8943.567
8944.057
8944.648
8944.057
obs-calc (MHz)
0.007
0.008
0.007
-0.003
0.009
-0.011
-0.005
0.006
0.008
0.006
-0.008
0.009
-0.020
0.008
0.003
0.008
0.003
191
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 6.A2. continued.
J= 1<—0 H216Q-BF3, highest frequency K=0 transition continued.
Mj"
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
M i"
1.5
1.5
1.5
1.5
-0.5
1.5
1.5
1.5
1.5
1.5
1.5
-0.5
1.5
1.5
1.5
1.5
-0.5
1.5
1.5
1.5
-0.5
1.5
1.5
1.5
1.5
-0.5
1.5
1.5
M j'
1
1
1
-1
1
0
0
1
1
1
-1
1
0
0
1
1
1
0
1
1
1
0
0
1
1
1
0
0
M,"
0
0
0
0
0
0
0
E(V/cm)________ Freq (MHz)
24.80
8944.026
8944.057
24.80
8944.608
24.80
8943.569
24.80
8944.071
31.05
8944.669
31.05
8944.071
31.05
31.05
8944.051
8944.071
31.05
31.05
8944.632
8943.572
31.05
8944.089
37.16
37.16
8944.666
37.16
8944.089
37.16
8944.055
37.16
8944.653
43.36
8944.115
43.36
8944.115
43.36
8944.060
8944.670
43.36
49.56
8944.139
49.56
8944.713
49.56
8944.139
49.56
8944.066
8944.691
49.56
8944.171
55.77
55.77
8944.735
55.77
8944.171
obs-calc (MHz)
-0.017
0.007
-0.022
-0.011
0.002
0.014
0.002
0.000
0.008
-0.007
-0.020
0.002
-0.008
0.002
-0.006
0.003
0.006
0.006
-0.013
0.007
0.005
-0.008
0.005
-0.021
0.012
0.008
-0.016
0.008
11
0
1
ll
HDlftO-BF
M i’
1.5
0.5
-0.5
1.5
-1.5
1.5
0.5
1.5
0.5
-0.5
1.5
-1.5
1.5
0.5
1.5
-0.5
-1.5
0.5
1.5
-0.5
-1.5
1.5
0.5
1.5
-0.5
-1.5
1.5
0.5
M," M,’ M,'
0.5
1 -1.5
0.5 -1 1.5
0.5 -1 0.5
0.5 0 0.5
0.5 0 -0.5
0.5 0 -1.5
0.5
1 -0.5
=0
E (V/cm)
17.75
17.74
17.74
17.75
17.75
17.75
17.75
Freq (MHz)
8629.496
8629.011
8629.011
8629.496
8630.050
8630.084
8630.050
obs-calc (MHz)
0.004
-0.002
-0.002
0.004
0.002
0.011
0.002
192
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 6.A2. continued.
HDlf,0-BF^ J=l<—0 K.-0 continued.
Mj"
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
M," Mj’ M,'
0.5 -1 1.5
0.5 -1 0.5
0.5 -1 -0.5
0.5 0 -0.5
0.5 0 -1.5
0.5
1 -1.5
0.5 -1 0.5
0.5 -1 -0.5
0.5 -t -1.5
0.5
1 -1.5
0.5 0 0.5
0.5
1 1.5
0.5
1 0.5
0.5
1 -0.5
0.5 -1 1.5
0.5 0 0.5
0.5 0 -0.5
1 0.5
0.5
0.5
1 -0.5
0.5
1 -1.5
0.5 -1 1.5
0.5 -1 0.5
0.5 0 0.5
0.5 0 -0.5
1 -0.5
0.5
0.5 -I
1.5
0.5 -1 0.5
0.5 -1 -0.5
0.5 0 -0.5
0.5
1 -1.5
0.5 -1 0.5
0.5 -1 -0.5
0.5 -1 -1.5
0.5
1 -1.5
1.5
0.5 0
1 1.5
0.5
0.5
1 0.5
0.5
1 -0.5
0.5 -1 1.5
E (V/cm)
17.74
17.74
17.75
17.75
17.75
17.75
17.74
17.75
17.75
18.44
18.44
18.44
18.44
18.44
18.44
18.44
18.44
18.44
18.44
18.44
18.44
18.44
18.44
18.44
18.44
18.44
18.44
18.44
18.44
18.44
18.44
18.44
18.44
24.49
24.91
24.49
24.51
24.50
24.50
Freq (MHz)
8629.011
8629.011
8629.481
8630.050
8630.084
8629.496
8629.011
8629.481
8629.461
8629.501
8629.501
8629.456
8629.487
8630.054
8629.013
8629.501
8630.054
8629.487
8630.054
8629.501
8629.013
8629.013
8629.501
8630.054
8630.054
8629.013
8629.013
8629.487
8630.054
8629.501
8629.013
8629.487
8629.456
8629.551
8630.123
8629.487
8629.520
8630.082
8629.052
obs-calc (MHz)
-0.002
-0.002
0.000
0.002
0.011
0.004
-0.002
0.000
-0.003
0.004
0.004
-0.010
0.002
0.003
-0.004
0.004
0.003
0.002
0.003
0.004
-0.004
-0.004
0.004
0.003
0.003
-0.004
-0.004
0.002
0.003
0.004
-0.004
0.002
-0.010
0.000
-0.014
-0.009
-0.008
-0.002
-0.005
193
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 6.A2. continued.
HD|6Q-BF, J=l<—0 K=0 continued.
nr
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Ml"
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
Mj’ M,’
0
0
0
1
1
1
-1
-1
1.5
0.5
-0.5
0.5
-0.5
-1.5
1.5
0.5
0.5
-0.5
E (V/cm
Freq (MHz)
obs-calc (MHz)
24.91
24.49
8630.123
8629.551
8630.082
8629.520
-0.014
24.50
24.51
24.50
24.49
24.50
24.50
8630.082
8629.551
8629.052
24.51
24.50
8629.052
8629.551
8630.082
I
-1
-1.5
-0.5
1.5
24.91
24.50
24.50
8630.123
8630.082
8629.052
-1
-1
0
0.5
-0.5
-0.5
24.50
8629.052
8629.520
8630.082
0
1
-1
-1
-1.5
-1.5
0.5
-0.5
-1
-1.5
-1.5
0
0
0
1
0
24.51
24.50
24.91
24.49
24.50
24.51
24.49
30.48
30.46
1
1
0.5
1.5
0.5
1
-1
-0.5
1.5
0
0
0.5
-0.5
30.46
30.46
1
0.5
-0.5
30.46
30.47
-1.5
1.5
0.5
30.48
30.48
30.47
30.46
30.46
30.47
30.48
0
0.5
0.5
0
0
0.5
0.5
0
0
0.5
0.5
-1
0
0
0
0
0.5
0.5
0.5
0.5
0
0
1
-1
0.5
-0.5
-0.5
30.46
30.46
30.47
1.5
0
0.5
-1
-0.5
30.48
30.46
1
1
-1
8630.123
8629.551
8629.052
8629.520
8629.487
8629.101
0.000
-0.002
-0.008
-0.002
0.000
-0.005
-0.005
0.000
-0.002
-0.014
-0.002
-0.005
-0.005
-0.008
-0.002
-0.014
0.000
-0.005
-0.008
-0.009
-0.005
8629.621
8629.524
0.001
-0.009
8629.585
0.005
-0.004
8630.121
8629.101
-0.005
8629.621
0.001
8629.621
8629.585
8630.121
8629.101
0.001
0.005
-0.004
8629.101
8630.121
-0.005
-0.004
8629.621
8629.621
0.001
0.001
-0.004
8630.121
8629.101
8629.585
-0.005
-0.005
0.005
194
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 6.A2 . continued.
HD'°Q-BF, J=l<—0 K=Q continued.
VI/'
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
M," Mj' M,’
0.5 0 -0.5
0.5
1 -1.5
0.5 -1 0.5
0.5 -1 -0.5
0.5 -1 -1.5
0.5
1 -1.5
0.5 0 0.5
0.5
1 1.5
0.5
1 0.5
0.5
1 -0.5
0.5 -1 1.5
0.5 0 0.5
0.5 0 -0.5
0.5
1 0.5
0.5
1 -0.5
0.5
1 -1.5
0.5 -1 1.5
0.5 -1 0.5
0.5 0 0.5
0.5 0 -0.5
0.5
1 -0.5
0.5 -1 1.5
0.5 -1 0.5
0.5 -1 -0.5
0.5 0 -0.5
0.5
1 -1.5
0.5 -I 0.5
0.5 -1 -0.5
0.5 -1 -1.5
0.5
1 -1.5
0.5 0 1.5
0.5 0 0.5
0.5
1 1.5
0.5
1 0.5
0.5
1 -0.5
0.5 -1 1.5
1.5
0.5 0
0.5 0 0.5
0.5
1 0.5
E (V/cm)
30.46
30.48
30.47
30.46
30.46
36.73
36.73
36.42
36.42
36.43
36.73
36.73
36.73
36.42
36.43
36.73
36.73
36.43
36.73
36.73
36.43
36.73
36.43
36.42
36.73
36.73
36.43
36.42
36.42
42.82
42.78
42.80
42.80
42.78
42.79
42.82
42.78
42.80
42.78
Freq (MHz)
8629.621
8629.101
8630.121
8629.585
8629.524
8629.168
8629.717
8629.584
8629.646
8630.179
8629.168
8629.717
8629.717
8629.646
8630.179
8629.168
8629.168
8630.179
8629.717
8629.717
8630.179
8629.168
8630.179
8629.646
8629.717
8629.168
8630.179
8629.646
8629.584
8629.229
8630.389
8629.820
8629.634
8629.721
8630.247
8629.229
8630.389
8629.820
8629.721
obs-calc (M!
0.001
-0.005
-0.004
0.005
-0.009
0.002
0.007
0.006
0.004
0.002
0.002
0.007
0.007
0.004
0.002
0.002
0.002
0.002
0.007
0.007
0.002
0.002
0.002
0.004
0.007
0.002
0.002
0.004
0.006
-0.005
-0.014
0.007
-0.002
0.005
0.003
-0.005
-0.014
0.007
0.005
195
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 6.A2. continued.
HDl60-BF; J=l<—0 K -0 continued.
Mj"
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
M," m ;
1
0.5
1
0.5
0.5 -1
0.5 -1
0.5 0
0.5 0
0.5 0
1
0.5
0.5 -1
0.5 -1
0.5 -1
0.5 0
0.5 0
1
0.5
0.5 -I
0.5 -1
0.5 -1
Ml'
-0.5
-1.5
1.5
0.5
0.5
-0.5
-1.5
-0.5
1.5
0.5
-0.5
-0.5
-1.5
-1.5
0.5
-0.5
-1.5
E (V/cm)
42.79
42.82
42.82
42.79
42.80
42.80
42.78
42.79
42.82
42.79
42.78
42.80
42.78
42.82
42.79
42.78
42.80
Freq (MHz)
8630.247
8629.229
8629.229
8630.247
8629.820
8629.820
8630.389
8630.247
8629.229
8630.247
8629.721
8629.82
8630.389
8629.229
8630.247
8629.721
8629.634
obs-calc (MHz)
0.003
-0.005
-0.005
0.003
0.007
0.007
-0.014
0.003
-0.005
0.003
0.005
0.007
-0.014
-0.005
0.003
0.005
-0.002
HD1t>0-BF, J=2«—I K=0
M,"
-1
-1
-1
-1
-1
-1
0
I
-1
-1
-1
-1
0
0
1
1
-1
-1
M," M,' Mi’
-1.5 -1 -1.5
-1.5 .2 -0.5
-0.5 0 -1.5
-0.5 -1 -0.5
0.5 -1 0.5
-1.5 -1 -0.5
-1.5 1 -1.5
-0.5 0
1.5
-1.5 -1 -1.5
-0.5 0 -1.5
-0.5 -I -0.5
0.5 -1 0.5
-1.5 0 -1.5
1.5 2 0.5
-0.5 0
1.5
0.5
1 1.5
.2
-0.5
-1.5
-0.5 0 -1.5
E (V/cm)
41.34
41.35
41.35
41.36
41.32
41.33
41.33
41.34
35.61
35.60
35.64
35.62
35.64
35.61
35.64
35.64
29.37
29.37
Freq (MHz)
17258.929
17259.508
17259.438
17258.871
17258.493
17258.962
17258.771
17258.916
17258.917
17259.434
17258.863
17258.475
17258.785
17258.769
17258.903
17258.837
17259.459
17259.428
196
obs-calc (MHz)
-0.002
0.001
-0.006
-0.002
-0.005
0.005
0.014
-0.002
0.007
0.000
0.001
-0.008
0.006
0.005
0.001
-0.006
-0.008
0.000
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 6.A2. continued.
HD16Q-BF3 J=2<—1 K=0 continued.
Mj"
M,"
M,'
-1
0
0
0
0.5
-1.5
-0.5
-1
0
-1
-1
0
1
1
-1
0
0
0.5
-1.5
-1.5
-1.5
0.5
1.5
-0.5
-0.5
0.5
0.002
0.009
0.009
17258.731
17258.876
23.54
1.5
-0.5
23.52
23.54
23.54
17258.853
17259.006
17258.913
17259.416
17258.853
17258.876
23.54
17258.844
47.26
47.26
47.23
44.49
17258.892
17258.892
17258.507
44.65
44.55
44.57
17258.888
17258.935
-0.5
-1
1
-1
-1
0
0.5
0.5
-1.5
-0.5
-I
-2
-0.5
-1
1
0
1
.2
1.5
-1.5
1
0.5
-0.5
17259.022
47.24
23.54
-1
-1
-I
-1
0
0
41.51
47.24
47.24
-1.5
-1.5
-0.5
0.5
1.5
1
1
.2
-1
0.010
0.010
0.003
0.002
0.007
1
-1
-1
.2
0.5
-0.5
-1.5
-1
17259.487
17258.912
17258.810
17258.843
17258.878
-0.5
0.5
1
.2
0.5
-1.5
-0.5
29.37
0
0
0.5
-0.5
0
0
-0.004
0.007
.2
-1
0
0
0
17258.463
17258.810
17259.395
17259.395
1.5
1.5
0.5
0.5
0.5
-0.5
-0.5
0.5
29.39
29.43
29.37
29.37
1
2
-1
0
1
-1
0.5
-1.5
-0.5
-1.5
-1.5
-0.5
-1
0
obs-calc (MHz)
0
-1
1
-1
-1
-1
I
Freq (MFIz)
1
-1
-1.5
-I
1
E (V/cm)
-1.5
-1.5
1.5
0
-0.5
M,'
.2
1.5
1.5
0.5
0.5
0.5
-0.5
-0.5
-1.5
29.43
29.43
29.36
23.52
23.54
17258.772
17258.772
17259.515
0.010
0.002
0.004
-0.003
0.014
0.011
-0.001
0.005
0.003
0.003
0.005
0.002
-0.005
0.007
0.001
44.59
44.65
17258.507
17257.913
17258.727
17258.774
0.001
-0.005
-0.004
0.002
0.5
-0.5
-1.5
-1.5
44.62
44.62
44.47
44.57
17258.910
17258.910
17259.551
17259.465
0.003
0.003
1.5
44.51
1
0.5
-1.5
1
0.5
44.48
44.62
44.59
0
0
0.5
1.5
-1.5
-0.5
29.36
0.005
0.005
44.49
17258.442
17259.377
17258.737
17258.757
0.006
0.006
-0.002
0.010
-0.001
0.000
197
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 6.A2. continued.
