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Structural study of hydrocarbon complexes with sulfur dioxide and water by microwave spectroscopy

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S tru c tu ra l stu d y o f h y d ro carb o n com plexes w ith sulfur dioxide
a n d w a te r by m icrow ave spectroscopy
Andrews, Anne Marie, Ph.D .
The University of Michigan, 1991
UMI
300N. ZeebRd.
Ann Arbor, MI 48106
STRUCTURAL STUDY OF HYDROCARBON COMPLEXES WITH
SULFUR DIOXIDE AND WATER BY MICROWAVE SPECTROSCOPY
A nne M. A ndrew s
A dissertation subm itted in partial fulfillm ent
of the requirem ents for the degree of
Doctor of Philosophy
(Chemistry)
in The U niversity of M ichigan
1991
Doctoral Committee:
Professor Robert L. Kuczkowski, Chair
Professor Lawrence S. Bartell
Professor Thomas M. D unn
A ssistant Professor Carol Korzeniewski
Professor T. Michael Sanders
RULES REGARDING THE USE OF
MICROFILMED DISSERTATIONS
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m itted to The U niversity of M ichigan and m ade available through
U niversity M icrofilms International or The U niversity of M ichigan are
open for inspection, but they are to be used only w ith due regard for the
rights of the author. Extensive copying of the dissertation or publication
of m aterial in excess of standard copyright lim its, w hether or not the
dissertation has been copyrighted, m ust have been approved by the
author as well as by the Dean of the G raduate School. Proper credit m ust
be given to the author if any m aterial from the dissertation is used in
subsequent w ritten or published work.
For Michael
ACKNOWLEDGEMENTS
I gladly take this opportunity to offer my appreciation to the m any
people who contributed to the success of this work. First and forem ost, I
thank Professor Robert L. Kuczkowski, for whom I have great adm iration and
respect. He has been a knowledgeable and patient m entor, providing advice,
direction, encouragem ent and the finest example of scientist and teacher.
The members of the research group have all contributed in some w ay
to this work. Particularly, I w ould like to thank Dr. M arabeth S. LaBarge for
teaching me the basics of m icrowave spectroscopy and for her enthusiastic
encouragem ent in my first m onths as a spectroscopist. Dr. K urt W. Hillig n
has been an invaluable resource for advice on com puting and all m atters
experim ental; I thank him for this, his valuable insights, lively conversations
and friendship. 1 thank my colleagues Amine Taleb-Bendiab, Jung-Jin Oh
and Iaonnis Iaonnou, who have provided valuable suggestions, enlightening
discussions and help in m any ways.
I thank m y colleagues in the Chem istry departm ent for support,
encouragem ent and friendship. I am particularly grateful to Fred Dulles, who
has helped m e w ith a host of com puter problems.
1 acknowledge the regents of the U niversity of M ichigan for financial
support through the Regents-Baer and Cornwell Fellowships, the N ational
Science Foundation for support the this research and the San Diego
Supercom puter Center for com puter time.
I am grateful to my fam ily and friends who have provided
encouragem ent through my m any years of education. Finally, I thank my
husband, Michael, for reasons too num erous to m ention, but particularly for
his unfailing love, support and good hum or.
TABLE OF CONTENTS
DEDICATION..............................................................................................................ii
ACKNOWLEDGEMENTS................................................................................... '....iii
LIST OF FIGURES.................................................................................................... v ii
LIST OF TABLES........................................................................................................ ix
LIST OF APPENDICES............................................................................................xiii
CHAPTER
1. INTRODUCTION....................................................................................... 1
M olecular Complexes
Fourier Transform M icrowave Spectroscopy
Thesis Proposition
References to Chapter 1
1
5
9
11
2. THE ETHYLENE-SULFUR DIOXIDE COMPLEX..................................13
Experim ental
Results and Analysis
Sum m ary
References to Chapter 2
14
17
37
48
3. THE ACETYLENE-SULFUR DIOXIDE COMPLEX............................... 50
Experim ental
Results and Analysis
Sum m ary
References to Chapter 3
v
51
52
65
72
4. THE CYCLOPROPANE-SULFUR DIOXIDE COMPLEX.......................74
Experim ental
Results and Analysis
Sum m ary
References to Chapter 4
75
76
88
97
5. THE CYCLOPROPANE-WATER COMPLEX........................................ 99
Experim ental
Results and Analysis
Sum m ary
References to Chapter 5
6.
101
102
118
125
INTERPRETATION AND DISCUSSION............................................ 127
Trends and Com parisons
Ab initio calculations
Electrostatic M odeling on the complexes
Legon-M illen M odel
Summary of Major Conclusions
References to Chapter 6
127
130
133
138
141
142
APPENDICES............................................................................................................144
vi
LIST OF FIGURES
Figure
1-1. Schematic of Fourier Transform M icrowave Spectrom eter
1 -2 .
6
3o3-2o2 Transition of cyclopropane-S 0 2 (a) Sample Free
Induction Decay. 1000 gas pulses samples at
0.2 ^sec/channel over 512 channels, (b) Fourier
transform ed pow er spectrum . The lineshape is dom inated
by Doppler broadening w ith depletion of intensity in the
center caused by favored production of larger clusters at the
center of the beam ................................................................................. 7
2-1. Structural param eters defining the geom etry of the C 2 H 4 -S0 2
complex. Perspective is dow n the C=C bond of C 2H 4 , w ith
the C and H atom s eclipsed and w ith the O atoms eclipsed
on the SO2 ............................................................................................. 23
2-2. D euterium nuclear quadrupole hyperfine patterns for the
I 10 -O00 transitions of (a) the A i tunneling state of 1 , 1 C2 H 2 D2 *SC>2 , (b) the A 2 state of 1 , 1 -C2 H 2 D 2 *S0 2 (c) the Ai
state of trans-Cz^ 2 ^ 2 'SOz and (d) the A 2 state of
fra«s-C2H2D2-S02................................................................................30
3-1.
Param eters defining the structure of the C2 H 2 -S0 2 complex....... 55
3-2. H yperfine pattern from deuterium nuclear quadrupole
coupling in C2 D2 -S0 2 - Stick diagram beneath represents the
predicted com ponents, w ith the solid lines arising from
even nuclear spin states and the dashed lines arising from
odd nuclear spin states........................................................................64
4-1.
Param eters defining the structure of the C3 H 6 -S0 2 complex....... 80
4-2.
Feasible perm utations of identical nuclei of CsHg-SC^. Likely
pathways associated w ith each are discussed in the tex t.............. 85
5-1.
Param eters defining the structure of C3 H 6 -H2 0 ........................... 108
v ii
5-2. Feasible perm utation of nuclei for C3 H 6 H 2 O. Pathw ays
between frameworks are discussed in the text............................. 1 1 2
5-3.
Positions for D in &asa/-l/l-C 3 H 4 D 2 ,H 2 0 for $ =
90°................ 115
5-4.
Positions for D in basal-1,1 -C 3H 4 D2 H 2 O for $ =
0°.................. 115
6-1.
Electrostatic Energy vs. 0 (SO 2 ) for C 2 H 4 SO 2 ..............................134
6 -2 .
Electrostatic Energy vs. 0 (SO2) for C2H2-S02.................................. 137
v iii
LIST OF TABLES
Table
1-1. Geometries of W eak Complexes Predicted by D istributed
M ultipole A nalysis and from Experim ent....................................... 3
1-2. Selected force constants predicted by the Legon and Millen
m odel and determ ined experim entally............................................ 4
2-1.
Rotational transitions for C2 H 4 -S0 2 ..................................................17
2-2.
Rotational and centrifugal distortion constants of C 2 H 4 SO2
2-3.
Stark effects and dipole moments of ethylene*S0 2 ........................ 22
19
2-4. Two structures w hich fit the moments of inertia from the A i
state........................................................................................................24
2-5. Predicted and observed (exp) rotational constants and dipole
components for the tw o isomers of cis-l,2-C2^hP2'S02............... 25
2-6.
Relative intensity of the tunneling doublets in
ethylene*S0 2 ......................................................................................... 29
2-7. M olecular constants for C 2 H 4 SO 2 derived w ith the internal
rotation H am iltonian.........................................................................32
2 -8 .
Calculated V2 barriers to internal rotation for isotopic species
of ethylene*S0 2 .................................................................................... 33
2-9.
Structure calculated from internal rotation constants.................. 34
2-10. D euterium nuclear quadrupole hyperfine structure and
coupling constants for C2 H 3 D-S0 2 ................................................... 34
2-11. N uclear quadrupole coupling constants of C2 H 3 D-S0 2
(MHz).................................................................................................... 36
2-12. Observed transitions for C 2 D 4 SO 2 .................................................... 38
ix
2-13. O bserved transitions for trans-C2 H 2 D 2 -S0 2 ..................................... 39
2-14. Observed transitions for 1 ,1 -C2 H 2 D 2 -S0 2 ..........................................40
2-15. Observed transitions for C2 H 4 *S180
160
............................................ 41
2-16. Observed transitions for C2 H 4 *S180 2 ................................................ .42
2-17. Observed transitions for C2 H 4 -3 4 S0 2 ................................................. 43
2-18. O bserved transitions for the d-in isom er of C 2 H 3 D-S0 2 ................ 43
2-19. Observed transitions for cis-C 2 H 2 D 2 -S0 2 ...........................................44
2 -2 0 .
Spectroscopic constants of isotopic species of ethylene-S 0 2
from W atson S-reduced H am iltonian............................................ 45
3-1.
Observed transitions of C2 H 2 -S0 2 / MHz........................................53
3-2.
Spectroscopic constants for C2 H 2 -S0 2 ..................
3-3.
Structural param eters from least-squares fits of the moments
of inertia of C 2 H 2 SO2, C2 H 2 S18 0 160 and C2 H 2 -3 4 S0 2 and
coordinates from K raitchm an substitution calculations............. 56
3-4.
Structure of C 2 H 2 -S0 2 from individual fits of the mom ents
of inertia for each isotopic species.................................................... 57
3-5.
Stark effects (Av/e2) and dipole moment of C 2 H 2 SO2 ..................58
3-6.
D euterium nuclear quadrupole coupling constants (MHz)
for C 2 H 2 and C2 H 2 -containing complexes.......................................60
3-7.
Observed transitions of C 2 D2 -S0 2 ..................................................... 67
3-8.
Observed transitions of C2 HD-S0 2 .....................................................67
3-9.
Observed transitions of C 2 H 2 *S180
160
54
............................................. 6 8
3-10. Observed transitions of C2 H 2 *3 4 S0 2 ...................................................6 8
3-11. Spectroscopic constants for acetylene*S0 2 ........................................ 69
3-12. D euterium nuclear quadrupole hyperfine com ponents for
C2 HDSO 2 ............................................................................................. 70
3-13. D euterium nuclear quadrupole hyperfine com ponents 4 of
C2 D2 S 0 2 ...............................................................................................71
4-1. Observed transitions for C3 H 6 -S0 2 .................................................... 77
4-2. Spectroscopic constants of C3 H$-S0 2 ................................................. 78
4-3. Planar second m om ents of cyclopropane-S 0 2 / cyclopropane
and sulfur dioxide............................................................................... 80
4-4.
4-5.
Structural param eters and atomic coordinates obtained from
least-squares fitting of mom ents of inertia and Kraitchman
equations................................................................
83
Predicted and observed dipole mom ents for basal-1,1C3 H 4 D2 SO2 for the tw o structures w ith 0(V) = 83.3° and0(V )
= 96.8°....................................................................................................84
4-6. Observed transitions for C3 H 6 ,34 S0 2 ................................................. 89
4-7. Observed transitions for C3H6*S180 2 ................................................. 90
4-8. Observed transitions for C3 H 6 -S180
160
............................................ 91
4-9. Observed transitions for C3 D6 -S0 2 ..................................................... 92
4-10. Observed transitions for basal-C3 tisD'S 0 2 ....................................... 93
4-11. Observed transitions for apical-1,l-CiH 4 D 2 -S180 2 ...........................93
4-12. Observed transitions for basal-l,I-C 3 H4 D 2 &O2 ................................94
4-13. Spectroscopic constants of isotopical species of C 3 H 6 SO2
from W atson S-reduced H am iltonian............................................ 95
5-1.
Observed transitions of C3 H 6 -H2 0 in MHz.................................... 103
5-2.
Spectroscopic Constants for C sH ^feO ............................................103
5-3.
Stark effects (Av/e2) and dipole m om ent of cyclopropanew ater................................................................................................... 105
5-4.
Planar second moments (amuA2) of C3 H 6 -H2 0 and selected
isotopomers........................................................................................ 107
5-5.
Experimental and predicted changes in rotational constants
(MHz) forC 3 H 6 H 2 0 ,C 3 H6 H D O andC 3 H 6 D 2 0 ......................... 109
5-6.
D euterium coordinates calculated using Kraitchm an's
equations/A ....................................................................................... 1 1 0
5-7.
Cyclopropane-water structures from least-squares fits of
m om ents of inertia lb and Ic............................................................I l l
5-8.
Relative intentsities of A i:A 2 tunneling states for C 3 H 6 H 2 O
and isotopom ers.................................................................................114
5-9.
Dipole m om ent com ponents and 170 nuclear quadrupole
coupling constants predicted from the structure and
experim ental...................................................................................... 117
5-10. Observed transitions of C3 H 6 H D O in M Hz..................................119
5-11. Observed transitions of C3 H 6 -D2 0 in M Hz................................... 119
5-12. Observed transitions of C3 H 6 *H2 lsO in MHz................................120
5-13. Observed transitions of apicaI-1,1-C 3 H 4 D 2 H 2 O in M Hz.............120
5-14. Observed transitions of C3 H 6 'H 2 170 in MHz................................121
5-15. Observed transitions of basal-1 , 1 -C 3 H 4D 2 ‘H 2 0 in MHz................122
5-16. Observed transitions of C3 D 6 -H2 0 in MHz.....................................122
5-17. Spectroscopic constants for C3 H 6 HDO and C3 H 6 -D2 0
isotopom ers........................................................................................ 123
5-18. C 3 H 6 HDO D euterium N uclear Q uadrupole H yperfine
S tructure.............................................................................................124
6-1.
Com parison of cyclopropane-, ethylene- and acetylenecontaining complexes.......................................................................129
6-2. Results of ab initio for C2 H 4 -S0 2 , C 2 H 2 -S0 2 and C3 H 6 *SC> 2 ......... 131
6-3. Results of ab initio calculations for C 3 H 6 H
2 0
...............................132
6-4.
Electroststic energies for different structures of C 2 H 4 -S0 2
from D istributed M ultipole Analysis............................................ 135
6-5.
Predicted and observed k® for S0 2 -containing complexes..........139
LIST OF APPENDICES
A.
Unassigned transitions........................................................................145
B.
Electrostatic Interaction Energies for the D istributed
M ultipole A nalysis........................................................................... 149
CHAPTER 1
INTRODUCTION
The weak forces betw een molecules play an im portant role in nearly all
aspects of science. They determ ine fundam ental physical properties of m atter
ranging from imperfections of gases to the structure of bulk phases. In
biological system s, interm olecular forces are responsible for such im portant
and diverse phenom ena as the conform ation of proteins and the function of
cell membranes. Such chemically im portant processes as solvation have
their origin here and weak m olecular interactions are thought to affect upper
atm osphere chemistry. As a result of such far-reaching consequences, much
effort has been devoted to the understanding of interm olecular forces.
M olecular Complexes
Historically, m olecular complexes have been studied as a means of
obtaining detailed inform ation about the interaction betw een isolated
molecules, w ith the goal of obtaining the binary interm olecular potential
energy function. Spectroscopic studies of charge-transfer complexes in the
ultraviolet and the visible have provided equilibrium constants and heats of
form ation for a host of complexes.1 M atrix isolation experim ents in the
infrared have been successful at indirectly determ ining the structures of a
num ber of charge-transfer, hydrogen-bonded and van der Waals type
1
2
com plexes.2 However, few of these studies have elicited structural
inform ation about the complexes and m ost have been carried o ut in
condensed phases where solvent and lattice effects can obscure purely binary
interactions.
More recently, molecular beam spectroscopy has allowed the study of
isolated dim eric complexes in the gas phase, thus elim inating the
com plications of condensed phases. Through a variety of experim ental and
theoretical techniques, various aspects of the interm olecular potential are
studied. In a few molecules, the entire potential surface has been m apped
out, but m ore often selected features are studied by a given technique: for
exam ple, the microwave region gives detailed inform ation about the
structures of complexes at the bottom of the potential w ell and often about
the large-am plitude motions which are typical of w eakly bound complexes.
In the infrared small changes in the intram olecular vibrations of the
m onom ers give inform ation on the bonds affected by com plexation and in
the far infrared the interm olecular vibrational m odes are studied directly.
Considerable effort has been paid to using theoretical m ethods to
predict and interpret the structures of complexes. However, because the
binding energy of a complex is only a sm all fraction of the total energy, very
elaborate calculations are required to reproduce all aspects of the
interm olecular potential. These have been carried out for a num ber of
molecules such as Ar-HCl and (H 2 0 )2 ,3 but the com putational expense has
lim ited this type of study to a sm all num ber of investigations. W hile lesssophisticated calculations w ill certainly be insufficient for producing a
com plete and accurate potential, the question arises w hether such
calculations, which are becoming alm ost universally accessible, are of any use
in predicting the structures and binding energies of complexes.
3
Because elucidation of a complete intermolecular potential energy
surface is an enormous undertaking, there is a desire to. understand the
nature of complexation in terms of simple, chemically-intuitive models,
which still have accurate predictive powers. Several have been proposed in
the literature. The interaction energy has been decomposed by Morokuma
into electrostatic, dispersion, polarization, charge-transfer, and exchange
repulsion terms.4 This analysis has indicated that the electrostatic interaction
plays a pivotal role in determining the structure of m any complexes,
particularly hydrogen-bonded complexes. Buckingham and Fowler have
Table 1-1 . Geometries of Weak Complexes Predicted by Distributed multipole
analysis and from Experiment.5
Prediction
Complex
Experiment
H3N...HF
C3v
C 3v
C3V
H3N...HCCH
Q3v
H3P...HCI
C3V
C3V
H3P...HCN
C3V
C 3v
C2H4...HF
C2v
C2v
C2H4...HCI
C2v
C2v
C2H2—.HF
C2v
C2v
C2H2....HCI
C2v
Q2v
N 2...HF
Linear
Linear
HCN...HCN
Linear
Linear
CO...HCN
Linear
Linear
01=72°, 02= 7 °a
01=60 - 70°
HF...HF
SO2—HF
cis h-bonded
cis h-bonded
SO2...HCI
cis h-bonded
cis h-bonded
a. For angle definitions, see Reference 5 and references therein.
4
dem onstrated success a t predicting the structures of a large num ber of
complexes using an electrostatic m odel em ploying point m ultipoles
distributed on various sites of the subunits and hard spheres of van der
W aals radii in place of a repulsive term .5 The results for some selected
complexes are show n in Table 1-1. Of note is that m ost of the complexes to
which this m odel has been applied are composed of small and often linear
subunits, and that the complexes generally have highly sym m etric structures.
Less w ork has been done on interpreting larger complexes, w here there are
m ore interm olecular coordinates to consider.
W hile the electrostatic models have been successful at interpreting the
structures of complexes, they do not attem pt to address the strength of
m olecular associations. Legon and M illen have developed a m odel whereby
from the stretching force constant for a hydrogen bond, which is readily
estim ated from spectroscopic data, the two subunits are assigned
nudeophilidties and electrophilidties .6 These are then used to predict the
Table 1 -2 . Selected force constants (10~2 m dyne/A ) predicted by the Legon and
M illen m odel and determ ined experim entally .6 __________________________
Experim ental
Com plex
Predicted
2.5
n 2...h c i
2 .8
n 2...h c n
2.3
2.3
3.9
4.2
CO...HQ
CO...HCN
3.3
3.6
5.9
PH 3 ...HCI
5.5
6 .8
H 2 S...HC1
6 .0
10.7
CH 3 CN...HCI
1 0 .1
12.5
12.5
H 2O...HCl
1 1 .1
h 2o ...h c n
1 0 .6
H 2O...HCCH
6.5
6 .0
5
force constants for other molecules. This m odel is chemically appealing
because one w ould like to think that the properties of a molecule w hich cause
it to bind strongly to one partner w ill play a major role in determ ining how it
will bind to another partner. It has proven quite successful in reproducing
the force constants of the hydrogen bonded complexes for which it was
devised, as shown in Table 1-2. It has not, however, been applied to other
weak complexes.
Fourier Transform M icrowave Spectroscopy
The pulsed m olecular beam Fourier transform microwave (FTMW)
spectroscopy technique was developed by Flygare at the U niversity of Illinois
and a spectrom eter based on this design was constructed by Hillig at the
U niversity of M ichigan .7' 8 A schematic of the spectrom eter is show n in
Figure 1-1. The molecules in the form of a pulsed supersonic beam are
introduced into an evacuated chamber containing a Fabry-Perot cavity. After
a short delay to allow the molecules tim e to travel to the center of the cavity,
a pulse of microwave radiation is coupled into the cavity, which has been
pre-tuned to be nearly on resonance w ith the microwave frequency. If there
is a rotational transition in the band-w idth of the cavity (1 MHz) the high
density of microwave radiation induces a bulk polarization in the gas sam ple
which has a long decay time
(2 0 0
jisec) relative to the decay tim e
(1 0
jisec) of
the initial pulse. After allowing the initial pulse to die aw ay, the free
induction decay (Figure 1-2) of the m olecular polarization is recorded,
digitized and Fourier transform ed to give a pow er spectrum in the frequency
dom ain.
Figure 1-1. Schematic of Fourier Transform
Vacuum
Chamber
Pulsed
MW Source
TT
3
FID Signal
Computer
Pulsed
Nozzle
Microwave Spectrom eter
Heterodyne
Detector
Fourier
Transform
Range:
7.2 -18.5 GHz
Bandwidth:
1 MHz
Resolution:
4 kHz
Repetition Rate: 23 Hz
Spectrum
Fabry-Perot
Cavity
Gas
Sample
e.g.
1%S02
98% Neon
ON
7
1.5
«
as
c
a
2*
&
as
■ e
£«
c
0
e
* 0
-1.5
Tima
600
«
c
3
&
e
as 300 ■oe
as
0
c
0
■E
0.0
0.1
0.3
0.2
0 .4
Frequency relative to 7311.520 MHz
0.5
Figure 1-2. 3 o3 -2 o2 Transition of cydopropane*S 0 2 (a) Sample Free
Induction Decay. 1000 gas pulses sam pled at 0.2 usee/channel over 512
channels (b) Fourier transform ed pow er spectrum . The lineshape is
dom inated by D oppler broadening w ith the depletion of intensity in
the center caused by favored production of larger clusters over dim ers
at the center of the beam .9
The m olecular beam aspect of the spectrom eter m akes it w ell-suited to
the study of w eak complexes. The expansion is typically carried out from a
sam ple containing 99% rare gas and 1% the molecule(s) of interest at a total
pressure of 1-2 atmospheres. The characteristics of the beam, therefore, are
8
dom inated by the rare gas. D uring the early p art of the expansion, w hen the
molecules are in the throat of the nozzle (in this case a
1
mm pinhole) there
is a large num ber of three-body collisions during which complexes m ay form
via
A + B + Rg -» A -B + Rg*
In the collision, the rare gas atom carries off excess kinetic energy which
w ould otherw ise dissociate a complex bound by only
1 -2
kcal/m ole of
energy . 10 The beam then enters a collisionless regim e w here the complexes
survive for the tim e of transit across the vacuum chamber, w hen the
spectroscopy is done.
In addition, the m olecular beam offers several spectroscopic
advantages. D uring the expansion, random kinetic energy is converted into
directed mass flow, resulting in trem endous cooling of rotational and
translational degrees of freedom (~ 1 K) and m oderate cooling of vibrational
degrees of freedom (~ 100 K). This produces a greatly sim plified spectrum
because only the ground vibrational state and low-energy rotational states are
significantly populated. A dditionally, the translational cooling virtually
eliminates pressure broadening and greatly reduces D oppler broadening, w ith
the result that the instrum ental resolution is on the order of kHz. Such
resolution allows the observation of transitions, hyperfine com ponents, or
m ultiplets from internal m otions which are separated by only a few kHz.
These features have proven extrem ely valuable in the study of weak, floppy
complexes which often exhibit large am plitude motions..
9
Thesis Proposition
A study of the complexes ethylene*S0 2 , acetylene*S0 2 ,
cyclopropane-S 0 2 and c y d o p ro p a n e ^ O is proposed. Analysis of their
FTMW spectra w ill provide detailed inform ation of the structures and large
am plitude internal m otions of the complexes. These complexes are selected
for a num ber of reasons. First, complexes of unsaturated hydrocarbons w ith
sulfur dioxide have been studied previously . 11' 12 These studies have elidted
equilibrium constants and heats of form ation for a num ber of complexes.
However, they have provided no structural data, although it has been
speculated that the prim ary interaction is between the sulfur atom and the it
system. A dditionally, these studies have not involved ethylene*S0 2 ,
acetylene-SC>2 or cyclopropane-S 0 2 . These are of particular interest because
ethylene and acetylene are the sim plest molecules in their dass and w ill
provide inform ation least contam inated by secondary interactions, w hile
cydopropane often exhibits properties sim ilar to unsaturated hydrocarbons.
Second, the series ethylene, acetylene, cydopropane has been studied
with a number of a d d binding partners, which exhibit hydrogen bonded
structures, induding HF, HC 1, and HCN.13"21 However, the series has not
been studied with non-hydrogen bonding partners. It is desirable to
determine if similar trends to those observed with the hydrogen-bonding
partners would be followed for a k acceptor such as SO2. Sulfur dioxide is an
excellent binding partner because it has a substantial dipole moment (1.6 D)
and appropriate molecular weight to have a significant portion of the
spectrum of the complex in the frequency range of the FTMW spectrometer.
(7 to 18 GHz)
10
Third, the acetylene and ethylene complexes w ith w ater have been
characterized, but the cyclopropane-water complex has not.22' 23 W hile the
ethylene-water complex has the H 2 O hydrogen bonded to the k system of the
ethylene, in acetylene-H 2 0 the acetylene is hydrogen bonded to the O of the
water. This gives a double reason for studying the cyclopropane-H 2 0 system:
w hat w ill the structure be like in com parison to the ethylene-H 2 0 and
acetylene-H 2 0 complexes; and how w ill the ethylene-, acetylene-,
cyclopropane-water series com pare to the HX and SO2 series?
The study w ill attem pt to address the following m atters.
1) Will the structure of the SO2 complexes be as predicted in earlier
w ork w ith the sulfur interacting w ith the n system? How w ill the gas phase
binding energies com pare to those of sim ilar complexes in solution?
2) W hat trends can be docum ented for the series ethylene, acetylene,
cyclopropane w ith SO2 and w ater? How do they com pare w ith the previously
studied series w ith HC1, HCN and HF?
3) Can the structures and large am plitude motions of the complexes be
interpreted using a sim ple electrostatic distributed m ultipole model?
4) Are low-level, com putationally accessible ab initio calculations
useful for reproducing and predicting the structures of complexes?
5) Can the Legon-Millen model for interpretation of force constants of
hydrogen-bonded dim ers be readily applied to non-hydrogen bonded
system s?
6)
W hat can be said about the nature of the interaction for each
complex? i.e. Are there indications the electronic structures of the subunits
are disturbed by complexation?
11
References to C hapter 1
1.
R. Foster, M olecular Com plexes, Vol. 1., (Paul Elek Scientific Books,
London, 1973).
2.
L. Andrew s, "Absorption Spectroscopy of M olecular Ions and Complexes
in Noble-Gas Matrices," in Chem istry and Physics of M atrix Isolated
Species, Edited by L. Andrews and M. M oskovits (Elsivier Science
Publishing, Am sterdam , 1989), pp 15-46.
3.
J. H. van Lanthe, T. van Dam, F. B. van Duijneveldt, L. J. M. KromBatenberg, Faraday Symp. Chem. Soc., 19,125 (1984).
4.
K. M orokuma, Acc. Chem. Res., 10,294 (1977).
5.
A. D. Buckingham and P. W. Fowler, Can. J. Chem., 63, 2018 (1985).
6.
A. C. Legon and D. J. Millen, J. Amer. Chem. Soc., 109,356 (1987).
7.
T. J. Balle and W. H. Flygare, Rev. Scient. Instrum ., 52, 33 (1981).
8.
K. W. Hillig II, J. M atos, A. Scioly, R. L. Kuczkowski, Chem. Phys. Lett.,
133,359,(1987).
9.
F. J. Lovas and R. D. Suenram, J. Chem. Phys., 87,2010, (1987).
10. See reference 7 and references therein.
11. D. Booth, F. S. Dainton and K. J. Ivin, Farad. Soc. Trans., 55,1293, (1959).
12. L. J. Andrews and R. M. Keefer, J. Amer. Chem. Soc., 73,4159, (1951).
13. J. A. Shea and W. H. Flygare, J. Chem. Phys., 76,4857 (1982).
14. S. G. Kukolich, P. D. Aldrich, W. G. Read and E. J. Campbell, Chem. Phys.
Lett., 90, 329(1982).
15. S. G. Kukolich, W. G. Read and P. D. Aldrich, J. Chem. Phys., 78, 3552
(1983)
16. W. G. Read and W. H. Flygare, J. Chem. Phys., 76, 2238 (1982).
17. A. C. Legon, P. D. Aldrich and W. H. Flygare, J. Chem. Phys., 75,625 (1981).
18. P. D. Aldrich, S. G. Kukolich and E. J. Campbell, J. Chem. Phys., 78, 3521
(1983).
12
19. L. W. Buxton, P. D. Aldrich, J. A. Shea, A. C. Legon and W. H. Flygare, J.
Chem. Phys., 75,2681 (1981).
20. a) A. C. Legon, P. D. Aldrich and W. H. Flygare, J. Amer. Chem. Soc., 104,
1486. (1982). b) P. D. A ldrich, S. G. Kukolich, E. J. Campbell and W. G.
Read, J. Amer. Chem. Soc., 105,5569 (1983).