HDlbO-BF-, J=2<—1 K=0 continued.
M," M,” M,' Mr
0
1.5 2 0.5
1
-0.5 0
1.5
I 0.5
1.5
1
-1
-1.5 _2 -0.5
-1
0.5
1
-1.5
-1
0.5 -1 0.5
0
-0.5 0 -0.5
0
-0.5 -1 0.5
0
0.5
0.5 0
-1
-1.5 0 -1.5
-1
1.5 1 0.5
0
-1.5 1 -1.5
0
-1.5 0 -1.5
0
0.5
0.5
1
0
1.5 1 1.5
1
-0.5 1 0.5
1
1
0.5
1.5
E (V/cm)
44.57
44.55
44.59
47.57
47.57
47.48
47.53
47.57
47.53
47.38
47.38
47.53
47.53
47.57
47.53
47.44
47.38
Freq (MHz)
17258.703
17258.920
17258.852
17258.965
17258.940
17258.519
17258.750
17258.896
17258.750
17259.559
17259.522
17258.723
17258.706
17258.880
17258.677
17258.506
17259.443
obs-calc (MHz)
-0.003
-0.007
0.000
0.007
-0 . 0 0 2
0.006
-0 . 0 1 2
0 .0 0 2
-0 . 0 1 2
-0 . 0 0 2
0 .0 0 2
0.004
-0.006
-0.006
-0.006
0 .0 0 1
0 .0 1 1
J=l<—0 H: isO-BF3, lower frequency fC=0 transition
Mj"
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
M," Mj'
-0.5 1
1.5 0
1.5 0
1.5 1
1.5 1
1.5 1
1.5 -1
-0.5 1
1.5 0
1.5 1
1.5 1
1.5 1
1.5 -1
-0.5 1
1.5 0
1.5 0
1.5 1
M,'
-1.5
1.5
0.5
1.5
0.5
-0.5
1.5
-1.5
0.5
1.5
0.5
-0.5
1.5
-1.5
1.5
0.5
1.5
E(V/cm)
18.59
18.59
18.59
18.59
18.59
18.59
18.59
21.58
21.58
21.58
21.58
21.58
21.58
24.68
24.68
24.68
24.68
Freq (MHz)
8537.487
8538.060
8537.487
8537.445
8537.471
8538.042
8536.989
8537.509
8537.504
8537.470
8537.490
8538.058
8537.014
8537.534
8538.099
8537.534
8537.485
obs-calc (MHz)
0.006
-0.003
0.006
-0.009
0.000
0.004
-0.013
0.005
0.000
0.004
0.001
0.006
-0.005
0.004
-0.014
0.004
0.005
198
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 6.A 2. continued.
J—1<—0 H2180 -B F 3, lower frequency K=0 transition continued.
J= l« -0 Hi
00
01
DO
^T|
Mj" Ml" Mj' M,'
0
1.5 1 0.5
0
1.5 1 -0.5
0
1.5 -1 1.5
0 -0.5 1 -1.5
0
1.5 0 1.5
0
1.5 0 0.5
0
1.5 1 1.5
0
1.5 1 0.5
0
1.5 -1 1.5
0 -0.5 1 -1.5
0
1.5 0 1.5
0
1.5 0 0.5
0
1.5 1 1.5
0
1.5 1 0.5
0
1.5 1 -0.5
0
1.5 -1 1.5
Mj" M," Mj'
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-0.5
1.5
1.5
1.5
1.5
1.5
1.5
-0.5
1.5
1.5
1.5
1.5
1.5
-0.5
1.5
1.5
1.5
1.5
1.5
M,
1 -1.5
0
1.5
0 0.5
1 1.5
1 0.5
1 -0.5
-1 1.5
1 -1.5
0
1.5
0 0.5
1 0.5
1 -0.5
-1 1.5
1 -1.5
0
1.5
0 0.5
1 1.5
1 -0.5
-1 1.5
E(V/cm)
24.68
24.68
24.68
27.75
27.75
27.75
27.75
27.75
27.75
30.85
30.85
30.85
30.85
30.85
30.85
30.85
Freq (MHz)
8537.515
8538.065
8537.030
8537.560
8538.139
8537.560
8537.499
8537.539
8537.056
8537.080
8538.167
8537.603
8537.523
8537.568
8538.109
8537.080
obs-calc (MHz)
0.005
-0.003
-0.009
0.000
-0.004
0.000
0.002
0.006
-0.005
-0.005
-0.011
0.008
0.008
0.009
0.002
-0.005
upper frequency K=0 transition
E(V/cm)
Freq (MHz)
obs-calc (MHz)
6.18
6.18
6.18
6.18
6.18
6.18
6.18
12.41
12.41
12.41
12.41
12.41
12.41
15.46
15.46
15.46
15.46
15.46
15.46
8593.373
8593.952
8593.373
8593.373
8593.373
8593.952
8592.908
8593.401
8593.965
8593.401
8593.388
8593.965
8592.934
8593.421
8594.017
8593.421
8593.394
8593.979
8592.947
0.002
-0.001
0.002
0.006
0.003
0.002
0.004
0.004
-0.014
0.004
-0.004
-0.001
0.009
0.004
0.019
0.004
0.001
0.002
0.007
199
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 6.A 2. continued.
J=l<—0 H2i80 -B F 3, upper frequency K=0 transition continued.
Mj
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
M," Mj' M,
-0.5 1 -1.5
1.5 0 1.5
1.5 0 0.5
1 0.5
1.5
1 -0.5
1.5
1.5 -1 1.5
-0.5 1 -1.5
1.5 0 1.5
1.5 0 0.5
1.5 1 0.5
1.5 1 -0.5
1.5 -1 1.5
1.5 1 0.5
1.5
1 -0.5
1.5 -1 1.5
1.5 1 0.5
1.5 0 0.5
1.5 1 0.5
-0.5 1 -1.5
1.5 0 0.5
1.5 0 0.5
E(V/cm)
18.49
18.49
18.49
18.49
18.49
18.49
21.64
21.64
21.64
21.64
21.64
21.64
24.72
24.72
24.72
27.75
30.78
30.78
24.72
24.72
27.75
Freq (MHz)
8593.444
8593.999
8593.444
8593.416
8593.994
8592.973
8593.475
8594.057
8593.452
8593.436
8594.018
8593.003
8593.461
8594.038
8593.015
8593.484
8593.591
8593.509
8593.508
8593.508
8593.547
obs-calc (MHz)
0.004
-0.023
0.004
-0.011
0.003
0.016
0.006
0.006
-0.017
-0.014
0.009
0.024
-0.014
0.009
0.012
-0.020
0.010
-0.025
0.006
0.006
0.008
Table 6.A3. Fit o f Observed Transitions o f Isotopomers o f H 2O-BF 3 to eq. (3) o f Chapter
6 . M=0 assigned to lower frequency K=0 component, opposite assignment yields nearly
identical results. See text for discussion.
H: lhO - " B F 3
J"
0
0
0
1
1
1
1
1
1
1
1
1
F"
1.5
1.5
1.5
1.5
1.5
2.5
2.5
0.5
1.5
0.5
0.5
0.5
K
J'
0
1
0
1
0
1
0
2
0
2
0
2
0
2
0
2
0
2
0
2
0
2
I
2
F
0.5
2.5
1.5
1.5
2.5
3.5
2.5
1.5
0.5
0.5
0.5
1.5
M
0
0
0
0
0
0
0
0
0
0
0
0
Freq (MHz)
8889.507
8889.980
8890.559
17780.056
17780.470
17780.470
17781.052
17781.111
17779.475
17780.526
17765.746
17766.065
obs-calc (tv
-0 . 0 0 2
0.004
-0 . 0 0 2
0 .0 0 1
-0.003
-0.003
-0.005
0.004
0.004
0.003
-0.007
0 .0 2 0
200
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 6.A 3, continued.
1■x
J
o
o
H ; 160 - 1'BF 3 continued.
J"
F"
K
1
I
2.5
1
1
2.5
1
1
1.5
0
0
1.5
0
0
1.5
0
0
1.5
1
0
1.5
0
1
1.5
0
1
1.5
0
1
2.5
1
0
2.5
0
1
0.5
1
1
0.5
1
1
0.5
1
1
2.5
1
1
2.5
1
1
1.5
1
1
1.5
-1
1
0.5
-1
1
0.5
-1
1
2.5
-1
t
2.5
-1
1
1.5
-1
1
1.5
J"
0
0
0
1
1
1
1
1
1
1
1
I
l0BF 3
F"
j
J•y
j
2
->
4
3
J■*»
j
4
4
2
K.
0
0
0
1
1
I
1
1
0
0
0
0
J'
2
2
2
1
1
1
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
F
3.5
2.5
2.5
0.5
2.5
1.5
0.5
1.5
2.5
3.5
2.5
1.5
0.5
1.5
3.5
2.5
1.5
2.5
0.5
1.5
3.5
2.5
1.5
2.5
M
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
I
1
1
Freq (MHz)
17766.189
17766.494
17776.761
8943.555
8944.032
8944.613
17886.770
17887.371
17887.776
17887.776
17888.364
17888.428
17842.178
17842.456
17842.626
17842.900
17843.012
17843.200
17904.149
17904.416
17904.565
17904.852
17904.941
17905.149
obs-calc (MHz)
-0.006
0.007
-0.018
-0.005
0.004
0.001
-0.009
0.008
-0.005
-0.005
-0.001
0.013
0.002
-0.013
0.007
-0.011
0.018
-0.003
0.023
-0.003
-0.004
-0.009
-0.003
-0.004
J'
1
1
1
•i
F
2
4
3
1
2
5
3
4
3
4
S
M
0
0
0
0
0
0
0
0
0
0
0
0
Freq (MHz)
8894.777
8895.121
8896.092
17775.365
17775.674
17775.789
17776.619
17776.719
17790.696
17791.805
17790.938
17791.422
obs-calc (MHz)
-0.004
0.001
0.005
-0.004
-0.006
0.009
-0.007
0.024
-0.005
-0.001
-0.005
0.003
2
2
2
2
2
2
2
2
2
201
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 6.A3, continued.
H: 160 - 'qBF3 continued.
J"
F"
K.
1
3
0
2
1
0
1
J
0
2
1
0
0
3
0
0
3
0
0
J"S
0
1
1
1
1
1
1
4
1
“S
1
J
1
1
J
I
2
1
1
I
j
0
1
3
0
4
1
0
2
I
0
4
1
0
1
4
-1
i
1
-1
1
j
-1
D: l60 - " b f 3
F"
J"
0
1.5
0
1.5
0
1.5
1
1.5
1
1.5
1
2.5
1
0.5
1
2.5
1
0.5
1
0.5
1
2.5
1
1.5
1
1.5
0
1.5
0
1.5
K.
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
J'
2
2
2
2
1
1
1
2
2
2
2
2
2
2
2
2
2
2
2
J’
1
1
1
2
2
2
2
2
2
2
2
2
2
1
1
F’
4
1
2
5
3
4
3
3
4
5
2
4
5
3
4
M
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
I
1
1
1
1
1
Freq (MHz)
17790.837
17790.815
17790.112
17792.015
8947.981
8948.319
8949.266
17852.281
17852.584
17852.708
17853.534
17853.604
17852.888
17896.319
17896.435
17896.551
17897.028
17897.392
17912.826
17912.030
17913.756
obs-calc (MHz)
-0.002
0.018
-0.001
0.008
0.007
0.007
-0.014
-0.001
-0.009
0.015
-0.006
-0.005
0.001
0.015
-0.007
0.006
0.006
-0.017
-0.006
0.005
0.009
F'
0.5
2.5
1.5
1.5
2.5
3.5
0.5
2.5
0.5
1.5
3.5
2.5
1.5
0.5
2.5
M
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
Freq (MHz)
8372.375
8372.838
8373.414
16745.245
16745.642
16745.642
16745.695
16746.216
16743.374
16743.660
16743.798
16744.368
16744.154
8375.363
8375.824
202
obs-calc (MHz)
-0.001
0.003
0.006
0.006
-0.007
-0.007
-0.003
-0.006
0.009
0.009
-0.001
-0.004
-0.013
-0.004
-0.001
3
2
4
3
1
■>
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 6.A 3. continued.
D : l0Q -11BF3 continued
J"
0
1
1
1
1
1
1
i
1
1
1
I
1
1
1
1
1
1
F”
1.5
1.5
1.5
2.5
2.5
0.5
0.5
2.5
2.5
1.5
0.5
1.5
0.5
0.5
2.5
2.5
1.5
1.5
D: lhO- ll)BF3
r
F"
0
3
0
3
0
3
->
1
J
2
1
1
1
1
1
1
1
1
1
1
1
0
0
0
j
4
2
4
3
2
4
2
j
j
3
3
3
K
0
0
0
0
0
0
1
1
1
1
1
I
-1
-1
-1
-1
-1
-1
K
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
J’
I
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
F
1.5
1.5
2.5
3.5
2.5
0.5
1.5
3.5
2.5
1.5
0.5
2.5
0.5
1.5
3.5
2.5
1.5
2.5
M
1
1
1
1
I
1
1
1
1
1
1
I
1
1
1
]'
I
1
1
2
2
2
2
2
2
2
2
2
2
2
2
F'
M
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
4
3
2
4
3
3
1
4
5
2
4
2
1
5
3
3
4
I
1
1
I
1
1
Freq (MHz)
8376.395
16751.171
16751.582
16751.582
16752.156
16751.645
16748.096
16748.224
16748.517
16748.608
16747.806
16748.815
16801.347
16801.634
16801.775
16802.046
16802.161
16802.356
obs-calc (MHz)
-0.003
-0.001
0.001
0.001
0.001
0.014
0.007
-0.013
-0.006
0.003
0.003
0.005
0.003
0.003
-0.003
-0.019
0.015
0.005
Freq (MHz)
8377.321
8377.664
8378.606
16755.246
16755.331
16755.390
16755.476
16755.927
16756.299
16754.664
16753.123
16753.542
16753.722
16754.345
16754.428
8380.281
8380.615
8381.571
203
obs-calc (MHz)
-0.004
0.007
0.000
0.010
0.000
0.018
0.002
-0.014
-0.022
0.004
-0.003
0.013
0.003
-0.015
0.001
-0.005
-0.003
0.005
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 6.A3, continued.