21. S. G. Kukolich, J. Chem. Phys., 78,4832 (1983).
22. K. I. Peterson and W. Klemperer, J. Chem Phys., 81 3842 (1984).
23. K. I. Peterson and W. Klemperer, J. Chem. Phys., 85 725 (1986).
CHAPTER 2
THE ETHYLENE-SULFUR DIOXIDE COMPLEX
Complexes of unsaturated hydrocarbons w ith sulfur dioxide have been
the subject of num erous investigations. In the early 1950s, A ndrew s and
Keefer observed charge-transfer bands in the ultra-violet for complexes of
sulfur dioxide w ith arom atics in solution . 1 Later, Booth, D ainton and Ivin
reported charge-transfer bands for
1 :1
complexes of olefins w ith sulfur
dioxide, also in solution . 2 From the tem perature dependence of the
equilibrium constants, they determ ined -AHf for the complexes to range from
0.73(6) kcal/m ole for the cydopentene-S 0 2 complex to 3.55(3) kcal/m ole for
the 2 ,3 -dim ethyl-2 -butene-S 0 2 complex. More recently, a photoionization
study has determ ined the gas phase dissociation energy for the trans-2 butene-S 0 2 complex as 3.75 kcal/m ole .3 The binding energy of the
ethylene*S0 2 complex, how ever, has not been detem ined.
The complex between ethylene and SO2 has been observed in m atrix
isolation and m olecular beam experiments. In the m atrix studies, Fredin 4
and N ord 5 observed several new bands which w ere attributed to the
ethylene-S 0 2 complex. However, no data on the structure or binding energy
were extracted. The m olecular beam study by M uenter, DeLeon and
Yokozeki6 com pared the relative abundances of C 2 H 4 -S0 2 , (C2 H 4 )2 , C2 H 4 -Ar,
(SC>2 )2 and SC>2 -Ar in a beam prepared by expanding a m ixture of C2 H 4 , SO2
13
14
and A t (1:1:98) and determ ined that C2 H 4 SO2 w as a relatively strong complex.
No attem pt was m ade to assign its spectrum.
N otably 7 none of the previous investigations has given definitive
inform ation of the structure of the complex or the exact nature of the
interaction, although it has been w idely accepted that the SO2 acts as an
electron acceptor from the hydrocarbon it system .1' 2 From the microwave
spectrum , it is established that this is indeed the case. The planes of the
ethylene and SO2 are stacked one above the other w ith the centers of mass
separated by about 3.5 A. The plane of die SO2 is tilted such that the prim ary
interaction is between the electropositive sulfur atom of the SO2 and the it
system of the ethylene.
Experimental
Instrum ental. The rotational spectrum of the complex w as m easured
in the region
6 .6
to 18 GHz w ith a Fourier transform m icrowave spectrom eter
using a modified Bosch fuel injector as a pulsed nozzle source .7
Experimental line w idths w ere 20 to 30 kHz and center frequencies w ere
estim ated to be accurate to ± 2 - 3 kHz for transitions unsplit by deuterium
nuclear quadrupole coupling. For m any of the deuterated species, the lines
were broadened up to 100 kH z by unresolved quadrupole splitting; center
frequencies were taken as the position of maximum intensity of the
broadened lines and are estim ated to be accurate to ± 20 - 30 kHz.
The spectrom eter is equipped w ith steel m esh plates for the
m easurem ent of Stark effects; the details are described fully elsew here .8
electric field was calibrated w ith the J = 1 - 0, Mj = 0 transition of OCS9 at
12162.980 MHz on each day th at Stark effects were m easured. Stark shifts
w ere typically m easured at 6 to
10
different field strengths.
The
15
Sam ples. The spectra were observed w ith a gas m ixture of
approxim ately 1% ethylene, 1 % S 0 2, and 98% rare gas at a total backing
pressure of 1 to 2 atm. In m ost cases the carrier gas w as neon, as this gave the
strongest and sharpest signals. Much of the early searching was done using
argon as the carrier gas and one of the isotopically substituted species was
observed in helium .
W ith the exception of C2 H 4 >34 S0 2 , which w as observed in natural
abundance (4%), the spectra of the isotopically substituted species were
observed in enriched samples. The deuterated ethylene sam ples were
purchased from MSD Isotopes w ith 298% enrichm ent and were used w ithout
dilution. S18 0 2 (99% enrichment) was purchased from Alfa Products and was
used w ithout dilution to assign the double-lsO species. The single-180 species
was observed by starting w ith a m ixture of 50% S18 0 2 and 50% S16 0 2; the SO2
underw ent rapid exchange to form approximately a
SI6 0 I8
0
2 :1 :1
m ixture of
: Sl602 : S180 2.
Relative Intensity Tests. In order to estim ate nuclear spin statistical
w eights for the tunneling doublets, the relative intensities of pairs of
transitions w ere determ ined by com parison of their signal to noise ratios in
the tim e domain. The S /N was estim ated as the ratio of the largest peak to
peak span in the early portion of the free induction decay (FID) to the largest
peak to peak span in the last 10% of the FID (where only noise is present.)
Due to the crudeness w ith which this value is determ ined, the S /N estim ates
from m any data sets had to be averaged to obtain m eaningful num bers for
com parison.
16
The FTMW spectrom eter is inherently not well suited for such a
m easurem ent of transition intensities. The prim ary difficulty is th at the
signal intensity changes greatly depending on the position of the pum p and
cavity resonant frequencies relative to the transition frequency. To obviate
this, relative positions for the pum p and the cavity w ere selected and held
constant for each com ponent of the pair of transitions. For one com ponent of
the tunneling doublet the FIDs from enough gas pulses w ere averaged to
attain a S /N between 5 and 20. This was repeated
8
to 10 tim es using the same
num ber of pulses (500-5000 depending on the strength of the transition) to
give an average S /N estim ate for the transition; this usually had a standard
deviation of about 10-15%. The pum p and the cavity w ere then positioned
the same relative distances from the other com ponent of the doublet and the
process was repeated using the same cavity and pum p frequency offsets and
the same num ber of shots.
The intensities of the signals are also dependent on both the total
backing pressure and the partial pressures of the ethylene and the S 0 2 in the
rare gas. Since die samples are held in 1 or 2 L glass bulbs, a choice had to be
m ade either to keep the partial pressures constant w hile allowing the backing
pressure to drop, or to keep the backing pressure constant through continued
dilutions w ith rare gas, allowing the partial pressures to decrease. The form er
gave m ore consistent results and was em ployed for all experim ents.
Relative intensity m easurem ents w ere m ade on the norm al isotopic
form, C 2 H 4 'S180
160
, 1 , 1 -C2 H 2 D2 ,S0 2 and fraws-l,2 -C 2 H 2 D 2 -S0 2 . (See Internal
Rotation...section.) O verall relative intensities w ere determ ined w ith an
estim ated accuracy of 10-15% from four to six pairs of transitions for each
isotopic species.
17
Results and A nalysis
Spectrum of the N orm al Isotopic Form. The m icrowave spectrum of
C2H4 SO2 was reported by LaBarge.1 0 Fiftysix a- and c-dipole transitions were
observed and their quantum num bers w ere assigned. They are listed in Table
Table 2-1. Rotational transitions3 for C2H4 SO2.
Aib
O-cd
<><*
Vobsc
Vobsc
8680.110 -0.004
-0.102
8653.913
ho-Ooo
12694.171
-0.005
12668.034
-0.142
211-I01
16890.173
0.009
-0.149
16864.198
3i2-2o2
13987.687
0.005
13925.001
-0.275
221-2h
13469.894
13407.194
0.005
-0.142
322“3i2
423-413
12788.710 -0.001
12726.062
0.026
11954.065 -0.004
0.232
11891.610
524-514
10980.941
-0.005
10918.920
0.468
625-6i 5
9891.021
0.006
9829.805
0.729
726-716
15061.264
0.002
-0.354
14998.963
220-212
32i-3i3
15673.111
-0.010
15611.482
-0.318
16581.117
0.002
-0.257
16520.810
422-414
8487.551
0.000
-0.084
8511.810
4o4-3i2
11121.917
0.002
-0.061
11144.326
505-413
13382.536
0.000
0.023
13402.311
606-514
15238.525
-0.002
0.007
707-615
7307.476 -0.002
7307.264
-0.098
202-l01
7677.424 -0.002
-0.094
7677.424
2li-llO
10449.790
0.003
-0.057
10449.466
3i3-2i2
-0.002
10913.461
-0.122
10912.906
303-202
10985.664 -0.010
0.007
10985.621
322-221
11061.646
0.001
-0.011
11061.982
321-220
11503.463 -0.004
3i2-2n
-0.120
11503.430
A2b
o-cd
-0.008
-0.003
0.000
-0.004
0.000
0.000
0.004
0.006
-0.007
0.001
0.009
-0.009
-0.008
-0.009
0.006
o-ce
0.100
0.131
0.185
0.278
0.145
-0.033
-0.244
-0.492
-0.781
0.349
0.302
0.246
0.054
0.073
0.043
0.001
0.004
0.001
-0.001
0.007
0.006
0.006
0.055
0.053
0.022
0.095
-0.024
-0.028
0.111
18
0.057
13911.752
0.002
0.005
13911.259
-0.052
4l4-3l3
-0.002
0.000
0.151
14464.251
-0.122
14463.109
404-303
0.004
0.021
14632.124
14632.196
-0.006
0.000
423-322
14820.594 -0.009
0.008
14819.750
0.009
0.028
422-321
15313.254
0.002
0.197
15313.382
0.002
-0.110
4i3-3i2
-0.092
17947.743 -0.002
5o5-4<)4
a* Q uantum num bers listed as J, Kproiate/ Koblateb- Symmetry label for tunneling state. See text.
c- Observed frequency in MHz.
d. O bserved - calculated frequency (MHz) using W atson H am iltonian to fit
each state.
e. Obs - calc (MHz) using internal rotation H am iltonian to fit both states.
2-1. The transitions occurred as doublets of unequal intensity w ith the c-type
transitions split by 25 to 65 MHz and the fl-type by a few kHz to 2 MHz. The
tw o components of each doublet exhibited nearly identical Stark effects and
this allowed the transitions to be appropriately paired as tunneling doublets
and their quantum num bers to be determ ined.
In the earlier report/ the spectrum w as assigned as tw o interacting
tunneling states (with transitions allowed between tunneling states). The
residuals for this assignm ent, however, were significantly larger than the
experim ental errors. In this w ork, the spectrum was re-assigned as tw o non­
interacting states (with no allowed selection rules between the tunneling
states) w ith all the stronger transitions assigned to one state and all the
w eaker transitions to the other. This assignm ent results in sum rule
differences of less than 10 kHz for all observed transitions connecting
common levels and residuals on the order of the experim ental uncertainties.
Each state was fit independently to A, B, C and five quartic distortion
constants using the W atson S-reduction in a F representation . 11 The derived
19
spectroscopic constants are listed in Table 2-2 and com parison of the observed
and calculated transition frequencies is shown in Table 2-1.
Table 2-2. Rotational and centrifugal distortion constants of C 2 H 4 SO 2 .
A /M H z
B/M Hz
C/M Hz
D j/kH z
D jx/kH z
Djc/kHz
d j/k H z
d2/kH z
Ai
6673.524(3)
2007.627(1)
1656.105(1)
4.941(19)
168.16(8)
504.1(8)
-1.1702(55)
-0.958(7)
na
■—
I
29
5
A2
6645.981(5)
2007.638(1)
1656.025(1)
4.829(28)
163.55(9)
-824.4(10)
-1.1256(93)
-0.933(11)
27
7
a- N um ber of transitions in the fit.
b- Av = v0bs “ Vcalc
Since the two sets of transitions w ere independently fit to a standard
W atson H am iltonian, a high barrier one-dim ensional tunneling m otion is
indicated; the nature of this m otion will be discussed below. By analogy to
C 2 H 4 O 3 , w here a sim ilar tunneling motion was observed , 12 the two
tunneling states of the C2 H 4 -S0 2 were labeled A i and A2 using the G 4
sym m etry group for the sym m etric and anti-sym m etric tunneling states,
respectively. The A i state gives rise to the m ore intense transitions, which
are generally the higher frequency components.
20
Spectra of Isotopically Substituted Species. To provide insight on the
internal motion(s) giving rise to the splitting in the spectrum and to
determ ine the structure of the complex, the spectra of nine isotopically
substituted species were studied. The spectra of C2 D4 SO2 (Table 2-12, at end of
chapter), frflws-l/2 -C 2H 2 D 2 -S0
2
(Table 2-13), U -C 2 H 2 D 2 SO2 (Table 2-14),
C 2 H 4 -S18 0 160 (Table 2-15), C2 H 4 *S180
2
(Table 2-16), and C2 H 4 -3 4 S 0 2 (Table
2-17) w ere characterized by doublets sim ilar to the norm al species. W ith the
exception of C 2 H 4 -34 SC>2 , for which too few transitions w ere m easured, they
w ere fit as two independent states to the same H am iltonian used for the
norm al species; the C2 H 4 -3 4 S0
2
was fit to only A, B and C for each state. The
spectra of C2 H 3 D-S0 2 (Table 2-18) and a s -l/2-C2 H 2 D2,S 0 2 (Table 2-19) did not
exhibit doublets. Intensive searches w ere m ade above and below the
observed lines in both species for a partner spectrum w ith no success. Their
transitions w ere fit w ith the same W atson H am iltonian. The spectroscopic
constants for all the isotopically substituted species are in Table 2-20.
Tunneling splittings result when an internal motion in a molecule
transforms it to an equivalent structure. The spectra of C2H3D-S02 and
cis-1,2-C2H 2D2*S02 were unsplit apparently because the internal motion did
not result in an equivalent form, but rather in a different structural isomer. It
has been observed in other systems where two "isotopic" structural isomers
can occur that one of the isomers has a significantly higher zero-point energy
than the other and is not substantially populated at the low temperature
(approx. IK) of a supersonic molecular beam.13/14 Thus, it seemed likely that
the lower energy isomers for cis-1,2 -C2H2D2 S0 2 and the Q H 3D SO2 had been
observed. This was confirmed by switching to H e as a carrier gas to raise the
temperature of the beam. Another spectrum for cis-1,2 -C2H 2D2-S0 2 was
observed which was very much weaker, b u t which had appropriate rotational
21
constants to be the other structural isomer. (See Structure section below.)
Because the spectrum was very weak, only
6
transitions were m easured; these
were fit to A, B and C. A second isomer of C2 H 3 D SO 2 should also be present,
how ever no search for its spectrum was attem pted.
The splitting in the transitions of the isotopically substituted spedes
scaled approxim ately linearly w ith deuteration, w ith the l 10-Ooo transition
split by 26 MHz in the normal isotopic spedes, by 13 MHz in
traHS-C2 H 2 D2 -S0 2 , by 12 MHz in 1,1-C2H2D2*S02 spedes and by 6 MHz in the
C 2 D4 ‘S0 2 spedes. The effect of substitution w ith lsO and
was m uch less
pronounced, w ith the splitting of the Ijq-Oqo transition decreasing to 20 MHz,
22 MHz and 19 MHz for C2 H 4 -34 S 0 2, C2 H 4 -S180
160
and C2 H 4 -S180 2 ,
respectively.
D ipole M om ents. The dipole moment of the complex was determ ined
from the Stark effect splittings of six transitions. The observed second order
Stark coeffidents are shown in Table 2-3. The values w ere obtained from
plots of Av vs. E2. A least squares fit of these data holding Hb = 0 yielded a total
dipole moment, |iT = 1.650(4) D, w ith components I |ia I = 0.629(6) D and I |xc I =
1.525(3) D. When Hb was not fixed to zero, the least squares fit determ ined a
value for it very nearly equal to zero.
The dipole moments of the two isomers of cis-1,2 -C 2 H 2 D 2 -S0 2 were
also m easured. The observed Stark effects and least squares fits are shown in
Table 2-3, as well. The dipole moment of the higher energy
cis-1 ,2 -C2 H 2 D 2 -S0 2 isom er is not as well determ ined as the others due to the
poor S /N of the transitions.
22
T able 2-3. Stark effects* and dipole moments of ethylene*S0 2 C2 H 4 SO2
IM I
1 1 0 "°0 0
0
2 11_101
0
2ir h i
1
2 0 2 '1 01
0
2 o2 _1oi
1
3 03-2 02
0
303_202
2
4 04'3 03
2
3 13"2 12
1
iMa'/D
iMcl/D
obs
3.066
0.245
3.983
1.439
3.656
-0.676
2.526
o-c
-0 .0 2 0
-0 .0 0 2
-0 .0 1 0
-0.016
cis -C2 H 2 D 2 ’S0 2
(d-itt)b
obs
o-c
3.323
- 0 .0 0 1
0.354
-0 .0 0 1
4.247
0 .0 0 0
cis -C 2 H 2 D2 -S0 2
(d-out)b
obs
o-c
3.337
-0.040
0.192
0.013
4.382
0.053
-0.004
-0.620
2.640
0 .0 0 1
0.778
-0 .0 0 2
-0.332
-0 .0 0 1
0.597(1)
1.531(1)
-0.884
2.592
0 .0 1 0
0 .0 0 2
0.029
0.629(6)d
1.525(3)
-0.150
-0.082
0.678(41)
1.525(22)
1.643(1)
1.650(3)
1.669(26)
Mt / d
*• Second order Stark coefficients. (Av/e2 in units of 105 M H z/[V /cm ]2)
b- See text.
c* Calculated values using the W atson H am iltonian rotational constants.
d* One standard deviation in the fit.
Structure. From planar mom ents and selection rules, it can be
established that the complex has an ac plane of symm etry. Com parison of the
out of plane second m om ent Pbb (Pbb = 0.5 [Ia + Ic - ItJ = ^ mi b*2, and sim ilarly
for Paa and PCc) of C2 H 4 -SC>2 (64.5803 amu-A2) and the C2 H 4 *3 4 S0 2 (64.6735
amu-A2) places the S atom in the ac symmetry plane. Also, Pbb of the
complex is nearly equal to the sum of Paa of free ethylene and Paa of free S 0 2
(16.8559 + 49.0507 = 65.9066 amu-A2).15 This indicates that SO2 and C 2 H 4
straddle the symmetry plane as shown in Figure 2-1, with the two molecular
planes stacked one above the other and their orientation defined by the
23
parameters R ^ , 0(C2H4> and 0(SO2). It is assumed that the C2H4 and SO2
subunits retain their uncomplexed structures, which are taken from reference
15.
cm
Figure 2-1. Structural param eters defining the geom etry of the
C2 H 4 SO2 complex. Perspective is dow n the C=C bond of C2 H 4 , w ith
the C and H atoms eclipsed and w ith the O atoms eclipsed on the SO2 .
In a weakly bound complex one w ould like to determ ine the structure
of each isotopic species separately. The changes in the vibrational am plitudes
of low frequency m otions in these complexes w ith isotopic substitution often
lead to different average structures for the substituted spedes, possibly giving
some insight on the low frequency motions. In the case of the C2 H 4 -SC>2
complex, however, this w as not possible. Changes in R ^ , 0 (C2 H 4 >, or 0 (SO2 >
will not affect the 5-coordinate of any of the atoms; thus the value of Pbb is
not useful. This leaves three structural param eters to be fit to Paa and Pcc.
24
Rcm can be uniquely determ ined from Ib = Paa +
= Ia(S02) + Ia(C2 H 4 > +
Rem2 n(C 2 H 4 -S0 2), but only a range of correlated values for 0 (C2 H 4 >and 0 (SO2 )
can be determ ined which are consistent w ith the observed m om ents of
inertia for an individual isotopic species.
A least squares fit to the A i state moments of inertia of all the isotopic
species can resolve some of the am biguity and results in the tw o sets of
structural param eters in Table 2-4.
T able 2-4. Two structures which fit the mom ents of inertia from the Ai state.
_________________________ P __________________________IP _____________
0 (SO2 )/d eg
10.2(2.7)b
10.3(2.7)
0 (C2 H 4)/d eg
19.8(2.1)
- 2 0 .0 (2 .1 )
Rcm/A
3.504(1)
3.504(1)
AIrmsc/am uA 2
0.45
0.45
a* The S-O bond distance was relaxed to match Pbb (see text) to 1.419 A.
b- Positive angles indicate counter-clockwise rotation, negative angles
clockwise. See figure 2-1.
c’ Alnns where AI = lobs’lcalc1
The m agnitude and direction of the angle 0 (SO2 ) are determ ined to be +10.3°
from the 34S and lsO substitution. U sing the data from the deuterated
ethylenes to determ ine the angle 0 (C2 H 4 ) is not so straightforw ard and values
of +19.8° and - 20.0° are consistent w ith the data. The isotopic species that are
sensitive to 0 (C2 H4 ) are C2 H 3 D 2 SO2 and cts-l,2 -C 2 H 2 D 2 ,SC)2 . Even considering
these tw o species, however, it is unclear how the ethylene m oiety is oriented
relative to the SOz. The tilt angle and deuterium positions for these fits place
the D atom s closer to the center of mass (d-in isomers) rather than away.
However, the deuterium substitution m ay lie tow ard either the sulfur side
25
(0 (C2 H 4 ) = +19.8°) or the oxygen side (- 20.0°) of the SOz. The a principal axis
is nearly collinear w ith the Rcm vector, therefore the deuterium coordinates
are nearly identical and the tw o possible orientations give fits of sim ilar
quality.
The data from the higher energy (d-out) isom er of the
cis- 1 ,2 -C2 H 2 D 2 -S0 2 species shed some light on the sign of 0 (C2 H 4 >. Rotational
constants w ere predicted for the d-out isom er for each value of 0 (C 2 H 4 ). As
can be seen in Table 2-5, the only significant difference is in the A constant,
Table 2-5. Predicted and observed (exp) rotational constants and dipole
components for the tw o isomers of cis-1 ,2 -C 2 H 2 D 2 SC>2 -______________
d-in a
d-out a
Exp
Exp
0 (C2H 4)
0 (C2H 4)
0 (C2H 4)
0 (C2H 4)
= +20°
= -20°
= +20°
= -20°
A /M H z
B/MHz
C/M Hz
Ha/D
6296
1934
1596
6301
1934
1596
6284
1937
1599
6312
1890
1565
0.60
0.65
0.597
0.66
1.53
1.50
1.530
1.51
Mc/°
a- See text for explanation of d-in, d-out labels.
6302
1890
1566
6300
1887
1566
0.60
1.54
0.678
1.526
which is 1 MHz larger in the d-out value for 0 (C2 H 4 > negative and 16 MHz
larger for 0 (C 2 H 4 > positive. The observed difference is 16 MHz, consistent
w ith 0 (C2 H 4 ) positive; however, as the absolute agreem ent in the A constants
is com parable to this difference, this is not a definitive test.
Small changes in the dipole m om ent com ponents caused by principal
axes rotation upon isotopic substitution provide a m ore com pelling
26
argum ent for the sign of 0 (C2 H 4 ). Because the sign of the dipole moment
cannot be determ ined directly, there are four choices for the orientation of the
dipole m om ent of the complex. The m ost reasonable choice puts the dipole
m om ent nearly parallel to the symm etry axis of the SO2 , as the dipole
m om ent of the complex is likely to be dom inated by the 1.63305 D 16
perm anent dipole m om ent of the SO2 . This requires only a 0.346 D induced
m oment, which is consistent w ith an ab initio calculation (below), w hile the
other three choices require induced moments of 0.925 D or larger. The two
cis-l,2 -C2 H 2 D 2 *SC>2 species provide the largest axis rotations upon substitution
and thus the m ost sensitive test of the structure. If 9 (C2 H 4 ) w ere positive, the
rotation w ould decrease the /4 ,-com ponent and increase the /Zc-component for
d-in and vice versa for d-out (Table 2-5). Conversely, the opposite should be
seen if 6 (C2 H 4 ) were negative. The changes are easily large enough to be
observed and significantly larger than w hat w ould be expected due to the
perm anent dipole m om ent of ci's-1 ,2 -C 2 H 2 D 2 .1 7 The observed dipole m om ent
com ponents for these two species are clearly consistent w ith the positive
value of
62
and inconsistent w ith the negative one.
The overall least-squares fit residual of 0.45 amu-A2, as well as the poor
agreem ent in the A constants for the cis-1,2 -C 2 H 2 D 2 -S0 2 isomers, can be
attributed to averaging effects of large am plitude vibrational motions. This is
m ost apparent w hen com paring Pbb for the norm al species w ith that
calculated from the free subunits. The large am plitude m otions in the
complex give a structure in which the average ^-coordinates of the atoms are
sm aller than they w ould be in a rigid structure, thus reducing Pbb; the other
inertial param eters w ill be sim ilarly contam inated. An attem pt to further
im prove the structural analysis w ill be. dealt w ith in the next section where
the internal motion will be discussed.
27
Finally, it is interesting to note that the dipole moment determined for
the C2H4-S02 complex (1.650 D) is very similar to the dipole moment of the
free S0 2 subunit (1.633 D). However, the dipole moment of the complex is
rotated some 12° away from the C2 axis of SO2. A projection of the dipole
moment of SO2 for 0 (SO2) = 10° predicts dipole components of |ia = 0.292 D
and ixc = 1.607 D, w hile the m easured values are |ia = 0.629 D and Me = 1.525 D.
This can be explained as arising from an induced dipole m om ent of
m agnitude 0.347 D w ith components of |ia = 0.337 D and Me = - 0.082 D.
Following analogous calculations in PF3 -rare gas complexes18, GAUSSIAN8 6
19
was used to calculate the electric field around SO2 (6-31G* basis set.) A sim ple
model treating ethylene as a point polarizability located at its center of mass
w ith components aaa = 5.53 A3, abb = 3*65 A3 and acc = 3.58 A3 2 0 in the
principal axis system of the ethylene) predicts an induced m om ent of 0.406 D,
w ith components M-a = 0.384 D and Me = ~ 0.131 D. The same approach was
used to estim ate the field that ethylene exerts on SO2 (with polarizability
components aaa = 5.32 A3, abb = 3-51 A3, OcC= 3.01 A3)21 w hich resulted in
induced dipole components from SO2 of Ma = 0.135 D and |ic = - 0.048 D.
A lthough this procedure overestim ates the total induced dipole com ponents
by about a factor of 2 , the signs and relative m agnitudes agree w ith the
experim entally derived values; it also suggests that the m ajority of the
induced dipole m om ent upon com plexation arises from the ethylene.
Internal Motion, Nuclear Spin Statistics and Barrier to Internal
Rotation. Apart from a few exceptions where the splitting is too small to be
observed, the transitions of C2H4 SO2 occur as doublets of unequal intensity.
A number of internal motion pathways can be envisioned which could
account for this: internal rotation of the SO2 about its C2 symmetry axis,
28
"over-the>top" inversion of the SO2 taking the complex through a C 2 V
transition state or rotation of the ethylene about one of its three sym m etry
axes. Since the strong and weak components can be fit independently w ith a
W atson S-reduced H am iltonian, the barrier to the internal m otion m ust be
relatively high. This also elim inates the inversion m otion of the SO2 as this
m otion w ould change the direction of the //c-dipole com ponent of the
complex and give selection rules between tunneling states. The possibility of
the S 0 2 subunit tunneling about its local C 2 axis can also be elim inated on the
grounds that tw o tunneling states are observed. This m otion w ould involve
the exchange of tw o 160 nuclei (1 = 0) and, as in the case of Ar-S0 2 , 2 2 half the
rotation-tunneling levels w ould be sym m etry forbidden.
Three possible pathw ays rem ain viz. the rotation of the ethylene about
each of its C 2 axes. To distinguish among these, the splittings in the spectra of
the three doubly deuterated isotopic species w ere considered. For a spectrum
to exhibit tunneling splitting in its transitions, the tunneling m otion m ust
result in an equivalent species w ith identical rotational constants. The
unsplit spectra of ris-l, 2 -C 2 H 2 D 2 -SC>2 and C 2 H 3 D-S0 2 , therefore, elim inated an
end-over-end flip of the ethylene (i.e. rotation about ethylene's b-axis) as this
m otion w ould give equivalent species w ith identical rotational constants.
In selecting between the tw o rem aining possibilities, the nuclear spin
statistics associated w ith the tunneling doublets in the trans- 1 ,2 -C 2 H 2 D 2 *S0 2
and the 1 ,1 -C2 H 2 D 2 -S0 2 w ere considered. Levels w ith different nuclear spin
statistical w eights occur only in cases w here equivalent nuclei are exchanged
by the m otion and the Pauli principle requires that the sym m etry of the
nuclear spin states be properly paired w ith the sym m etry of a given rotationtunneling level. The expected statistical w eights for the exchange of two
29
protons and tw o deuterons are 1 :1.4 (A i: A 2 ). The results of the relative
intensity m easurem ents are given in Table 2-6 (see also experim ental);
T able 2 -6 . Relative intensity of the tunneling doublets in ethylene-SC?2 a.
Ai
1.55
C2H4S02
C2H 4-S180 160
1.68
1.00
tram-CjJcliP 2 ’S0 2
1.00
1,1-C2H 2D2-S0 2
a- The ratios have an uncertainty of ±15%.
A2
1.00
1.00
1.34
1.02
fra«s-C 2H 2 D 2 ’S0 2 exhibits these spin statistics, w hereas 1 ,1 -C 2 H 2 D 2 -S0 2 does
not. This indicates that equivalent nuclei are exchanged in trans-CjHzPl'SOz
but protons are exchanged for deuterons in 1 , 1 -C2 H 2 D 2 -S0 2 . The pathw ay
consistent w ith this is the rotation of the ethylene in its m olecular plane
(about its local c axis). To ensure that the m easured spin statistical weights
w ere not sim ply fortuitous, the relative intensities of the tw o states in the
norm al isotopic species and C 2 H 4 *S180
160
w ere also examined. For the
exchange of two pairs of protons, statistical w eights of 1.67:1 ( A i : A 2 ) w ould
be expected, and again the m easured values (Table 2-6) are in reasonable
agreem ent.
Further evidence for the effect of the tunneling m otion on spin
statistics can be seen in the deuterium nuclear quadrupole coupling patterns
in frans-C 2 H 2 D 2 -S0 2 and 1 , 1 -C2 H 2 D 2 -S0 2 , as shown in Figure 2. In the case of
1 , 1 -C 2 H 2 D2 -S0 2
, each com ponent of the doublet (a,b) exhibits identical nuclear
quadrupole coupling patterns, whereas in tr a n s ^ jh ljU x S ^ (c,d), the patterns
for the two components are distinctly different. As w ith the relative
intensities, this difference arises because identical nuclei are exchanged upon
30
internal rotation in trans-C 2 H 2 D 2 *S0 2 w hile in 1 , 1 -C2 H 2 D 2 ,S0 2 they are not.
Thus, in the frans-C 2 H 2 D 2 -SC>2 spectrum only the hyperfine transitions
allowed by the Pauli principle appear in each state. In 1 ,1 -C2 H 2 D 2 *S0 2 , there is
no exchange of identical nuclei and therefore all nuclear spin states are
allow ed for each rotation-tunneling level.