D216Q -‘qBF 3 continued.
J"
F"
K
J'
2
1
3
0
2
2
1
0
2
1
4
0
2
1
3
0
■)
2
1
1
2
1
4
1
2
1
4
1
2
1
4
1
2
1
3
1
4
M
1
1
1
1
1
1
1
1
1
Freq (MHz)
16761.108
16761.209
16761.356
16760.531
16757.494
16757.897
16758.264
16758.350
16758.827
obs-calc (MHz)
-0.001
0.005
0.010
-0.002
-0.014
-0.014
-0.003
0.015
0.018
F
M
0.5
2.5
1.5
1.5
3.5
2.5
0.5
2.5
1.5
0.5
2.5
1.5
1.5
3.5
2.5
0.5
1.5
2.5
1.5
0.5
3.5
2.5
1.5
2.5
0.5
1.5
3.5
0
0
0
0
0
0
0
0
0
1
1
I
I
I
I
1
1
I
1
1
I
1
1
I
0
0
0
Freq (MHz)
8536.942
8537.416
8538.008
17074.419
17074.830
17074.830
17074.893
17075.417
17075.485
8592.901
8593.365
8593.937
17185.123
17185.531
17185.531
17185.593
17185.711
17186.106
17186.170
17186.596
17187.020
17187.315
17187.380
17187.602
17053.976
17054.279
17054.428
204
obs-calc (MHz)
-0.009
-0.001
0.008
0.000
-0.005
-0.005
0.008
0.000
0.018
0.005
0.003
-0.008
0.004
-0.004
-0.004
0.008
0.009
-0.012
0.002
0.018
0.001
0.005
-0.014
0.000
-0.005
0.007
0.006
F
3
1
5
2
1
5
j
4
H ^ O - 1'BFs
J"
F"
K
0
0
0
1.5
1.5
1.5
1.5
2.5
1.5
0.5
2.5
0.5
1.5
1.5
1.5
1.5
2.5
1.5
0.5
2.5
2.5
0.5
0.5
2.5
2.5
1.5
1.5
0.5
0.5
2.5
0
1
1
1
1
1
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
I
1
1
I
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-1
-1
-1
-1
I
1
I
J'
1
1
1
2
2
2
2
2
2
1
I
1
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 6.A3, continued.
H ; 180 - 11BF3 continued.
J"
F"
K
J’
2
1
1.5
1
2
I
1.5
1
2
1
0.5
1
2
1
2.5
1
2
1
1.5
1
2
1
1.5
1
H :lsO- ioBF3
J"
F"
■>
0
J
K.
0
0
j
1
1
3
2
1
1
3
4
1
->
1
1
0
0
4
0
0
0
0
0
0
0
0
0
->
0
j
0
3
3
0
0
0
0
0
0
0
0
0
0
1
1
1
1
I
1
1
1
1
1
1
1
1
J
3
j
->
3
4
->
4
2
4
4
3
3
I
j
1
1
1
2
2
4
-1
-1
-1
-1
-1
-1
1
1
1
F
1.5
2.5
0.5
3.5
1.5
2.5
M
0
0
1
1
1
1
J'
1
F
2
1
1
4
3
M
0
0
0
0
0
0
0
0
0
0
1
1
1
I
1
1
1
1
1
1
1
1
1
1
I
I
1
1
1
1
2
2
2
2
■>
2
2
1
1
1
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
j
1
4
5
T
4
3
2
4
3
2
3
1
4
5
2
4
1
2
5
4
2
3
4
1
2
5
Freq (MHz)
17054.795
17055.008
17029.087
17029.522
17029.901
17030.101
obs-calc (MHz)
-0.002
0.003
0.003
-0.003
0.002
-0.006
Freq (MHz)
8542.778
8543.121
8544.093
17086.185
17086.296
17086.335
17086.439
17086.911
17087.308
17087.507
8596.968
8597.306
8598.255
17192.924
17193.503
17193.605
17193.635
17193.744
17194.207
17194.588
17202.270
17202.572
17202.668
17203.094
17203.217
17203.501
17203.577
17040.398
17040.723
17040.826
205
obs-calc (MHz)
-0.020
-0.013
-0.003
-0.020
-0.005
-0.007
-0.006
-0.008
0.004
0.004
0.007
0.009
-0.004
0.008
0.003
0.009
-0.002
0.004
-0.007
-0.011
0.012
0.005
0.001
-0.002
0.001
-0.007
0.000
-0.021
-0.006
-0.002
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 6.A3, continued.
H: l8O -l0BF3continued.
J"
J'
F"
K.
■>
2
1
1
J
2
2
1
1
2
2
1
1
2
1
4
1
2
4
1
1
**
2
1
j
1
2
1
3
1
2
1
3
1
F'
2
3
1
5
4
2
j
4
M
I
1
0
0
0
0
0
0
obs-calc (MHz)
-0.011
0.021
-0.009
0.003
-0.004
0.002
-0.018
-0.019
Freq (MHz)
17041.367
17041.041
17068.172
17068.592
17069.015
17069.141
17069.413
17069.480
Table 6.A4. Assigned Transitions from Starred State in Figure 6.2.
H:",0-"BF,
J"
F"
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1.5
1.5
1.5
0.5
0.5
0.5
1.5
1.5
1.5
1.5
1.5
2.5
2.5
2.5
J'
F'
K
Freq (MHz)
Obs-Calc(MHz)
1
1
1
2
T
0.5
1.5
2.5
0.5
1.5
1.5
0.5
1.5
1.5
2.5
2.5
2.5
2.5
3.5
0
0
0
1
0
1
0
0
1
0
1
0
1
0
8907.262
8908.326
8907.735
17814.826
17816.118
17815.086
17814.458
17815.041
17815.641
17815.457
17815.846
17816.055
17815.550
17815.457
0.008
0.010
0.009
0.016
0.007
-0.019
-0.001
-0.008
0.005
-0.013
0.000
-0.005
-0.001
-0.013
F'
2
K
Freq (MHz)
Obs-Calc(MHz)
0
0
0
1
1
0
0
8912.244
8913.565
8912.591
17824.658
17825.266
17824.533
17825.122
0.004
0.004
0.009
0.002
-0.001
-0.003
-0.008
2
■>
2
2
2
2
2
2
2
H;'60 - l0BF-,
J"
F"
J'
0
0
0
1
1
1
1
3
3
3
2
2
**
j
1
1
1
2
2
2
2
3
4
1
3
2
3
206
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 6.A4. continued.
H: l(,0 - l(>BF-, continued.
J"
F"
1
1
1
1
F
3
4
4
5
FC
Freq (MHz)
Obs-Calc(MHz)
3
3
j
4
J’
2
2
2
2
1
0
1
0
17825.92
17825.266
17826.005
17825.37
-0.008
-0.004
0.007
-0.005
D;'°0- "BF-,
J"
F"
J'
F
Freq (MHz)
Obs-Calc(MHz)
1
1
1
2
2
2
2
2
2
2
2
2
0.5
1.5
2.5
0.5
0.5
1.5
1.5
1.5
2.5
2.5
2.5
3.5
K
0
0
0
0
1
I
0
1
0
1
0
0
8372.375
8373.414
8372.838
16745.695
16743.374
16743.66
16745.245
16744.154
16745.642
16744.368
16746.216
16745.642
-0.002
0.007
0.003
-0.002
0.008
0.008
0.006
-0.013
-0.005
-0.003
-0.004
-0.005
F
2
K.
Freq (MHz)
Obs-Calc(MHz)
0
0
0
0
1
0
1
0
0
1
0
1
0
8377.321
8378.606
8377.664
16755.331
16753.123
16755.927
16753.722
16754.664
16755.246
16754.345
16755.39
16754.428
16755.476
-0.003
0.004
0.009
-0.005
-0.001
-0.018
0.006
-0.003
0.004
-0.010
0.013
0.005
-0.002
0
0
0
1
1
1
1
1
I
1
1
1
1.5
1.5
1.5
0.5
0.5
0.5
1.5
1.5
1.5
1.5
2.5
2.5
D;'60- mBF,
J"
F"
J'
0
0
0
1
1
1
1
1
1
1
1
1
1
3
3
3
2
2
2
2
1
1
1
2
2
2
■>
3
3
3
3
j
4
2
2
2
2
2
2
3
4
1
1
2
3
2
3
3
4
4
5
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 6.A 4. continued.
H;I80 - ' iBF3
J"
F"
J’
F’
K.
Freq (MHz)
Obs-Calc(MHz)
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1.5
1.5
1.5
0.5
0.5
0.5
0.5
1.5
1.5
1.5
1.5
1.5
2.5
2.5
2.5
2.5
1
1
1
2
2
2
2
2
2
2
2
2
2
->
0.5
1.5
2.5
0.5
0.5
1.5
1.5
0.5
1.5
1.5
2.5
2.5
1.5
2.5
2.5
3.5
0
0
0
0
1
0
1
1
1
0
0
1
1
0
1
0
8536.942
8538.008
8537.416
17074.893
17074.211
17075.485
17074.508
17074.725
17075.017
17074.419
17074.83
17075.225
17074.725
17075.417
17074.934
17074.83
0.002
0.012
0.007
0.002
0.010
0.007
0.014
-0.004
-0.005
-0.003
-0.011
-0.007
-0.004
-0.011
-0.004
-0.011
F
2
K.
Freq (MHz)
Obs-Calc(MHz)
0
0
0
0
1
0
1
0
1
0
1
0
1
0
1
0
8542.778
8544.093
8543.121
17086.296
17085.739
17086.911
17086.066
17087.507
17086.703
17086.185
17087.011
17086.335
17087.085
17087.308
17086.586
17086.439
0.006
0.007
0.008
0.002
-0.005
-0.009
0.010
-0.003
-0.010
-0.012
0.003
-0.001
0.007
-0.001
-0.005
-0.001
2
2
H;IS0- 10BF,
J"
F"
J’
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
3
3
3
1
1
1
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3
4
4
4
3
4
1
1
2
2
“
t
j
2
3
3
4
4
4
4
5
208
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 6.A4. continued.
h d I6o - " b f 3
J"
0
0
0
1
1
1
I
1
1
i
1
1
1
1
1
F”
1.5
1.5
1.5
0.5
0.5
0.5
0.5
1.5
1.5
1.5
1.5
2.5
2.5
2.5
2.5
HDlftO- °BF;
J"
F"
0
0
0
1
1
1
1
I
1
1
I
1
1
1
1
3
3
3
2
2
2
j
j
j■>
4
4
4
4
J’
F
K
Freq (MHz)
Obs-Calc(MHz)
1
1
1
2
2
2
2
2
2
->
0.5
1.5
2.5
0.5
0.5
1.5
1.5
1.5
1.5
2.5
2.5
1.5
2.5
2.5
3.5
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
8628.962
8630.008
8629.427
17258.898
17257.551
17259.498
17257.828
17258.438
17258.348
17258.848
17258.547
17259.006
17259.428
17258.258
17258.848
0.005
0.010
0.007
-0.006
0.013
0.016
0.001
-0.004
0.001
-0.007
-0.007
-0.014
-0.005
-0.007
-0.007
F
2
K.
Freq (MHz)
Obs-Calc(MHz)
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
8633.828
8635.134
8634.169
17268.376
17267.137
17267.473
17269.585
17267.753
17267.698
17268.283
17268.441
17267.927
17269.376
17268.004
17268.527
0.005
0.008
0.008
-0.009
-0.016
0.009
-0.006
-0.004
-0.004
-0.005
0.015
0.001
-0.015
0.010
-0.002
2
2
2
2
2
J’
1
1
1
2
2
2
2
2
2
2
2
2
2
2
2
3
4
1
1
2
3
3
2
3
4
3
4
4
5
209
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 6.A 4. continued.
HD'*Q-I1BF3_______
J"
F"
J’
F’
K
Freq (MHz)
Obs-Calc(MHz)
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1.5
1.5
1.5
0.5
0.5
0.5
1.5
1.5
1.5
1.5
2.5
2.5
2.5
2.5
1
1
1
2
2
2
2
2
2
2
2
2
2
2
0.5
1.5
2.5
0.5
0.5
1.5
1.5
1.5
2.5
2.5
1.5
2.5
2.5
3.5
0
0
0
0
1
0
0
1
0
1
0
0
1
0
8291.895
8292.938
8292.363
16584.780
16583.546
16585.378
16584.314
16584.350
16584.730
16584.542
16584.899
16585.314
16584.274
16584.730
0.001
0.002
0.006
-0.005
0.007
0.014
-0.008
0.000
-0.005
-0.014
-0.002
0.000
0.007
-0.005
J'
F’
2
K
Freq (MHz)
Obs-Calc(MHz)
0
0
0
0
1
1
1
0
1
0
1
0
0
8297.629
8298.920
8297.968
16595.992
16594.867
16595.201
16595.468
16595.904
16596.136
16596.052
16596.191
16596.970
16596.136
0.000
0.003
0.005
-0.004
-0.015
0.012
-0.011
0.003
0.014
0.015
0.000
-0.021
-0.003
HD1sO-'°BF-,
J"
F"
0
0
0
1
1
1
1
1
1
1
1
1
3
3
3
2
2
2
■)
3
j
3
3
4
4
1
1
1
2
2
2
2
2
2
2
2
2
2
3
4
1
1
2
3
3
3
4
4
4
5
210
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Chapter 7. Partially Bonded Systems as Sensitive Probes o f Microsolvation:
Rotational Spectrum and Structure of HCN—HCN—BFj.
D. L. Fiacco and K..R. Leopold
Department of Chemistry
University of Minnesota
207 Pleasant St., SE
Minneapolis, MN 55455
211
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Abstract
The structure of HCN-HCN-BF3 has been determined by rotational spectroscopy. The
N-B bond distance is 2.274(22) A, which is 0.199(36) A shorter than that in HCN-BF3 .