50 kHz
8224.075
8206.570
8210.750
8193.715
Figure 2 -2 . D euterium nuclear quadrupole hyperfine patterns for the
liO-Ooo transitions of (a) the A i tunneling state of 1 , 1 -C 2 H 2 D 2 *S0 2 , (b)
the A2 state of 1 ,1 -C2 H 2 D 2 *S0 2 (c) the A i state of frans-C 2 H 2 D 2 -SC>2 and
(d) the A2 state of trans-C2 l h P 2 'S0 2
The splittings in the spectrum thus result from an internal rotation of
the ethylene in its molecular plane. Given this and the geom etry of the
31
complex, the spectrum was fit by Taleb-Bendiab 23 using the following internal
rotation H am iltonian .2 4
H = A Ja2 + BJb2 + C Jc2 + Dac(Ja Jc + JcJa>
0)
- 2 (QaJa + QcJc) j + Fj2 + § V 2 (l-cos2<x)
w here
A=^
+ FP“2
B=l s
c- ^
+ Fp<?
Dac = F Pa Pc
Qa = F Pa
Qc = F pc
H2
F — 2 rla
r —1 —A.apa —^-cPc
Pa “ •■
I •aa
P c-
t
Joc
Ja, Jb and Jc are the projections of the total angular m om entum onto
the principal axes, a, b and c, respectively; j is the angular mom entum of the
internal rotor, a is the internal rotation coordinate, and V2 is the two-fold
barrier height; laa/ Ibb and Icc are the principal mom ents of inertia of the rigid
rotor; la is the moment of inertia of the internal rotor; A.a (Xc) is the direction
cosine between the internal rotor axis (c-axis of the ethylene subunit), and the
a- (c-) inertial axis. The m om ent of inertia of the internal rotor, Ia, was set
equal to Icc of free ethylene. To account for centrifugal distortion effects, the
W atson S-reduction quartic centrifugal distortion H am iltonian was added to
the internal rotation H am iltonian. The H am iltonian m atrix of H was
constructed using IJK M ^ [(2 rc)-1/ 2] e*1™*, where IJK M ^ are asym m etric rotor
wavefunctions and [(2jc)-1/ 2] e11™1 are free rotor wavefunctions. The resulting
infinite matrix was diagonalized w ith the free-rotor basis set truncated at m =
±13.
32
The constants obtained from this fit for the norm al spedes are given in
Table 2-7 and agreem ent w ith experim ental frequences is show n in Table 2-1.
Barriers w ere calculated for all isotopes exhibiting internal rotation splitting;
these are presented in Table 2-8. The agreem ent is quite good, w ith all
barriers about 31 cm-1.
Table 2-7. M olecular constants for C2 H 4 -S0 2 derived w ith the internal
rotation H am iltonian (see equation 1).____________________________
Fixed param eters
Fitted param eters
F/M H z
32747.868
A /M H z
8741.25(23)
Qc/MHz
2009.697(20)
601.245
B/M Hz
Q a/M Hz
8255.867
1664.542(12)
C/M Hz
Dac/M H z
151.576
D j/kH z
DjK /kH z
Dk /k H z
d i/k H z
d2/kH z
V2 /c m _1
nc
A ^nns/kH z
3.98(39)
162.9(33)
-159.3(300)
-1.26(21)
-1.64(19)
30.159(13)
56
244
a* A,a = cos 0 a.
*>• A' = K2 /2Iaa = A - Fpa2, etc.
c- N um ber of transitions in fit.
A 'b/M H z
B’/M H z
C '/M H z
9aa
0C
6659.912
2009.697
1653.504
20°
74o
33
Table 2-8. Calculated V2 barriers to internal rotation for isotopic species of
ethylene-SQ 2 Barrier / cm ”1
n
AVnns
C2 H 4 S0 2
30.16(2)a
56
0.244
C2H 4 S1 8 0 2
30.39(2)
43
0.154
C2D4*S02
31.59(2)
44
0.039
frans-C 2 H 2 D 2 *S0 2
30.97(2)
41
0.068
1 ,1 -C2 H 2 D 2 'S0 2
30.84(2)
40
0.086
26
0.103
C 2 H4-S180 160
30.32(2)
a- U ncertainty in parentheses is 2a.
Given the dependence of the effective rotational constants on the
direction cosines of the internal rotation axis w ith respect to the principal
inertial axes, and noting that the A constant is m ost affected by the internal
rotation, it is clear that the internal rotation axis is close to the a principal axis,
confirm ing a tunneling m otion of ethylene in its m olecular plane. A ttem pts
by Taleb-Bendiab to fit the transitions to the other possible m otions of the
ethylene resulted in AVrms (obs - calc) values of several MHz.
The original W atson H am iltonian fit to independent states produces a
better Avrms than the internal rotation fit by about a factor of 10. Nevertheless,
the internal rotation fit and its transferability to the various isotopes is quite
compelling. The structure derived from least squares fitting of the "internal
rotation-corrected" m om ents of inertia is quite sim ilar to th at determ ined
from the A i constants and is listed in Table 2-9. The differences can be used to
estim ate lim its for the uncertainties of die structural param eters. The
structure in Table 2-9 is preferred since the internal rotation effects have been
m inim ized. The structural param eters are still contam inated by vibrational
34
averaging effects and should be considered analogous to those of an rQ
structure.25
T able 2-9. Structure calculated from internal rotation constants.®
0(SO2)/d eg
13.2(2.7)
0 (C2 H 4)/d eg
21.1(2.1)
3.502(1)
Rcm/A
0.43
AIrmsb/am uA 2
a- Preferred structure.
b* AI = lobs = Icalc-
D euterium N uclear Q uadrupole C o u plin g. For the C2 H 3 D SO 2 spedes,
the deuterium n u d ear quadrupole hyperfine structure w as resolved and
assigned for several transitions. The assigned hyperfine com ponents are
Table 2-10. D euterium n u dear quadrupole hyperfine structure and coupling
constants for C2 H 3 D-SQ2.___________________________________________
obs-calc
vobs
Kp* Ko' F ’ J"
(MHz)
K0" F" (MHz)
V
1
8443.448
1
1
0
1
0
0
0.0005
0
8443.412
1
1
2
0
1
-0.0028
0
0
0
1
8443.368
1
1
0
0
0
0
0.0023
0
V
3
3
3
2
2
2
2
2
2
2
4
3
2
2
2
2
2
2
1
1
1
1
3
2
10787.829
10787.809
10787.770
-0.0006
0.0007
3
3
3
2
2
2
2
2
2
3
4
2
3
3
3
1
1
1
2
2
2
3
4
2
12998.799
12998.786
12998.779
0.0003
0.0010
-0.0013
2
2
1
3
2
1
1
3
13505.709
0.0010
0 .0 0 0 0
35
2
2
1
1
2
1
1
1
13505.684
-0 .0 0 1 0
4
4
0
4
4
5
4
3
3
1
2
1
2
4
3
8415.703
8415.665
0.0030
-0.0030
0
2
2
2
4
4
3
5
3
14368.568
-0.0013
4
2
2
2
14368.554
4
3
3
3
0.0013
Xaa= - 0.119(1) MHz
%bb = 0.010(1) MHz
Xcc = 0.109(1) MHz
listed in Table 2-10, along w ith the calculated nuclear quadrupole coupling
constants. The coupling constants were determ ined by a least-squares fitting
procedure which treats the quadrupole interactions as perturbations on the
rotational energies .'2 6
To interpret the nuclear quadrupole coupling constants, the electric
field gradients at the deuterium site arising from unperturbed (i.e.
uncomplexed) ethylene and SO2 w ere calculated using GAUSSIAN86.19 The
calculations w ere initially done at the Hartree-Fock level using a 6-31G* basis
set. To test the reliability of the electric field gradients, the calculations w ere
repeated w ith STO-3G and 4-31G basis sets and the three calculations agreed to
w ithin 10%. These ab initio electric field gradients w ere rotated into the
principal inertial axis system of the complex to estim ate the contributions
from each subunit to the nuclear quadrupole coupling constants, shown in
Table 2-11. The calculations indicate that the quadrupole coupling in the
complex is due alm ost entirely to the electric field gradient arising from the
ethylene charge distribution w ith
<1
kHz contribution from the SO2 field
gradient. There does not appear to be any previous m easurem ent of the
coupling constants for free C 2 H 3 D and the accuracy of the calculated values is
36
difficult to estim ate, precluding any firm conclusion regarding the effects of
complex form ation of the coupling constants except that they are small.
Table 2-11. Nuclear quadrupole coupling constants of C2 H 3 D-S0 2 (MHz).
Exp
Calculated
so 2
C2H4
Xaa
Xbb
Xcc
-0.119
0.010
0.109
-0.1029
0.0182
0.0847
0.0005
0.0000
-0.0005
It m ay be useful for com parison purposes to use the coupling constants
of the complex to estim ate the quadrupole principal axis com ponents in
ethylene. The ab initio calculations on free ethylene suggest that the principal
axis of the electric field gradient tensor at the deuterium site is nearly
cylindrically symmetric about the C-D bond (6-31G* values: Xxx = -0.2257
MHz, %yy = 0.1609 MHz, Xzz = 0.1188 MHz, x along the C-D bond, z
perpendicular to the m olecular plane). N eglecting the off-diagonal
com ponents, which cannot be determ ined, and rotating the observed
quadrupole coupling tensor into the same orientation using the
experim entally determ ined structure gives %xx = -0.2581 MHz, Xyy = 0.1504
MHz, and Xzz = 0.1077 MHz.
Force Constants and Binding Energy. Treating the complex as a
pseudo-diatom ic molecule, the Dj distortion constant may be related to the
stretching force constant of the van der Waals bond using the m odel of
M illen .2 7
37
ko =
[4B4 + 4C4 - (B+C)2 (B-C)2]
From this, a force constant of 0.05713 m dyne/A is obtained and, using a
Lennard-Jones 6-12 potential, the binding energy is calculated as 490 cm-1.
Sum m ary
The study of the ethylene-S0 2 complex by m icrowave spectroscopy has
determ ined that the complex has a stacked structure w ith the S atom of SO2
apparently interacting w ith the k system of ethylene. This is in agreem ent
w ith the structural predictions of previous workers. A dditionally, the
spectrum of the ethylene-S 0 2 complex is perturbed by tunneling doublets
because the ethylene subunit undergoes a high-barrier internal rotation
motion about its local c axis. The pseudo-diatom ic model estim ates the
binding energy of the complex as approxim ately 1.4 kcal/m ole, which falls
w ithin the range of previously determ ined binding energies for sim ilar
complexes.
38
Table 2-12. Observed transitions for C2D4-S02T ransition
lio-Ooo
2 1 1 -1 0 1
312-202
2 2 1 -2 h
322-312
423-413
524-514
2 2 0 -2 1 2
321-313
4o4-3i2
2 0 2 -1 0 1
2 li-llO
3l3-2l2
3o3“2o2
322-221
321-220
3i2-2n
4i4-3i3
404-303
422-321
4i3-3i2
5i5-4l4
A i State
A2 State
Vobsa
o-cb
o-c0
v0 bsa
7786.229
11438.960
15251.990
12394.900
11938.552
11338.108
10602.269
13340.817
13879.568
7921.025
6670.542
6996.451
9555.100
9963.980
10027.211
10093.827
10483.588
12721.475
13209.035
13520.649
13956.662
15873.487
0.007
0.005
-0.007
-0 .0 1 0
0.008
-0.023
-0.009
-0 .0 2 1
-0.048
0.005
0.043
0.095
-0.060
-0.023
-0.023
-0.013
7779.638
11432.282
15245.391
12381.631
11925.287
11324.893
10589.141
13327.612
13866.597
7927.187
6670.486
6996.451
9554.996
9963.831
10027.241
10093.891
10483.571
12721.365
13208.751
13520.879
13956.601
15873.333
0 .0 0 1
-0 .0 0 1
-0.009
0 .0 1 1
0.005
-0 .0 2 0
0.015
0 .0 0 1
0 .0 0 0
-0 .0 1 0
0.004
0.009
-0.004
-0 .0 0 2
-0.008
0.007
0 .0 0 1
0 .0 1 1
0.013
-0.017
0.016
0.025
-0.009
0.006
-0.027
0.006
-0 .0 1 1
-0 .0 1 0
o-cb
0.064
-0.038
-0.014
-0.005
0 .0 0 0
0 .0 0 1
-0 .0 0 2
-0.035
0.041
0 .0 1 2
0.003
0 .0 2 1
o-cc
-0.008
-0.019
-0.003
0.032
-0 .0 0 1
-0.046
-0.096
0 .0 2 0
0.077
0.044
0.024
0.034
-0.007
-0.013
-0 .0 0 1
0.023
-0.026
0.004
0.003
0.004
-0.005
-0.004
-0 .0 2 0
-0.006
0 .0 0 1
0 .0 0 1
0 .0 2 2
-0.003
-0.039
0.015
0.006
0 .0 2 2
was not
resolved and assigned. v0bs are frequencies of the most intense peaks in the
hyperfine pattern
b. Calculated using Watson S-reduced Hamiltonian.
c. Calculated using Internal Rotation Hamiltonian.
39
Table 2-13. Observed transitions for fraws-C2H2D2-S02A i State___________
A 2 State
o-cb
o-cb
o-c*
v0bsa
8193.775
-0.009
-0.001
-0.009
-0.022
-0.001
12016.495
0.006
16010.066
-0.003
-0.028
0.003
-0.052
0.005
-0.017
13116.109
0.005
0.010
12629.982
0.005
-0.002
0.078
11990.472
0.007
-0.007
11206.937
0.151
0.000
0.009
-0.088
14124.245
0.016
-0.008
-0.079
14698.906
-0.006
-0.041
-0.003
15551.858
-0.005
d
-0.005
-0.076
o-cc
Vobsa
8206.594
-0.019
lio-Ooo
12029.276
-0.003
2n -lo l
16022.763
0.003
3i2-2o2
13144.230
0.058
221-2h
12658.062
0.012
322-312
12018.478
-0.074
423-413
11234.795
-0.188
524-514
14152.163
0.108
220-212
14726.505
32l-3i3
0.046
15578.808
0.017
422-414
8181.873
404-312
9973.020
-0.003
-0.019
9972.865
0.001
0.005
3i3-2i2
10408.398
-0.006
-0.055
10408.120
-0.005
0.035
3o3-2o2
10962.302
-0.027
0.016
10962.252
-0.004
0.027
3i2-2n
13277.399
0.001
-0.016
13277.167
0.002
0.016
4l4-3l3
13796.239
13795.677
4o4“3o3
0.000
-0.048
-0.005
0.055
13953.794
0.021
13953.759
0.059
-0.013
-0.033
423-322
14129.701
0.005
0.021
0.007
14130.123
-0.009
422-321
14593.325
-0.025
-0.062
0.014
14593.298
0.082
4i3-3i2
16566.379
0.000
16566.055
0.027
-0.013
-0.003
5l5-4l4
17120.940
0.001
-0.035
0.000
17119.995
0.081
5o5-4q4
a. H ypertine structure from deuterium nuclear quadrupole coupling was not
resolved and assigned. v0bs are frequencies of the m ost intense peaks in the
hyperfine pattern
b. Calculated using W atson S-reduced H am iltonian.
c. Calculated using Internal Rotation H am iltonian.
d- N ot observed. Predicted at 8193.7. Falls under lio-Ooo-
40
Table 2-14. Observed transitions for 1,1-C2H2D2*S02.
A i State
o-cb
A 2 State
O-cb
o-c0
o-c0
Vobsa
Vobsa
8224.106
0.024
0 .0 1 2
0.054
-0.013
8210.885
lio-Ooo
12044.452
0.007
-0.045 12031.279
0.005
0.061
2 1 1 -1 0 1
0 .0 0 2
16034.233
-0.009
0.072
-0.085 16021.186
3i2-2o2
12720.814
-0.080
-0.087 12691.792
-0.041
-0.031
322-312
12085.847
0 .0 1 0
0.060 12056.902
0 .0 1 1
-0.042
423-413
11307.507
0.054
0.167 11278.730
0.017
-0.106
524-5i4
-0.007
10399.424
-0.025
0.080 10371.053
-0.198
625-615
14772.763
0.024
0.058
-0.049 14744.234
0.134
321-313
-0.004
15616.369
-0.018
-0.152 15588.669
0.128
422-414
8176.304
0 .0 2 1
0.062
8188.408
0 .0 1 1
-0.003
4o4-3i2
5()5-4i3
10714.558
0.054 10725.697
0 .0 0 1
0.009
-0.056
-0.037
7313.931
-0.061
7313.931
-0.030
-0 .0 0 1
l l 0 -2 ll
0.004
9977.528
0 .0 2 2
9977.324
0.005
0 .0 0 2
3i3-2i2
10410.296
0.008
-0.018 10409.272
-0.003
0.027
303-202
10959.272 -0 .0 2 0
-0.028 10959.253
0.006
0.026
3l2-2ll
0 .0 0 2
13283.749
0.016 13283.451
-0.003
-0 .0 1 1
4l4-3l3
13800.242
0.006
-0.024 13799.614
0 .0 0 1
0.027
404-303
14589.799
0.013
-0.052 14589.724
0.000
0.054
4l3-3l2
16574.833
-0.010
0.009 16574.418
-0.015
-0.032
5l5-4l4
-0.007
-0.034 17127.016
17128.053
0 .0 0 1
0 .0 1 2
505“404
a. Hypertine structure from deuterium nuclear quadrupole coupling was not
resolved and assigned. v0bs are frequencies of the most intense peaks in the
hyperfine pattern
b. Calculated using Watson S-reduced Hamiltonian.
c. Calculated using Internal Rotation Hamiltonian.
41
Table 2-15. Observed transitions for C2 H 4 -S180
160
.
A i State__________________ A 2 State
0 -c3
0 -c3
o-cb
Vobs
Vobs
0.004
8368.266
0.003
0.000
8390.548
lio-Ooo
12340.522
0.003
0 .0 0 1
-0.028
12362.749
2 1 1 -1 0 1
-0.067
0 .0 0 1
16499.425
-0.005
16521.490
312-202
11977.935
0.000
12023.622
0.000
423-413
14300.624
0.000
0.000
14345.465
2 2 0 -2 1 2
8502.544
-0.131
0 .0 0 1
0 .0 0 1
8482.140
4o4-3l2
7205.857
0.000
- 0 .0 0 1
-0.066
7206.061
2 0 2 -1 0 1
7858.816
0.003
0.003
0.070
7585.816
2 ll- ll 0
-0.034
-0.007
10287.644
-0.003
10287.338
3i3-2i2
-0.094
10756.647
10756.108
-0.003
-0.003
303-202
-0.004
0.105
11364.768
- 0 .0 0 1
11364.800
3i2-2n
-0.047
13693.139
0.007
0.003
13693.608
4i4-3i3
14246.982
-0.106
14245.861
-0 .0 0 2
0.003
404-303
15125.987
15125.854
0.004
0 .0 0 1
-0.139
4i3-3i2
0 .1 2 2
17662.927
17664.841
-0.003
-0.003
505-404
a. Calculated using W atson S-reduced Hamiltonian.
b. Calculated using Internal Rotation Hamiltonian.
o-cb
-0.005
0.032
0.066
0.134
0.063
-0.064
0.031
0.089
-0.107
0.045
0.111
0.140
-0.123
42
Table 2-16. Observed transitions for C2H4*S1802.
A i State_____________________ A 2 State
o-c®
o-c®
o-cb
Vobs
Vobs
8089.782
12023.632
0 .0 0 0
2 1 1 -1 0 1
16149.212
0 .0 0 1
3i2-2o2
0.004
12470.506
2 2 1 -2 h
0 .0 0 2
11930.790
322-312
423-413
11222.723
-0 .0 0 1
-0.003
10359.119
524-514
0.003
9359.676
625-615
-0 .0 0 2
13598.196
2 2 0 -2 1 2
-0 .0 0 1
14254.458
32i-3i3
8493.227
4o4-3i2
-0 .0 0 2
-0.024 10931.763
10916.343
505-413
7500.304
-0 .0 0 2
-0.067
7500.304
2 n - li0
10132.067
0.003
-0.030 10131.777
3i3-2i2
10606.581
-0.003
-0.086 10606.054
3o3“2o2
10695.367
-0 .0 0 2
10695.317
0 .0 0 1
322-221
10787.710
0.003
0.005 10788.042
321-220
11235.075
-0 .0 0 1
-0.097 11235.036
3l2-2ll
-0.041
13483.927
0.003
13483.476
4l4-3l3
14037.505
0.000
-0.098 14036.407
404-303
14241.959
-0.003
-0 .0 0 2
14241.870
423-322
0.004
14950.085
-0 .1 2 0
14949.923
4i3-3i2
a. Calculated using W atson S-reduced H am iltonian.
b. Calculated using Internal Rotation Ham iltonian.
lio-Ooo
8108.756
12042.549
16167.988
12517.645
11977.936
11269.815
10406.013
9406.086
13644.973
14300.617
-0.003
-0.068
-0.099
-0.134
-0.139
-0.042
0.082
0.226
0.392
-0.213
-0.188
-0.005
0.004
-0.006
o-cb
-0.009
0.003
0.066
0.108
0.135
0.137
0.044
-0.087
-0.248
-0.400
0 .0 0 2
0 .2 1 0
-0.004
-0 .0 1 1
0.004
-0 .0 0 2
0.189
0.017
0.018
0.057
0.029
0.077
-0 .0 0 1
0 .0 0 1
0.006
0 .0 0 2
0 .0 0 2
0 .0 0 1
0.007
-0 .0 0 1
0.005
-0.003
0.003
0.005
-0.005
0 .0 1 1
0.095
0.041
0.098
0 .0 0 1
0.118
43
Table 2-17. Observed transitions for C2H4<34S02.
Vobs
A i State___________________________ A 2 State
o-cb
o-c3
o-cb
o-c3
Vobs
8632.754
-0.395
-0.033
8612.464
lio-Ooo
12593.532
12614.155
0.405
0.070
2n -lol
10377.607
0.444
-0.175
10377.285
3l3-2l2
10833.222
-0.474
-0.380
10833.010
3o3-2()2
-0.082
14360.411
-0.366
14360.411
404-303
a. Calculated using W atson S-reduced H am iltonian.
b. Calculated using Internal Rotation H am iltonian.
-0.182
0.177
0.025
-0.566
0.363
0.096
-0.144
-0.096
0.074
0.820
Table 2-18. Observed transitions for the d-in isomer of C 2 H 3 D-S0 2 .
T ransition
0 -c 3
T ransition
Vobs
8443.435
0.005
lio-Ooo
3i3-2i2
12384.103
-0.006
3<)3-2o2
2 n -lo i
16502.950
-0.005
312-202
322-221
13505.642
-0.009
221-2h
321-220
12998.793
0 .0 0 1
3l2-2ll
322-312
12332.152
0 .0 1 1
423-413
4i4-3i3
11515.579
-0.007
524-514
404-303
14556.739
0 .0 1 1
2 2 0 -2 1 2
423-322
15156.556
-0.005
422-321
321-313
8415.697
-0.005
4o4-3i2
4i3-3i2
7538.121
-0.005
2 ll- ll 0
505-404
a. Calculated using W atson S-reducec H am iltonian.
VobS
10263.304
10716.378
10787.807
10863.143
11294.663
13663.338
14202.272
14368.566
14554.489
15035.217
17621.682
0 -c 3
0.000
0 .0 0 1
0 .0 1 1
0.007
0.008
0.003
-0.007
-0 .0 0 1
0.008
-0 .0 0 2
0.006
44
Table 2-19a. Observed transitions for the d-in isomer of cis-C2 H 2 D 2 -SQ2 o-ca
T ransition
o-c3
T ransition
Vobs
Vobs
10087.544
-0.007
-0.001
8227.558
3i3-2i2
lio-Ooo
10531.202
12099.807
0.017
-0.005
303-202
2n -loi
10601.997
16146.849
-0.002
-0.010
322-221
3i2-2o2
0.012
10676.896
0.001
13063.378
221-2h
321-220
0.002
3i2-2n
12566.131
11099.239
0.003
322-312
-0.004
13429.162
4i4-3i3
11912.281
-0.001
423-413
11111.718
-0.003
4o4-3q3
13955.976
-0.002
524-514
14120.957
0.003
-0.001
10179.405
423-322
6 2 5 -6 1 5
14094.672
-0.012
14744.807
0.005
4i3-3i2
220-212
14684.037
-0.003
16754.721
321-3i3
0.005
5i5-4i4
8340.328
0.003
17314.881
-0.002
4o4-3i2
505-4q4
-0.003
10880.403
5o5-4i3
a. Calculated using W atson S-reduced Hamiltonian.
Table 2-19b. Observed transitions for the d-out isom er of cfe-C2 H 2 D 2 -SQ2 .
T ransition
o-c
Vobs
llO-Ooo
2 n -lo i
3l3-2l2
303-202
3i2-2n
8188.861
11964.492
9868.519
10294.917
10833.702
0 .1 0 0
-0.107
-0.336
0.514
0.140
45
Table 2-20. Spectroscopic constants of isotopic species of ethylene-S02 from
W atson S-reduced H am iltonian.
Q H ^SC ^
C2 H 4 *S^®0 2
C2H4-S180160
A i State
A /M H z
B/M H z
C/M H z
6412.063(3)a
1967.460(1)
1599.404(1)
6404.769(4)
1986.679(2)
1627.301(1)
D j/kH z
D jx/kH z
DR/kHz
d i/k H z
d2/kH z
4.44(2)
160.41(9)
255.2(6)
-1.17(7)
-1.03(9)
4.7(1)
162.7(3)
368.5(8)
-0.99(2)
-0.30(5)
nb
0.003
15
0.003
A /M H z
B/M H z
C/M H z
6122.247(5)
1967.473(1)
1599.332(1)
6380.668(6)
1986.689(2)
1627.234(2)
D j/kH z
DjK/kHz
DR/kHz
d i/k H z
d2
4.36(3)
156.7(2)
-565(1)
-1 .2 0 (1 )
-0.99(2)
5.02(2)
154.1(5)
-143(1)
-0.73(4)
0 .2 1 (8 )
V0bs-Vcal im s/M H z
21
6643.3(8)
1990.9(3)
1645.5(2)
-
-
5
0.612
A 2 State
nb
6621.4(6)
1990.9(3)
1645.5(2)
-
-
15
5
0.006
0.005
0.509
vobs-Vcal rm s/M H z
a. Uncertainties are one standard deviation in the least squares fit.
b. N um ber of transitions in the fit.
22
46
T able 2-20 (cont'd). Spectroscopic constants of isotopic species of ethylene-SC>2
from W atson S-reduced H am iltonian.
frans-C2H2D2-S02 I4 -C2H2D2SO2
C2D4 SO2
A i State
A/M H z
B/MHz
C/MHz
5959.945(8)
1826.734(2)
1516.985(2)
6295.478(9)
1911.902(3)
1581.871(2)
6314.135(28)
1910.742(8)
1583.210(6)
Df/kHz
DjK/kHz
DR/kHz
di/kH z
d2/kH z
3.91(5)
149.5(2)
138(2)
-0.87(3)
-0.79(3)
4.50(5)
159.0(2)
279(2)
-1.09(3)
-0.93(3)
4.6(2)
158(1)
289(8)
-1.14(9)
-0.8(1)
22
0.010
21
0.011
20
0.038
A/M H z
B/MHz
C/MHz
5952.735(22)
1826.737(6
1516.963(4)
6281.795(9)
1911.902(3)
1581.828(2)
6300.036(14)
1910.739(4)
1583.152(3)
Dj/kHz
DjK/kHz
DK/kH z
di/kH z
d2
3.9(1)
146.8(5)
-416(5)
-0.9(8)
-0.73(7)
4.46(5)
155.3(2)
-581(2)
-1.09(3)
-0.94(2)
4.56(8)
151(6)
-582(4)
-1.10(5)
-0.78(6)
22
0.028
20
0.010
20
0.019
n
V0bs"vcal rms/MHz
A2 State
n
vobs*vcal rms/MHz
47
Table 2-20 (cont'd). Spectroscopic constants of isotopic species of ethylene*S02
from W atson S-reduced H am iltonian.
cis-C2 H 2 D 2 -S0
2
C2 H 3 DSO 2
d-in
A /M H z
B/M Hz
C/M Hz
6291.227(6)
1936.741(2)
1599.219(1)
6472.873(6)
1970.948(2)
1626.878(1)
D j/kH z
DjK/kHz
DK/kHz
d i/k H z
d 2 /kH z
4.23(3)
183.2(2)
-173(1)
-1.07(2)
- 1 .0 2 (2 )
4.53(3)
175.2(1)
-163(1)
-1.03(3)
-0.99(2)
n
V0bs"vcal rms/MHz
23
0.008
d-OUt
A /M H z
B/M Hz
C/M Hz
6300.8(4)
1887.9(1)
1566.1(1)
D j/kH z
DjK/kHz
DK/kHz
d i/k H z
d2
-
n
vobs“Vcal rms/MHz
5
0.354
-
22
0.008
48
References To C hapter 2
1.
L.J. Andrews and R. M. Keefer, J. Amer. Chem. Soc., 73,4169 (1951).
2. D. Booth, F. S. Dainton and K. J. Ivin, Farad. Soc. Trans., 55,1293 (1959).
3. J. R. Grover, E. A. W alters, J. K. Newm an, M. G. W hite, J. Amer. Chem.
Soc., 107,7329 (1985).
4. L. Fredin, Chem. Scr., 4 ,97 (1973).
5. L. N ord, J. Molec. Struct., 96,27 (1982).
6.
a.) J. S. M uenter, R. L. DeLeon, A. Yokozeki, Farad. Disc. Chem. Soc. 73,
63 (1982). b.) R. L. DeLeon, J. S. M uenter, Atmos. Environ., 18,995
(1984).
7.
K. W. Hillig n, J. Matos, A. Sdoly, R. L. Kuczkowski, Chem. Phys. Lett.,
133,359(1987).
8.
R. K. Bohn, K. W. Hillig
(1989).
9.
K. Tanaka, H. Ito, K. H arada, T. Tanaka, J. Phys. Chem., 80, 5893 (1984).
n, R. L. Kuczkowski, J. Phys. Chem.,
93, 3456
10. M. S. LaBarge, K. W. H illig n, R. L. Kuczkowski, Angew. Chem., Int't
English Edn., 27, 1356 (1988).
11. J. K G. W atson, J. Chem. Phys., 46,1935 (1967).
12. C. W. Gillies, J. Z. Gillies, R. D. Suenram, F. J. Lovas, Ohio State M olecular
Spectroscopy Symposium, Columbus, OH, Paper TF4, June, 1989.
13. T. R. Dyke, B. J. H ow ard, W. Klemperer, J. Chem Phys., 56, 2442 (1972).
14. H. S. Gutowsky, C. Chuang, J. D. Keen, T. D. Klots. T. Emilsson, J Chem.
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15. M. D. Harmony, V. W. Laurie, R. L. Kuczkowski, R. H. Schwendeman,
D. A. Ramsay, F. J. Lovas, W. J. Lafferty, A. G. Maki, J. Chem. Phys. Ref.
Data, 8,619 (1979).
16. F. J. Lovas, J. Chem. Phys. Ref. Data, 14, 395 (1985).
17. A pparently, the dipole moment of cis-C 2 H 2 D 2 has not been determ ined.
The value for LI-C 2 H 2 D2 is 0.0091 D. E. H irota, Y. Endo, S. Saito, K.
Yoshida, I. Yamaguchi, K. M ochida, J. Mol. Spec., 89, 223 (1981).
49
18. A. Taleb-Bendiab, M. S. LaBarge, L. L. Lohr, R. C. Taylor, K. W. H illig
R. L. Kuczkowski, R. K. Bohn, J. Chem. Phys., 90,6949 (1989).
n,
19. J. M. Frisch, J. S. Binkley, H. B. Schlegel, K. Raghavachari, C. F. Melius,
R. L. M artin, J. J. P. Stewart, F. W. Bobrowicz, C. M. Rohlfing, L. R.
Kahn, D. J. DeFrees, R. Seeger, R. A. W hiteside, D. J. Fox, E. M. Fluder
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Publishing U nit, Pittsburg, PA 1986).
20. Y. Chen, T. Oka, J. Chem. Phys., 88,5282 (1988).
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22. R. L. DeLeon, A. Yokozeki, J. S. M uenter, J. Chem Phys, 73,2044 (1980).
23. A. Taleb-Bendiab, Ph.D. Thesis, 1991.
24. J. D. Swalen, D. R. Herschbach, J. Chem. Phys., 27,100 (1957).
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27. D. J. Millen, Can. J. Chem., 63,1477 (1985).
CHAPTER 3
THE ACETYLENE-SULFUR DIOXIDE COMPLEX
Because the study of a series of related complexes has been valuable in
determ ining the nature of interm olecular interactions, the characterization of
the C 2 H 4 -S0 2 complex was followed by the study of the C 2 H 2 -S0 2 complex,
w ith the object of determ ining the sim ilarities and differences w hich occurred
upon a change in the hydrocarbon moiety. The C2 H 2 *S0 2 complex was first
observed by M uenter and coworkers in a m olecular beam m ass spectrom etry
focusing experim ent. 1 From the com petition for form ation am ong C 2 H 2 -S0 2 ,
(C2 H 2>2 C 2 H 2 *Ar, (S0 2 )-Ar and (S0 2 >2 / they inferred that a relatively strong
van der W aals interaction occurred between C 2 H 2 and SO2 . No attem pt was
m ade to observe the spectrum and consequently no inform ation on the
structure or internal dynam ics of the complex was obtained. Solution studies
have shown th at SO2 forms charge-transfer complexes w ith electron donors
such as olefins2 and arom atic system s,3 how ever the acetylene-S 0 2 system
apparently has not been the subject of such investigations.
We were uncertain of w hat to expect for the structure of this complex.
The C2 H 4 SO 2 complex, and sim ilarly the C 2 H 4 O 3 and C 2 H 2 O 3 complexes,4 ' 5
have a stacked near-parallel planes structure. It appears that the prim ary
interaction in C 2 H 4 -S0 2 occurs between the S atom of the SO2 and the n
system of the hydrocarbon. This is consistent w ith inferences from earlier
charge-transfer studies .2 However, the hydrogens of C2 H 2 are considerably
50
51
more acidic than those of C2 H 4 6 and complexes of ad d s w ith SO2 , such as
S 0 2 -HC1 and SC>2 -HF,7 are characterized by hydrogen bonding of the acid to an
O atom of SO2 . A dditionally, in C2 H 4 H 2 O, the H 2 O is hydrogen-bonded to
the jc system of C 2 H 4 , while in C2 H 2 -H2 0 , the C 2 H 2 hydrogen bonds to the O
of H 2 O. The question arises w hether this interaction m ight dom inate in
C 2 H 2 S 0 2. Regarding internal dynamics, it was anticipated that the spectrum
of the complex m ight display evidence of internal rotation, espedally if its
configuration resembled that of the C2 H 4 -S0 2 , C2 H 4 O 3 , and C2 H 2 O 3
complexes. The spectra of the latter all are characterized by tunneling
splittings from an internal rotation of the hydrocarbon subunit about an axis
nearly collinear w ith the Rem vector. A dditionally, the structurally-unrelated
acetylene dim er exhibits com plicated internal m otions w hich m anifest
themselves in its infrared and microwave spectra .8 This chapter reports an
analysis of the rotational spectrum of the C 2 H 2 SO2 complex which is
consistent w ith the stacked structure. Surprisingly, no evidence for a
tunneling motion was detected.
Experim ental
In stru m e n t The rotational transitions of C 2 H 2 SO2 w ere observed in
the Fourier transform microwave (FTMW) spectrom eter at the U niversity of
M ichigan using a m odified Bosch fuel injector as a pulsed supersonic nozzle
source ;9 initial searches were m ade on a sim ilar instrum ent at the U niversity
of Exeter. 10 Line w idths for transitions not split by deuterium nuclear
quadrupole coupling w ere typically 20 kH z full w idth at half maximum and
center frequencies w ere reproducible to ± 2 kHz. For the deuterated species,
the nuclear quadrupole hyperfine structure w as resolved in only a sm all
52
num ber of the observed transitions, so the center frequencies w ere estim ated
as the m ost intense of the unresolved hyperfine peaks. These lines w ere very
broad (in some cases up to 150 kHz) and center frequencies were estim ated to
be accurate only to ± 20 - 30 kHz.
For the m easurem ent of Stark effects, the spectrom eter was fitted w ith
two parallel steel mesh plates to which up to 10 000 V DC can be applied w ith
opposite polarity. The electric field was calibrated on each day that Stark
effects were m easured using the 2 o2 - 1 ii, Mj = 0 and ±1 transitions of SO2 .11
Sam ples. The spectra w ere observed w ith a gas m ixture of 1% C2 H 2 ,
1% SO2 and 98% Ar at a total backing pressure of 1 - 2 atm. The C 2 D 2 sample
(98%) was purchased from MSD Isotopes and used w ithout dilution. The
C 2 HD sample was prepared by reacting a 70:30 m ixture of D2 O /H 2 O w ith
CaC 2 . The gases evolved w ere passed through a dry ice trap to remove any
rem aining w ater and the acetylene was collected in a liquid nitrogen trap.
(The trapping of small am ounts of acetylene did not appear to be hazardous.)
This produced a mixture of approxim ately 2 : 1 : 1 C2 HD : C2 H 2 : C 2 D 2 . The
S18 0 160 sample was prepared by mixing equal am ounts of S160 2 and S180 2
(Alfa Products, 99% lsO) in a glass bulb. Immediately upon mixing, the
sam ple exchanged to give an approxim ately 2 : 1 : 1 m ixture of S18O ieO : S16C>2
: SI8 O 2 . The C2 H 2 i3 4 S0 2 spectrum was observed in natural abundance (4%).
R esults and A nalysis
Spectrum of C2 H 2 *S0 2 . In the initial search of the region from 8.5 to
12.5 GHz by H ow ard and Legon at the U niversity of Exeter, 17 transitions were
observed which required both C2 H 2 and SO2 to be seen. All subsequent
53
measurem ents w ere done at the University of M ichigan.
Because the Exeter
spectrom eter is not equipped to do Stark effect m easurem ents, the transitions
w ent unassigned. W ith the aid of Stark effect m easurem ents perform ed in
the U niversity of Michigan spectrom eter,
8
w ere assigned as the C 2 H 2 SO 2
dimer. The rem aining 9 lines are believed to arise from another structural
isom er of the dim er or a trim er species. Attem pts to fit these transitions have
Table 3-1. Observed transitions of C2 H 2 ‘SQ2 / MHz.
T ransition
T ransition
Vo-Vc
Vobs
-2
9411.619
2 i 2 - lll
iio-Oooa
13881.003
0
2 n -lo i
2 l 2 -l 01
9251.510
1
404-312
2 n - li 0
2
11935.979
5()5-4l3
3l3-2l2
14130.081
-3
303-202
606-514
15807.753
2
707-6l5
322-221
2
14825.595
221-2i i
321-220
4
14184.888
3 i 2 -2 n
322-312
13344.347
2
423-413
4i4-3i3
12319.228
0
524-514
404-303
11132.961
-1
6 2 5 -6 1 5
423-322
9819.733
-3
726-716
432-331
8 2 7 ^8 1 7
8426.488
2
431-330
16169.819
0
2 2 0 -2 1 2
422-321
16954.977
-3
321-313
4l3“3l2
7357.151
3
5i4-422
11981.716
-1
615-523
16361.052
0
716-624
a. Q uantum num bers are J’kp Ko -J"k pk o
Vobs
7622.854
8033.840
8500.363
11416.987
11981.219
12091.228
12202.147
12731.937
15191.898
15849.392
16099.084
16171.716
16178.374
16371.571
16939.618
Vo-Vc
2
2
1
1
-1
0
0
0
1
0
2
1
5
-2
-3
been unsuccessful. Following the initial assignm ent, a total of 33 a- and cdipole transitions arising from levels up to J = 8 and Kp = 3 were observed in
54
the region 7 to 18 GHz. These are listed in Table 3-1. The transitions were fit
to a W atson S-reduced H am iltonian using the F representation.12 The
derived spectroscopic constants are listed in Table 3-2.
Table 3-2. Spectroscopic constants for C2 H 2 -SQ2 .
A /M H z
7176.804(2)
B/M H z
2234.962(1)
C/M H z
1796.160(1)
D j/kH z
7.617(3)
DjK/kHz
42.19(2)
D k /1cH z
-42.6(4)
d i/k H z
-1.681(1)
d2/kH z
-0.354(1)
na
AVrrns/ kHz^
a. N um ber of transitions in fit.
b. Av = v0bs“Vcalc.
33
2
The spectra of C2D2-S02 (Table 3-7, at end of chapter), C2 HD-SC>2
(Table 3-8), C2H2-S180 160 (Table 3-9) and C2H2-34S02 (Table 3-10) w ere also
observed. These w ere fit to the same W atson H am iltonian and their
spectroscopic constants are listed in Table 3-11.
Structure. The small difference in the planar second moment P bb13 for
C2 H 2 SO 2 (62.8303 amu-A2) and C2H2,34S02 (62.8228 amu-A2) places the S
atom in the a-c plane. A comparison of Pbb of the C2H2-S02 complex
(62.8303 amu-A2) with the sum of Paa of free acetylene and Paa of free SO2 14
(14.2352 + 48.7828 = 63.0180 amu-A2) indicates that the two subunits both
55
straddle an a-c symm etry plane, w ith the C 2 axis of the SO2 rotated 90° to the
Coo axis of the acetylene, as shown in Figure 3-1. W ith this orientation
established, the structure of the C2 H 2 SO2 complex is defined by the two
param eters Rem and 6 (S0 2 >, w here Rcm is the distance between the centers of
mass of the acetylene and SO2 and 0 (SO2 > is the tilt angle between the C2 axis
of the SO2 and the perpendicular to Rcm. It is assum ed that die C2 H 2 and SO2
subunits retain their uncom plexed geom etries.
c
cm
Figure 3-1. Param eters defining the structure of the C 2 H 2 -S0 2 complex.
A least-squares fit of the m om ents of inertia of the norm al isotopic
species yielded two structures which had fits of the same quality: both had
Rcm = 3.43 A, bu t the tw o had nearly equal and opposite values for 0 (SO2 )
(+14° and -16°). The isotopic species sensitive to the sign of 0(SO2> are
C 2 H 2 *S180
160
and C2 H 2 ,34 S0 2 , however addition of their rotational constants
to the least-squares fit again produced tw o structures as show n in Table 3-3.
56
Table 3-3. Structural param eters from least-squares fits of the m om ents of
inertia of C2 H 2 SO2 , C2 H 2 -S180 160 and C2 H 2 *34 S0 2 and coordinates from
Kraitchm an substitution calculations.
na
P
K raitchm an
RcmM
0(SO2)/degb
Alrms/ amu-A2 c
a(0)/A d
fc(0)/Ad
c(0)/A d
3.431
13.9
0.28
1.08
1.23
0.34
3.431
-16.0
0.50
0.89
1.23
0.36
a(S)/Ad
-0.90
- 1 .1 0
fc(S)/Ad
0 .0
0 .0
c(S)/Ad
-0.34
-0.36
a. Two least squares fits of m om ents of inertia. See text.
b. Positive angle indicates clockwise rotation. See Figure 3-1.
c. AI =Iobs ” Icalc
d. a,b,c coordinate of atom.
1.04
1.24
0.35
0.90
0 .0
0.38
The fit of the structure w ith the positive angle, w here the S atom is nearer the
C2 H 2 , is of slightly better quality than that of structure w ith the negative
angle, but the difference is not great enough to be conclusive. A more
compelling argum ent for the correct geom etry results from the com parison of
the a coordinates of the oxygen and sulfur atoms for the tw o structures to
those calculated using K raitchm an's equations , 15 also given in Table 3-3. The
Kraitchman coordinates are consistent w ith the structure labeled 1. This
structure is sim ilar to the structure of C2 H 4 -S0 2 , w here the S atom is also
nearer the C2 H 4 . The structures calculated for each of the isotopically
substituted species separately, along w ith that from a least-squares fit of all of
the mom ents of inertia sim ultaneously, are show n in Table 3-4.
57
Table 3-4. Structure of C2H2-S02 from individual fits of the mom ents of
inertia for each isotopic spedes.____________________________________
A lla
C2H2
C2H2
C2 H 2 SO2 C2HD
C2D2-S02
.S18Q160
•S02
•34502
3.429(2) 3.426(2)
3.430(2)
3.432(2)
3.431(l)c
3.430(1)
Rcm/A
14.1(1)
14.2(1)
14.0(1)
13.9(1)
14.1(1)
e (s o 2) 13.9(1)
/deg
0.312
0.315
0.316
0.314
0.319
0.353
Alrmsk
a. All isotopic species least-squares fit together.
b. AI = lobs - Icalc / amuA2
c. Uncertainties represent one standard deviation in the least-squares fit.
It is difficult to estim ate the accuracy of this structure in relation to a
physically w ell-defined average or equilibrium structure. The large
am plitude vibrations of a floppy molecule certainly contam inate the
mom ents of inertia from which the structure is derived. This is m ost easily
seen in the discrepancy between the observed value of Pbb and the one
calculated from the structures of C 2 H 2 and SO2 . However, this difference of
0.19 amu-A2 is not as large as in C 2 H 4 -S0 2 (1.33 amu-A2) and other complexes.
Also, a comparison of the structures calculated for each isotopic species shows
that there is very little change upon isotopic substitution. Because the
mom ents of inertia of each isotopic species will be contam inated differently
due to changes in vibrational am plitudes, this suggests that the effects of
vibrational averaging are not so apparent in this complex. It, therefore, seems
reasonable to estim ate that the average structure (so-called ro)16 is w ithin
±0.03 A for Rcm and ±5° for 0 (SO2 ) of the equilibrium structure.
D ipole M om ent The dipole moment of the complex was determ ined
by measuring the Stark effect of 9 transitions and fitting the observed Stark
shifts using a least-squares procedure. Owing to the symm etry of the
58
complex, it was expected that Pb w ould be identically zero. To test this, Pb was
initially allowed to vary in the fit. This resulted in Pb2 = 0.01 ± 0.09 D2,
consistent w ith pb equal to zero. Therefore, in the final fit shown in Table 3-5,
Pb w as constrained to zero. This resulted in a total dipole m om ent of
1.683(5) D, w ith components, lpa l = 0.721(2) D and IMe I = 1.521(5) D.
Table 3-5. Stark effects (Av/e2)a and dipole moment of C2 H 2 -SQ2 .
IMI
obs
1
33.97
202-l01
6.22
0
2 l2 -lll
1
56.32
2i2 -lll
1
-60.76
2 ll-ll0
0
31.33
lio-Ooo
1
38.40
2 ll-lo i
7.44
0
404-312
2
-13.27
4o4-3i2
3
-39.50
4o4-3i2
o-cb
0.28
-0.04
-0.75
-0.81
0.13
-0.23
0.02
0.21
0.13
Pt = 1.683(5) D
1Pa 1= 0.721(2) D
Ipc 1= 1.521(5) D
a. Second order Stark effect in M H z/(kV /cm )2.
b. Stark coefficients calculated using rotational constants listed in Table 3-2.
As in the C2H4-S02 complex, the dipole moment of the C2H2-S02
complex (1.683 D) is quite sim ilar to the dipole m om ent of free SO2
(1.633 D).11 However, the dipole m om ent of the complex is rotated some 14°
from the C 2 axis of the SO2 subunit. (The direction of the dipole m om ent of
the complex is selected such that it is dom inated by the perm anent dipole
m om ent of SO2 .) If the dipole moment of SO2 is projected onto the principal
axes of the complex using the structure determ ined above, the com ponents
are estim ated to be pa = 0.395 D and Pc = 1.584 D. A positive sign im plies that
59
the com ponent points along the positive axis in Figure 3-1. To explore
w hether the discrepancy between the projections and the observed
components can be explained by polarization, we em ployed a sim ple model
in which the acetylene was treated as a point polarizability at its center of
mass w ith components a M= 4.86 A3 and <x_l = 2.94 A3.17 A G A U SSIAN 8618
calculation was undertaken (HF/6-31G*) to estim ate the electric field around
free SO2 at the site of the center-of-mass of the acetylene. From this electric
field induced dipole components pa = 0.342 D and Pc = 0.118 D were calculated.
The same approach was used to estim ate the dipole m om ent induced in the
SO2 by the acetylene. From the calculated electric field and SO2 polarizability
com ponents a aa = 5.32 A3, abb = 3-51 A3 and OcC= 3.01 A3,19 components |ia =
0.181 D and |ic = -0.031 D w ere calculated. The total dipole components |xa=
0.521 D and pc = 0.087 D compare favorably w ith the difference between the
experim ental and projected values, which gives components pa = 0.326 D and
He = 0.063 D.
D euterium N u d ear Q uadrupole Coupling. The hyperfine structure
from deuterium nud ear quadrupole coupling w as resolved and assigned for
several transitions in both C2 HD-S0 2 and C2 D 2 -S0 2 - The assigned hyperfine
com ponents are shown in Tables 3-12 and 3-13. Q uadrupole coupling
constants w ere determ ined from a least-squares fit of the hyperfine
com ponents treating the quadrupole interaction as a perturbation on the
rotational energy .20 The quadrupole coupling constants for both C2 HD SO2
and C 2 D 2 -S0 2 are shown in Table 3-6. Also induded in Table 3-6 are
quadrupole coupling constants that have been determ ined for C 2 HD and C2 D 2
in previous studies .21' 2 6 It should be noted that the labels Xaa, Xbb, Xcc are
strictly correct only for the C2 H 2 -S0 2 complexes. The observed x's for C 2 HD,
60
C 2 D 2 and C2 D 2 *Ar have been relabeled to facilitate discussion so that %bb
corresponds to the field gradient along the C-D bond axis for all species. For
the values determ ined from the excited bending vibrational states of
acetylene, this appears to be a good approximation.
Table 3-6. Deuterium nuclear quadrupole coupling constants (MHz) for C 2 H 2
and C 2 H 2 -containing complexes._______________________________________
C2HDS02
C2D2*S02
C2D2-Ar
C2P 2
C2HD
C2P 2/
c 2h d
C2HD V4=l
C2HD V5 =l
C2P 2 V4 =l
C2P 2 V5=l
Xaa
-0.101(3)
-0.098(4)
Xbb
Xcc
0.198(3)
-0.097(3)
0.199(7)
-0.101(4)
0.2044(10)
0.225(30)
0.231
0.1986(7)
Xbb
0.221(2)
0.207(6)
0.20916
0.20870
Xaa"Xcc
-0.006(4)
-0.031(22)
M ethod
FTM W
FTM W
MBER
MBMR
ab initio
NM R
Ref
MBER
MBER
MBER
MBER
25
25
26
26
21
22
23
24
The first point to make is that for C2 H 2 SO2 qaa = qcc = - 0.5 qbb (within
experim ental uncertainty). A lthough the location of the principal axis of the
quadrupole tensor is not known, this relationship betw een the observed q's,
as well as the geometric arrangem ent of the complex, suggests that the
gradient along the C-D bond is nearly cylindrically symmetric. Secondly, the
scatter in the values in Table 3-6 does not provide a very clear-cut reference
point for XD- This makes it difficult to estim ate how greatly the electric field
gradient at the D site has been affected by complexation to SO2, except to
suggest that any effect m ust be 10% or less.
To explore the effect of complexation m ore quantitatively, GAUSSIAN86
w as used to estim ate w hether the electric field gradient of the SO2 moiety w ill
directly affect the coupling constant of the D. The field gradient produced by
free SO2 at the position of the D in the complex w as calculated w ith both the
GAUSSIAN 6-31G* and 4-31G basis sets and indicated a negligible contribution
of £ 0.003 MHz to the coupling constant. The calculated value for free
acetylene in the 6-31G* basis set was Xi 1= ~ 0.128 M Hz and
x ± = 0.256 M H z , in
reasonable agreem ent w ith the observed values, b u t considerably poorer than
the literature value in Table 3-6, for which a larger basis set was em ployed. Of
course, this calculation does not estim ate w hether an electronic perturbation
of the acetylene by the SO2 can afreet the field gradient at the D site. W hen a
superm olecule calculation is perform ed for the C 2 H 2 -S0 2 complex, Xaa =
0.127, Xbb = -0.255 and Xcc = 0.128 are obtained. These are quite sim ilar to the
constants obtained for free acetylene, suggesting little or no perturbation by
the SO2 .
The contrast betw een the small or negligible electronic perturbation
effects on (eqQ)o hi acetylene upon complexation com pared to the larger
polarization effects indicated by the dipole m om ent data is striking. One
possible resolution is that considerable polarization of the acetylene occurs,
b u t that it is confined prim arily to the O C bond w hile the C -H bonds are
relatively unaffected. A nother is that the electron density in the C -H bond is
affected m ore significantly b u t in a m anner that does not m arkedly alter the
electric field gradient at the deuterium site.
Internal Rotation. Recent studies of C2H4-S02, C2H2O3,5 and C2 H 4 O3 4
have show n that all three complexes have an internal m otion that splits their
rotational transitions into tunneling doublets. It has been shown in C 2 H 4 SO 2
62
that the motion is an internal rotation of the hydrocarbon about the axis
perpendicular to its plane and hindered by a V2 barrier of about 30 cm”1. The
same m otion has been postulated for C 2H 2 O 3 and C2 H 4 -0 3 . It w as expected,
therefore, that the structurally sim ilar C 2 H 2 SO2 complex w ould also exhibit
internal rotation splittings. Spectra w ere predicted for barriers between V2 = 0
and 30 cm -1 using the internal rotation H am iltonian applied to the C2 H 4 -S0 2
problem 3 2 and searches were carried out over the predicted regions. For low
barriers, V2 £ 5 cm-1, a series of transitions was predicted on the low and high
side of an R-branch band center (B+CXJ+l) which converged to it for high
internal rotation quantum num bers. For higher barriers, V2 ^ 10 cm-1, each
assigned line was expected to be accompanied by an internal rotation doublet.
The largest doublet splitting w as 500 to 700 MHz and occurred for barriers of
V2 = 10 to 20 cm”1. Extensive searches in the predicted regions produced a
num ber of lines w ith low-J second order Stark effects which required both
C 2 H 2 and SO2 , but the Stark effects and patterns w ere inconsistent w ith the
predicted spectra. For example, the Stark effects w ere not sim ilar to any of the
Stark effects of the observed transitions, indicating that the transitions were
not tunneling doublet m ates arising from a high barrier. N either did any of
the transitions exhibit the first order Stark effects expected for the low barrier
case. We have concluded that these unassigned transitions belong to one or
m ore structural isomers of the C2 H 2 -S0 2 complex a n d /o r a trim er species.
Several tunneling m otions can be envisioned w hich w ould involve
the exchange of equivalent oxygen atoms in the C 2 H 2 -S0 2 species. These
include an SO2 inversion m otion and a rotation of the SO2 about its
sym m etry axis. As these involve the exchange of tw o equivalent spin zero
nuclei, zero spin w eight w ould be expected for one of the sym m etry states in
the norm al isotopic species and result in a missing set of transitions.
63
Therefore, intensive searches w ere m ade above and below several of the
observed transitions in the C2H2-S180 160 species, w here Pauli restrictions
leading to the zero spin w eight of one symm etry state in C2 H 2 -S0 2 are lifted.
These searches w ere also unsuccessful. A dditionally, an SO2 inversion
m otion w ould change the sign of |Xc and lead to perturbations in the
spectrum ; thus the good centrifugal distortion fit precludes this motion.
A dditional insights w ere obtained from the quadrupole coupling
patterns of the C2D2-S02 species. If the C2H2-S02 complex w ere undergoing
an internal rotation sim ilar to that observed in C2 H 4 *S0 2 , w ith the acetylene
rotating about an axis nearly coincident w ith the Rem vector, equivalent
deuterium atoms w ould be exchanged in C2D2-S02- The Pauli principle
requires that the sym m etry of the rotational (or rotation-tunneling) level be
appropriately m atched w ith the sym m etry of the nuclear spin function such
that the overall wavefunction is sym m etric w ith respect to interchange of two
bosons. For m oderate and high barrier problem s there is a clear distinction
between sym m etric and antisym m etric tunneling states. Therefore, if
internal rotation occurred, the nuclear quadrupole coupling pattern for a
given transition w ould display only the hyperfine com ponents resulting
from either the even or the odd nuclear spin functions, depending on
w hether the tunneling state w as sym m etric or asymmetric, as was observed
in frans-C2H2D2-S02• Figure 3-2 shows the hyperfine pattern of the I 10 -O0 0
transition of C2 D 2 SO2 . Beneath it is a stick diagram of the hyperfine
transitions w ith the even nuclear spin com ponents show n in solid lines and
64
0.4
Frequency relativ e to 8786.600 MHz
Figure 3-2. Hyperfine pattern from deuterium nuclear quadrupole
coupling in the lio-Ooo transition of C2 D2 SO2 . Stick diagram beneath
represents the predicted com ponents, w ith the solid lines arising from
even nuclear spin states and the dashed lines arising from odd nuclear
spin states.
the odd in dashed lines. All the hyperfine components are observed,
indicating that the complex is not undergoing any internal rotation. This
argum ent can also be applied to the low barrier or free internal rotation
situation in which case the assigned transitions w ould arise from the m = 0
non-degenerate state and should also exhibit only one nuclear spin
sym m etry.
The internal rotation H am iltonian em ployed in the C2H4-S02
system 27*28 was used to estim ate a lower lim it to the barrier to internal
rotation for die C2H2-S02 complex. This was obtained by varying the barrier
until the largest predicted splittings w ere below the instrum ental resolution.
As the observed transitions were very sharp in the norm al isotopic species
(FWHM was about 20 kHz), a splitting of 5 to 10 kHz was selected for this
65
lim it; anything larger w ould result in broader lines, if not distinct, split peaks.
A t V2 = 135 cm-1, the largest of the splittings collapsed to < 10 kH z and a t V2 =
150 cm -1 to < 5 kHz.
Force Constant and B inding Energy. If the van der W aals complex is
treated as a pseudo-diatom ic molecule, the Dj distortion constant m ay be
related to the stretching force constant of the van der W aals bond. From the
m odel of Millen , 29 the force constant is calculated as 0.0497 m dyne/A . From
this and a Lennard-Jones 6-12 potential, the binding energy is determ ined to
be 390 cm-1.
Sum m ary
The structure of the C2 H 2 -S0 2 complex is sim ilar to that of the
C 2 H 4 SO2 complex, w ith the principal interaction apparently betw een the S
atom of the SO2 and the n system of the C2 H 2 . The Rem distance in the
C 2 H 2 -S0 2 is considerably shorter than that in the C 2H 4 -S0 2 (3.430 A versus
3.504 A). A better com parison is perhaps the distance from the S atom to the
center of mass of the hydrocarbon. For C2 H 2 -S0 2 , this distance is 3.363 A,
w here it is 3.438 A in the C 2 H 4 -S0 2 complex, the difference being 0.065 A. The
binding energy for C2 H 2 -SC>2 is calculated as
1 .1
kcal/m ole.
The m ost perplexing finding of this study is the observation that the
C 2 H 2 -S0 2 complex does not undergo an internal rotation of the C 2 H 2 subunit.
It is certainly inconsistent w ith the series C2 H 4 -S0 2 , C2 H 4 O 3 , C2 H 2 O 3 , where
the splitting in the I 10 -O00 transition is 25 MHz, 10 MHz and 5 MHz
respectively. Extrapolating, one w ould expect from chemical intuition that
66
the same transition in the C2H2-S02 complex w ould be split by 10 -15 MHz.
W hat is giving rise to this difference is unclear.
1
h
VO
Table 3-7. Observed transitions (MHz) of C2P2*S02T ransition
T ransition
Vo-vc
Vobs
8786.862
9
iio-Oooa
2i2-l01
17
13048.453
2 li-lo i
2 n -lio
1
17537.228
3i2-2o2
3l3-2l2
8844.597
29
4o4-3i2
3q3-2o2
13575.007
2 2 1 -2
322-221
-1 2
12942.311
322-312
321-220
12113.581
9
3l2-2ll
423-413
11105.514
6
4i4-3i3
524-514
9944.037
-42
6 2 5 -6 1 5
404-303
7
14908.089
220-212
423-322
14
15695.350
422-321
321-313
4i3-3i2
5l5-4l4
a. Q uantum num bers are JkpKo*
Table 3-8. Observed transitions (MHz) of C2 HD SO2 .
T ransition
T ransition
Vo-Vc
Vobs
9099.849
-2
2 1 2 -I 11
liO-Oooa
4
13460.696
2 n -lo i
2i2-l01
9034.997
2
4o4-3i2
2 ll-ll0
11610.607
-2
505-413
3i3"2l2
1
13694.845
6o6-5l4
3q3-2q2
14215.982
-25
221-2h
322-221
13580.769
-12
322-312
321-220
12748.032
423-4i3
44
3i2-2n
-17
11733.450
524-514
4i4-3i3
15551.235
-3
220-212
4o4-3q3
16334.938
6
321-313
423-322
17515.650
6
4 3 2 -3 3 1
422-4i4
15956.612
11
422-321
16510.270
-5
4i3-3i2
a. Q uantum num bers are JkpKo*
Vobs
7624.937
8089.045
10811.980
11363.434
11481.036
11599.232
12113.719
14383.491
15018.355
15284.099
15573.722
16112.841
17930.746
Vo-vc
-8
5
-9
"6
Vobs
7415.457
7822.446
8286.493
11105.477
11662.409
11775.427
11889.129
12410.644
14775.893
15421.489
15677.488
15752.488
Vo-Vc
10
7
14
1
3
4
-40
-5
5
-2
6
-7
3
-1 1
-18
-4
-1
4
4
-3
-8
68
Table 3-9. Observed transitions (MHz) of C2H2-S18Q 160 .