In contrast, the N—H distance, 2.197(6) A, is only slightly shorter (0.033(6)A) than that
in (HCN):. The results indicate significant changes in geometry at the dative bond site
upon the addition of a single HCN "solvent" molecule to the HCN-BF3 complex. This
result is consistent with that observed for the structurally analogous HCN-HCN-SO 3
complex. The hypersensitivity of both the HCN-SO3 and the HCN-BF3 complex to the
presence of first near neighbor interactions arises because the dative bond is only
partially formed, and we suggest that partially bound systems are extremely sensitive
probes of microsolvation effects.
212
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Introduction
Understanding the role of solvent in molecular systems and specifically its
effect on energetics, reactivity, and geometry is vital to many diverse fields of
chemistry. [1] Intermolecular interactions oftentimes significantly alter the energy
levels of the solute, resulting in vastly different behavior between the gaseous and
condensed phases. [2] This situation is exacerbated in the regime where the presence
of the solvent acts as a large perturbation on the solute, and the distinction between
inter- and intra-molecular interactions is not as well defined. Partially bonded
systems, where the dative linkage lies in the intermediate regime between a van der
Waals and a fully formed chemical bond are examples o f such systems. [3,4]
Complexes of this class have demonstrated an extreme sensitivity to near neighbor
interactions, evidenced as large structural differences between the gas and solid
phases. Recently, we have reported the first study o f microsolvation effects in
partially bonded systems in the structurally analogous HCN—HCN-SO3 complex. [5]
Here, we provide further compounding evidence for the measurable effect o f adding a
single "solvent” molecule to a partially formed dative bond by measuring the effect of
adding a single HCN unit to HCN-BF3 .
Partially bonded molecules are systems in which the bonding interaction is not
fully realized in the gas phase, as is evidenced by the large differences in bond distances
and angles between the gas and crystalline phases. Our interest is in probing the onset of
these structural changes by adding a single near neighbor in close proximity to a
partially formed dative bond. As stated above, we have successfully applied this
approach to the HCN-SO3 molecule by bonding an additional HCN unit to the terminal
hydrogen, resulting in the formation o f HCN—HCN-SO3 . [5] The presence o f the remote
HCN unit resulted in a 0.107(21) A contraction o f the N— S dative bond and an
enhancement in the dipole moment o f 1.238(19) D over the sum of the dipole moments
of HCN and HCN-SO3 , while the N-H interaction was not perturbed by the presence of
the remote SO3 unit. This result demonstrated that even the slightest degree of
"solvation” was enough to cause real chemical change only at the partially bonded
213
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
interaction site, where there was still “bonding left to happen”. While this result provides
strong evidence for partially bonded systems as sensitive probes o f microsolvation, the
inability to prepare HCN-SC^fs) does not allow for a direct comparison to the structural
changes that accompany the formation of the entire lattice. In the case o f HCN-BF3 ,
however, both the gas and crystal structures have been determined, [6,7] and the
corresponding changes between the gas and solid phases are indeed striking.
The gas phase structure of HCN-BF3 determined from microwave spectroscopy
is shown in Figure 7.1 below.
F
91.5 ± 1.5
€=N 2 .4 7 3 (2 9 )A
Vv
Figure 7.1. Gas phase structure o f HCN-BF3 .
The B-N bond distance is shorter than in the sum o f van der Waals radii for nitrogen
and boron yet longer than a fully formed N-B bond. The angular distortion o f the BF3
unit could not be determined from the spectroscopic data, and was reported as shown
in Figure 7.1. This value incorporates a range from 90-93°, where 93° represents the
ab initio value, argued as an upper limit to the degree o f bend-back of the BF3 moiety.
[8 ] In the original study, it was argued that the shorter N-B distance in HCN-BF3 as
compared to N:-BF3 and NCCN-BF3 provided evidence for a measurable progression
toward covalent bonding throughout the series o f Lewis acid-base adducts containing
BF3. [6 ]
In order to test this hypothesis and confirm a progression o f the N-B bonding
interaction,
the
crystal
structure
o f HCN-BF3
was
determined
by
crystallography. [7] The structure is shown in Figure 7.2 below.
214
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
X-ray
105.5°, 105.9°, 105.4°
1.638(2)A
Figure 7.2. Solid phase structure o f HCN-BF 3.
From a comparison of Figures 7.1 and 7.2, it is evident that the N-B bond
distance contract by 0 . 8 3 5 ( 2 9 ) A while the N-B-F bond angle widens by 14.1(18)°
between the gas and solid phases. These changes are enormous by any measure and
provide an unparalleled example o f the large medium effects that are characteristic of
partially bonded systems. The origin o f these effects has remained an outstanding
question since the earliest observation o f large medium effects in Lewis acid-base
complexes. For HCN-BF3, it was argued that a cooperative mechanism in which bond
shortening is favored by the near proximity of anti-aligned dipoles could account for
the large structural changes. [7] This hypothesis followed from a previous paper by
Jiao and Schleyer, who used SCRF calculations to demonstrate a rapid rise in the
dipole moment o f HCN-BF3 and concurrent contraction o f the N-B bond distance
with an increase in the dielectric constant o f the surrounding medium. [9]
This theory was subsequently challenged by Iglesias et al., who calculated the
geometry, energy and dipole moment o f HCN-BF3 and (HCN-BF3)2 at the HF and
MP2 levels using the 6-31G** basis set. [10] Their results demonstrated a contraction
of the N-B bond distance o f 0 . 1 5 2 A accompanied by an increase in the N-B-F bond
angle o f 2.0° upon addition o f the second HCN-BF3 unit. The distance between the
HCN-BF3 optimized at 3 . 2 3 A , which is shorter than the
3 .8 A
distance observed in the
crystal. From these results, the authors argue that a cooperative mechanism does not
play a decisive role in the phase dependent structure. [1 0 ] They assert that further
215
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
distance neighbors are unlikely to account for the remaining 0 . 5 9 2 A contraction in
the N-B bond and ~ 1 1° in the out-of-plane distortion o f the BF 3 unit. In a subsequent
paper by Cabaieiro-Lago et al., the calculations were repeated using two larger basis
sets; D95** and 6-31++G** at the HF, MP2, and DFT/B3LYP levels. [11] O f the two
basis sets used, the 6-31++G** basis set provided better agreement with the structural
parameters for HCN-BF 3 monomer, and was hence utilized for comparison with
(HCN-BF3):. The two HCN-BF 3 units were optimized at a distance o f 3 .8 A . in
agreement with that in the solid state. The contraction o f the N-B bond distance at the
MP2/6-31-'-*-G** level o f theory/basis set was 0 . 7 0 8 A accompanied by a widening o f
the N-B-F bond angle o f 9.3°. The authors conclude that the majority o f the structural
changes in HCN-BF 3 are indeed due to first near neighbor interactions. This is in
agreement with Hankinson et al., who contend that 30% o f the total lattice energy can
be accounted for by near neighbor interactions, highlighting the importance o f both
close and distant contacts in systems where the propensity for bond formation exists.
[12]
In this light, and because HCN-BF 3 remains the premier example o f large gassolid structure differences, it is o f immense interest to examine the effect o f single
distant near-neighbors at the level o f de'ail provided by microwave spectroscopy. As
in the case o f H C N -H C N -SO 3 , the simplest perturbation to HCN-BF 3 is to bond a
second HCN unit to the terminal hydrogen. In the case o f HCN-BF 3 , however, the
addition o f a second HCN unit complicates the analysis o f the rotational spectrum due
to the presence o f three quadrupolar nuclei. Nevertheless, the spectral analysis is
simplified by the substitution o f either or both nitrogen atoms with l5 N. As an
outstanding candidate as a probe o f microsolvation, the spectrum and structure o f
HCN—HCN-BF 3 is reported in this chapter. In order to examine the changes in
energetics and electronic redistribution in the HCN-HCN-BF 3 complex, calculations
were carried out using the BLW -ED method derived by Mo, Gao, and Peyerimhoff.
[13] These are presented along with a discussion o f the potential utility o f partially
bonded systems as sensitive probes o f solvation.
216
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Experimental
Rotational spectra of ten isotopomers of the HCN—HCN-BF3 complex were
obtained using a pulsed-nozzle Fourier transform microwave spectrometer, the details of
which have been described elsewhere [14,15]. The complex was produced using a co­
injection source [16-20] where the HCN was injected into a pulsed (nozzle rate 6.5 Hz)
expansion of 2% BF3 seeded in argon. A mixture o f 32% HCN in Ar was flowed
through a 0.016" I.D. stainless steel needle into the early stages of the Ar/BF3 expansion
at a backing pressure of 125 torr. Isotopic substitution on the HCN moieties was
accomplished using enriched samples. DCN was prepared by reaction o f KCN with dry
D 3PO 4
dry
while HCI5N was prepared by reacting 99 atom % KCi5N (Icon Services) with
H 3PO 4.
Due to relatively weak signals, spectra due to the l0B isotopomer were
observed only in the case of the parent, 15N /ISN, and fully deuterated species.
Initial spectral searches were guided using the contraction o f the N-S distance in
HCN-HCN-SO 3 as an estimate to the change in the N-B bond distance. Spectral
patterns were identified as belonging to HCN—HCN-BF3 by the large number of
transitions characteristic of a symmetric rotor with three quadrupolar nuclei. Once the
parent species was located, initial searches for the H C N - H C I5N-BF3 isotopomer failed.
Returning to spectral predictions that were based on the expected complex geometry, it
became evident that the boron bound nitrogen is positioned almost precisely at the
center of mass of the complex. If the atom were exactly on the center o f mass,
substitution of this atom by the heavier ,5N isotope would have absolutely no effect on
the rotational constant as compared to the parent isotopomer. However, substitution by a
heavier atom decreases the frequency o f vibration, and the averaging o f the ground state
rotational constant over the zero point motion results in an increase in the effective
rotational constant. Returning to spectral searching, the transitions for the l5N substituted
species were readily located, with the H C I4N —H C 15N -n BF3 spectrum lying slightly
higher in frequency than H C l4N —H C l4N -n BF3.
217
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Results
The spectra of the isotopomers o f HCN—HCN-BF3 were all consistent with a
symmetric top with quadrupole coupling by either one, two, or three quadrupolar nuclei.
A spectrum of the J = 7
6 transition o f the parent isotopomer is shown in Figure 7.3
below. The observed frequencies for all four l3N substituted isotopomers are provided
in Table 7.1. The frequencies for these isotopomers were readily fit to the usual
symmetric rotor expression with one or two quadrupolar nuclei, as appropriate, viz.
v = 2(J"+1)[B-DjkK2] - 4Dj(J"+1 )3 + AE0
(1)
Here. AEq is the difference in hyperfine energies between the upper and lower states and
was adequately calculated via the usual first order treatment. [21] The other symbols
have their usual meanings. [21] Least squares fits o f the observed spectral frequencies
were earned out for the four l5N containing isotopomers, and the fitted spectroscopic
constants are given in Table 7.2.
\r.
u
-C
Urn
<
6333.5
6334
6334.5
6335
Frequency (MHz)
Figure 7.3. J = 7 <— 6 Transition o f HCI4N —HCl4N -n BF 3, where the splitting due to
ail three quadrupolar nuclei is apparent. Total collection time for this spectrum was
-47 s.
218
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 7.1. Transitions for 1SN substituted isotopomers o f HCN—HCN-BF3.
H C 1SN - H C '5N - " B F 3
J"
F"
J'
F
K
5
5
5
5
5
5.5
6.5
4.5
3.5
6
6.5
6
6
6
6
7.5
5.5
4.5
4.5
0
0
0
0
0
6
6
6
6.5
I
7.5
4.5
6
6.5
7.5
1
1
2
2
2
5
5
5
5
5
5
5
5
5
5
5
6
6
4.5
5.5
6.5
3.5
5.5
6.5
4.5
3.5
5.5
6.5
4.5
3.5
7.5
6.5
6
6
5.5
4.5
6
6
7.5
6.5
6
6
6
5.5
4.5
6
6
6
6
6
6
6
7
7
7
7
7
7
5.5
4.5
6.5
7.5
6.5
0
0
6.5
5.5
6
6
5.5
4.5
6
6
7.5
6.5
6
6
6
6
5.5
4.5
7
7
7
7.5
4.5
7
7
7
7
8.5
7.5
8.5
7.5
6.5
5.5
8.5
5.5
0.001
0.003
5340.885
5341.437
5341.414
0.002
0.003
-0.002
-0.001
0.001
-0.002
0.001
5341.437
5341.291
5341.216
5341.291
5341.052
5340.885
5341.018
5340.852
6231.673
6231.673
3
0
0
7
6
7.5
6.5
5341.512
5341.514
3
3
4.5
8.5
7.5
6.5
5.5
-0.001
-0.001
5341.216
j
7
7
7
7
5341.481
5341.481
2
5.5
5.5
8.5
7.5
Freq (MHz) Obs-Calc (MHz)
1
1
6231.695
6231.695
6231.595
6231.609
1
1
2
2
6231.630
6231.609
2
6231.423
6231.375
2
3
3
3
3
4
4
6231.375
6231.423
6231.008
6231.113
6231.095
6230.993
6230.487
6230.462
-0.003
0.002
-0.004
0.003
-0.002
0.002
0.002
0.003
0.003
-0.003
0.000
0.004
-0.005
-0.002
0.002
-0.004
-0.007
0.000
0.004
-0.001
-0.002
-0.005
0.009
219
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 7.1. continued.
HC15N -H C 15N -10BF3
J"
J’
F"
F
K
5
5
8
6
6
6
9
7
0
0
5
5
5
5
5
5
5
5
4
2
6
6
6
6
6
6
6
5
3
6
9
8
0
0
0
0
1
I
6
5
7
1
1
2
2
2
5
5
5
5
5
5
5
5
6
8
7
4
7
6
3
6
6
6
6
6
5
3
7
6
6
6
5
2
6
3
6
4
0
6
4
1
1
6
0
HCI5N -H C I4N -"B F3
J"
FI"
F"
J’
5372.992
0.010
5373.125
5372.813
-O.om
5372.671
5372.726
5373.056
5372.953
5372.973
5373.087
-0.008
-0.001
-0.007
7.5
7.5
6.5
6.5
5.5
5.5
8.5
6.5
7.5
6.5
6.5
4.5
0
0
5.5
4.5
8.5
7.5
5
5
5
5
5
5
3.5
3.5
6.5
6.5
6.5
5.5
4.5
3.5
7.5
6.5
5.5
6.5
6
6
6
6
6
6
4.5
4.5
7.5
7.5
7.5
6.5
5
5.5
6.5
6
6.5
0.000
0.009
0.002
-0.002
0.000
0.007
K.
5.5
6.5
6.5
5.5
3.5
6
-0.005
-0.008
0.009
-0.005
0.002
-0.002
F
6.5
6.5
5.5
5.5
4.5
4.5
6
6
6
6
6
5372.953
5372.973
5373.005
5373.037
5373.020
5372.863
5372.885
5372.885
FI'
5
5
5
5
5
5
7.5
Freq (MHz) Qbs-Calc (MHz)
0
0
0
0
Freq (MHz) Qbs-Calc (MHz)
5336.138
5336.138
5336.138
5336.020
5336.077
5336.138
0.000
0.000
-0.004
0.005
-0.007
0.007
6.5
7.5
0
0
1
1
1
I
5336.166
5336.138
5336.077
5336.020
5336.064
4336.108
0.003
-0.003
-0.004
-0.004
0.006
0.006
6.5
1
5335.983
-0.002
220
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 7.1.continued.
H C i5N -H C I4N -"B F3
J" F I” F" J’ FI'
5
5
5
5
5.5
3.5
5.5
5.5
5
6
6
6
6
4.5
7.5
7.5
6.5
6.5
6.5
6.5
6
6
6
6
6
5.5
5.5
4.5
4.5
7.5
6
6
7.5
7.5
4.5
8.5
7.5
8.5
6
6
6
6
6
6
6
7.5
7.5
6.5
6.5
5.5
5.5
4.5
7.5
6.5
7.5
6.5
6.5
4.5
4.5
6
4.5
3.5
6
6
4.5
2.5
6.5
4.5
3.5
8.5
6.5
7.5
7.5
6.5
5.5
6.5
6.5
5.5
6 6.5
6 4.5
6 6.5
6
6
7
7
7
7
7
7
6.5
5.5
8.5
8.5
7.5
7.5
7.5
7.5
7 6.5
7 6.5
7 5.5
7 5.5
7 8.5
7 8.5
7 8.5
7 8.5
7 8.5
F
K
Freq (MHz)
Obs-Calc (MHz)
5.5
3.5
7.5
5.5
1
1
2
2
5336.064
5336.064
-0.005
-0.004
5335.983
5335.983
4.5
9.5
7.5
8.5
7.5
7.5
6.5
7.5
6.5
6.5
5.5
9.5
2
5335.983
6225.430
6225.430
6225.430
6225.325
6225.451
6225.404
-0.001
-0.001
-0.003
0.000
8.5
9.5
7
7
7
7
7
7.5
7.5
6.5
6.5
5.5
8.5
7.5
8.5
9.5
7.5
5.5
5.5
7
5.5
4.5
0
0
0
0
0
0
0
0
0
0
1
1
2
2
2
2
2
2
2
2
2
6225.390
6225.065
6225.451
6225.430
6225.359
6225.325
6225.155
0.002
-0.003
0.005
0.004
0.004
-0.001
-0.002
0.004
-0.003
-0.003
0.002
-0.003
6225.047
6225.105
6225.206
6225.206
6225.142
6255.206
6225.047
-0.001
0.007
6225.155
0.001
0.002
0.000
-0.004
0.004
-0.004
221
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 7.1 continued.
HC14N - H C l5N - n BF3
J"
FI"
F"
J'
F I’
F'
K
6
6.5
7.5
7
7.5
8.5
0
5434.837
0 .0 0 2
6
6.5
5.5
7
7.5
6.5
0
5434.837
0 .0 0 2
6
5.5
6.5
7
6.5
7.5
0
5434.837
-0 . 0 0 2
6
5.5
6.5
7
6.5
6.5
0
5434.715
0.003
6
5.5
5.5
7
6.5
6.5
0
5434.865
0.009
6
4.5
3.5
7
5.5
4.5
5434.837
0.009
6
3.5
4.5
7
4.5
5.5
0
0
5434.865
0.005
6
6.5
7.5
7
7.5
8.5
1
5434.776
-0.004
6
6.5
6.5
7
7.5
7.5
I
5434.735
0 .0 1 2
6
5.5
6.5
7
6.5
7.5
1
5434.807
0.006
6
5.5
6.5
7
6.5
6.5
1
5434.683
6
5.5
4.5
7
6.5
5.5
I
5434.776
0.000
0.008
6
3.5
4.5
7
4.5
5.5
1
5434.776
0 .0 0 1
6
3.5
3.5
7
4.5
4.5
1
5434.735
-0.005
6
3.5
2.5
7
4.5
3.5
I
5434.776
0.009
6
6.5
6.5
7
7.5
7.5
2
5434.449
0.004
6
5.5
6.5
7
6.5
7.5
2
5434.688
0 .0 0 2
6
5.5
6.5
7
6.5
6.5
2
5434.598
0.003
6
5.5
5.5
7
6.5
6.5
2
5434.683
0 .0 0 1
6
5.5
6.5
7
6.5
5.5
2
5434.865
0.009
6
5.5
4.5
7
6.5
5.5
2
5434.683
-0.003
6
5.5
6.5
7
5.5
6.5
2
5 4 3 4 .4 4 9
0 .0 1 0
6
3.5
3.5
7
4.5
4.5
2
5 4 3 4 .4 4 9
0.006
6
5.5
6.5
7
6.5
6.5
3
5434.449
0.000
6
5.5
5.5
7
6.5
6.5
3
5434.464
0 .0 0 1
6
5.5
5.5
7
6.5
5.5
3
5434.598
0.004
6
6.5
5.5
7
5.5
6.5
3
5434.510
-0 . 0 0 1
6
4.5
3.5
7
5.5
4.5
3
5434.510
-0.003
6
3.5
4.5
7
4.5
3.5
3
5434.464
-0 . 0 0 1
7
7.5
8.5
8
8.5
9.5
6340.576
-0 . 0 0 1
7
7.5
7.5
8
8.5
8.5
6340.551
-0 . 0 1 2
7
7.5
6.5
8
8.5
7.5
0
0
0
6340.576
0 .0 0 1
7
6.5
7.5
8
7.5
8.5
6340.576
-0.004
7
6.5
6.5
8
7.5
7.5
0
0
6340.596
0 .0 0 2
Freq (M Hz) Qbs-Calc (M Hz)
222
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
h c
14n -
h c
15n - " b f 3
J"
FI"
F"
J'
F I’
F
K.
7
6
6
6
6
6
6.5
5.5
4.5
8
6.5
6.5
5.5
5.5
8.5
8.5
7.5
7.5
6.5
5.5
9.5
8.5
0
6
6.5
6.5
5.5
7.5
6.5
5.5
4.5
8.5
7.5
6.5
5.5
6.5
5.5
7.5
7.5
6.5
5.5
8.5
7.5
7.5
6.5
7.5
6.5
7.5
1
6.5
9.5
8.5
6.5
7.5
1
2
6.5
6.5
5.5
4.5
2
6
6
6
6
6
6
6
4.5
7.5
7.5
4.5
7.5
6.5
6.5
5.5
8.5
7.5
5.5
6.5
6
5.5
6.5
5.5
5.5
6
4.5
3.5
6
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
6.5
5.5
0
0
0
1
1
I
1
Freq (MHz) Obs-Calc (MHz)
6340.187
6340.535
6340.596
6340.576
6340.501
6340.467
6340.535
6340.501
6340.476
6340.501
6340.307
6340.346
6340.346
6340.299
-0.005
-0.003
0.002
-0.004
-0.010
-0.006
-0.001
0.004
-0.003
-0.009
2
6340.307
6340.237
-0.005
-0.011
-0.003
-0.001
-0.005
-0.004
2
6340.307
-
2
2
2
0.001
Table 7.2. Spectroscopic Constants for Isotopomers o f HCN|—HCN 2-BF 3.
Isotopomer
B(MHz)
HC,5N-HCi5N-'1BF; 445.1364(6)
Dj(kHz) DJK(kHz) eQq(B)
eQq(Nl) eQq(N2)
0.169(6) 4.97(1)
—
HCI4N-HCI5N-"BF3452.91479(7) 0.169*
—
2.509(33) -3.984(33)
—
HC15N-HCI4N-"BF, 444.6899( 1) 0.170(1) 5.03(2)
2.498(13) —
-3.994(22)
HCI5N-HCI5N-I0BF3447.7600( 1) 0.17*
5.047(85)
—
HCI4N-HCI4N-MBF3452.91(1)
0.17*
HCI4N-HCI4N-I0BF3455.09( 1)
0.17*
5.041(3)
2.509(20)
4.81(7)
—
DC14N-DC l4N-'1BF; 434.09( 1)
DCi4N-DC,4N-'0BF3436.66( 1)
0.17*
DC^N-HCN-1'BF3435.42( 1)
0.17*
HC,4N-DCI4N-"BF3450.90(1)
0.17*
*D; was fixed at this value in the rotational constant determination.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
The observed frequencies and relative intensities for all isotopomers containing three
quadrupolar nuclei are listed in Table 7.A1 in the Appendix to this chapter. Due to the
large number of transitions predicted in the case o f three coupling nuclei, attempts at
fitting the hyperfme structure for these six isotopomers were unsuccessful. This
difficulty was intensified due to the three fluorine atoms, as the spin-spin interaction
results in additional spectral splitting. For this reason, the rotational constants for
these isotopomers were estimated from the position o f the strongest transition, which
is expected to correlate with the K=0 transition in the absence of hyperfme. From the
spectral predictions, (obtained from both an internally written program and the Pickett
program [22]) the strongest hyperfme component was predicted to lie within 10kHz
(in the J= 7<—6 ) o f the K=0 transition in the absence o f hyperfme. The error bars
reported for these isotopomers in Table 7.A1 are chosen to encompass the uncertainty
in this approach.
Structure Analysis
The relevant structural parameters for the HCN-HCN-BF 3 complex are defined in
Figure 7.4, and are identical to those used in HCN-HCN-SO}.[5] As in the case of
HCN-BF3 and HCN—HCN-SO3, the possibility of large amplitude vibration o f the HCN
and BF3 subunits is accounted for by including the angles x, Yi and y> in the analysis.
Since the complex is a symmetric top, <x>=<Yi>=<Y2>=0- In the case of HCN-BF3, a
value of yeiT = cos'l<cos;Y>12 = 17.5 ± 0.2° was determined from the N quadrupole
coupling constant and Xcfr = cos' 1<cos2x > 1/2 = 13.1 ± 1.3° was determined from the B
coupling constant.
224
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Figure 7.4. Definition o f angles used to describe the structure of HCN—HCN-BF3 . yi
and Y; give the instantaneous deviations o f HCNi and HCN? from the equilibrium C3
axis of the complex. x is the analogous angle for the C3 axis of the BF3 . a measures the
distortion of the BF3 unit from planarity and is equal to the NBF angle at the equilibrium
geometry of the complex. R is the N-B distance and r is the length of the HCN—HCN
hydrogen bond.
As in the case of HCN-BF3, (and HCN—HCN-SO3 ) the H-C, ChN, and B-F bond
distances were fixed to those in free HCN [23] and BF3 [24], respectively. Preliminary
fits using the rotational constants reported in Table 7.2 confirmed the expectation that a
(NBF angle) and x (excursion o f the BF3 unit) were highly correlated and thus not
independently determinable from the rotational constants. For this reason, a was
allowed to float in the rotational constant fits while the value of x was varied, utilizing
the 13.1° value in HCN-BF3 as an upper limit [6], For 72, a Kraitchman analysis o f the
hydrogen and nitrogen coordinates gives 11(2)°, where the large error bar accounts for
the average rotational constants used for the deuterated species. A similar analysis could
not be carried out for yi since the inner nitrogen lies so close to the center o f mass o f the
complex. For this reason, the value ofysO 1°) was utilized as a conservative upper limit
for yi, which appears reasonable since the N-B bond is likely stronger than the N—H
hydrogen bond, and the inner HCN is constrained by binding partners on both sides.
This approach is similar to that utilized in the structure analysis o f the analogous
HCN—HCN-SO3 complex.
The preferred structural parameters were obtained from a series of non-linear least
squares fits in which R, r, and a were varied with y> fixed at 11° and yi and x
constrained to values representing the maximum and minimum values as discussed
above (0° and 11° for yt; 0° and 13.1° for
x)- The
fitted structural parameters for
HCN—HCN-BF3 are reported in Table 7.3, where the quoted uncertainties reflect the
total range o f values obtained from the series o f fits.
225
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Table 1 3 . Structural Parameters for HCN—H O -B F 3 .
Parameter
Value
R(N— B)
2.274(22)A
r(N2—H)
2.197(6)A
a(NBF)*
93.0(4)°
11(2)°
*b
a. Averaged value of two sets o f rotational constant fits.
b. Determined from double-substitution Kraitchman analysis.
The following equation derived from previous results for BF3 complexes with N
donors was utilized to provide a confirmation of the fitted value for a. [25]
R(BN)
= ( 1.580 A ) -(0.441 A ) log[9 cos2 a]
(2 )
R(BN) is the measured B-N bond distance and a (or its complement) is the N-B-F bond
angle. Using this equation, a value of 93.1(6)° is obtained for a, in near agreement with
the 93.0(4)° value obtained in the first series o f fits in Table 7.3. As can be seen from the
Table, the uncertainties in R and r are small, indicating that those parameters not well
determined from the rotational constants have little effect on the determination o f the
more salient structural features. The fitted structure o f the complex is shown in Figure
7.5 below.
2.274(22)A
Figure 7.5. Fitted Structural Parameters o f HCN—HCN-BF 3.
Finally, it is necessary to comment on the use o f rotational constants averaged
over hyperfme structure in the case of the six isotopomers with three quadrupolar nuclei.
As discussed above, the rotational constant determination was carried out by assigning
the most intense spectral feature to the K=0 transition, which was predicted to lie within
226
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
10 kHz (in the J = 7<—6 transition) from its corresponding transition in the absence of
hyperfme structure. The rotational constants were therefore assigned an error o f 10 kHz
in the rotational constant fits. This degree of uncertainty propagates as an error in the
fourth decimal place of a single structural parameter, thus the error bars reported in
Table 7.3 certainly exceed any degree of uncertainty entered by utilizing averaged
rotational constants.
Discussion
The structural and spectroscopic properties can be utilized to examine the
effect of a single near neighbor interaction on the partial bond in HCN-BF 3. The
structure and electronic properties o f the HCN—HCN-BF 3 complex are summarized
in Table 7.4 and compared to HCN-BF 3, the analogous HCN—HCN-SO 3 complex,
(HCN);, and (HCN)3.