T ransition
T ransition
Vo-vc
Vobs
Vobs
7503.124
9079.281
1
212-In
iio-Oooa
13502.197
-2
7920.225
2n -loi
2i2-loi
9246.171
-1
8398.499
4o4-3i2
2 n -lio
0
5q5-4i 3
11815.592
11235.740
3l3-2l2
13873.924
0
11803.970
303-2Q2
606-514
11925.042
221-2h
0
13967.980
322-221
-1
12047.027
13315.746
321-220
322-312
1
12461.449
12577.279
3i2-2n
423-413
11422.369
-1
14947.437
524-514
4i4-3i3
10225.288
0
15601.456
625-615
404-303
15341.822
0
15875.337
423-322
220-212
16153.114
4
15955.212
321-313
432-331
17379.871
-3
15963.109
422-414
431-330
7930.124
0
16174.198
422-321
5i4-422
16729.636
0
4i3-3i2
a. Q uantum num bers are Jkp Ko-
Table 3-10. Observed transitions (MHz) of C 2 H 2 -34SQ2 T ransition
T ransition
Vo-Vc
Vobs
Vobs
9368.132
-12
8435.764
ho-0ooa
2 n -lio
11
13801.226
11344.847
3i3-2i2
2n -loi
9187.032
-1
11900.229
404-312
303-202
7574.372
-9
3i2-2n
12635.765
2 i2 -lll
7978.281
13
12745.514
2i2-l01
4q4-3q3
a. Q uantum num bers are JkpKo-
Vo-vc
1
2
2
-1
-1
-3
-2
1
1
1
0
3
1
-2
Vo-Vc
-16
-1
2
1
-3
69
Table 3-11. Spectroscopic constants for acetyleneS 0 2 .a
C2 H 2 S18 0 16 0
C2 D 2 S 0 2
C2 HDSO 2
6655.943(10)
6919.318(15)
6867.696(2)
A /M H zb
2131.012(2)
2211.727(1)
B/M Hz
2180.661(3)
1696.556(2)
1763.992(1)
C/M H z
1745.100(3)
D j/kH z
DjK/kHz
DR/kHz
d i/k H z
d2/kH z
7.00(6)
28.7(3)
-40(2)
-1.66(3)
-0.25(3)
7.24(7)
34.4(2)
-33(3)
-1.63(3)
-0.33(3)
7.363(5)
42.45(2)
-43.1(3)
-1.691(3)
-0.375(2)
c 2 h 2 -3 4 s o 2.
7151.505(17)
2216.789(10)
1786.069(8)
7.1(1)
41.1(18)
-43c
-0.8(3)
1 .0 C
24
nd
26
29
10
AVnns/kHz
13
17
2
15
a. W atson S-reduction, Ir representation.
b. Uncertainties represent one standard deviation in the least-squares fit.
c. Param eter fixed in least-squares fit.
d. N um ber of transitions in the fit.
e. Av = vQbs"vcalc*
70
Table 3-12. Deuterium nuclear quadrupole hyperfine components (MHz) for
c 2 h d s o 2._______________________ _____________________
F"
T ransition
F’
v0 -vc
Vobs
1
1
9099.822
0 .0 0 2
lio-Ooo
1
2
9099.849
0 .0 0 0
1
0
9099.892
- 0 .0 0 2
1
1
13460.761
-0 .0 0 1
2 n -lo i
2
3
13460.701
0.005
1
2
13460.629
-0 .0 0 1
2
2
13460.629
-0.003
3
13580.837
3
0 .0 0 1
322-312
4
4
13580.762
-0 .0 0 1
2
2
13580.738
0.000
1
0
7415.526
-0 .0 0 1
2 i 2 - lll
2
2
7415.487
0.000
2
3
7415.457
0 .0 0 1
2
1
0 .0 0 2
7415.429
1
1
7415.377
-0 .0 0 2
1
1
7822.490
-0 .0 0 2
2 o2 -loi
2
3
7822.447
0.000
1
0
0 .0 0 2
7822.419
1
1
8286.557
-0 .0 0 1
2 il-llO
3
3
8286.494
0 .0 0 1
2
1
8286.459
0.000
2
1
11775.425
0.004
322-221
4
3
11775.401
-0 .0 0 2
2
3
11775.368
-0.003
71
T able 3-13. D euterium nuclear quadrupole hyperfine components* (MHz) of
C 2D 2‘S Q 2»__________________________________________________________
T ransition
F’
I’
F"
I"
Vobs
2
2
1
2
8786.953
iio-Ooo
1
1
1
1
8786.917
2
2
2
3
8786.899
1
2
2
2
8786.880
2
2
2
2
8786.859
1
1
1
0
8786.833
2
2
3
3
12942.464
322-312
4
4
2
2
12942.428
2
2
1
1
12942.412
1
4
4
1
12942.382
2
2
5
5
12942.324
1
1
3
3
12942.295
4
2
2
3
8844.632
4q4-3i 2
2
4
2
5
8844.602
1
2
1
3
8844.595
1
1
4
5
8844.561
2
2
6
5
8844.525
a. Coupling scheme is I = Ii + I2; F = J + 1.
v0 -vc
-0.003
0 .0 0 2
0.000
0.008
0.006
-0.005
-0 .0 0 2
0 .0 1 0
0.005
0 .0 0 1
-0 .0 0 2
-0 .0 1 2
-0.005
0.003
0.005
-0.006
0.003
72
References to Chapter 3
1.
J. S. M uenter, R. L. DeLeon, A. Yokozeki, Farad. Disc. Chem. Soc., 73 63
(1982).
2.
D. Booth, F. S. D ainton, K. J. Ivin, Farad. Soc. Trans. 55 1293 (1959).
3.
L. J. Andrews, R. M. Keefer, J. Am. Chem. Soc., 73 4169(1951).
4.
C. W. Gillies, J. Z. Gillies, R. D. Suenram, F. J. Lovas, J. Am. Chem. Soc.,
subm itted.
5.
C. W. Gillies, J. Z. Gillies, R. D. Suenram, F. J. Lovas, Ohio State M olecular
Spectroscopy Symposium, 1989, Columbus, OH, Paper TF4.
6.
R. T. M orrison, R. N. Boyd, Organic Chemistry, 4th Ed. (Allyn and Bacon,
N ew ton, MA, 1983) pp. 566 - 568.
7.
A. J. Fillery-Travis, A. C. Legon, Chem. Phys. Lett., 123 4 (1986).
8.
G. T. Fraser, R. D. Suenram, F. J. Lovas, A. S. Pine, J. T. Hougen,
W. J. Lafferty, J. S. M uenter, J. Chem. Phys., 89 6028 (1988).
9.
K. W. H illig n, J. M atos, A. Sdoly, R. L. Kuczkowski, Chem. Phys. Lett.,
133 359 (1987).
10. A. C. Legon, L. C. W illoughby, Chem. Phys., 74 127 (1982).
11. F. J. Lovas, J. Chem. Phys. Ref. Data, 14 395 (1985).
12. J. K. G. W atson, J. Chem. Phys., 46 1935 (1967).
13. Pbb = 0.5(Ia + I c - I b ) = X m ibi2
14. M. D. H arm ony, V. W. Laurie, R. L. Kuczkowski, R. H. Schwendeman,
D. A. Ramsay, F. J. Lovas, W. J. Lafferty, A. G. Maki, J. Chem. Phys. Ref.
Data, 8 619 (1979).
15. J. Kraitchman, Am. J. Phys., 2117 (1953).
16. R. H. Schwendem an, Critical Evaluation of Chemical and Physical
Structural Information; D. R. Lide, M. A. Paul, Ed., (National Academy
of Sciences, W ashington, D.C., 1974), 74-115.
73
17. Landolt-B ornstein, Zahlenwert und Funktionen, (Springer, Berlin, 1962)
Vol. 2, Pt. 8,871.
18. J. M. Frisch, J. S. Binkley, H. B. Schlegel, K. Raghavachan, C. F. M elius,
R. L. M artin, J. J. P. Stewart, F. W. Bobrowicz, C. M. Rohlfing,
L. R. Kahn, D. J. DeFrees, R. A. W hiteside, D. J. Fox, E. M. Fluder,
J. A. Pople, GAUSSIAN86, (Camegie-M ellon Q uantum Chem istry
Publishing U nit, Pittsburg, PA, 1986).
19. W. F. M urphy, J. Raman. Spec., 11 339 (1981).
20. W. Gordy, R. L. Cook, Microwave Molecular Spectra, 3rd Ed. (Wiley, N ew
York, 1984) p 413.
21. J. S. M uenter, R. L. DeLeon, J. Chem. Phys, 72 6020 (1980).
22. N. Ramsey, American Scientist, 49 509 (1961).
23. M. R. Asdjodi, R. V. Gregory, G. C. Lickfield, H. G. Spencer, J. W.
Huffman, G. B. Savitsky, J. Chem. Phys., 861653 (1987).
24. S. E. Emery, G. C. Lickfield, A. L. Beyerlein, G. B. Savitsky, J. Mag. Res., 56
323 (1984).
25. M. D. M arshall, W. Klemperer, J. Chem, Phys., 81 2928 (1984).
26. R. L. DeLeon, J. S. M uenter, J. Mol. Spec., 126 13 (1987).
27. A sim plified H am iltonian was em ployed w hich neglects the effects of
internal rotation on the A and C rotational constants. Thus, the
estim ates of splittings and barriers are only approxim ate. See ref. in
C hapter 2 for additional discussions of the calculation.
28. The program used for this calculation was supplied by A. Taleb-Bendiab.
29. D. J. Millen, Can. J. Chem., 63 1477 (1985). This equation is strictly correct
only for 0 (SO2 ) = 0 °, w here the C2 H 2 and SO2 lie in parallel planes.
CHAPTER 4
THE CYCLPROPANE-SULFUR DIOXIDE COMPLEX
Complexes of HF, HC1 and HCN w ith the hydrocarbon series
ethylene , 1*3 acetylene,4 *6 cyclopropane 7*9 have been studied recently. In each
complex, the ad d is hydrogen bonded to the
11
(ethylene and acetylene) or
pseudo-TC (cydopropane) system .10 It has been noted that for each HX series
there is a decrease in hydrogen-bond length, an increase in pseudo-diatom ic
stretching force constant and an increase in induced dipole m om ent from
ethylene to acetylene to cydopropane . 11' 12 As these properties are often
correlated w ith the strength of the interaction, this has led to discussion that
the pseudo-7E system of cydopropane is a better hydrogen bond acceptor than
the dassical it systems of ethylene and acetylene. Legon and M illen, studying
the pseudo-diatom ic force constants of the HC1 and HCN series, have
assigned nudeophilidties to C 2 H 4 (4.7), C2 H 2 (5.1) and C 3 H 6 (6.4) .12
W hile these trends are well-docum ented for the hydrocarbon-add
complexes, which are hydrogen bonded, there is less know n about this
hydrocarbon series complexed to a non-hydrogen bonding partner. The
complexes of ethylene and acetylene w ith sulfur dioxide both have a stacked
structure w ith die C2 axis of the SO2 crossed at 90° to the C=C or C^C bond.
The sulfur of the SO2 apparently interads w ith the it system of the ethylene
and acetylene. Like the acid complexes, it was observed that the interaction
distance, as m easured from the C-C bond center to the sulfur, is shorter for
74
75
C2 H 2 -S0 2 (3.359 A) than C2 H 4 SO2 (3.446 A) and that the induced dipole
moment is greater for C2 H 2 SO 2 . The force constants for the stretching
vibration between the hydrocarbon and the SO2 are not easily com pared due
. to the effect of internal rotation in C 2 H 4 SO 2 .
This chapter focuses on the cyclopropane-S 0 2 (C3 H 6 SO2 ) complex. The
sulfur atom interacts w ith the pseudo-7C system as expected, however the
structure is different from the C2 H 4 -S0 2 and C2 H 2 -S0 2 complexes in th at the
C2 axis of the SO2 is nearly parallel to the C-C bond, rather than crossed at 90°.
The interaction distance (S to C-C bond center) of 3.203 A is shorter than in
C 2 H 2 -S0 2 and the induced dipole m om ent and the pseudo-diatom ic force
constant are both greater.
Experim ental
Spectrom eter. The spectrum was observed in a Fourier transform
microwave spectrom eter of the Balle-Flygare type which has been described
previously . 13' 14 The m olecular beam was generated w ith a m odified Bosch
fuel injector. Line w idths w ere typically 20-30 kHz full w idth at half
maximum and center frequencies were estim ated to be accurate to ± 2 - 3 kHz.
For deuterated isotopomers, transitions were broadened to 100 kHz or more
(fwhm) from unresolved nuclear quadrupole hyperfine structure and line
centers were accurate to ± 20 - 30 k H z . Stark effects were m easured by
applying up to 10 000 V w ith opposite polarities to two parallel steel mesh
plates separated by about 30 cm.
Sam ples. The spectrum of C3 H 6 SO2 was observed w ith a m ixture of
approxim ately 1 % each of C3 H 6 (Aldrich) and SO2 (Matheson) in Ar at a total
76
pressure of 1.5 atm. S180 2 (98%
18 0 )
was purchased from Alfa Products and
used w ithout dilution to observe the C3 Hg-S180 2 spectrum. A 50 : 50 m ixture
of S180 2 and S16 C>2 was used to produce the C3 H 6 *S180
160
spectrum ; the
sam ples exchanged im m ediately upon mixing. The C3 H 6 i3 4 S0 2 spectrum was
observed in natural abundance (4% ^S ). C3 D 6 (98% D) and I 4 -C 3 H 4 D 2 (98%)
w ere purchased from MSD Isotopes.
C 3 H 5 D was synthesized in poor yield as follows. C ydopropyl G rignard
reagent was produced by reacting cydopropyl brom ide (Aldrich) w ith Mg
(Baker) in dry diethyl ether in the usual m anner. The flask containing the
G rignard reagent was then placed in line w ith a trap cooled w ith a CCI4 slush
(-25° C) followed by a liquid nitrogen trap (-196° C) w hich was isolated from
the atm osphere by a m ercury bubbler. N itrogen gas was passed through the
apparatus while D2 O (Cambridge Isotope Labs) was slowly added dropwise to
the cydopropyl Grignard. Excess D 2O and ether were trapped in the CCI4 trap
and a sm all am ount of C3 H 5 D was collected in the liquid nitrogen trap.
Results and A nalysis
Spectrum . The spectrum of C 3 H 6 SO2 exhibited a- and c-dipole
selection rules. The c-type R-branch transitions w ere split into doublets of
unequal intensity and the strong and weak c-type transitions were each fit
independently w ith the a-type transitions to a W atson S-reduced
H am iltonian15. The observed transitions are listed in Table 4-1 and the
derived constants are shown in Table 4-2. The splitting of the c-type
transitions arises from an internal rotation of the cydopropane subunit
exchanging three pairs of protons (see internal rotation section below) and the
A i and A 2 symm etry labels of the states are taken by analogy to ethylene*S0 2
77
which has a sim ilar tunneling path. For C3 H 6 SO 2, the A i label corresponds
to the w eaker transitions and the A2 to the stronger.
Table 4-1. Observed transitions for C3 H 6 -SQ2 .
T ransition
T ransition
v0 -vcb
v0 bsa
A i/A 2 c
7311.753
1
6l6-5l5
3<)3-202d
7315.089
-1
322-221
606-5Q5
7318.850
7
6i5-5i4
321-220
7432.386
3i2-2n
3
7l7-6l6
9595.002
1
4i4-3i3
707-606
9744.449
-2
7l6-6l5
404-303
9752.487
-4
2 2 1 -2 h
423-322
432-331
9754.511
2
2 2 0 -2 1 2
9754.584
2
32i-3i3
431-330
9761.865
-1
422-4i4
422-321
9908.517
3
4l3-3l2
523-515
11991.722
4
5i5-4i4
12173.271
2
505-404
12189.058
-9
524-423
12207.788
-3
523-422
5i4-4i3
12383.484
-1
Vobs
A 1 /A 2
14387.127
14597.283
14856.965
16780.978
17015.605
17382.667
14754.456
14990.582
15112.216
15279.080
15495.147
v0 -vc
9
3
-1 2
2
-7
10
4
0
1
1
-5
■
a
2
Ai
7435.084
-S
7435.245
-2
lio-Ooo
9951.926
A
9952.070
-14
2 ll-lo i
12508.184
0
12508.346
7
3i2“2o2
15105.949
2
15105.104
2
413-303
9026.565
A
9026.412
-7
606-514
11185.201
-3
11185.039
-1
707*6i 5
a. Observed frequency in MHz.
b. Vobs-Vcalc in kHz.
c. Symmetry label of tunneling state. A 1 /A 2 indicates only one transition
was observed.
d. Q uantum num bers are JkpKo*
78
Table 4-2. Spectroscopic constants of C3H6-S02.
A /M H z
B/M H z
C/M H z
A2
6176.635(5)
1258.500(1)
1180.101(1)
Ai
6176.828(5)
1258.500(1)
1180.101(1)
D j/kH z
DjK/kHz
Die/kHz
d i/k H z
d2/kH z
H iq/kH z
113/k H z
1.958(5)
15.5(1)
-18.1(9)
-0.078(4)
0.179(6)
0.9(1)
0.04(1)
1.959(6)
15.4(2)
20.5(11)
-0.77(5)
0.178(7)
0 .8 (2 )
0.04(1)
n
AVntis/kHz
33
6
33
7
The spectra of C3 H 6 i34 S0 2 (Table 4-6, at end of chapter), C3H6-S1802
(Table 4-7) and C3 H 6 -S180
160
(Table 4-8) were also all split into doublets, w ith
the sam e relative intensity pattern as the norm al isotopic species. For
C 3 H 6 -S180 2 and C3 H 6 -S18OieO, the m agnitude of the splitting of the 2 n -lo i
transitions decreased by 30% and 10% respectively. For C 3 H 6 -3 4 S0 2 , the
splitting increased by 10%. In the C3 D6 -SC>2 (Table 4-9) the doublets were
unresolved due to deuterium nuclear quadrupole broadening. For
C 3 H 5 D SO2 (Table 4-10) the transitions w ere unsplit. Two different spectra
w ere observed for the 1 ,1 -C3 H 4 D 2 *S0 2 isotopic species (Tables 4-11 and 4-12);
one was split into doublets (labeled apical) and the other was unsplit (labeled
basal). These labels w ill be discussed in the structure section. For the
spectrum of the apical species both tunneling doublets w ere very weak,
m aking it difficult to assign strong and weak com ponents. Therefore, the
79
symm etry labels were assigned by higher/low er frequency to be consistent
w ith the other isotopic species. The m agnitude of the splitting decreased by
30%. The rotational constants for the isotopom ers are given in Table 4-13 at
the end of the chapter.
D ipole M oments. The dipole m om ent of the complex was m easured
by tracking the Stark effect of seven M components from 4 transitions w ith
increasing electric field. The electric field was calibrated using the J = 1 <—0,
M = 0 <- 0 transition of OCS at 12162.980 M Hz .16 The observed Stark effects
w ere least-squares fit to dipole components, I |la I = 0.815(1) D and IjLLc I =
1.470(1) D resulting in J lj = 1.681(1) D. W hen [lb w as included in the fit, the
value for |lb 2 was 0.030(50) D, indicating that |lb was zero. The dipole
m om ent components of basal-C^H^DxSOz w ere also determ ined as I |l a I =
0.803(3) D and IJlc I = 1.482(3) D from
6
M components from 2 transitions.
Structure. It was assum ed in the structural analysis that the geom etries
of the cyclopropane and sulfur dioxide w ere not changed upon complexation
from their free gas-phase structures . 17' 18 The moments of inertia and planar
second m om ents of the stronger set of transitions w ere used for the isotopic
species which exhibited splittings. Because the difference in rotational
constants is very small (<200 kHz), this choice will not m arkedly affect the
determ ination of the structure. The planar moments for C3 H 6 -S0 2 ,
C3 Hg-3 4 S0 2 , cyclopropane and sulfur dioxide are listed in Table 4-3.
80
Table 4-3. Planar second moments8 of cydopropane-SC>2, cydopropane and
sulfur dioxide.
C3H6
S 02
C3H6-34S02
C3H6-S02
374.0012
Paa/amu-A2
377.8599
20.1254
48.7679
8.3574
Pbb/amu-A2
54.2495
54.2460
20.1254
Pcc/am uA2
27.5716
27.8239
5.0262
0.0
a. Paa = 0.5 Ck + lb - la) = X miai2 an<* sim ilarly for Pbb/ Pcc-
The a- and c-type selection rules and absence of a |Ib dipole com ponent
suggest that the complex has an ac symm etry plane. Com parison of the
planar moment Pbb of C3 H 6 SO2 (54.2495 amuA2) w ith Pbb of C3 H 6 ,34S0 2
(54.2460 amuA2) indicates that the S atom lies in this plane. Pbb for the
complex is also equal to the sum of Paa of free SO2 and Pcc of free
cydopropane, pladng the C 2 axis of SO2 and the ab plane of cydopropane in
the ac plane of the complex. This orientation is shown in Figure 4-1 w ith the
cm
Figure 4-1. Param eters defining the structure of the C3 H 6 -S0 2 complex.
81
S and C atoms in the ac symm etry plane and the O and H atoms straddling it.
Once this is established, the geometry of the complex can be described by the
three coordinates in Figure 4-1: Rom, the distance between the centers of mass
of. the SO2 and the cyclopropane; 0 (SO2 >/ the angle between the C2 axis of SO2
and Rem and 6 (V), the angle subtended by Ron and a line through the center of
mass of cyclopropane parallel to the C-C bond to which the SO2 is bonded.
These angles define the tilt of the cyclopropane or the SO2 from perpendicular
to Rem/
0(V) = 0(SO2) = 90° corresponds to no tilt.
W ith the sym m etry of the molecule deduced, a brief comment about
the spectra of the deuterated isotopes is appropriate before proceeding w ith a
discussion of the structure. The relative orientation of the cyclopropane and
the SO2 perm its three different isomers to exist for both C 3 HsD-S0 2 and
C 3 H 4 D 2 SO2 . In each case the isotopic substitution could be on either of the
CH 2 groups in the C-C bond which is closest to the SO2 (labeled basal species)
or on the CH 2 group opposite that bond (apical). In the case of CsHsD-SC^,
due to difficulties w ith the synthesis, only one spectrum w as observed before
the sam ple was depleted. The rotational constants indicated that it was one of
the basal isomers. For the C 3 H 4 D 2 -S0 2 , two spectra were observed: one was
consistent w ith the D2 in the apical position and the other w ith D2 in one of
the basal positions. A lthough efforts w ere m ade to find the spectrum of the
third species, it was not observed.
Little inform ation could be gleaned from the m om ents of inertia of the
norm al isotopic species alone. Because the b coordinates of all the atom s are
fixed by sym m etry and the geometries of the monomers, only the Paa and Pcc
mom ents of inertia are useful for structure determ ination. The result is that
Rem can be determ ined from lb as approximately 3.73 A but a series of
82
correlated values for 0 (SO2 ) and 0(V) are obtained from a single isotopic
species.
In determ ining the structure by least-squares fitting of the moments of
inertia of all the isotopic species, a choice m ust be m ade about assignm ent of
the C3 H 4 D 2 *SC>2 isotopic spectra. The assignm ent of one spectrum to the
species substituted at the apical position and one substituted at the basal
position was unam biguous based on the isotope shifts. However, the latter
could be assigned to the CD2 group either at the S or O atom side of the SO2 .
(see figure 4-1). The same am biguity occurs in the location of the basal
deuterium in the C 3 HsD-S0 2 . Both assignments w ere tried and they resulted
in the two fits shown in Table 4-4. It was evident th at the CH 2 -C D 2 or CH 2 CHD bond is tilted slightly to the SO2 and that the D 2 (or Di) substitution
occurs at the carbon closer to the SO2 . The quality of the fits is sim ilar because
the coordinates of the deuterium are nearly identical in both structures.
Kraitchman's equations w ere used to calculate the positions of the
substituted atom s .1 9 They are compared w ith the values from the leastsquared fit in Table 4-4. The coordinates determ ined for the CaHsD-SC^
species and the basal-CjHjDz-SOz species are the same and indicate the basal
substitution w ith the CD 2 group nearer the SO2 . The coordinates determ ined
for the aptca/-C3 H 4 D 2 -S0 2 species place the hydrogen atom near to the a axis
and much further from the SO2 . The substitution coordinates do not,
how ever, distinguish between the two structures. The S and O coordinates
from Kraitchman's equations are included in Table 4-4 for completeness.
83
Table 4-4. Structural param eters and atomic coordinates obtained from leastsquares fitting of m om ents of inertia and Kraitchman equations.___________
Fit 2®
K raitchm an
Fit I®
3.729(1)
3.729(1)
Rem/^
73.3(1.7)
73.2(1.7)
0 (SO2)/d eg
96.8(2.4)
0(V)/deg
83.3(2.4)
Alrms/arnuA2
0.52
0.52
lal
Ibl
Icl
1.37 A
1.38 A
1.40 A
0 .0
0 .0
0 .0
0.36
0.36
0.36
O
lal
Ibl
Icl
1.58
1.24
0.38
1.58
1.24
0.38
1.52
1.24
0.32
He
(basal)
lal
Ibl
Icl
1.38
0.91
1.17
1.39
0.91
1.15
1.26e
0.89
S
1 .2 1
Hd
(apical)
lal
3.67e
3.69
3.69
Ibl
0.91
0.91
0.89
Icl
0.19
0.15
0.26
a. Least-squares fit of 24 m om ents of inertia (A2 sym m etry state) from the 8
isotopic species. Fit 1 is preferred. See text.
b. See figure 4-1 for definition of coordinates.
c. H(basal) is the hydrogen at the carbon position in the CH 2 -CH 2 bond which
is closest to the SO2 . (See figure 4-2).
d. H (apical) is the hydrogen at the carbon most distant from the SO2 . (See
figure 4-2.)
e. Calculated from the 1 /1 -C3 H 4 D 2 *S0 2 species.
A sim ilar am biguity about the sign of an angle w as encountered in the
C 2 H 4 SO 2 complex, w here the tilt angle of the ethylene was difficult to
determ ine. This was resolved by examining the change in the dipole
m om ent projections upon isotopic substitution. A sim ilar analysis was
84
em ployed here. W hen a molecule is isotopically substituted its principal
inertial axes translate and rotate. The result of the rotation is a sm all change
in the projections of the dipole m om ent on the principal axes. It is assum ed
th at the change in the total dipole m om ent upon isotopic substitution is
negligible. This should be a reasonable assum ption for C 3 H 4 D 2 SO2 . The
dipole m om ent of I 4 -C3 H 4 D 2 has been m easured as 0.011(5) D, 2 0 and the total
dipole moments of die C3 H 4 D 2 -S0 2 and C3 H 6 SO2 differ by only 0.006 (4) D.
The tw o options for the assignm ent of the basal CD 2 spectrum rotate the axes
in opposite directions. For both rotations the a- and c-dipole com ponents
w ere predicted and they are show n in Table 4-5. (The direction of the dipole
m om ent of the complex is selected such that it is dom inated by the
perm anent dipole m om ent of SO2 .21) The observed dipole com ponents for
basal-C 3 H 4 D 2 SO2 indicate 0(V) = 83.3°.
T able 4-5. Predicted and observed dipole moments for basal-l,I-C3 H4 D 2 S O 2
for the tw o structures w ith 0(V) = 83.3° and 0(V) = 96.8°.
Ha/D
Mc/D
0(V) = 83.3°
0(V) * 96.8°
0.802
1.478
0.829
1.463
Experim ental
0.803(3)
1.482(3)
The uncertainties for Rem and the tilt angles in Table 4-4 are the statistical
uncertainties arising from the fitting process. The structural param eters are
the so-called ro values .2 2 It is difficult to estim ate how closely they
approxim ate the equilibrium values due to the large am plitude vibrational
m otions in such complexes; it is probably reasonable to expect these values to
be w ithin ±0.03 A for Rcm and ±5° for the tilt angles.
85
Internal Rotation. The splitting in the c-type transitions signifies that a
tunneling m otion occurs between tw o or m ore equivalent configurations in
the complex. In an attem pt to determ ine the tunneling path the feasible
perm utations of identical nuclei shown in Figure 4-2 w ere considered.
8
Figure 4-2. Feasible perm utations of identical nuclei of C3 H 6 -SO2 .
Likely pathw ays associated w ith each are discussed in the text.
86
Possible tunneling paths for the perm utations are: 1—>2, rotation of SO2 about
its C 2 axis; 1 —>3, inversion of SO2 through a C 2 V interm ediate structure; 1 —>4
and 1 —>5, rotation of cyclopropane about its C 3 axis; 1 —>6 and l-» 7 , rotation of
cyclopropane about either of its C2 axis including the basal CH 2 groups (the
sym m etry argum ents are the same for both); 1 —>8 , rotation of cyclopropane
about its C2 axis including the apical CH 2 group.
The
1 —> 2
and 1 —>3 motions can be elim inated as the source of the
tunneling doublets based on the spectrum of the norm al isotopic species. If
the tunneling path w ere l-* 2, tw o identical oxygen atom s (I = 0) w ould be
exchanged and half the levels w ould have zero nuclear spin weight. For the
l-» 3 m otion, the direction of the c-dipole m om ent reverses, resulting in cdipole selection rules between the A i and A 2 sym m etry states. Since the two
sets of c-type transitions may be fit separately, the observed selection rules are
inconsistent w ith this tunneling path.
The rem aining tunneling paths involve the cyclopropane subunit,
therefore the deuterated isotopom ers w ere instrum ental in exploring them.
From structural considerations alone, three isom ers w ould be expected for the
1 , 1 -C 3 H 4 D 2 *S0 2
: one w ith the CD2 group in the basal position at the the S of
the SO2 , a second in the basal position a t the the O of the SO2 and the third in
the apical position. Referring to fram ework 1 in Figure 4-2, these correspond
to substitution in positions 3 and 4, positions 1 and 2, and positions 5 and 6 ,
respectively. The tunneling paths under consideration, how ever, w ould
result in different splitting patterns for the different isomers. For the l-» 4
and l->5 motions, rotation of cyclopropane about its C 3 axis, none of the
C3 H 4 D 2 SO2 spectra should be split. This path w ould exchange the CD2 group
am ong three structurally inequivalent fram eworks w hich have different
moments of inertia. W ith the exception of H 3 5 C1-H3 7 C1, tunneling doublets
87
are generally not observed under those conditions .2 3 The l - » 6 and 1 —>7
m otions w ould produce a split spectrum for the basal CD2 group on the C2
axis about which the cyclopropane rotates as this w ould exchange identical
nuclei. However, unsplit spectra w ould be expected for the the CD2 group at
the other basal and the apical positions. For the l - > 8 path, the CD 2 group in
the apical position results in the exchange of identical atoms and tunneling
doublets, while both the basal CD2 groups are distinct and w ould be unsplit.
The observation of splittings in the spectrum of the CD 2 group in the apical
position and an unsplit spectrum for the CD 2 group in the basal position then
indicates that the
1 —> 8
m otion is the correct tunneling path. This w ould
produce nuclear spin statistical weights of approxim ately 1:1.3 and although
the relative intensities of the tw o states could not be m easured, they are
estim ated to be between
1 :1
and 1 :2 .
It should be noted that the 1—> 8 path is described as rotation of
cyclopropane about its C 2 axis. This facilitates the discussion of the symm etry
but does not necessarily im ply that the SO2 is a fixed fram ework on which the
cyclopropane rotates. A lthough this division is common and a good
description w hen the masses of the two parts are very different, such a
separation is not obvious for C 3 H 6 SO2 . Perhaps a geared rotation of the two
subunits against one another w ould be a more appropriate description. There
is some suggestion of this since the m agnitude of the tunneling splitting is
affected not only by isotopic substitution on the cyclopropane, b u t also on the
sulfur dioxide. It is not trivial to estim ate the barrier from the observed
splittings and this was not attem pted.
Finally, it is interesting that out of three possible structural isom ers for
1 , 1 -C 3 H 4 D 2 -S0 2
, only tw o w ere observed. While it is not uncom mon under
supersonically cooled beam conditions for only the isotopom er w ith die
88
low est zero-point energy to be populated ,2 4 the observation of tw o out of
three isom ers is puzzling. The tunneling path seems to shed some light on
this. Based on statistical argum ents, it is equally likely th at the SO2 w ill bond
to any of the three C-C bonds in the 1 , 1 -C3 H 4 D 2 spedes w hen the complexes
are form ed in the nozzle. If the tw o bond positions have different zero-point
energies a path exists for cooling to the lower energy basal position through
the tunneling coordinate, i.e. the internal rotation pathw ay is a m eans for
equilibrating between the tw o CD 2 bond isomers. However, there is no ready
pathw ay for cooling between the basal and apical positions if the barrier to
exchange for this m otion is very high, and both of these forms rem ain
populated at the level determ ined by the beam kinetics.
Sum m ary
The structure of C3 H 6 -S0 2 is sim ilar to the structures of C2 H 4 SO2 and
C2H2 SO2 in that the S atom apparently interacts w ith the pseudo-7C system of
the cyclopropane. The sym m etry, how ever, is different w ith the dihedral
angle (a) between the C2 axis of the SO2 and the C-C bond equal to 0° for
C3 H 6 SO 2 compared to 90° for C2 H 4 -S0 2 and C2 H 2 *S0 2 - Like the C2 H 4 SO 2
complex, C3 H 6 -S0 2 undergoes an internal rotation of the cyclopropane about
its local C2 axis.The pseudo-diatom ic stretching force constant for C 3 H 6 -S0 2
w as calculated using M illen's model2 5 as 0.059 m dyne/A and from this the
binding energy was estim ated as 650 cm "1 or 1.9 kcal/m ole.
89
Table 4-6. O bserved transitions for C 3 H 6 -34SQ2 .
T ransition
T ransition
Vo-vcb
Vobsa
3()3-202d
3i2-2n
4i4-3i3
404-303
4i3-3i2
T ransition
A l/A 2c
7242.123
7359.271
9506.431
9651.854
9811.094
1
3
1
-2
3
a2
5l5-4l4
505-404
606-505
5i4-4l3
Vobs
Vo-vc
A 1 /A 2
11881.103
12057.907
12261.818
14459.410
4
2
3
-1
Ai
7403.587
-5
7403.741
-2
lio-Ooo
-t.1
9894.945
9895.104
-14
2n-l0l
12424.588
0
12424.744
7
312-202
14993.558
2
14993.719
2
413-303
a. Observed frequency in MHz.
b. V0bs-VCalc bl kHz.
c. Symmetry label of tunneling state. A 1 /A 2 indicates only one transition
was observed.
90
Table 4-7. Observed transitions for C3 H 6 -S18Q 2 .
T ransition
T ransition
v0-vcb
V0 bsa
A i /A 2c
1
7242.826
3l2-2ll
5i5-4i4
1
9295.386
505-404
4i4-3i3
-2
5i4-4i3
9464.759
4o4-3o3
-4
9476.560
606-505
423-322
-1
9490.029
422-321
9655.286
3
4i3-3i2
a2
Vobs
A 1 /A 2
11616.492
11820.635
12066.152
14169.756
Vo-vc
4
2
-1
3
Ai
9407.874
-<1
-14
9704.978
2ll-l01
11912.787
7
0
11912.891
312-202
14464.672
2
2
14464.763
4l3-303
a. Observed frequency in MHz.
b. Vobs-Vcalc in kHz.
c. Symmetry label of tunneling state. A 1 /A 2 indicates only one transition
was observed.
91
Table 4-8. Observed transitions for C3 H 6 -S18 Q 160 .
T ransition
T ransition
Vote
Vo-vc
v0-vcb
V0bsa
A 1 /A 2
A i/A 2 c
7204.747
1
9621.962
-1
422-321
3<)3-202d
7208.844
-1
9778.040
3
322-221
4l3-3l2
7
11799.390
4
7213.358
321-220
5l5-4l4
7334.698
11992.417
3
2
3i2-2n
505-404
9441.707
1
5i4-4i3
1 2 2 2 0 .0 2 1
-1
4l4-3l3
-2
9600.896
14155.851
9
404-303
6i6-5i5
9610.684
-4
14378.225
3
423-322
606-505
a2
Ai
-A[
9676.028
9676.158
-14
2 ll- l 01
12205.618
0
12205.749
7
3i2-2o2
14778.921
2
14779.036
2
413-303
a. Observed frequency in MHz.
b. Vobs-Vcalc in kHz.
c. Symmetry label of tunneling state. A 1 /A 2 indicates only one transition
was observed.
d. Q uantum num bers a JkpKo-
92
Table 4-9. Observed transitions for C3 D 6 -SQ2 .
v0 -vc
T ransition
T ransition
v0 -vcb
Vobs
Vbbsa
A 1 /A 2
A l/A 2 c
-4
13168.348
9
8851.200
6l6-5l5
2 n -lo i
0
13333.516
3
11168.850
606-505
3i2-2o2
2
13352.544
-1 2
13517.715
413-3(0
625-524
2
13358.515
-1 2
15899.180
5i4-4o4
634-533
1
13358.775
-1 2
4i4-3i3
8781.476
633-532
-2
13375.327
8898.074
-1 2
4()4-3o3
624-523
-4
-1 2
8903.725
13533.130
6i5-5i4
423-322
-1
15360.197
2
8910.253
422-321
7l7“6l6
9024.846
3
15545.550
-7
4i3-3i2
707-606
4
10975.387
15575.683
-7
5i5-4i4
726-625
2
-7
11117.481
15612.015
505-404
725-624
11128.502
-9
15785.460
10
7l6-6l5
524-423
11131.782
-9
15112.216
1
321-313
533-432
5 3 2 -4 3 1
11131.871
-9
12740.400
1
322-3i2
11141.545
-3
523-422
-1
11279.513
5i4-4i3
a. Observed frequency in MHz.
b. Vobs-Vcalc in kHz.
c. Symmetry label of tunneling state. A 1 /A 2 indicates only one transition
was observed.
d. Q uantum num bers a JkpKo-
93
T able 4-10. Observed transitions for b a s a l-C ^ H s D -S O zT ransition
T ransition
v0 -vcb
v0 -vc
Vobs
Vobsa
4
7263.862
1
11918.715
3o3-202d
5l5-4l4
12093.932
2
7380.262
3
3l2-2ll
505-404
5i4-4i3
-1
9536.547
1
12296.761
4l4-3l3
-2
7311.752
-5
9680.765
4o4-3()3
lio-Ooo
9809.891
-4
9839.058
3
4i3-3i2
a. Observed frequency in MHz.
b. Vobs-Vcalc in kHz.
c. Symmetry label of tunneling state. A 1 /A 2 indicates only one transition
was observed.
Table 4-11. Observed transitions for ap/ca/-l,l-C3H4D2-S18 02«
T ransition
T ransition
v0 -vcb
V0 bsa
Vobs
A i /A 2c
A 1 /A 2
1
11248.950
4i4-3i3
9000.556
5i5-4i4
-2
9139.714
11418.305
505-404
4()4-3o3
9146.734
-4
11432.093
423-322
524-423
-1
11448.382
9154.891
422-321
523-422
9291.601
3
11615.640
4i3-3i2
5i4-4i3
13692.702
606-505
13716.568
625-524
13745.006
624-523
A2
v0-\
4
2
-1
3
-1
3
3
3
Ai
-4
-14
9589.050
9589.150
11985.441
7
11985.335
0
3i2-2o2
14419.172
2
14419.282
2
4l3-303
a. Observed frequency in MHz.
b. Vobs-Vcalc in kHz.
c. Symmetry label of tunneling state. A 1 /A 2 indicates only one transition
was observed.
2 n -lo i
94
T able 4-12. Observed transitions for basal-1,l-Cs^D^SOz.
T ransition
T ransition
v0 -vc
v0 -vcb
Vobs®
Vobs
9577.077
-4
4
11848.225
5l5"4l4
2 n -lo i
12093.137
0
12016.714
2
3i2-2o2
505-404
4i 3-3q3
14646.758
2
12031.243
-9
524-423
14072.658
1
-1
12211.498
2 2 0 -2 1 2
5i4-4i3
14185.448
32i-3i3
1
14215.132
9
6i6-5i5
14340.141
1
14410.259
3
606-505
422-414
9480.090
1
14435.352
-1 2
4i4’3i3
625-524
9618.737
-2
14650.816
-1 2
404-303
6l5-5l4
9626.160
-4
423-322
9634.778
-1
422-321
9770.806
3
4i3-3i2
a. O bserved frequency in MHz.
b. Vobs-Vcalc in kHz.
c. Symmetry label of tunneling state. A 1 /A 2 indicates only one transition
was observed.
Table 4-13. Spectroscopic constants of isotopic species of C3H6-S02 from
W atson S-reduced H am iltonian.
c 2 h 4 -s18 o 16 o C3H4D2’S02
C2 H4-S1802
C3H6-34S02
apical
A 2 State
A /M H z
B/M H z
C/M H z
6157.911(7)
1245.745(2)
1169.571(2)
5718.558(2)
1229.851(1)
1139.843(1)
5945.514(3)
1243.685(1)
1159.500(1)
6049.426(5)
1179.925(1)
1107.162(1)
D j/kH z
DjK/kHz
Die/kHz
d i/k H z
d2/kH z
1.90(2)
14.2(6)
OP
OP
OP
1.861(3)
15.4(3)
18.2°
-0.111(5)
0.183(3)
1.92(5)
15.2(6)
18.2C
-0.092(7)
0.179(7)
1.62(1)
1 2 .6 (1 )
18c
0°
0.133(5)
13
0 .0 0 1
17
0.003
16
0.006
nb
13
vG-Vc img/M Hz 0.009
A i State
A /M H z
B/M Hz
C/M H z
6158.066(7)
1245.745(2)
1169.571(2)
5718.664(5)
1229.850(1)
1139.845(1)
5945.350(3)
1243.684(1)
1159.501(1)
6049.523(5)
1179.926(1)
1107.162(1)
D f/kHz
DjK/kHz
DK/kHz
d i/k H z
d2
1.89(2)
14.1(7)
OP
OP
OP
1 .8 6 (8 )
1.92(5)
15.2(5)
18.2C
-0.085(6)
0.181(6)
-
nb
15.5(1)
18.2C
-0.098(1)
0.184(9)
-
13
13
17
15
v0-vc rm s/M H z 0.009
0.003
0 .0 0 2
0.006
a. Uncertainties are one standard deviation in the least squares fit.
b. N um ber of transitions in the fit.
c. Fixed in the least-squares fit.
96
Table 4-13 (cont'd). Spectroscopic constants of isotopic species of C3H6-S02
from W atson S-reduced H am iltonian.
C3 D6 SO2
A 2 /A 2 State
C3H 5 DSO 2
basal
C3H4D2‘S02
basal
A/M H z
B/MHz
C/MHz
5420.840(57)
1143.558(1)
1082.701(1)
6062.694(14)
1249.091(3)
1173.358(4)
5857.749(6)
1239.833(1)
1167.135(1)
Dj/kHz
1.63(4)
8.2(3)
-2 0 C
-0.063(7)
0.179(2)
2 .2 (6 )
1.958(7)
11.3(8)
-9(1)
-0.080(7)
0.232(5)
DjK/kHz
D k /I cH z
di/kH z
d2/kHz
OP
0°
0°
0c
nb
10
30
19
0.018
0.004
V0bs_Vcal rms/MHz 0.006
a. U ncertainties are one standard deviation in the least squares fit.
b. N um ber of transitions in the fit.
97
References to C hapter 4
1. J. A. Shea and W. H. H ygare, J. Chem. Phys., 76,4857 (1982).
2. S. G. Kukolich, P. D. Aldrich, W. G. Read and E. J. Campbell, Chem. Phys.
Lett., 90, 329(1982).
3.
S. G. Kukolich, W. G. Read and P. D. Aldrich, J. Chem. Phys., 78, 3552
(1983)
4. W. G. Read and W. H. H ygare, J. Chem. Phys., 76,2238 (1982).
5. A. C. Legon, P. D. Aldrich and W. H. Hygare, J. Chem. Phys., 75,625 (1981).
6.
P. D. Aldrich, S. G. Kukolich and E. J. Campbell, J. Chem. Phys., 78, 3521
(1983).
7.
L. W. Buxton, P. D. Aldrich, J. A. Shea, A. C. Legon and W. H. Hygare, J.
Chem. Phys., 75,2681 (1981).
8.
a)A. C. Legon, P. D. Aldrich and W. H. Hygare, J. Amer. Chem. Soc., 104,
1486. (1982). b) P. D. Aldrich, S. G. Kukolich, E. J. Campbell and W. G.
Read, J. Amer. Chem. Soc., 105,5569 (1983).
9.
S.G. Kukolich, J. Chem. Phys., 78,4832 (1983).
10. a) C. A. Coulson and W. E. Moffit, J. Chem. Phys., 15,151 (1947). b) C. A.
Coulson and W. E. Moffit, Phil. Mag., 40,1 (1949)
11. D. D. Nelson, Jr, G. T. Fraser and W. Klemperer, J. Chem Phys., 82, 4483
(1985).
12. a) A. C. Legon and D. J. Millen, J. Amer. Chem. Soc., 109,356 (1987). b)
A. C. Legon and D. J. Millen, J. Chem. Soc. Chem. Comm., 1987,986.
13. T. J. Balle and W. H. H ygare, Rev. Sd. Instr., 52,33 (1981).
14. K. W. Hillig n, J. M atos, A. Sdoly and R. L. Kuczkowski, Chem. Phys.
Lett., 133,359(1987).
15. J. K. G. W atson, J. Chem. Phys., 46,1935 (1967).
16. K. Tanaka, H. Ito, K. H arada and T. Tanaka, J. Phys. Chem., 80, 5893 (1984).
17. Y. Endo, M. C. Chang and E. Hirota, J. Mol. Spec., 126,63 (1987).
98
18. M. D. Harm ony, V. W. Laurie, R. L. Kuczkowski, R. H. Schwendeman,
D. A. Ramsey, F. J. Lovas, W. J. Lafferty and A. G. Maki, J. Chem. Phys.
Ref. Data, 8,619 (1979).
19. a) J. Kraitchman, Am J. Phys., 21,17 (1953). b) A. Chutjian, J. Mol.
Spectrosc., 14,361 (1964)
20. O. Bottcher, N. H eineking and D. H. Sutter, J. Mol. Spec., 139,236 (1990).
21. F. J. Lovas, J. Chem. Phys. Ref. Data, 14,395 (1985).
22. R. H. Schw endem an, Critical Evaluation of Chemical and Physical
Structural Information; edited by D. R. Lide and M. A. Paul, (National
Academy of Sciences, W ashington, D.C., 1974), pp. 74-115.
23. N. Ohashi and A. S. Pine, J. Chem. Phys., 81, 73 (1984).
24. a) T. R. Dyke, B. J. H ow ard and W. Klemperer, J. Chem. Phys., 56,2442
(1972). b) H. S. Gutowsky, C. Chuang, J. D. Keen, T. D. Klots and T.
Emilsson, J. Chem. Phys., 83,2070 (1985).
29. D. J. M illen, Can. J. Chem., 63,1477 (1985).
CHAPTERS
THE CYCLOPROPANE-WATER COMPLEX
Because interm olecular interactions involving w ater are im portant in
m any aspects of chemical, biochemical and atm ospheric sciences, w atercontaining m olecular complexes have been the subject of a great deal of
study . 1 Complexes of w ater w ith hydrocarbons such as ethylene and acetylene
have been studied as models of hydrophobic inter actions. la'b The
cydopropane-w ater complex is of particular interest due to the anesthetic
nature of cydopropane. W hile it is w idely accepted that anesthetic properties
result from m olecular assodations, as opposed to chemical reactions, the
nature of this interaction is not well understood. Relationships between lipid
solubility and anesthetic potency have provided evidence th at these
interactions occur prim arily in the lipid bilayer of the cell wall, but it has been
proposed that polar interactions involving the interruption of hydrogen
bonding by the anesthetic could be an im portant factor.2
In an ab initio study exploring this relationship, H obza et al sought the
m ost stable structure of the cydopropane-w ater dim er .2 They determ ined
that the w ater sat above the cydopropane ring w ith the oxygen pointing
tow ard the ring. This structure had an interaction energy of -2.88 kcal/m ole.
The cydopropane-w ater complex has also been the subject of a m atrix IR
study by Barnes and Paulson .3 Their investigations suggested that both w ater
hydrogens w ere involved in hydrogen bonding and they proposed a
bifurcated structure for the complex. However, because the experim ent
99
100
reveals only which bonds are affected by complexation, they w ere unable to
determ ine any details of the structure.
H igh resolution gas-phase spectra have been observed by Fourier
transform microwave spectroscopy for complexes of cyclopropane w ith HC1,4
HF5 and HCN .6 In each case, HX w as hydrogen bonded to the center of a C-C
bond, w ith the ad d in the CCC plane. This is analogous to the structures of
HX w ith ethylene 7 and acetylene8 in so far as the pseudo-n: system of
cydopropane is analogous to the n systems of ethylene and acetylene .9
Similarly, complexes of ethylene, acetylene and cydopropane w ith sulfur
dioxide all involve the S atom of the sulfur dioxide interacting w ith the n or
pseudo- 7i system of die hydrocarbon.
The complexes of w ater w ith ethylene and acetylene have been studied
using the molecular beam electric resonance technique by Peterson and
Klem perer. la'b Their studies revealed that w hile the w ater was hydrogen
bonded to the n system of the ethylene, the acetylene was hydrogen bonded to
the O atom of the water.
Considering these related studies, it w as not obvious w hat m odel to
choose to predict the spectra of the gas-phase cydopropane-w ater complex
(C3 H 6 H 2 O). W ould the complex have a stacked type structure as the ab initio
study indicated (hereafter referred to sim ply as stacked), bifurcated w ith two
hydrogen bonds to a C-C edge as suggested by the m atrix ER work (hereafter
bifurcated), or hydrogen bonded in the traditional sense as suggested by the
cydopropane-HX, ethylene-HX and ethylene-w ater system s (hereafter
hydrogen bonded)? This chapter w ill provide evidence that the w ater is
hydrogen bonded to a C-C edge w ith the oxygen in the CCC plane. The w ater
undergoes a high barrier internal rotation about its local C 2 axis interchanging
101
the free and bonded hydrogens and a nearly free internal rotation about the
hydrogen-bonded
O -H bond.
Experim ental
Spectrom eter. The rotational spectrum of the complex was observed in
a Fourier transform microwave spectrom eter of the Balle-Flygare type using a
m odified Bosch fuel injector as a pulsed nozzle source .10' 11 Line w idths were
typically 20-30 kH z full w idth at half maximum w ith partially resolved
D oppler doubling. Center frequencies have an estim ated accuracy of ± 2 kHz.
The spectrom eter is fitted w ith tw o steel m esh plates separated by 30 cm
which can be charged to ± 10 000 V for the m easurem ent of Stark effects.
For the resolution of the deuterium nuclear quadrupole hyperfine
structure, a new m odification of the spectrom eter was em ployed. A nozzle
was placed in the center of one of the m irrors of the Fabry-Perot cavity so that
the gas jet expanded along the cavity axis.12 This increased the splitting
between components of each D oppler doublet to 60-70 kHz. Furtherm ore, the
combination of a m uch longer free induction decay (because the molecules
are in the active region of the cavity for a longer time) and a narrow er spread
in the on-axis velocity distribution decreased the w idth of each com ponent to
~5 kHz, giving m uch better resolution of the closely spaced hyperfine
structure.
Sam ples. The spectrum of C3 H 6 -H2 0 was observed by placing about
1 mL of de-ionized w ater in a 1 L glass sam ple bulb. The w ater was degassed
by freezing to liquid nitrogen tem perature and pum ping on it for several
m inutes followed by w arm ing to room tem perature; this was repeated for two
102
or three freeze/thaw cycles until no further gas was evolved. A bout 10 torr of
C3 H 6 (Aldrich) and 1.5 atm of Ar (Linde) were then added to the bulb. The
vapor pressure of w ater at room tem perature was sufficient to produce the
spectrum w ith good signal/noise.
The spectra of C3H 6 HDO and C3 H 6 -D2 0 were observed by placing a 75 :
25 m ixture of D 2 O (Cambridge Isotope Labs) and HfeO in a chamber
im m ediately behind the nozzle orifice. A sam ple containing 1%
cyclopropane in A r at 1.5 atm was passed over this solution. The spectra of
L 1 -C3 H 4D2 -H2 0 , CaDs-EfeO, C 3 H 6 *H2 170 and C3 H^ H 2 180 w ere produced w ith
the sam e procedure as the norm al isotopic species using commercial samples.
U -C 3 H 4 D2 H 2 O (98%), C 3 D6 H 2 O (98%) and C3 H 6 H2170 (38%) w ere purchased
from MSD Isotopes. C3 Hg-H2 180 (99%) was obtained from Cambridge Isotope
Labs.
R esults and A nalysis
Spectrum . The spectrum of die C3 H 6 H 2 O complex was predicted using
a hydrogen-bonded model analogous to C2 H 4 -H2 O and transitions were found
in the appropriate region for J = 2 <—1 fl-type transitions. This led to
predictions for the J = 3 <- 2 transitions of the same series, which were readily
found, b- and c-type Q-branch series were then predicted in the region 16 to 18
GHz, but despite considerable searching, no other transitions w ere found.
The observed transitions, listed in Table 5-1, w ere all split into doublets w ith a
3:1 relative intensity ratio. The strong and weak sets were each fit
independently to a A, B, C, Dj and D jk in the W atson S-reduction F
representation . 13 The labels A i and A 2 are taken by analogy to the C3 H 6 *SC>2
103
system. The fitted constants are shown in Table 5-2. The A constant is poorly
determ ined because only a-type transitions w ere observed.
Table 5-1. Observed transitions of C3 H 6 H 2 O in MHz.
A ia
w eak
A2a
strong
T ransition
Vobs
Vobs
Vo-Vc
9539.715
9171.080
9895.676
14308.359
14571.827
-0.015
14578.252
14842.236
0 .0 0 1
Vo-Vc
-0 .0 1 2
9538.013
-0 .0 0 2
9715.940
2 0 2 -1 0 1
9895.087
0.014
2 ll- ll 0
0 .0 1 2
14305.798
3i3-2l2
14570.094
-0.004
303-202
-0.004
14571.018
322-221
14576.470
0 .0 0 2
321-220
14841.344
-0.006
3 i 2 -2 n
a. Symmetry label of tunneling state.
b. Q uantum num bers are JkpKo2 i 2 - lllb
Table 5-2. Spectroscopic Constants for C3H 6 -H2 Q.
a2
Ai
strong
weak
A /M H z
19950(150)
19950(100)
2518.843(7)
B/M Hz
2518.845(5)
2340.876(7)
C/M H z
2340.321(5)
D j/kH z
6.7(2)
6.7(3)
DjK/kHz
184(4)
189(1)
na
8
Av/kHz
14
Ha/D
1.209(2)
a. N um ber of transitions in fit.
7
16
0 .0 0 2
0 .0 1 2
0.009
0.000
-0.009
104
The spectra of C 3 H 6 HDO and C3 H<s-D2 0 w ere predicted, again using a
hydrogen bonded m odel, and searches w ere begun. For CsHgT^O, the
transitions w ere split into doublets of unequal intensity, but the intensities
were reversed. In the norm al isotopic species the low er frequency lines were
three times as strong as the higher frequency lines, w hile in the C 3 Hg*D2 0 , the
higher frequency lines w ere about tw o tim es stronger than the lower
frequency transitions. The m agnitude of the splittings decreased by about 50
to 60% for the deuterated form. For C 3 H 6 HDO, tw o different isotopic isomers
w ere expected for a hydrogen bonded structure, one w ith the D in the
hydrogen bond and the other w ith the D in the non-bonded position. Only
one spectrum was observed and no doubling of the transitions was found.
The rotational constants indicated the deuterium -bonded isom er. Extensive
searches above and below the observed transitions produced no partner and
intensive searches for another isom er w ere not fruitful.
The spectra of C3 H 6 -H2 180 and C3 H 6 *H2 170 w ere also split into
doublets. For C 3 Hg-H2 180 the splitting decreased by 30% The relative
intensities of the tw o components paralleled the norm al isotopic species and
were approxim ately 3:1. C3 H 6 *H2 170 also exhibited split transitions with
strong and weak components. The 170 nuclear quadrupole hyperfine
structure prevented a m ore quantitative determ ination of their relative
intensities.
The spectra of 1 ,1 -C3 H 4 D2 *H2 C and C3 D 6 H 2 O were also m easured. For
1 , 1 -C 3 H 4 D 2 -H2 0
two different spectra were observed and both were split into
doublets w ith a 3:1 intensity ratio sim ilar to the norm al isotopic species.
These tw o spectra correspond to deuteration at the position opposite the C-C
bond to which the w ater is bonded (labeled apical) and at one of the carbons
making up the C -C bond to which the w ater is bonded (labeled basal). The
105
splitting decreased by about 2 0 % for die apical position and by about 1 0 % for
the basal position. The spectrum of C3 D 6 H 2 O w as split into doublets w ith a
3:1 intensity ratio and w ith a decrease in the splitting of about 30%.
The observed transitions and spectroscopic constants for all the
isotopically substituted species are shown in Tables 5-10 through 5-17 at die
end of the chapter.
D ipole M om ent The dipole m om ent of C3 H 6 H 2 O was determ ined by
m easuring the Stark effects of all 15 M com ponents available from the
Table 5-3. Stark effects (Av/e2)a and dipole
IMI
C 3H 6 H 2 O
obs
0
-12.14
2 0 2 -1 0 1
1
9.88
2 0 2 -1 0 1
0
10.05
2 l 2 - lll
1
499.83
2 i 2 - lll
0
9.75
2 n -lio
1
-498.91
2 ll- ll 0
0
-2 .0 0
3(53-202
1
0.54
3o3-2<)2
2
3.81
303-202
0
-0.56
3i3-2i2
1
17.32
3i3-2i2
2
70.80
3i3-2i2
0
0.54
3l2-2li
1
-16.55
3i2-2n
2
-66.77
3l2-2n
momenl of cyclopropane-water.
C 3 H 6 HDO
o-c
obs
o-c
-0.53
0.44
0.44
-5.90
0.48
-5.60
-0.07
-2.166
0.057
-0.627
-0.024
0 .0 0
0.17
-0.00
-0.580
0.004
0.15
0.47
0 .0 0
-0.398
-0.000
-0.07
-0.25
Ha/D
1.209(10)
a. Second order Stark effect in M H z/(kV /cm )2.
1.277(8)
106
observed transitions. The electric field was calibrated using the J = 1 «- 0, M =
0
<—0 transition of OCS at 12162.980 MHz.14 The observed Stark effects of
C 3 H 6 H 2 O, shown in Table 5-3, w ere least squares fit to the dipole components
using Stark coefficients calculated from the rigid rotor rotational constants,
resulting in \ia=l .209(10) D; \i\p- was a small negative num ber (-0.033 D2) and
He2 was 0.021(68) D2. This im plied that Mb " Vc * 0 D* Therefore, for the fit
shown in Table 5-3 the |ib and He components w ere constrained to zero; the
resulting jia com ponent w as the same. The dipole m om ent of C3 H 6 HDO was
also m easured (Table 5-3), resulting in |ia=1.277(8) D and (lb * He " 0 D.
Nuclear quadrupole coupling constants for CaH^HDO and
C 3 H 6 ‘H 21 7 0 . H yperfine structure arising from deuterium nuclear
quadrupole coupling in the C3 H 6 HDO species w as resolved and assigned.
The assigned hyperfine com ponents are shown in Table 5-18 at the end of the
chapter. The quadrupole interaction was treated as a perturbation on the
rotational energy levels and the coupling constants w ere derived by least
squares fitting to die observed splittings, resulting in Xaa - 0.242(3) MHz, Xbb =
-0.107(7) MHz and Xcc = -0.135(7) MHz. 15
The 170 hyperfine w as assigned for both the strong and weak
com ponents of the tunneling doublets as show n in Table 5-13. For the strong
com ponent a com plete assignm ent was possible, w hile for the w eaker
com ponent only the strongest hyperfine transitions w ere observed, giving a
much sm aller data set. The coupling constants w ere fit as in the C 3 H 6 HDO to
give ^
= -5.352(10) MHz, %bb = 2.353(12) MHz and Xcc = 2.999(22) MHz for the
stronger transitions and Xaa = -4.798(165) MHz, %bb = 2.091(95) MHz and Xcc =
2.707(270) MHz for the weaker.