Table 7.4. Structural and Electronic Properties for HCN—HCN-BF3 and Related
HCNrBF3a
R(N,-B) = 2.473(29) A
a(NBF) = 91.5(1.5)°
y, = 17.53(16)°
h c n 2 h c n , - s o 3c
R(N,-S) = 2.470(20) A
a(NSO) = 92.2(6)°
r(N:- H ) = 2.213(29) A
0
<>
11
&
eQq(N,) = -4.080(13)MHz
eQq(n B) = 2.731(36)MHz
eQq('°B) = 5.683(46)MHz
|i = 4.1350(73)D
HCN2 HCN,-BF3b
R(N,-B) = 2.274(22)A
0t(NBF) = 93.0(4)°
r(N2-H ) = 2.197(6)A
72 = 1 K2 )°
eQq(Ni) = -3.994(22)MHz
eQq(N2) = -3.984(33)MHz
eQq("B) = 2.509(20)MHz
eQq('°B) = 5.047(85)MHz
eQq(N,)=-3.882(15)MHz
eQq(N2)= -4.053( 15)MHz
(X= 8.640(19)D
y, = 13.7°
Y: = 9.0°
HCN, HCN2 HCNV
KN, —H) = 2.17 A
r(N 2—H) = 2.18 A
Yi = 12.6°
72 = 6 °f
eQq(N,) = -4.097(20) MHz
eQq(N:) = -4.440( 19) MHz
p. = 6.552(35)D
73 =
eQq(Ni) = -4.049(2) MHz
eQq(N2) = -4.251(2) MHz
li = 10.6(1)D
OO
On
0
HCN, HCN2d
r(N |-H ) = 2.230 A
(a) Ref. [6 ]. (b) This work, (c) Ref [5]. (d) Ref. [26]. (e) Ref. [27]. (f) Assumed value of
Ref. [27],
227
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
A comparison of the structural parameters o f HCN-BF3 and HCN—HCN-BF3
reveals a 0.199(36) A contraction of the N-B bond distance. This is an extraordinary
degree of bond contraction brought on by the addition of a single "solvent” molecule,
and represents the most striking example to date of microsolvation effects in partially
bonded systems. Indeed, the dative bond shrinks by an additional 0.092(46) A in
comparison to the analogous HCN-HCN-SO3 complex. [5] The changes in the N-B-F
bond angle are not as clear due to the large uncertainty in this angle in HCN-BF3,
however, some degree of widening of this angle is apparent. The N— H distance differs
from that in (HCN); [26] by only 0.033(6)A, which is consistent with the degree of
hydrogen bond contraction observed in (HCN)3. [27] Table 7.5 compares the structural
changes in HCN—HCN-BF3 to other complexes with the general HCN—HCN-Y
formula.
Table 7.5. Structural and Electronic Changes for Complexes with the General
Formula HCN HCN-Y.
Complex
HCN-HCN-BF'/
HCN-HCN-S03g
HCN-HCN-CO;h
HCN-HCN-HCF3h
HCN-HCN—HFh
HCN-HCN—HClh
A(N—Y)a A
A(N—H)b A
A(eQq(N;))°
A(eQq(N,))d
0.199(36)
0.107(21)
0.052
0.042
0.043
0.062
0.033(6)
0.017(29)
0.004
0.030
0.069
0.054
0.086(26)
0.096(16)
-0.280(15)'
0.113(39)
0.044(25)
0.022(20)
e
e
0.003(6)’
0.037(20)
e
e
(a.) (distance in respective dimer)-(distance in trimer) (b.) (distance in (HCN);)(distance in trimer) (c.) (value in dimer (MHz)) - (value in trimer (MHz)) (d.) (value in
(HCN);:Ref. [26])-(value in trimer) (e.) value not measured in trimer. (f.) This work, (g.)
Ref. [5]. (h.) Ref. [28]. (i.) calculated from difference in value in HCN-CO;: Ref. [29]
and HCN—HCN-CO;: Ref. [28] (j.) calculated from difference in value in HCN-HF:
Ref. [30] and HCN-HCN-HF: Ref. [28],
The changes reported in Table 7.5 are most dramatic when the N—Y bond can be
described as partially formed prior to the addition of the second HCN unit From Table
7.5. the evidence suggests that when the Y in the N-Y bond is also hydrogen, the ratio
A(N— Y)/ A(N— H) is closer to unity. This is sensible if the interaction in the trimer can
be dissected as either a perturbation on (HCN); by the addition o f an acid unit or a
228
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
perturbation on an HCN-acid molecule by a second HCN. In the case where the trimeric
species is joined by two hydrogen bonding interactions, the two perturbations would
seemingly be of similar magnitude. This is clearly demonstrated in the case of (HCN)3For the partially bonded systems and the CO: complex, however, the evidence suggests
that a larger perturbation on the HCN— (B, S, C) interaction is brought about by the
remote HCN unit than the opposite. Although the ratio of the changes is largest for the
HCN-HCN-CO 2 species, the largest changes in the N-Y interaction occur when Y is a
Lewis acid. This provides evidence that Lewis acid-base complexes indeed exhibit an
extreme sensitivity to remote interactions, which is heightened in comparison to
Bronsted Lowry acid-base pairs.
The nitrogen and boron quadrupole coupling constants are consistent with an
increased interaction at the dative bond site as well as a perturbation at the hydrogen
bond site. Both nitrogen and the boron coupling constants are reduced in magnitude in
the trimer as compared to HCN-BF3 and (HCN):. The magnitude o f this reduction for
eQq(N:) is in near agreement with that observed for HCN—HCN-SO3, while the
reduction in eQq(N 1) appears larger. Due to the larger than normal error bar on eQq(N 1),
however, it is difficult to draw any conclusions regarding the change in the magnitude of
this constant between (HCN): and HCN—HCN-BF3 . Nevertheless, the reduction at both
sites opposes that expected based on a decreased vibrational amplitude and suggests
some degree of electronic rearrangement in HCN—HCN-BF3 as compared to HCN-BF3 .
While an analysis of the differences in quadrupole coupling constants provides
some degree of insight into the change in the electric field around a particular nucleus,
the details concerning the migration o f charge are difficult to ascertain. O f additional
interest are the energetic changes accompanying the formation o f the donor acceptor
bond, specifically a decomposition o f these changes into electrostatic, deformation,
charge transfer, and polarization terms. Therefore, in order to fully examine the
energetic and electronic changes that accompany the addition o f a microsolvent to a
partially formed bond, the contributions to the energy and dipole moments were
calculated at using the BLW-ED method developed by Mo, Gao, and PeyerimhofF. [13]
229
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
The
B L W -E D
calculations were carried out at the HF level using Gaussian 98
[31], while corrections to the final energy were determined at the MP2 level using the 631G(2df,2pd) basis set. The energy was decomposed into five terms,
A E „,
and
A E corT.
The
AEdist
A E dlst, A E ^ , AEpoi,
term represents the contribution to the total energy arising
from the deformation o f the monomer units in the complex. This term always represents
a positive contribution to the energy. The second term, AEes represents the electrostatic
energy. AEpoi represents the energy due to electronic polarization and is calculated as the
difference in energy between the block-localized wavefunction and the antisymmetrized
product of the wavefunctions for the two monomers at the complex geometry. [13] The
AEa term represents the change in energy arising from intermolecular charge transfer
and is computed from the difference in energy between the Hartree-Fock wavefunction
and the block-localized wavefunction, correcting for
B S S E . A E Corr
is essentially the
difference in the interaction energy between the HF and MP2 levels of theory. In the
case of HCN—HCN-BF3, the molecule was divided at the dative bond site, since our
interest was in the energetic and electronic changes occurring at the N— B bond. Table
7.6 summarizes the results of the calculations.
Table 7.6. Results of BLW-ED calculations for HCN-BF3 and HCN HCN-BF3
HCN-BF3*
1.15
-0.77
-1.89
- 1.11
-1.47
-4.09
0.804
0.119
4.568
Difference
HCN •HCN-BF3b
2.57
1.42
AEdist (kcal/mol)
-0.57
-0.20
AEd (kcal/mol)
-3.07
-1.18
AEpoi (kcal/mol)
-2.06
-0.95
AEct (kcal/mol)
-1.76
-0.29
AEcorT(kcal/mol)
-4.89
0.8
AEWi (kcal/mol)
1.101
0.297
A|ipoi (D)
0.179
0.060
APct(D)
9.251
4.683
M-tot ( D )
a.) A refers to the difference between the HCN-BF3 complex and the HCN and BF3
monomers, b.) A refers to the difference between the HCN—HCN-BF3 complex and
HCN-H CN and BF3 units.
230
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
From the Table, the largest energetic differences between the dimer and trimer
appear to be in the deformation, polarization, and charge transfer energies, while the
largest change to the total dipole moment arises from polarization effects. This result
confirms the notion obtained from an analysis of the changes in the nuclear quadrupole
coupling constants; i.e. that electronic rearrangement indeed occurs with the addition of
the second HCN unit. This reorganization of electron density in the trimeric species
seems to arise from a combination o f polarization and charge transfer effects, with the
larger contribution arising from electronic polarization. This is consistent with the
picture in HCN-HCN-SO3, where it was demonstrated that the largest contribution to
the induced dipole moment arose from polarization effects. [5] In order to visualize
these effects, electron density difference (EDD) maps were generated for both HCN-BF3
and HCN-HCN-BF3, and are shown in Figures 7.6 and 7.7, respectively.
Figure 7.6. Electron difference density (EDD) map for HCN-BF3 complex. Left;
Polarization (contour 0.001 e/auJ), Right: Charge-transfer (contour 0.0005 e/auJ) — =
gain of electrons.
= loss of electrons.
231
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 7.7. Electron difference density (EDD) map for HCN—HCN-BF 3 complex.
Top: Polarization (contour 0.001 e/au^), Bottom: Charge-transfer (contour 0.0005
e/auJ) — = gain of electrons.
= loss o f electrons.
The EDD maps have a similar appearance for both the dimeric and trimeric species. In
both cases, electron flow is from the nitrogen to the boron arising from polarization and
charge transfer. Charge also migrates from the boron to the fluorine atoms as a result of
electronic polarization. Although the differences in the degree of electron flow between
HCN-BF3 and HCN—HCN-BF3 are difficult to ascertain from the diagrams, the
information provided in Table 7.6 along with the Figures paints a clear picture o f the
dominant contributions to the charge flow. Clearly, from the magnitude of the bond
contraction (0.199(36) A) upon addition of the remote HCN, additional charge migration
into the bonding region has occurred. From the BLW-ED analysis, it is clear that the
major contribution to this added electron density in the dative bonding region is due to
electronic polarization, and a smaller degree can be attributed to charge transfer. It is
reassuring that the map in Figure 7.7 illustrates very little change in the hydrogen
bonding region, consistent with the picture in HCN—HCN-SO 3.
232
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
In summary, the HCN—HCN-BF3 complex demonstrates a remarkable degree o f
bond contraction in comparison to the dimeric species HCN-BF3 . The bond contraction
is on the order of 20% of the difference in the N-B bond distance between the gas and
solid phases. This in agreement with the conclusion by Hankinson et al. who contended
that nearly 30% of the total lattice energy for partially bonded systems can be attributed
to first near neighbor interactions. [12] This bond contraction is also consistent with that
previously reported for the HCN—HCN-SO3 complex, in which case there was no solid
phase data for comparison. [5] This situation makes partially bonded molecules very
sensitive probes of their local environment and suggests their use as test systems for
evaluating microsolvation effects. Indeed, these systems represent an unusual and
challenging case for solvation models, where the separation between inter- and intrainteractions is not distinct.
Conclusions
1. The structure o f the HCN|—HCN2-BF3 complex has been determined using
microwave spectroscopy. The motivation for this study was to perturb the partially
formed donor-acceptor bond between N; and B from its value in gas phase HCN-BF3.
Indeed, the contraction of the dative bond in comparison to HCN-BF3 is 0.199(36)A,
which is 0.092(46) A greater than that observed in the analogous HCN—HCN-SO3
complex. The N r H distance, on the other hand, remains unperturbed in comparison to
(HCN);, which is consistent with HCN-HCN-SO 3 .
2. A comparison of the nitrogen quadrupole coupling constants between HCNBF;., HCN—HCN-BF3, (HCN); and (HCN)3 reveals some electronic reorganization in
HCN-HCN-BF 3. This restructuring has been analyzed in detail using the BLW-ED
method. [13] The contributions to the total energy as well as the dipole moment o f the
complex have been decomposed into electrostatic, deformation, polarization, and charge
transfer terms. This analysis has revealed that the major contribution to the induced
dipole moment of the complex arises from electronic polarization, while the major
contribution to the binding energy arises from a sum o f deformation, charge transfer,
233
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
and polarization effects. The binding energy of HCN—HCN-BF3 is 0.8 kcal/mol greater
than HCN-BF3. This additional degree of stabilization appears to arise from further
charge migration into the dative bonding region, hence the measured contraction in the
N-B bond.
3.
The changes in structure and bonding resulting from the addition o f a single
solvent molecule provides further evidence that partially bound systems offer unusually
sensitive probes of microsolvation effects. The bond contraction observed here upon the
addition of a single solvent molecule accounts for nearly 20% o f the difference in the NB bond distance in HCN-BF3 between the gas and crystalline phases. This value is
astounding and further compounds the contention o f Hankinson et al. that nearly 30% of
the total lattice energy in these systems can be accounted for by first near neighbor
interactions. [ 12]
Acknowledgement. This work is supported by the National Science Foundation, and
the donors of the Petroleum Research Fund, administered by the .American Chemical
Society. We are grateful to Dr. Y. Mo for his assistance with the BLW-ED calculations.
234
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References:
1. See for example: Solvent Effects and Chemical Reactivity; Tapia, O., Bertran, J.,
Eds.; Kluwer: Dordrecht, 1996 and references therein.
2. Cramer, C.J.; Truhlar. D.G. Chem. Rev. 1999, 99, 2161.
3. Leopold, K.R. in Advances in Molecular Structure Research, Hargittai, M.;
Hargittai, I. Eds., JAI Press: Greenwich CT, 1996, Vol. 2, p. 103 and references
therein.
4. Leopold, K.R.; Canagaratna, M.; Phillips, J.A. .4cc. Chem. Res. 1997, 30, 57 and
references therein.
5. Fiacco, D.L.; Hunt, S.W.; Leopold, K.R. J. Phvs. Chem. A 2000,104, 8323.
6 . Reeve, S.W.; Bums, W.A.; Lovas, F.J.: Suenram, R.D, Leopold, K.R. J. Phvs.
Chem. 1993, 97, 10630.
7. Bums, W.A.; Leopold, K.R. J. Am. Chem. Soc. 1993,115, 11622.
8 . Jurgens-Lutovsky, R.; Almldf, J. Chem. Phys. Lett. 1991, / 76, 263.