107
Structure. Because the A rotational constants w ere poorly determ ined
for all isotopomers, only B and C were used in the structure calculations w ith
the exception that the A constants were used in calculating the planar second
m om ents, Pxx- Reasonable errors in the A constants propagate into errors of
~0.3 amu-A 2 in the planar moments. For isotopic species w ith split
transitions, the constants from the m ore intense state w ere used. Since the
differences in B and C between the tw o states were very sm all, this choice will
not m arkedly affect the structure. It was assum ed that the cyclopropane and
w ater structures w ere unchanged upon complexation . 16' 1 7
T able 5-4. Planar second moments3 (amuA2) of C3 H 6 H 2 O and selected
isotopom ers.___________________________________________________
180b
C3 H6 -D2 0
apicalc
C3H 6H D O
C 3H 6H 20
206.4537
195.5852
208.1714
208.9615
197.7425
Paa
20.4517
20.3592
20.3523
20.2998
20.3748
Pbb
5.1434
4.9745
5.0437
6.7597
5.0446
Pcc
C3H6
20.1539
20.1539
Pbb
5.0403
Pcc
a. Paa = 0.5 [lb + Ic - lal and sim ilarly for Pbb and Pcc.
b. C3 H6 H 2 lsO.
c. flp/cfl/-l,l-C 3 H 4 D2 -H2 0 .
Paa
H 2O
1.1916
0.6344
0 .0
Shown in Table 5-4 are the moments of inertia and planar second
m om ents for the A2 states of selected isotopic species, as w ell as for
cyclopropane and w ater. Com parison of the planar second mom ents of the
complex w ith those of free cyclopropane reveals that Pbb(complex) ~
Pbb(cyclopropane) and Pcc(complex) « Pcc(cydopropane). These relationships
im ply that the w ater does not contribute to Pbb and PCC/ i.e. the b and c
108
coordinates of the oxygen are zero or nearly so. Also, Pcc implies th at the
cydopropane ring lies in the ab plane of the complex or nearly so . 16 Such an
arrangem ent is consistent w ith either a hydrogen bonded or a bifurcated
structure but not w ith a stacked structure. Indeed, if one tries to reproduce
the observed B and C constants w ith a stacked structure it proves to be
impossible. Placing the w ater above the ring results in a very near prolate top
w ith (B - C) < 20 MHz com pared to the observed (B - C) of 180 MHz.
Once it is established that the heavy atoms all lie in a plane, the
geom etry of the complex is defined by the param eters show n in Figure 5-1,
0(H2Q)
Figure 5-1. Param eters defining the structure of C3 H 6 -H2 0 .
w here Rcm is the distance between the centers of mass of w ater and
cydopropane, OOHfeO) is the angle between the C 2 axis of the w ater and Rcm,
0(V) is the angle between the C2 axis of cydopropane and Ron/ and <|>is the
torsional angle between the CCC plane of cydopropane and the plane of the
water. Rcm, being prim arily defined by the positions of the heavy atoms, can
be determ ined from the moments of inertia of the norm al isotopic spedes to
109
be approxim ately Ron = 3.93 A. These moments/ however, are relatively
insensitive to the angles. 0(H 2 O) is defined by the positions of the hydrogens
and either a hydrogen bonded or a bifurcated structure can match B and C.
A lthough Fbb(complex) = Paa(V), this does not give inform ation about 0(V);
because cyclopropane is a symmetric top, Fbb(complex) can be reproduced for
all angles
0
of cyclopropane. <|>is also a function of the positions of the w ater
hydrogens and any $ between 0° and 90° gives a reasonable match for the
rotational constants.
The angle 0(H 2 O) can be determ ined from die mom ents of inertia of
C 3 H 6 HDO and C3 H 6 D 2 O. The m easured changes in rotational constants
upon deuteration AB(HDO) = B C C ^ ^ O ) - B C C ^ HDO) and AB(D2 0 ) =
B(C3 H6-D2 0 ) - B(C3H 6 -H20 ) are shown in Table 5-5.
Table 5-5. Experimental and predicted differences in rotational constants
(MHz) for C3 H 6 -H2 Q/ C 3 H 6 HDO and C3 H 6 D2 O.______________________
A (D20)b
A (HDO)a
Expc
Expc
Bifd
h-bonde
Bifd
h-bonde
B
104
26
52
33
49
105
C
23
51
29
91
48
85
a. Difference between rotational constants of C3 H 6 -H2 0 and C3 H 6 HDO.
b. Difference between rotational constants of C3 H 6 -HDO and C3 H6-D2 0 . See
text for details
c. Experimental.
d. Calculated for bifurcated structure.
e. Calculated for hydrogen bonded structure.
The small change upon substitution of one deuterium followed by the
large change for a substitution of a second suggests that the two w ater
hydrogens are in significantly different positions. To test this inference Rcm
was adjusted for the bifurcated and hydrogen bonded structures to best match
B and C for C3 H6*H2 0 . From these structures/ changes in lb and Ic were
110
predicted for the tw o deuterated w ater isotopes (Table 5-5). The agreem ent
was very poor for the bifurcated structure and quite good for the hydrogen
bonded structure.
A lthough the A constants w ere poorly determ ined, Kraitchman
calculations w ere carried out first using the norm al isotopic species as the
parent to calculate the position of the first deuterium , then using C3 H 6 HDO
as the parent to calculate the position of the second deuterium . 18 The results
are shown in Table 5-6. The a coordinates are small for the first hydrogen
atom and large for the second, consistent w ith the hydrogen bonded
structure. It should be noted that the b and c coordinates reported in Table 5-6
are very poorly determ ined, as they are greatly affected by the A rotational
constant; changing the A constant by ± 1 GHz results in b and c coordinates
between 0 and 1 A. Therefore, these coordinates cannot be used to determ ine
<|>. The a coordinates, however, are defined by the B and C rotational constants
which are well-known, and are reliable to ±0.05 A for the same change in A.
Table 5-6. D euterium coordinates calculated using Kraitchm an's equations.
h-bonda
1.46
0.19
freeb
a/A
2.97
b /k
0.44
c /k
0 .2 2
0.29
a. Calculated using C3 H 6 H 2 O as parent and C 3H 6 HDO as substituted species.
b. W ater hydrogen not involved in hydrogen bond. Calculated using
C3 H6 HDO as parent and C3 H 6 D2 O as substituted species.
The orientation of the cyclopropane can be determ ined from the
1 , 1 -C 3 H 4 D 2 -H2 0
isotopes. The sim ilarity of Pbb(C3 H$-H2 0 ) to Fbb(apical-
I ll
C 3 H 4 -D2 -H2 0 ) places the substituted hydrogens in or nearly in the ac plane of
the complex and requires that 0(V) be approxim ately zero.
The torsional angle <|>is not readily determ ined from the m om ents of
inertia. It is defined prim arily by the b and c coordinates of the non-bonded
hydrogen on the w ater. The moments of inertia, being subject to vibrational
averaging effects of the sam e m agnitude as the inertial contributions from the
b and c coordinates of a hydrogen atom, are not reliable indicators of these
coordinates. All the experim ental data were fit to Rem and 0 (H 2 O) for
0
= 0°
(non-bonded H in the CCC plane) and <j>= 90° ( non-bonded H perpendicular
to the CCC plane). The results are shown in Table 5-7. A lthough the quality
of the fit is slightly better for $ = 0 °, the difference is too small to be
conclusive. The structure of C 3 H 6 H 2O is determ ined to be hydrogen bonded
w ith an approxim ately linear hydrogen bond, as m easured by the angle
between the C-C bond center, the bonded hydrogen atom and the oxygen
atom. The position of the free hydrogen, however, is uncertain.
Table 5-7. Cyclopropane-water structures from least-squares fits of moments
of inertia lb and Ic.____________________________________________________
1 2 4 .1 (4 .5 )
0
0
ON
II
-©•
0
0
II
®o-cm-cc/°a
Rem/Aa
(lobs'Icalc)rms/ amu*A^
1 2 3 .0 (6 .3 )
3 .9 3 1 (2 )
3 .9 3 1 (2 )
0 .4 8
0 .6 8
2 .3 4 0
2 .3 4 0
Rh-bond/A*5
3
4
0h-bond/°k
a. Fitted param eters.
b. Calculated param eters (not explicitly fit). Rh-bond is the distance from the
hydrogen-bonded H to the C -C bond center. 0h-bond is the deviation of the
angle subtended by the C-C bond center, the hydrogen-bonded H and the O
from 180°.
112
Internal Rotation. The splitting observed in the transitions indicates
that the molecule is tunneling betw een equivalent conform ations through
perm utations of identical nuclei. To explore the nature of this tunneling
m otion, feasible perm utations of equivalent nuclei w ere considered, w here
’<C$
o(5
o
( 3
o
( 3
o(3
o
( 3
8
o
( 3
® (3
Figure 5-2. Feasible perm utation of nuclei for C3 H 6 H 2 O. Pathways
between frameworks are discussed in the text.
113
feasible restricts the consideration to perm utations which do not require the
breaking of covalent bonds. The am biguity of the free hydrogen position will
not affect the num ber of frameworks considered. However, it w ill be a
consideration in the sym m etry argum ents used to choose am ong them , as
discussed below. The eight frameworks shown in Figure 5-2 w ere considered.
Likely pathw ays between the frameworks are as follows: 1 -* 2 and 1 -* 3,
rotation of cyclopropane about its C 3 axis; 1 -» 4, rotation of cyclopropane
about the bonded O-H bond (this is symm etrically equivalent to rotation of
cyclopropane about its C2 axis which lies nearly along the a principal axis of
the complex);
1
-» 5 , rotation of w ater about its C2 axis;
1
-» 6 , inversion of
w ater through a bifurcated interm ediate exchanging the bonded and nonbonded hydrogens; 1 —>7 and 1 -> 8 , rotation of cyclopropane about either of
its rem aining C 2 axes.
The 3 :1 relative intensities of the Ai and A 2 states in the norm al
isotopic species are suggestive of a tunneling path which exchanges two
hydrogen atom s of the w ater. The decrease in the m agnitude of the splittings
upon isotopic substitution lends support to this theory as the splittings
collapse m uch more upon substitution of the w ater than on the cyclopropane.
This is confirm ed by the relative intensities of the tw o states in the
isotopom ers shown in Table 5-8. For C3 H 6 -D2 0 the relative intensities
reverse for the tw o states, consistent w ith the
1
: 2 nuclear spin statistical
w eights for the exchange of tw o deuterons. The lack of tunneling splittings in
the C3 H 6 -HDO suggests that the tunneling m otion involved the exchange of
the two w ater hydrogens and that they are in tw o inequivalent positions in
the complex. A dditionally, the apical-CjtbiPxHiO, basal-CztLiDzfyO and
C 3 D6 H 2 O all exhibit 3 :1 relative intensities as observed in the norm al
isotopic species, indicating that the cyclopropane does not take p art in the
114
tunneling m otion. These considerations elim inate all the tunneling paths in
Figure 5-2 except 1 -» 5 and 1 -»
6
as the cause of the doubling.
Table 5-8. Relative intensities 3 of A 2 :Ai tunneling states for C 3 H6-H20 and
isotopom ers.
C3H6*H20
2.6:1
C3 H 6 -HDO
b
C3H6-D20
(1 :2)
C3 H6-H2180
(3:1)
C3 H6-H2170
(3:1)
Q H 6-H 20
(3:1)
1 /1 -C 3 H 4 D 2 -H2 0 (apica/)
2.8:1
l /l-C3H4D2*H 2 O(&asa0
______________ 2.9:1
a. Relative intensities m easured as described in Chapter 2. U ncertainties are
about 15%. N um bers in parentheses are estim ated.
b. Only one set of transitions observed.
In selecting between the 1 -» 5 and 1 -> 6 motions and the tw o
structures, tw o experim ental observations w ere em ployed. The first is the
3 :1 spin statistical w eights in the norm al isotopic species. Indistinguishable
structures for frameworks
1
and
6
require perm utations of identical nuclei
(14)(23)(56)(ab), giving statistical w eights approxim ately 1 :1 .2 . The second
consideration is the spectrum of &asa/-C3 H 4 D 2 -H20 w here the transitions
were split into doublets w ith a 3 :1 intensity ratio. For die <j>= 90° structure
with the tunneling path
1
—> 6 , split transitions are expected because the
starting and ending fram eworks have the same mom ents of inertia.
However, the relative intensities w ould be 1 :1 because the m otion does not
result in indistinguishable configurations, i.e. the CD2 group w ould be
exchanged w ith a CH 2 group, as shown in Figure 5-3, resulting in no nuclear
115
Figure 5-3. Positions for D in basal-1 /1 -C 3 K^D2 -H2 0 for <|>= 90°.
spin restrictions. For the <j>= 0° structure w ith the 1 -»
6
m otion, tw o different
isotopomers for basal-1 ,1 -C 3 H 4 D 2 -H2 0 (Figure 5-4) are expected, one w ith the
free hydrogen on the side of the CD2 group and the other on the side of the
non-deuterated CH 2 group. W ith the exception of the H35 C1-H3 7 C1 dim er,
tunneling doublets are not generally observed in such a situation . 19 While it
is possible that the two isotopom ers w ould have 3 :1
Figure 5-4. Positions for D in &asa/-l,l-C 3 H 4 D 2 -H2 0 for <j>= 0°.
relative intensities due to a Boltzman distribution, this w ould be highly
fortuitous. Therefore, for either structure the tunneling path consistent w ith
the relative intensity data is the rotation of w ater about its local C2 axis; for
116
both structures the l-» 5 m otion exchanges identical nuclei (the tw o w ater H)
in both apical- and basal-l,I-C 3 H 4 D2 H 2 O and 3:1 intensities are expected.
To distinguish between the <j>= 0° structure and the 0 = 90° structure
again the f?asa/-C3H4D2*H20 spectrum was considered. For <)>= 90°, the CD2 in
the 1 and 2 positions (Figure 5-2, fram ew ork 1) gives the sam e moments of
inertia as the CD2 group in the 3 and 4 positions, resulting in only one
spectrum. Rotation of w ater exchanging a and b w ould split it into doublets
of 3 :1 relative intensities. For $ = 0° , however, deuteration at the 1 and 2
positions gives a different isom er w ith different m om ents of inertia than
deuteration a t the 3 and 4 positions, resulting in tw o basal isomers. For both
isotopom ers the rotation exchanging a and b w ould result in doubled
transitions w ith 3:1 statistical weights. The observation of only one
spectrum , split into tunneling doublets, seems to favor the <|>= 90° structure.
However, it should be noted that it is not uncom mon for m olecular beam
conditions to produce only one of tw o or m ore possible isotopic isom ers in
significant am ount due to differences in zero-point energy and the cold
tem perature of the supersonic beam.20 Therefore, the position of the non­
hydrogen bonded hydrogen rem ains an open question. Finally, although
m ost van der W aals molecules show some degree of symm etry, there is no a
priori reason that the molecule should have either <j>= 0° or <|>= 90° symm etry
i.e. it is equally possible that 0°«|><90o.
The determ ination of the structure as hydrogen bonded and the
rotation of w ater about its C2 axis as the cause of the tunneling doublets
leaves tw o puzzles. The first is that the observed dipole m om ent is not
consistent w ith a hydrogen bonded structure. If die dipole m om ent of w ater
is projected into the principal axis system of the complex, com ponents na =
1.15 D and p.± = 1.45 D are expected w here p.j_ = [m,2 + n*2]0-5. 17 The
117
experim entally m easured components are (ib * M-c “ 0 D. The second is that
the 170 quadrupole coupling constants are also quite different from those
predicted by a projection of the quadrupole tensor into the complex principal
axis system. This is show n in Table 5-9.21
Table 5-9. Dipole m om ent com ponents and 170 nuclear quadrupole coupling
constants predicted from the structure and experimental.*_________________
Predicted
O bserved
1.15
1.209(2)
M-a
1.45
0.0
Ho.
-6.039
-5.342(10)
Xaa
-4.129
2.356(12)
Xbbb
10.169
2.986(22)
Xccb
a. Experimental values are as m easured for the A i tunneling state.
b. Xbb and Xcc are for the <j>= 0° structure. The values will be reversed for the $
= 90° structure.
The m ost plausible explanation is that the w ater subunit, in addition to
a high barrier tunneling m otion about its local C 2 axis, is involved in a nearly
free internal rotation about the hydrogen-bonded O-H bond. W ith a small
barrier and a light top, the excited torsional states w ould be very high in
energy. Such a m otion w ould also change the direction of the b- or c-dipole
m oment, resulting in perpendicular (b- or c-type) selection rules between
tunneling states The b- or c-type transitions resulting w ould yield Stark
coefficients considerable different from those determ ined using the rigid rotor
rotational constants. For example, if a tunneling m otion produced a
difference in energy between the states on the order of 100 GHz, as is not
uncom mon for w ater tunneling m otions,22 the coefficients w ould be an order
of m agnitude sm aller that those determ ined from the rigid rotor constants
118
and the determ ined perpendicular dipole m om ent w ould be artificially small.
Additionally, for a low barrier, w here the top can be thought of as classically
rotating, rather than tunneling, both the dipole m om ent and the nuclear
quadrupole coupling constants w ould be averaged over the tunneling
coordinate, reducing < |ij> and giving Xbb and Xcc sim ilar to the observed
values.
Despite considerable searching, no evidence for a second tunneling
splitting is observed, but the excited torsional states are likely not populated at
the IK tem perature of a supersonic beam.
Sum m ary
Following the trend of the complexes C3 H 6 HX, C 2 H 4 HX, C2 H 2 HX and
C2 H 4 *H2 0 , the C3 H 6 H 2 O complex has the H 2 O hydrogen-bonded to a C-C
edge which behaves as a pseudo-n system hydrogen-bond acceptor. From
M illen's m odified pseudo-diatom ic m odel the stretching force constant for
the hydrogen bond is calculated as 0.065 m dyne/A .
23
W ith a Lennard-Jones 6-
12 potential this gives a binding energy of 731 cm-1 or 2.1 kcal/m ole. The
w ater subunit is involved in tw o internal motions: the first is a high barrier
internal rotation about its local C2 axis which results in doubling of the
rotational transitions; the second is a low barrier rotation about the hydrogenbonded O-H bond which m anifests itself in anom alous dipole moment
components and 170 quadrupole coupling constants.
119
Table 5-10. Observed transitions of C3H 6 HDO in MHz.
T ransition
Vo-vc
Vote
-0.012
9442.739
2 i2 -lllb
-0.002
9616.855
202-101
9792.232
0.014
2 n -li0
14162.871
0.012
3l3-2l2
-0.004
14421.638
303-202
-0.004
14422.640
322-221
0.002
14427.873
321-220
14687.147
-0.006
3i2-2n
a. Symmetry la oel of tunneling state.
b. Q uantum num bers are jKpKo-
Table 5-11. Observed transitions of CsHfrDzO in MHz.
A2a
weak
T ransition
v0-vc
v6bs
9065.161
-0.012
2 i2 -lllb
9226.922
-0.002
202-101
0.014
9389.470
2 n -lio
0.012
13596.719
3i3-2l2
14837.241
-0.004
3q3-2o2
14083.121
-0.006
3l2-2ll
a. Symmetry label of tunneling state.
b. Q uantum num bers are JKpKo-
A ia
strong
Vote
9065.815
9227.469
9389.846
13597.716
13838.056
14083.758
Vo-Vc
-0.015
0.002
0.012
0.009
0.000
-0.009
120
Table 5-12. Observed transitions of C3 Hg-H2 18Q in MHz.
A ia
weak
A2a
strong
T ransition
Vo-Vc
Vobs
-0.014
8971.496
2i2 -lllb
9128.807
0.000
2<)2-l01
9286.827
0.014
2 ll-ll0
0.009
13456.259
3l3-2i2
13690.210
0.000
303-202
-0.009
13929.190
3l2-2ll
a. Symmetry label of tunneling state.
b. Q uantum num bers are JkpKo*
Vobs
8972.631
9129.426
9286.950
13457.961
13691.210
13929.381
Vo-Vc
-0.012
0.000
0.012
0.008
0.000
-0.008
T able 5-13. Observed transitions of apical-lfl-C stU P T ^O in MHz.
A ia
A2a
strong
weak
T ransition
v0-vc
Vo-Vc
Vobs
Vobs
-0.012
8985.945
8987.006
-0.015
2 i2 -lllb
-0.002
9125.652
0.002
9124.775
202-101
0.014
9264.341
0.012
9264.725
2 n -lio
0.012
13477.573
13479.648
0.009
3i3-2i2
-0.004
13685.942
13684.611
0.000
303-202
13687.682
0.002
13688.986
0.001
321-220
13895.603
-0.006
13896.190
-0.009
3i2“2 ii
a. Symmetry label of tunneling state.
b. Q uantum num bers are JKpKo-
121
Table 5-14. Observed transitions8 of C3 H 6 -H2 17Q in MHz.
a2
Ai
strong
weak
F'-F"
T ransition
Vo-Vc
Vobs
Vobs
9241.774
0.5-1.5
0.009
2i2-lll
1.5-1.5
-0.004
9241.375
4.5-3.5
9241.163
-0.004
2.5-1.5
0.004
9420.955
3.5-3.5
-0.004
9240.585
2.5-2.S
9240.242
-0.003
3.5-2.5
9240.096
0.001
2.5-2.5
9408.260
-0.002
202-101
3.5-2.5
9407.987
-0.007
9409.856
4.5-3.5
9407.903
0.000
9409.764
1.5-1.5
9407.430
0.009
3.5-3.5
9406.869
-0.002
2.5-1.5
9406.659
0.003
4.5-3.5
9575.991
0.004
9576.583
2 n -lio
2.5-1.5
9575.920
-0.001
9576.530
3.5-3.5
9575.531
-0.003
2.5-2.5
9575.002
0.000
3.5-2.5
9574.904
0.000
1.5-1.5
13860.420
-0.001
13862.482
3i3-2i2
5.5-4.5
13860.311
0.006
13862.402
4.5-3.5
13860.084
-0.005
13862.196
4.5-3.5
14108.428
-0.004
14109.738
303-202
5.5-4.5
14108.383
0.002
14109.691
3.5-2.5
14108.167
0.003
14109.505
5.5-4.5
3i2-2n
14362.505
0.000
14363.014
4.5-3.5
14362.280
-0.002
14362.793
3.5-2.S
13462.162
-0.002
4.5-4.5
14361.831
0.003
a. Coupling scheme is F = J + I.
Vo-Vc
0.005
-0.005
-0.001
0.001
-0.012
0.012
0.000
-0.002
-0.004
0.005
0.010
-0.010
122
Table 5-15. Observed transitions of b a s a l - l / L - C j ^ ^ T ^ h P in MHz.
A ia
A2a
strong
weak
T ransition
Vo-Vc
Vobs
Vobs
-0.012
9416.565
9414.996
2i2 -lllb
-0.002
9406.113
9605.159
202-101
0.014
9795.425
9575.980
2 n -lio
0.012
14120.999
14123.350
3i3-2i2
-0.004
14401.073
14402.666
303-202
-0.004
14403.933
322-221
14411.472
0.002
321-220
14691.535
-0.006
14692.346
3i2-2ii
a. Symmetry label of tunneling state.
b. Q uantum num bers are JKpKo*
Vo-Vc
-0.015
0.002
0.012
0.009
0.000
-0.009
Table 5-16. Observed transitions of C3 D 6 -H2 Q in MHz.
A ia
weak
A2a
strong
T ransition
v0-vc
Vobs
8770.707
-0.012
2 i2 -lllb
-0.002
8932.969
202-101
0.014
9097.243
2 ll-ll0
13151.734
3l3-2l2
-0.004
13394.800
303-202
13644.444
-0.006
3l2-2ll
a. Symmetry label of tunneling state.
b. Q uantum num bers are JKpKo-
Vobs
8771.939
8933.760
9097.602
13156.582
13396.006
13644.988
Vo-Vc
-0.015
0.002
0.012
0.009
0.000
-0.009
123
Table 5-17. Spectroscopic constants for C3 H 6 HDO and C3 H 6 -D2 Q isotopomers.
C3H6HDO
C3H6-D20
Ai
A2
A/M H z
19881(70)
20000(500)
19676(200)
B/MHz
2492.166(6)
2388.319(20)
2388.403(9)
C/MHz
2317.410(6)
2226.178(19)
2226.385(9)
Dj/kHz
5.9(7)
6.7(3)
5.2(3)
DjK/kHz
177(1)
180(12)
191(6)
n
8
6
6
AVrms
17
22
10
Ma/D
1.277(8)
Xaa/MHz
0.242(3)
Xbb/MHz
-0.107(7)
Xcc/MHz
0.135(10)
Table 5-17 (cont'd). Spectroscopic constants of C3 H 6 -H2 18Q and C3 H 6 -H2 17Q
C3H6-H2180
C3H6-H2170
A2
Ai
A2a
A ia
A/M H z
19908(500)
20422(500)
19882(300)
18162(5000)
B/MHz
2361.527(22)
2361.412(19)
2436.196(15)
2436.3(6)
C/MHz
2203.876(21
2204.265(19)
2268.787(15)
2269.3(6)
Dj/kHz
5 .9 (7 )
6.3(6)
6.1(5)
6 .1 b
DjK/kHz
183b
176(13)
164(12)
183(9)
n
3
6
6
6
24
21
16
731
Xaa/MHz
-5.352(10)
-4.798(165)
Xbb/MHz
2.353(12)
2.091(95)
X cc/ M H z
2.999(22)
2.707(170)
unsplit frequencies. As a complete set was not available for the Ai state, the
constants w ere determ ined using the m ost intense of the hyperfine
transitions.
b. Fixed at this value in the least-squares fit.
124
Table 5-17 (cont'd). Spectroscopic constants of a p i c a l - l / l - C s ^ A ^ ' ^ h P ,
b a sa l-1 ,1- C 3H 4 D 2 H 2O and C3D6-H2Q._____________________________
C3D6-H20
basal-1,1apical-1,1-
A /M H z
B/M H z
C/M H z
D j/kH z
DjK/kHz
n
^Vmns
C3H4D2-H20
C3H4D2-H20
A2
Ai
A2
Ai
18676(100)
18633(13)
16791(50)
16805(50)
2351.318(3)
2351.283(4)
2211.972(3)
2212.431(4)
5.7(2)
5.4(2)
A2
Ai
13656(250)
13654(250)
2496.852(8) 2496.85(4)
2315.85(3)
2315.51(3)
2306.660(8) 2307.17(4)
2152.29(3)
2152.70(3)
6.2(4)
6.5(11)
190(25)
4.5(9)
186(18)
4.7(9)
182(17)
170(2)
168(2)
195(2)
7
7
8
6
6
6
7
9
22
45
32
30
T able 5-18 . C 3H 6 HDO Deuterium Nuclear Q uadrupole H yperfine Structure
O-Cc
v(obs)
J'KDKo-I"KDKoa
F - F'b
9792.304
2 -1
-0.001
2 n -lo i
3 -2
9792.232
0.002
1 -0
9792.149
-0.001
2 -1
9443.744
-0.001
212- I 11
3 -2
9443.671
0.002
1 -0
9443.596
-0.001
4 -3
14687.133
0.000
3 i2 -2 n
3 -2
14687.155
0.000
0.002
4 -3
14162.865
3 i3 -2 i2
3 -2
14162.883
-0.002
a. Rotational quantum num bers J, Kproiate/ Koblateb. F = J+I.
c. Observed - calculated frequencies.
125
References to C hapter 5
1.
a) K. I. Peterson and W. Klemperer, J. Chem Phys., 813842 (1984). b) K. 1.
Peterson and W. Klemperer, J. Chem. Phys., 85 725 (1986). c) D. Yaron,
K.I. Peterson, D. Zolandz, W. Klemperer, F. J. Lovas and R. D.
Suenram, J. Chem. Phys., 92 7095 (1990). d) P. H erbine and T. R. Dyke,
J. Chem. Phys., 83 3768 (1985). e) H. O. Leung, M. D. M arshall, R. D.
Suenram and F. J. Lovas, J. Chem. Phys., 90 700 (1989). f) K. I. Peterson
and W. Klemperer, J. Chem, Phys., 80 2439 (1984).
2.
P. Hobza, F. M ulder and C. Sandorfy, J. Amer. Chem. Soc., 103 1360 (1981).
3.
A. J. Barnes and S. L. Paulson, Chem. Phys. Lett., 99 326 (1983).
4.
a) A. C. Legon, P. D. Aldrich and W. H. Flygare, J. Amer. Chem. Soc., 102
7584 (1980). b) A. C. Legon, P. D. Aldrich and W. H. Flygare, J. Amer.
Chem. Soc., 104 1486 (1982).
5.
L. W. Buxton, P. D. Aldrich, J. A. Shea, A. C. Legon and W. H. Flygare, J.
Chem. Phys, 75 2681 (1981).
6.
a) P. D. Aldrich, S. G. Kukolich, E. J. Campbell and W. G. Read, J. Amer.
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(1983).
7.
a) S. G. Kukolich, P. D. Aldrich, WQ. G. Read and E. J. Campbell, Chem.
Phys. Lett., 90 329 (1982). b) J. A. Shea and W. H. Flygare, J. Chem.
Phys., 76 4857 (1982). c) S. G. Kukolich, W. G. Read and P. A. Aldrich, J.
Chem. Phys., 78 (1983).
8.
a) A. C. Legon, P. D. Aldrich and W. H. Flygare, J. Chem. Phys., 75 625
(1981). b) W. G. Read and W. H. Flygare, J. Chem. Phys., 76 2238 (1982).
C) P. D. Aldrich, S. G. Kukolich and E. J. Campbell, J. Chem. Phys., 78
3521 (1983).
9.
A. de Meijere, Angew. Chemie, Intl. Engl. Ed., 18 809 (1979), and
references therein.
10. T. J. Balle and W. H. Flygare, Rev. Sd, Instr., 52 33 (1981).
11. K. W. Hillig, J. Matos, A. Sdoly and R. L. Kuczkowski, Chem. Phys. Lett.,
133 359 (1987).
12. W. Stahl and D. Sutter, Rev. Scient. Instr., 61 3695 (1990).
13. J. K. G. W atson, J. Chem. Phys., 46,1935 (1967).
126
14. K. Tanaka, H. Ito, K. H arada and T. Tanaka, J. Chem. Phys., 80 5893 (1984).
15. W. G ordy and R. L. Cook, M olecular Microwave Spectra (Wiley, New
York, 1984) pp 413-418.
16. Y. Endo, M. C. Chang, E. Hirota, J. Mol Spec, 126 63 (1987).
17. D. Heming, F. C. D eLuda, W. Gordy, P. A. Staab, H. W. M organ, Phys.
Rev. A, 5 2785 (1973).
18. J. Kraitchman, Am. J. Phys., 2117 (1957).
19. N. Ohashi and A. S. Pine, J. Chem. Phys., 81, 73 (1984).
20. a.) T. R. Dyke, B. J. H ow ard, W. Klemperer, J. Chem Phys. 56 2442 (1972).
b.) H. S. Gutowsky, C. Chuang, J. D. Keen, T. D. Klots. T. Emilsson,
J Chem. Phys, 83 2070 (1985).