9. Jiao. H.; Schleyer. P.v.R. J. Am. Chem. Soc. 1994, 116. 7429.
10. Iglesias, E.; Sordo, T.L.; Sordo, J.A. Chem. Phys. Lett. 1996, 248, 179.
1 1. Cabaleiro-Lago, E.M.; Rios, M.A. Chem. Phys. Lett. 1998, 294, 72.
12. Hankinson, D.J.; Almlof, J.; Leopold, K.R. J. Phys. Chem. 1 996,100, 6904.
13. Mo. Y.; Gao. J.; Peyerimhoff, S.D. J. Chem. Phys. 2 0 0 0 ,112, 5530.
14. Balle, T.J.: Flygare, W.H. Rev. Sci. Instrum. 1981, 52, 33.
15. (a) Phillips, J.A.; Canagaratna, M.; Goodffiend, H.; Grushow, A.; Almlof, J.;
Leopold, K.R. J. Am. Chem. Soc, 1995, 117, 12549. (b) Phillips, J.A.; Ph.D. Thesis,
University o f Minnesota, 1996.
16. Legon, A.C.; Wallwork, A.L.; Rego, C.A. J. Chem. Phys. 1990, 92, 6397.
17. Gillies, C.W.; Gillies, J.Z.; Suenram, R.D.; Lovas, F.J.; Kraka, E.; Cremer, D. J. Am.
Chem. Soc. 1991, 113,2412.
18. Gutowsky, H.S.; Chen, J.; Hajduk, P.J.; Keen, J.D.; Emilsson, T., J. Am. Chem. Soc.
1989, 111. 1901.
19. Emilsson, T.; Klots, T.D.; Ruoff, R.S.; Gutowsky, H.S. J. Chem. Phys. 1990, 93
6971.
235
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
20. Canagaratna, M.; Phillips, J.A.; Goodfriend, H.; Leopold, K.R., J. Am. Chem. Soc.
1996,118, 5290.
21. Townes, C.H.; Schawlow, A.L. Microwave Spectroscopy, Dover: New York, 1975.
22. Picket, H. M. J. Mol. Spec. 1991, 148, 371.; http://spec.jpl.nasa.gov/
23. Winnewisser, G.; Maki, A.G.; Johnson, D.R. J. Mol. Spectrosc. 1971, 39, 149.
24. Brown, C.W.; Overend, J. Can. J. Phys. 1968, 4 6 ,977.
25. Bums. W.A.; Phillips, J.A.; Canagaratna. M.; Goodfriend, H.; Leopold, K.R. J.
Phys. Chem. A 1999, 103, 7445.
26. (a) Legon. A.C.; Millen, D.J.; Mjoberg, P.J. Chem. Phys. Lett. 1977, 47, 589. (b)
Buxton. L.W.; Campbell, E.J.; Flygare, W.H. Chem. Phys. 1981, 56, 399. (c)
Brown, R.D.: Godfrey, P.D.; Winkler, D.A. J. Mol. Spectrosc. 1981, 89, 352. (d)
Campbell, E.J.; Kukolich, S.G. Chem. Phys. 1983, 76, 225.
27. Ruoff. R.S.; Emilsson, T.; Klots, T.D.; Chuang, C.; Gutowsky-, H.S. J. Chem. Phys.
1988, 89. 138.
28. Ruoff. R.S.: E Emilsson, T.; Klots, T.D.; Chuang, C.; Gutowsky, H.S. J. Chem.
Phys. 1989, 90, 4069.
29. Leopold, K.R.; Fraser, G.T.; Klemperer, W. J. Chem. Phys. 1984, 80, 1039.
30. Legon, A.C.; Millen, D.J. Chem. Rev. 1986,86, 635.
31. Frisch, M.J.; Trucks, G.W.; Schlegel, H.B.; Scuseria, G.E.;
Robb, M.A.;
Cheeseman, J.R.; Zakrzewski, V.G.; Montgomery, J.A., Jr.,; Stratmann, R.E.;
Burant, J.C.; Dapprich, S.; Millam, J.M.; Daniels, A.D.; Kudin, K.N.; Strain, M.C.;
Farkas, O.; Tomasi, J.; Barone, V.; Cossi, M.; Cammi, R.; Mennucci. B.; Pomelli,
C.: Adamo, C.; Clifford, S.; Ochterski, J.; Petersson, G.A.; Ayala, P.Y.: Cui, Q.;
Morokuma, K.; Malick, D.K.; Rabuck. A.D.; Raghavachari, K.; Foresman, J.B.;
Cioslowski. J.; Ortiz, J.V.; Baboul, A.G.; Stefanov, B.B.; Liu, G.; Liashenko, A.;
Piskorz, P.; Komaromi, L; Gomperts, R.; Martin, R.L.; Fox, D J.; Keith, T.; AlLaham, M.A.; Peng, C.Y.; Nanayakkara, A.; Challacombe, M.; Gill, P.M.W.;
Johnson, B.; Chen, W.; Wong, M. W.; Andres, J.L.; Gonzalez, C.; Head-Gordon,
M.; Replogle, E.S. and Pople, J.A.
Gaussian 98, Revision A.9, Gaussian, Inc.,
Pittsburgh PA, 1998.
236
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Appendix to C hapter 7.
Table 7.A1. Transitions for Isotopomers of HCN— HCN-BF3 with Three
Q uadupolar Nuclei.
HCUN-HCI4N -MBF»
J = 5 <— 1
Freq (MHz) Intensity Freq (MHz)
Freq <MHz)
Intensity
4524.442
7.0
4524.471
14.0
4524.506
9.1
4524.513
4524.546
12.8
108.1
97.4
79.9
4524.555
4524.584
4524.635
13.5
J = 6 4—5
Freq (MHz)
Intensity
5429.240
11.3
5429.270
3.8
5429.298
8.0
5429.335
19.4
5429.349
33.0
24.4
5429.363
5429.380
29.1
5429.388
19.5
6334.114
6334.046
6334.017
6334.003
6333.979
69.2 Freq (MHz) Intensity
7238.984
37.6
146.2
7239.004
144.8
89.5
6333.972
6333.953
6333.943
6333.907
6333.855
6333.845
6333.814
6333.789
70.5
20.7
6333.482
6333.460
6333.443
Freq (MHz)
Intensity
6334.314
29.3
6334.294
39.2
6334.279
712.6
6333.422
6333.405
6333.307
51.8
73.2
49.9
43.1
7239.022
7239.050
7239.059
7239.084
135.5
21.2
21.0
14.2
7239.104
7239.121
33.3
8.4
6333.732
6333.720
6333.559
6333.545
6333.527
6333.517
5429.443
5429.464
T
461.8
55.6
57.0
283.3 J = 8 <- 7
21.6
7.1
O'
6334.168
6334.124
6334.088
6334.065
5429.393
5429.410
II
30.7
Intensity
7238.931
7238.965
7238.984
30.8
64.8
83.7
257.2
23.5
31.6
83.2
45.7
37.6
15.9
6.8
4.3
3.8
6.0
9.4
1.2
3.8
4.1
6334.270
6334.247
506.5
226.7
6333.236
6333.218
6333.341
6334.233
6334.203
237.8
311.9
6333.322
6334.146
4.3
1.2
8.3
5.6
6.4
3.7
18.9
6334.185
241.6
6334.139
28.1
237
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 7.A1. continued.
HCI4N-HCI4N - 10BF3
J=6
5
J=7
6
Freq (MHz) Intensity Freq (MHz)
5460.495
0.5
6370.514
5460.574
0.9
6370.543
5460.590
2.6
6370.571
5460.601
1.6
6370.596
5460.633
1.5
6370.648
5460.651
2.1
6370.659
1.4
5460.672
6370.670
5460.712
5460.770
1.1
8.1
5460.796
5460.816
24.6
5460.827
5460.838
11.6
8.2
5460.920
27.1
2.8
5460.862
5460.887
23.1
37.8
5460.898
5460.936
20.9
1.8
3.0
4.0
5460.960
5460.973
5460.986
5461.004
2.3
1.1
Intensity
2.3
3.7
4.0
8.5
5.0
9.1
8.2
6370.692
6370.763
18.3
3.8
2.3
6370.775
6370.793
6370.817
6370.826
4.4
5.3
4.3
6.3
6370.868
6370.879
18.3
8.9
6370.900
6370.911
6370.924
6370.971
20.1
5.4
7.6
9.8
6370.985
6371.000
6371.014
4.2
5.2
6371.077
1.9
238
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 7.A1. continued.
DCUN-DCUN-"BF? DCu N-DClJ n -,wb f 3 DCUN-HCUN-UBF', HCUN-DCUN-mBFi
jJ=6
5
J = 7 <— 6
J = 6 <- 5
J=6
5
t
i
IFreq (MHz) Intensity Freq (MHz) Intensity Freq (MHz) Intensity Freq (MHz) Intensity
T1
4.2
; 5208.869
23.4
5410.597
6112.982
6.3
5224.708
5208.898
2.1
14.9
6113.005
2.5
5410.619
3.3
5224.633
5208.924
12.5
6112.960
2.7
15.2
5224.537
18.4
5410.655
27.1
i
5208.946
18.9
6112.936
2.7
5410.667
5224.779
20.4
1 5208.956
20.3
7.9
4.1
5410.678
6112.913
5224.797
23.8
9.1
; 5208.993
6112.905
7.2
3.9
5410.706
5224.860
14.3
5209.008
18.5
6112.896
5410.514
7.2
1.5
5.3
5224.825
| 5209.029
5.1
6112.881
5410.474
7.3
3.2
2.8
5224.882
5209.054
1.2
5410.534
6112.850
4.8
5.7
2.7
5224.916
J = 7 <- 6
6112.841
6.8
6.2
5410.556
1.7
5224.931
6076.967
6076.990
6077.010
: 6077.024
6077.040
6077.066
6077.1 14
6077.144
6076.955
6076.944
6076.913
6076.870
6076.826
; 6076.802
6076.766
■ 6076.706
1 6076.673
| 6076.648
| 6076.606
6076.594
6076.567
; 6076.556
13.7
25.3
70.7
228.1
85.3
106.1
109.5
7.0
4.7
6.5
30.0
30.1
6112.831
6112.816
6112.782
6112.771
6112.761
6112.756
6112.714
6112.703
6112.688
6112.723
6112.663
6112.641
17.8
16.4
6113.037
6113.047
16.9
7.5
2.8
6.0
2.7
6113.062
6113.092
6113.117
3.3
1.9
2.0
6113.129
6113.160
6113.179
6113.199
5.4
5.0
10.7
10.1
10.1
9.1
17.8
13.2
9.6
9.0
6.1
6.9
13.1
11.0
5.6
9.4
10.2
10.2
8.1
8.7
5224.942
5224.975
5224.991
5224.998
5224.022
J = 7 <r—6
6095.560
6095.546
6095.400
6095.430
6095.446
6095.465
6095.692
6095.721
6095.731
6095.753
6095.672
6095.688
6095.710
13.1
7.5
10.1
7.6
1.6
8.0
1.1
4.2
3.3
3.2
3.4
8.8
6.2
6.2
12.0
4.9
4.2
5410.486
1.0
5410.415
5410.443
5410.385
5410.363
5410.732
5410.747
2.6
4.3
3.1
3.9
22.3
7.3
J =7«- 6
6312.344
6312.356
7.3
12.7
6312.672
6312.244
6312.294
6312.335
6312.394
6312.405
6312.416
6312.435
4.8
7.9
239
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
11.6
8.8
6.5
7.6
6.1
12.9
14.8
17.0
A p pendix A. Unassigned Transitions dependent on H (D bO and HlDl-’SO.t-
H;Q-H:S 04 triplet
v(MHz)
I
3631.183
3638.606
41.1
109.3
51.6
72.8
3645.238
7195.482
7261.196
1146.5
34.0
7268.721
7272.810 165.0
7272.893 192.0
7275.971 1710.0
7289.272 1226.0
7317.157 428.4
10863.195
10888.869
10906.276
10906.567
10910.856
10922.640
10930.901
DiO-DjSOg triplet
I
v(MHz)
3590.637
3590.662
3600.561
3609.851
7180.203
7199.883
7218.558
10717.224
H:0-HDS0g triplet
2.0
1.1
6.4
0.8
781.0
2195.9
651.0
3257.4
10767.542 128.2
10796.700 313.1
v(MHz)
I
7254.839
122.90
7269.669
7269.681
7238.840
7238.853
10855.606
10855.612
10879.379
71.70
34.80
10901.736
3619.938
3627.989
354.6
4157.6
788.3
687.6
6000.0
270.0
3635.376
41.80
10.20
5.90
17.90
1110.80
75.00
3.20
8.40
1.60
302.1
14513.042 11.1
14542.025 13.7
14568.926 3.0
240
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
H ;S 0 .-H ;0
v(MHz)
4344.476
4344.309
6560.038
6563.565
6879.426
7064.631
7222.877
7222.888
7393.594
7410.770
7424.272
7430.264
7436.356
7442.1 15
7456.396
7865.192
7945.705
8585.281
8598.039
8600.154
8602.455
8610.612
8617.606
8619.281
8624.509
8621.992
8625.779
8626.653
8627.134
8628.124
8629.887
8632.746
8637.084
1
48.2
15.1
40.2
65.8
103.4
80.0
268.1
162.7
83.7
6.6
558.8
11.8
41.8
2.1
162.2
37185.5
93.9
2378.4
80.2
623.6
74.1
3466.2
1796.0
85.7
4092.3
24992.0
29384.9
3486.4
32214.6
2899.4
12012.7
676.7
873.9
v (M H z )
I
8645.272
9.3
8652.050 297.8
8656.305 61.6
8658.742 66.9
8659.973 38.0
8660.819 55.1
8661.283 72.3
8662.248 28.8
8663.636 439.0
8663.778
13.4
8663.949
12.4
8687.604
9.6
8687.430
14.2
8687.407
5.8
8724.211
24.0
8743.869 589.6
13.9
8744.115
8755.336 281.0
8760.440 147.3
8766.457
8.0
8773.373
7.2
8774.547 33.0
8783.560
4.0
8783.749 65.1
8784.055 56.5
8784.242 21.1
8786.015 461.8
8790.113
16.3
8845.959
1.7
8845.975
3.5
8854.114
19.6
8862.113 33.0
8866.009
5.9
8870.308 505.8
v (M H z )
8870.159
8877.824
8884.910
8888.397
8893.718
8894.306
8894.362
8982.748
9011.654
9014.810
9022.364
9036.822
9044.630
9056.420
9064.497
9075.398
9084.819
9089.910
9090.079
9093.801
9110.463
9119.119
9129.982
9130.444
9130.451
10144.457
10222.859
10233.909
10304.447
10304.438
10586.429
10588.038
10597.319
10598.928
I_
32.7
182.7
31.8
13.8
224 2
32.0
60.3
6.7
69.9
13.7
10.5
25.3
2814.9
21.8
7274.3
740.4
57.0
221.0
180.0
904.9
2079.2
12.1
30.7
65.0
21.0
2339.9
58.0
60.5
51.5
15.6
708.8
695.8
1439.1
801.9
v (M H z )
I
10599.684
10632.229
10671.069
10717.224
10745.695
10768.893
10785.549
10785.829
10823.779
10828.112
10930.901
10964.555
10965.835
10970.513
10982.278
10987.822
10987.975
11001.233
11005.498
11010.429
11023.809
13937.431
13937.449
13937.399
14542.025
14513.042
14568.926
406.7
310.5
578.3
3257.4
180.8
96.9
2627.2
883.0
4.8
6.5
44.8
19200.7
131.2
86.9
28.5
145.2
63.7
444.6
59.0
53.0
8173.8
j .j
2.3
1.5
13.7
11.1
3.0
241
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
D ;0-D ;S04
v(MHz)
3988.811
3988.822
3892.827
3892.849
4091.427
I
2.3
2.9
2.6
2.6
46.6
6567.522 12.2
6640.078 27.0
6693.035 203.5
6694.961 40.8
6694.991 21.7
6784.474
6865.263
6865.363
6865.384
6865.426
6865.540
6947.401
7479.334
7486.854
7487.423
7487.439
7556.722
7556.756
7556.803
7556.830
7621.832
7643.757
7648.864
7664.870
7664.877
7664.887
7664.912
25.0
22.1
360.9
1413.0
47.7
222.1
30.0
192.8
1365.6
16.8
44.4
134.3
370.0
30.2
30.3
162.6
17.0
1097.8
18.8