21. R. C. Cohen, K. L. Busarow, K. B. Laughlin, G. A. Blake, M. Havenish, Y.
T. Lee, R. J. Saykally, J. Chem. Phys., 89 4494 (1988).
22. R. M. Garrey and F. C. D eLuda, Can. J. Phys., 551115 (1977).
23. D. J. Millen, Can. J. Chem., 63 1477 (1985).
CHAPTER 6
INTERPRETATION AND DISCUSSION
Trends and Com parisons
The trends in bond distances and bond energies and the sim ilarities
and differences docum ented in series of related complexes have been useful
in developing sim ple, chem ically-intuitive rules for predicting and
interpreting the structures of complexes. Legon and M illen have developed a
hierarchy of hydrogen bonding preferences w ith respect to lone pairs and it
system s . 1 Nelson, Fraser and Klem perer have studied the trends in induced
dipole mom ents for a series of hydrocarbons w ith HF as a m eans of exploring
trends in interaction strength am ong related complexes.2 The sim ilarities
and differences among the ethylene, acetylene, cyclopropane series w ith SO2
and w ater are com pared to previous observations of the series w ith HF, HC1
and HCN.
The appropriate hydrocarbon-X distances, stretching force constants,
w ell depths and induced dipole moments for the cyclopropane, ethylene and
acetylene complexes w ith SO2 , HC1, HCN and HF are shown in Table 6-1. The
psuedo-diatom ic stretching force constants w ere calculated using M illen's
m odel. The induced dipole mom ents for the HF complexes w ere taken from
N elson, Fraser and Klemperer2 as Jlmd = JX- <cos 0>Ji-HF w here <cos 0> is
approxim ated by <cos2
0 > 1/ 2
which is determ ined from hyperfine interaction
127
128
constants. For the SO2 complexes an estim ate of the averaging effects from
bending m otions on the dipole mom ents is not so straightforw ard as there
are no hyperfine interactions giving inform ation on the SO2 bending
vibration. As the am plitude of the vibration is probably less than 10° ( for
PF3 -Ne <cos2
0 > !/2
= 8 °, for PF3 *Ar, PF3 *Kr <cos2
0 > * /2
=1 0 ° ) 3' 4 these effects
w ere neglected and the induced m om ents were taken as the difference
between the observed dipole com ponents and the projections of the SO2
perm anent dipole m om ent on the principal axes of the complex.
The structures of C2 H 4 -S0 2 , C 2 H 2 SO2 and C3 H 6 -S0 2 are sim ilar in that
the S atom apparently interacts w ith the it or pseudo-rc system of the
hydrocarbon. The SO2 complexes exhibit the same decrease in sulfur to C-C
bond center distance previously noted for the hydrogen bonded complexes.
There is an increase in induced dipole m om ent in the series ethylene,
acetylene, cyclopropane, w hile in the HF complexes the induced dipole
m om ent is about the same for C2 H 2 HF and C2 H 4 HF and larger for C3 H 6 HF.
The force constants and binding energies are also greater for C 3 H 6 SO2 than
C 2 H 2 SO 2 . The values for C2 H 4 SO2 are anom alously high, m ost probably
because of perturbations in the spectrum due to a tunneling m otion which
contam inates the distortion constants. The difficulty w ith the C 2 H 4 SO 2
distortion constants aside, it is reasonable to conclude from the other data that
C 3 H$-S0 2 is the m ost strongly bound of the three, consistent w ith the finding
of Legon and M illen that C 3 H 6 is the best nucleophile .5
The C3 H 6 H 2 O complex is sim ilar to the C 2 H 4 -H2 0 complex w ith the
w ater hydrogen-bonded to the it system. The C 2 H 2 -H2 0 complex is different
w ith the C 2 H 2 hydrogen-bonded to the O of water. The bond distance is
shorter and the pseudo-diatom ic force constant is greater for C3 H 6 H 2 O, as in
the CxHy*S0 2 series. Across the a d d series the force constants vary
129
Table 6-1. Com parison of cyclopropane-, ethylene- and acetylene-containing
Sp2
h 2o
HC1
HCN
HF
Ra
kb
EC
pa(ind)d
Pc(ind)
|XT(ind)
Cyclopropane
3.31
0.059
652
0.349
0.095
0.361
R
k
E
Ref
3.283
0.065
731
R
k
E
Ref
3.567
0.087
959
R
k
E
Ref
3.475
0.062
862
8
11
Ethylene
3.483
0.057
490
0.326
0.063
0.332
Acetylene
3.363
0.047
390
0.289
0.072
0.298
3.412
0.046
3.958
6
7
3.724
0.061
575
9
3.699
0.067
614
3.711
0.046
575
3.656
0.053
642
13
12
10
R
3.021
3.143
3.121
p(ind)
0.78
0.65
0.67
14
Ref
15
16
a. R = distance from hydrocarbon C-C bond to center of mass (SO2 ) or nearest
heavy atom (HX) / A
b. k = pseudo-diatomic force constant / mdyrteA' 1
c. E = pseudo-diatom ic w ell-depth / cm-1.
d. Induced dipole m om ent /D .
130
as HC1 > HCN > H 2 O as m ight be expected from the acidity trends am ong the
hydrogen donors.
A b initio calculations
Because the binding energies of complexes are very small com pared to
the total m olecular energy, the m ajority of theoretical calculations done on
van der W aals complexes have been very sophisticated, involving large basis
sets, configuration interaction and basis set superposition error corrections. 17
W hile these calculations have produced results in agreem ent w ith the
experim ental work, the large com putational cost involved in such elaborate
calculations makes them prohibitively expensive for routine structure
predictions. To explore w hether Hartree-Fock level ab initio theory is useful
for predicting and interpreting the structures and internal m otions of
complexes, the interm olecular structural param eters w ere optim ized using
the GAUSSIAN8 6 and GAUSSIAN8 8 program packages . 18 In all calculations
the basis set used was 6-31G* and the subunits were held rigid at their
experim entally determ ined m onom er geom etries.
For the C2 H 4 -S0 2 , C 2 H 2 -S0 2 and C3 H 6 SO2 complexes, the center of
mass distances and tilt angles were optim ized for both the a = 0° and a = 90°
structures, w here a is the angle between the C-C bond and the C 2 axis of the
SO 2 . The results are shown in Table 6 -2 . The ab initio calculations agree w ith
the experim ental results that a = 90° for C2 H 4 SO2 and C2 H 2 -S0 2 , w hile a = 0°
for C 3 H 6 *S0 2 . The optim ized values for Rcm and the tilt angles are in good
agreem ent w ith the experim ental values although in each case the
experim ental Rcm is about 0.1 A shorter than the calculated value.
131
T able 6-2. Results of ab in itio for C2 H 4 -SQ2 , C2 H 2 SO2 and C3 H 6 -SQ2 .
C2H4 SO2
C2H2 SO2
C3H6 SO2
calc
exp
calc
exp
calc
exp
90
90
90
0
a /0
90
0
3.58
3.43
3.50
3.49
3.83
3.73
K anM
14
10.1
12.7
10
10
16
0(SO2)/°
0(CXHy)°
19.7
20
8
6
-AE/cm-1
V'2 /cm ' 1
890
173
490
30
910
315
390
>135
383
21
650
From the difference in energy between the a = 0° and a = 90° structures,
the V2 barrier to internal rotation was estim ated for each complex (also in
Table 6-2). Q ualitatively, the results compare favorably w ith the experiment.
The C 2H 2 -S0 2 is predicted to have a barrier larger than C2 H 4 -S0 2 by a factor of
two, in qualitative agreem ent w ith experim entally determ ined estim ates of
the barriers. The barrier for C 3 H 6 -S0 2 is predicted to be significantly lower
than that for C 2 H4 -S0 2 ; how ever, there is no experim ental barrier to compare
to this. Also included in Table 6-2 are estim ates of the binding energies which
were calculated by subtracting the energies calculated for the rigid subunits
from the total complex energies. The binding energies are com pared w ith
those estim ated from the pseudo-diatom ic m odel (exp) for each complex. The
agreem ent here is som ew hat poorer w ith the ab initio calculations giving
about the same binding energy for C 2 H 4 SO2 and C 2 H 2 SO2 and a smaller
binding energy for C3 H 6 SO2 . Experimentally, the C 3 H 6 SO2 complex has the
largest binding energy.
The discrepancy in the binding energies is perhaps not surprising. For
weak complexes a significant am ount of the binding energy calculated is
attributed to basis set superposition error, which has not been included in the
132
calculations. W hile one m ight expect this to be of com parable m agnitude for
the same complex at a = 0° and a = 90°, thus allow ing relative energy
com parisons for the same complex, it m ay not be com parable for tw o different
complexes. Therefore, energy com parisons am ong complexes are considered
less reliable.
For the C 3 H 6 -H2 0 complex, geom etry optim izations w ere carried out
for the experim entally determ ined hydrogen-bonded structure, the bifurcated
structure reported from the m atrix IR study and the stacked structure reported
in the previous ab initio work. For the hydrogen bonded and bifurcated
structures, calculations w ere perform ed for the C 3 H 6 and H 2 O planes coplanar
(a = 0°) and perpendicular (a = 90°). The results are show n in Table 6-3.
T able 6-3. Results of ab initio calculations
h-bonded
a = 0°
a = 90°
Ron/A
4.160
4.150
126.3
129.1
Ocm-o-cm/0
-A E /c n r 1
405
398
for C3H 6 -H2 Q.
bifurcated
a = 0°
a = 90°
3.182
3.238
76
32
stacked
3.614
330
The hydrogen bonded structure is the m ost strongly bound am ong those
considered, followed by the stacked (~ 70 cm "1 higher in energy) and then the
bifurcated (> 300 cm *1 higher in energy). It should be noted that in the
previous ab initio study, neither the hydrogen bonded nor the bifurcated
structures was considered. Unfortunately, because the energy difference
between the a = 0° and a = 90° hydrogen-bonded structures is very small (7
cm*1), it is not possible to settle the experim ental am biguity about the
structure by com paring binding energies.
133
W hile it is gratifying that the Hartree-Fock level ab initio calculations
are successful at duplicating the experim ental structures, the reason for its
success is unclear. However, it seems reasonable to suggest that it is due to
the electrostatic nature of the interactions. The ab initio calculations are
generally reliable for calculating the electrostatic properties of molecules at
large distances ( 3 - 5 A). If the total interaction energy is dom inated by the
interaction of these electrostatic properties, the structural predictions m ight be
quite good.
O ther factors generally considered to render such calculations
less useful, such as basis set superposition error and configuration interaction,
perhaps contribute to the large errors in the absolute energy, bu t do not seem
to interfere w ith the correct determ ination of the structure.
Electrostatic M odeling of the Complex.
There has been considerable discussion in the literature on the
interpretation of the structure and dynam ics of w eakly bound complexes.
Ideally, one w ould like a com putationally sim ple m odel which is physically
easy to interpret, but which also has accurate predictive power. Electrostatic
models have proven to be useful in predicting the structures of complexes.
M orokuma has show n, through an energy decom position analysis, that for
hydrogen bonded complexes in particular the overall interaction energy
follows very closely the electrostatic contribution w hen plotted against a
structural coordinate . 19 H e finds that the other contributions to the
interaction energy (dispersion, charge transfer, polarization and exchange
repulsion) tend to cancel one another out. Further, Buckingham and Fowler
have had considerable success at predicting the structures of a large num ber of
134
complexes using a sim ple distributed m ultipole m odel of the electrostatic
interactions .20' 21
To investigate w hether electrostatic considerations alone
can be used to interpret the structure of the C2 H 4 SO 2 , C2 H 2 SO2 , and
C3 H 6 SO2 complexes, a distributed m ultipole analysis proposed by
Buckingham and Fowler was explored. In this m odel, all polarization,
dispersion, and charge transfer effects are ignored. Point m ultipoles are
placed on atoms and bond centers to approxim ate the electronic charge
distribution in the molecule. The repulsive term is m odeled by hard spheres
of van der Waals ra d ii 2 2 placed on the atoms.
The values calculated by Buckingham and Fowler for the distributed
m ultipoles of ethylene and SOz were used directly .2 0 Except w here noted
otherw ise, the energies w ere calculated using the experim ental
distance.
Table 6-4 shows calculated electrostatic interaction energies for a num ber of
different geom etries. Of the geom etries considered, the experim ental
01
-200
-400&
0
-600’
scn
a
4 -800
W
-1000t
•100
-50
0 1
0
(degrees)
50
100
Figure 6-1. Electrostatic Energy vs. 0 (SO2 ) for C 2 H 4 -S0 2
Table 6-4. Electrostatic energies (cm*1) for different structures of CjHJSO, from Distributed Multipole Analysis
i*
cD
h i*
-569
-875
• • •
IIb
CD
ccb
IV'
-715
-512
136
structure (I) has the largest stabilization energy. For structure I, a shallow
electrostatic m inim um is obtained as 0i is varied (Figure 6-1) at about 6 (S0 2 >
=
0
10
-15°, consistent w ith the experim ental structure. As
62
is varied, w ith
(SO2 ) fixed at the experim ental value, a minimum is obtained at +20° (875
cm-1). Considering the experim ental difficulty in determ ining the sign of
0 (C2 H 4 ),
it is interesting to note that a substantially lesser interaction (549 cm-
l) is obtained for 0 (C2 H 4) = - 2 0 °.
In the analysis of the C 2 H 2 -S0 2 system, the distributed m ultipoles
calculated by Buckingham and Fowler for C2 H 2 and SO2 were again used
directly and the van der W aals radii were taken from Pauling .22 A global
search of all possible geom etries in which the center of mass distance and five
angles were varied produced tw o electrostatic minima. The d s hydrogen
bonded structure, sim ilar to SO2 HF and S0 2 -HC1,23 has the largest
stabilization energy (-1600 cm-1), while the stacked structure, sim ilar to the
experim ental geom etry, is at the second minimum (-815 cm-1). This is
sim ilar to the result reported for the S0 2 -HCN
24
complex, w here initial
predictions from the distributed m ultipole m odel indicated that the structure
w ould be d s hydrogen bonded .2 3 However, experim ental evidence revealed
that the HCN sat perpendicular to the SO2 plane w ith the N atom pointed
tow ard the S in an anti-hydrogen bonded configuration. It was only w hen the
N-S distance was perm itted to be shorter than the sum of the N and S van der
W aals radii, as was determ ined experim entally, that the distributed m ultipole
m odel found a global m inim um at the experim ental structure. In the case of
the C 2 H 2 SO2 , however, the point of dosest contact determ ined
experim entally is not shorter than the hard sphere sum s, so it has not been
explored w hether relaxing the hard sphere contact constraint w ill reverse the
stability order of the two isomers. Using the stacked structure, it is interesting
137
to examine w hether electrostatics can be used to predict correctly the
experim entally determ ined tilt angle of the S02- Figure 6-2 show s the
calculated electrostatic energy as the angle 0 is varied from 0 to 90° at the
experim ental distance, Rcm = 3.430 A. There is a shallow m inim um at 9 = 10 20°, consistent w ith the observed value of 14°.
<300
Iu
-500
IS
8
aXJ -700
at
W
-900
-100
-50
0
6 / degrees
50
100
Figure 6-2. Electrostatic Energy vs. 0 for C2H2-S02-
For the C 3 H 6 SO2 complex, distributed m ultipoles for SO2 were taken
directly from Buckingham and Fowler, while those for cyclopropane w ere
calculated using the CADPAC program w ith a DZP basis set.25 The structure
of C3 H 6 SO2 is sim ilar to the structures of C 2 H 4 -S0 2 and C2 H 2 *SC>2 in that the
S atom apparently interacts w ith the pseudo-rc system of cyclopropane. The
sym m etry, however, is different w ith the dihedral angle between the C 2 axis
of SO2 and the C -C bond equal to 0° for C 3H 6 SO2 compared to 90° for
C 2 H 4 SO2 and C2H2-S02. To explore w hether this could be attributed to
electrostatic considerations alone, the distributed m ultipole (DMA) m odel of
138
Buckingham and Fowler was em ployed.
The DMA gives a m inim um of
energy at the a = 0° geom etry w ith 0(SO2) = 90° and 0(V) = 75°, which are
considerably different from the experim ental angles. The well seems to be
very shallow, however, and the experim ental geom etry 0(SO2) = 74°, 0(V) =
84° is only 13 cm-1 higher in energy. The low est energy structure for a = 90°
is 75 cm-1 higher in energy.
Electrostatic interactions as m odeled by the Buckingham-Fowler
paradigm certainly are not sufficient to com pletely rationalize the binding,
structure and internal dynam ics of these complex. The m easured differences
between dipole m om ent com ponents and those projected from the SO2
perm anent dipole m om ent indicate that polarization effects are also
im portant. N evertheless, the com parisons m ade above indicate that
electrostatic interactions play a significant role in determ ining the structures
of these complexes.
Legon-M illen M odel
In addition to determ ining the geom etry of a complex, it is often
desirable to know about the strength of the interaction and how it compares
to related complexes. Legon and M illen's m odel involves assigning
nucleophilicities and electrophilidtes to binding partners so that interaction
strengths, as m easured by the pseudo-diatom ic stretching force constants for
the van der W aals bond, m ay be predicted for new complexes.5 This has been
quite successful in interpreting hydrogen bonded complexes, b ut it has not yet
been applied to other weak complexes. Because m any SO2 complexes have
been characterized in recent years, the CxH yS 0 2 complexes seem ed an ideal
139
situation to test it. The form ula for relating nudeophilidties and
electrophilidties to the pseudo-diatom ic stretching force constant is5
ko = c N E
w here k<j is the force constant, c is a proportionality constant (equal to about
0.25), N is the nudeophilidty of the nudeophile and E is the electrophilidty
of the dectrophile. The proportionality constant is necessary because, for a
starting point, w ater was arbitrarily assigned N = 10, w hile HF was assigned E
= 10.
W ith N = 6.4 for cydopropane as determ ined by Legon and M illen, E
for SO2 was calculated as 3.7. This was then used to predict k<j for a num ber of
SO2 complexes w ith molecules for which the nudeophilidties have been
calculated. These are shown in Table 6-4 along w ith the experim entally
determ ined k<j.
Table 6-5. Predicted3 and observed kq for S02-containing complexes
Predicted
Observed
Reference
5.9
5.9
C3H6-S02b
4.7
4.7
C 2 H 2 SO2
4.1
5.7
C2 H 4 SO2
9.3
8.4
H 2 OSO 2
13
4.4
H 2 SSO 2
5.3
14
6.7
2.7
HCN SO 2
15
10.4
6.8
16
(CH3)20 S 0 2
a. Predicted using nudeophilidty from Ref 5b and electrophilidty of SO2 =
3.7. (See text)
b. C3 H 6 SO2 was used to determ ine the electrophilidty of SO2 , therefore the
match is required to be exact.
There is excellent agreem ent for C2 H 2 SO2 and quite good agreem ent for
S02-H2026 and PfeS-SO*27 The difficulty w ith k<j for C 2 H 4 SO2 is discussed in
140
Chapter 3. The agreem ent for HCN-S0224 and (CH3)20S0228 is rather poor.
These complexes, how ever, are unusual in that the tw o subunits are
som ewhat closer than the sum of their van der W aals radii. In the case of
(CH3)20 S 02 the interaction m ay involve some charge transfer interaction.
This raises questions about the validity of the psuedo-diatom ic
approxim ation, but also suggests that the nudeophilidty m odel is perhaps
only applicable to complexes which are bound by prim arily electrostatic forces.
A larger data set is needed to test w hether these complexes represent an
anom aly or w hether the m odel does not readily transfer to non-hydrogen
bonded weak complexes.
141
Sum m ary of M ajor Conclusions
From this study detailed structures and internal m otions have been
experim entally determ ined for C 2 H 4 *SC>2, C2 H 2 SO2 , C3 H 6 SO2 and C3 H 6 H 2 O.
The characterization of C3H6*H20 has provided the m issing com ponent in
the hydrocarbon series w ith hydrogen bonding partners. C2 H 4 -S0 2 , C2 H 2 -S0 2
and C3 H 6 *SC>2 complexes have extended that series to non-hydrogen-bonding
partners.
Various models have been applied to interpret the experim ental
results. The Buckingham and Fowler distributed m ultipole m odel has
show n m oderate success, w ith very good results for C2 H 4 -S0 2 and C3 H 6 SO2 .
The results for C2H2-S02 w ere poorer, w ith the m odel predicting a hydrogen
bonded structure, com pared to a rc-bonded structure determ ined
experim entally. Low level Hartree-Fock ab initio calculations have been
surprisingly successful at determ ining the structures and dynam ics of these
complexes, although less so a t calculating binding energies. The Legon-
Millen model for calculating stretching force constants for hydrogen-bonded
complexes was extended to the ic-bonded SO2 complexes w ith m ixed success.
W hile results were poorer for other SO2 containing complexes, the model
was quite successful for the hydrocarbon-S02 complexes presented here.
142
References to Chapter 6
1.
A. C. Legon and D. J. M illen
2.
D.D. Nelson, G. T. Fraser, W. Klemperer, J. Chem. Phys., 82 (1985) 4483.
3.
K. W. H illig n, M. S. LaBarge, A. Taleb-Bendiab, R. L. Kuczkowski, Chem,
Phys. Lett., 171 (1990) 542.
4.
A. Taleb-Bendiab, M. S. LaBarge, L. L. Lohr, R. C. Taylor, K. W. Hillig n, R.
L. Kuczkowski, J. Chem. Phys., (1989) 6949.
5.
(a) A. C. Legon and D. J. Millen, J. Amer. Chem. Soc., 109 (1987) 356. (b).
A. C. Legon and D. J. M illen, J. Chem. Soc. Chem. Comm., 1987,986.
6.
K I. Peterson and W. Klemperer, J. Chem Phys., 81 (1984) 3842.
7.
K. I. Peterson and W. Klemperer, J. Chem. Phys., 85 725 (1986).
8.
a.) A. C. Legon, P. D. Aldrich and W. H Flygare, J. Amer. Chem. Soc., 102
7584 (1980). b.) A. C. L egon, P. D. Aldrich, and W. H. Flygare, J. Amer.
Chem. Soc., 104 1486 (1982).
9.
P. D. Aldrich, A. C. Legon and W. H. Flygare, J. Chem. Phys., 75 2126
(1981).
10. A. C. Legon, P. D. A ldrich and W. H. Flygare, J. Cham. Phys., 75 625 (1981).
11. a.) P. D. A ldrich, S. G. Kukolich, E. J. Campbell and W. G. Read, J. Amer.
Chem. Soc., 105 5569 (1983). b.) S. G. Kukolich, J. Chem. Phys., 78 4832
(1983).
12. S. G. Kukolich, P. D. Aldrich, W. G. Read and E. J Campbell, Chem. Phys.
Lett., 90 329 (1982).
13. S. G. Kukolich, P. D. Aldrich, W. G. Read and E. J Campbell, Chem. Phys.
Lett., 90 329 (1982).
14. L. W. Buxton, P. D. Aldrich, J. A. Shea, A. C. Legon and W. H. Flygare, J.
Chem. Phys., 75 2681 (1981).
15. J. A. Shea and W. H. Flygare, J. Chem. Phys., 76 4857 (1982).
16. W. G. Read and W. H. Flygare, J. Chem. Phys., 76 2238 (1982).
143
17. J. H. van Lanthe, T. van Dam, F. B. van Duijneveldt, L. J. M. KromBatenberg, Faraday Symp. Chem. Soc., 19,125 (1984).
18. J. M. Frisch, J. S. Binkley, H. B. Schlegel, K. Raghavachari, C. F. M elius,
R. L. M artin, J. J. P. Stewart, F. W. Bobrowicz, C. M. Rohlfing, L. R.
Kahn, D. J. DeFrees, R. Seeger, R. A. W hiteside, D. J. Fox, E. M. Fluder
and J. A. Pople, GAUSSIAN86, (Camegie-M ellon Q uantum Chem istry
Publishing Unit, Pittsburg, PA 1986).
19. K. M orokuma, Acc. Chem. Res., 10 294 (1977).
20. A. D. Buckingham and P. W. Fowler, Can J. Chem., 63 2018 (1985).
21. A. D. Buckingham and P. W. Fowler, J. Chem. Phys., 79 6426 (1983).
22. L. Pauling, The Nature of the Chemical Bond, (Wiley, N ew York) p. 260.
23. A. J. Fillery-Travis and A.C. Legon, Chem. Phys. Lett., 123 4 (1986).
24. E. J. Goodwin and A. C. Legon, J. Chem. Phys., 85 6828 (1986).
25. R. D. Amos and J. E. Rice, Cambridge Analytical Derivatives Package.,
Issue 4.0, (Cambridge, 1987).
26. K M atsum ura, F. J .Lovas, R. D. Suenram, J. Chem. Phys., 91 5887 (1989).
27. a.) R E. Bumgarner, D. J. Pauley, S. G. Kukolich, J. Chem. Phys., 87 3749
(1987). b.) D. J. Pauley, S. G. Kukolich, J. Chem. Phys., 93 1487 (1990).
28. J.-J. Oh, K. W. Hillig n , R. L. Kuczkowski, Inorg. Chem., in press.
APPENDICES
145
APPENDIX A
UNASSIGNED TRANSITIONS
Searches for the spectra of G |H 2 -S0 2 , C2 H 2 -S0 2 and C 3 H 6 SO2 produced
a num ber of transitions w hich w ere not assigned to the dim ers reported here.
M ixing experim ents dem onstrated that the transitions required both sulfur
dioxide and the appropriate hydrocarbon. It is believed that they arise from
another structural isom er of the dim er, a higher m olecular w eight aggregate
or, m ost likely, a com bination of tw o or more such spectra. Extensive efforts
to assign these transitions have been unsuccessful. H ow ever, their
assignm ent is unlikely to affect the analysis presented here.
146
U nassigned Transitions of C2H4*S02
Regions Searched (MHz): 7200-7450,7850-8800,8950-9100,9500-10 050,
10 300-10 400,10 900-11500,12 200-12 275.
J__________________________Frequency (MHz)
7323.720
3-2
7323.976
3-2
7450.231
8190.114
3-2
8270.883
4-3
8296.143
4-3
8307.174
3-3
8397.098
4-3
9604.421
9756.143
9794.058
9802.663
9802.904
9891.008
U nassigned T ransitions of C2H2*S02
Regions Searched (MHz): 7700-13000,15300-15850
J
2-2 or 2-1
2-2 or 2-1
4-4
2-2 or 2-1
(3-3)
3-3
3-2
3-2
2-2 or 2-1
2-2 or 2-1
4-4
2-2 or 2-1
3-3
2-2 or 2-1
(3-3)
Frequency (MHz)
8119.908
8153.794
8355.368
8389.667
8423.554
8434.765
8435.820
9740.573
9915.375
10383.814
10501.078
11359.788
11367.226
11847.325
11900.221
12506.305
Intensity
w
s
m
vs
s
s
m
s
vs
s
m
s
s
vw
m
s
148
U nassigned Transitions of C3 H 6*SC>2
Regions Searched (MHz): 8000-9900,10335-10410,10550-10800,1086010960,12700-12850, also many small (< 20 MHz) regions.
J
4-3
4-3
4-3
4-3
2-2 or 2-1
£3
£3
£3
£3
Frequency (MHz)
8273.734
8436.652
8484.533
8535.873
8539.782
8541.374
8541.770
8567.597
8605.611
8622.32
8707.868
8712.030
8729.996
8733.160
8736.823
8829.441
8829.711
J
Frequency (MHz)
8837.419
8917.448
9148.568
9161.214
10336.508
10591.417
10670.267
10679.267
10683.369
10722.2677
10870.891
10938.636
10951.766
11024.850
12370.985
149
APPENDIX B
ELECTROSTATIC INTERACTION ENERGIES FOR THE DISTRIBUTED
MULTIPOLE ANALYSIS
The program MULTIPOLE w ritten in FORTRAN to ru n on the
M ichigan Term inal System (MTS) calculates the interaction energies for point
m ultipole m om ents (up to the quadrupole) distributed over u p to 10 sites on
tw o m onom er subunits; it follows the m ethod outlined by Stone1 and
Buckingham and Fow ler.1 The coordinates of the m ultipole sites and the
m ultipole values are input, along w ith a center-of-mass separation and angles
defining the relative orientation of the tw o subunits. The electrostatic
energies then calculated by
+
+
+
R qR p ~ R2 8aB
r
R55
i
R a Rfi ~
+ ®ap j qi)
5 [ Rq Rfl R*y~ R2 (Rq &By ^ Rp ^cy ^ y SaB)]
R7
SaB
R5---------
(M<x i ®py j + M>qj 6pyi)
105 Rq Rb Ry R§
w here i, j are sum m ed over all m ultipole sites of the top and bottom
repectively, a , p, y, 5 are over x, y, z cartesian axes, R is the total distance
between sites i and j and Rq is the distance along a between sites i and j.
150
The inpu t to the program is as follows:
CARD 1
A80
TITLE
CARD 2
6(F10.6)
Rem/ 01/ 02/ $/ Yl/ Y2
w here
Rem = distance between the centers of mass in A
9i = rotation of top about local a axis in degrees
82
= rotation af bottom about local a axis in degrees
<j>= torsional angle between the tw o subunits in degrees
Yl = rotation of top about local c axis in degrees
\|/2
= rotation of bottom about local c axis in degrees.
N ote: Geometries of subunits are input, each in its ow n coordinate system,
such that the b axis is the direction of Rcm (i.e. in a stacked complex of planar
molecules all b coordinates w ould be zero). The tilt angles are therefore
defined by how the user chooses to input the structure of the subunits.
CARD 3
3CF10.6)
x, y ,z
w here x, y, z are the coordinates of the m ultipole sites in bohrs. See note
above. Repeat as needed
CARD 4
(FI 0.6)
q
CARD 5
3CF10.6)
Moo My/ Mz
CARD 6
3 X 3(F10.6)
0xx/
°xx/ 0xv/
°xy/ 0:
°xz
0yx/ 0yy/ 0yz
0zx/
zx/ «zy,
0zv/ °zz
0;
151
where, q, p, 0 are m ultipole moments in atomic units at each site. These
m ust be input in the same order as the coordinates of the sites. Repeat as
needed.
N ote: The m ultipole moments from the CADPAC program are in a spherical
expansion. They m ust be transform ed to a cartesian expansion for use in this
program . The form ulae are w orked out by Price, et al.3
152
References to A ppendices
1.
A. J. Stone, Chem. Phys. Lett., 83,233 (1981)
2.
A. D. Buckingham and P. W. Fowler, Can J. Chem., 63 (1985) 2018.
3.
S. L. Price, A. J. Stone and M. A lderton, Molec. Phys., 52 (1984) 987.
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