19.4
38.5
6.7
v(MHz)
I
v(MHz)
I
v(MHz)
I
v(MHz)
I
7671.983
7674.966
8038.297
8038.306
8038.286
8058.152
8058.165
8058.182
8147.354
8162.740
8162.747
8162.765
8162.793
8163.710
8163.733
8174.698
8181.569
8181.600
8185.514
8185.541
8185.492
8187.527
8187.511
8187.550
8188.844
8188.866
8188.902
8188.915
8188.938
8190.094
8191.201
8191.230
8194.006
12.0
16.2
42.5
32.9
21.1
7.7
13.1
12.7
51.0
14.6
16.5
29.3
22.6
33.0
12.0
170.2
246.6
6.3
153.4
197.7
44.9
10.6
214.2
142.3
176.3
304.1
62.4
243.0
35.5
23.8
61.0
268.9
52.5
8194.027
8195.475
8198.522
8198.544
8205.402
8205.412
8215.360
8275.886
8275.862
8429.410
8429.425
8429.433
8454.145
8470.648
8472.455
8478.630
8718.047
8746.076
8746.093
8746.126
8746.148
8754.906
8754.951
8754.970
8754.993
8754.956
8770.285
8770.322
8770.359
8770.371
8772.439
8787.487
8827.646
17.2
52.4
22.5
44.8
6.7
13.7
11.0
52.7
21.2
12.1
9.3
6.2
863.7
4534.5
94.9
543.8
15.8
92"> 2
8846.082
8846.092
8846.098
8861.402
8861.439
8916.946
8916.957
8916.967
9660.049
9695.942
9716.877
9798.265
9798.292
9815.468
9815.438
9815.421
9817.237
9818.996
9819.022
9819.070
9819.117
9819.153
9819.161
9819.190
9997.476
9997.492
10010.291
10013.818
10016.820
10016.846
10044.242
10220.791
10220.812
32.0
17.6
16.3
159.3
31.7
11.5
5.7
7.9
50.7
282.1
7.8
396.0
397.3
103.7
9.4
9.1
105.4
20.1
26.3
19.0
18.7
30.4
18.9
21.1
10316.347
10316.374
10366.755
10366.790
10456.394
10516.563
10523.880
10523.906
10523.927
10523.937
10547.864
13289.744
13289.705
13269.223
13269.267
28.0
155.0
16.0
42.7
64.4
16.6
5.0
32.0
5.0
3.5
36.3
2.6
1.3
49.1
29.5
1799.3
2692.9
429.2
3.2
5.5
4.4
2.6
7.8
189.5
3511.3
41.9
46.8
6.2
15.8
8.1
11.1
12.8
2”* "*
26.0
19.6
59.2
22.9
62.8
11.1
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
M ixed isotopomers
v(MHz)
I
v(MHz)
I
v(MHz)
I
v(MHz)
I
6801.213
6932.496
6932.512
6941.859
6950.179
6962.457
6987.394
6987.656
6993.856
7006.657
7006.688
7010.315
7025.814
7025.830
7025.854
7029.796
7067.964
7073.922
7074.039
7074.174
7074.291
7084.136
7084.159
7084.219
7084.246
7085.406
70S8.830
7090.021
7092.041
7092.257
7092.307
7095.086
7095.120
7096.541
22.1
93.9
29.4
16.4
30.5
18.5
917.0
174.9
22.1
18.4
105.2
59.4
26.2
9.3
4.9
11.5
26.5
41.2
21.7
32.2
6.6
12.4
17.0
51.4
39.5
181.7
8.8
5.8
16.8
28.8
133.6
2.8
5.4
7.2
7096.567
7103.601
7138.505
7138.521
7138.549
7139.016
7139.357
7152.337
7152.323
7154.206
7154.230
7154.429
7154.305
7154.323
7154.330
7155.485
7166.377
7180.198
7180.209
7186.439
7192.943
7192.964
7193.344
7193.715
7197.453
7197.470
7200.508
7201.297
7203.057
7203.073
7203.087
7203.096
7205.117
7208.790
31.3
16.9
16.5
10.2
8.7
6.2
21.8
63.2
44.0
14.5
4.2
7.8
5.1
15.8
16.8
19.2
6.9
28.1
14.7
70.3
31.7
75.1
119.7
34.9
77.4
11.0
31..6
20.0
18.6
25.6
77.7
20.0
123.8
21.1
7210.685
7210.722
7215.725
7229.461
7229.495
7237.632
7241.068
7252.237
7252.253
7252.281
7252.345
7252.358
7252.374
7252.386
7257.693
7271.226
7867.520
7867.527
7867.537
7867.541
8225.309
8488.904
8503.581
8503.605
8506.314
8519.461
8519.935
8519.967
8553.358
8553.382
8561.912
8575.794
8575.774
8727.868
24.5
8.6
12.5
7.9
5.2
13.5
34.1
4.5
27.7
23.0
13.7
17.3
8.5
13.3
68.7
32.7
5.9
4.0
5.5
4.0
3381.5
103.2
29.9
8.3
46.4
12.9
26.3
11.7
12.8
60.8
5.0
19.5
6.5
6.0
8727.884
10414.427
10414.450
10414.495
10414.500
10414.522
10414.551
10414.575
10414.588
10454.378
10468.257
10468.323
10474.753
10485.312
10486.091
10494.773
10494.778
10494.914
10505.277
10505.320
10505.377
10510.663
10510.676
10510.684
10510.691
10523.073
10523.100
10523.115
10545.518
10545.542
10545.559
10545.586
10545.606
10545.670
3.7
2.8
6.1
4.2
11.7
16.2
0.8
11.4
9.3
3.2
172.7
8.4
30.2
">T ^
68.1
19.9
4.5
3.9
23.3
31.8
179.5
120.6
60.0
53.9
55.3
15.0
4.7
5.9
3.1
37.5
4.0
10.6
95.1
2.6
243
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
M ixed Isotopomers continued.
v(MHz)
I
10546.468
10554.388
10547.862
10567.469
10567.508
10571.691
10595.010
10595.066
10595.093
10609.682
10609.900
10628.998
10629.040
10629.976
10630.017
10630.026
10631.844
10632.197
10632.251
10632.267
10638.447
10641.233
10641.314
10643.393
10645.120
10645.143
10645.168
10653.957
i 0671.067
10672.799
10694.716
10695.098
10695.996
10695.993
10864.571
10869.329
5.0
7.4
161.3
108.4
13.2
5.4
10.5
6.9
7.0
5.6
8.5
1.6
3.0
359.2
47.4
46.4
14.8
32.1
62.9
13.2
4.4
7.0
4.3
38.8
27.7
377.2
224.3
17.9
22.5
24.0
14.5
4.8
17.0
32.8
11.1
904.5
v(MHz)
I
10929.901
117.2
11556.462 523.3
10696.016 104.0
10696.082
16.0
10700.684
7.2
12.7
10700.732
10700.712
7.0
10721.158
5.8
10721.175
5.0
10722.870 281.4
10723.184
76.2
10738.935 43.7
10738.997 20.0
46.9
10739.023
10739.081
16.2
10739.102
14.5
10739.063
11.8
10767.539 777.8
36.9
10767.603
10779.696
10.5
10781.311 158.1
10781.331
18.3
10783.044
1.8
3.4
10783.081
10788.772
13.6
10793.378 44.9
10796.708 515.8
i 0799.090
11.1
10801.421 3676.4
10801.438 5543.5
10801.457 618.6
10805.245
6.9
10815.985
3.5
10824.891 130.0
10864.516
6.7
10864.527
9.7
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Mixed Isotopomers continued.
v(MHz)______ I______ v(MHz)
10869.335
10877.332
1585.1
20.3
10864.552
I
7.5
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
A ppendix B. Syntheses
I. (C H ;b '?N
l'N substituted tritnethvlamine was prepared via the literature reaction between
paraformaldehyde and ammonium chloride [I]:
3 (CH:O b - 2 I5NH4C1 -» 2 (C H 0 ji5N*HC1 - 3 CO; - 3 H ;0
(CHo.’, 15N*HCI - NaOH -> (CH-,blfN - NaCI * H:0
( 1)
(2)
The second step allows for the release o f the free amine from its respective hydrochloride
salt.
In the final preparation. 5.0g ' '\ H 4Cl
(9 9
atom
°o .
Icon Services) was thoroughly
mixed with 13.63g (CH;Ob (Aldrich) in a l.OL three-necked round bottom flask.
(Thorough mixing is important in order to obtain high yields of the free amine). The flask
was equipped with a reflux condenser and immersed in an oil bath. A thermometer was
positioned in the oil bath away from the coils such that the temperature could be easily
monitored throughout the reaction. The reaction vessel was slowly heated up to -130°C.
where the mixture eventually liquefies with the release CO;(g). The reaction was allowed
to continue for approximately 5 hours, at which time evolution of CO; had essentially
ceased. At this time, the oil bath was removed and the reaction vessel allowed to cool to
room temperature. The flask was then immersed in a dry ice/ ethanol bath in order to
evacuate the vessel without the loss of any uncomplexed amine. The reflux condensor
was removed and replaced by a glass tube housing two columns, the first contained BaO
(to remove H ;0) and the second contained Ascarite (to remove any residual CO;). The
tube was connected to a manometer and vacuum line. The flask was evacuated and a
saturated solution of NaOH (9.2g'l6.7mL) was added via syringe. The dry ice/ethanol
mixture was subsequently removed and the liberated trimethylamine was collected in a
liquid nitrogen cooled ballast which was evacuated and preweighed. The reaction yield,
determined by comparison of the pre- and post- weight o f the ballast, was
94%
by mass.
The substituted trimethylamine was successfully utilized to measure the Strark spectrum
of (C H .b'-N -B F; and (CH;,b'5N-(CH 3bB and to obtain the spectrum of the “ S. ''N
isotopomer of (CHOr.N-SO;.
246
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Nitrogen 15-substituted ammonia was synthesized according to the following
reaction:
NH4CI * KOH -» N'Hj - KCl - H:0
As the two reactants immediately react to form products, it is necessary to keep them
separate prior to beginning the reaction. In order to accomplish this, the following vessel
was constructed from two round bottom flasks and a 3-wav adapter:
To manifold
5Ox KOH
■stir bar
In the final procedure, lg of ''N H jC l (99 atom%, Icon Services) was placed in the side
vessel while 50 times the molar equivalent o f finely ground (important for high yield)
KOH (51.52g) was placed in the larger round bottom flask. The reaction vessel was
evacuated and the two reactants were mixed by tilting the entire vessel, allowing the
NH4C1 to fall into the flask containing the finely ground KOH. The reaction proceeded
immediately, with the formation of NH 3(g) apparent as bubbles arising from the solid
mixture. The magnetic stirrer was engaged and heat was periodically applied with a heat
gun in order to push the reaction towards products. The amount of NH 3 evolved was
monitored using a calibrated manometer and collected in an evacuated N':(l) cooled
vessel. The reaction yield was 98%. determined by the total change in pressure viewed on
the manometer over the course o f the reaction.
247
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
HI. HCCCN (Cyanoacetvlene)
Cyanoacetvlene was synthesized in a two step reaction as follows [2]:
1. HCCCOOCH; liq. NH*
2. HCCCONH- -------►
'
P-Ch.A
HCCCONH;
HCCCN
In step 1 of the final preparation. -10ml of methyl propriolate (HCCCOOCH-.) was added
dropwise to a large excess (7.5g) of liq. NH;. The NH-.(I) was obtained by trapping
aliquots of NH;(g) in a reaction tube immersed in a dry ice acetone bath. The methyl
propriolate was added as slowly as possible to prevent the reaction from proceeding too
rapidly. The reaction initially forms a yellowish liquid. The liquid was allowed to warm
slowly while the excess NH; and CH-.OH formed in the reaction were pumped off. The
product. HCCCONH: forms as a flesh colored precipitate. The precipitate was initially
wet and was pumped overnight to dry and remove all excess NH;. The weight o f the
amide after drying was 7.84g. resulting tn a 95° o yield.
In Step 2. the HCCCONH; was thoroughly mixed with 3 1.36g of sand and 20.9 Ig
of P; 0 < in a 100ml 3-necked flask. ** H C C CO NH 2 must be handled with extreme
care as it is a skin irritant. The flask was equipped with a thermometer and cpnnected
to a vacuum line, which was also connected to an evacuated liquid N; cooled ballast for
the collection of the HCCCN(g). The flask was evacuated and immersed in an oil bath,
where the temperature was gradually raised to 250°C over a period of 3 hours. The
pressure of the HCCCN produced was monitored with a manometer. The HCCCN gas
was collected at 10 intervals, yielding a total amount o f 5.795g or 87 mass°o.
248
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
References:
1. Organic Synthesis. 2nd ed.: Wiley. New York. 1964: Collect. Vol. 1.
2. Miller. F.A.; Lemmon. D.H. Spectrochim. Acta. 1967. 23A. 1415.
249
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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