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Fourier transform microwave spectroscopy of gas phase acids and acid-base complexes

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Fourier Transform Microwave Spectroscopy of Gas Phase
Acids and Acid-Base Complexes
A THESIS
SUBMITTED TO THE FACULTY OF THE GRADUATE SCHOOL
OF THE UNIVERSITY OF MINNESOTA
BY
Galen Sedo
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
Dr. Kenneth R. Leopold, Advisor
October 2008
UMI Number: 3334428
INFORMATION TO USERS
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© Galen Sedo 2008
Abstract
Fourier transform microwave spectroscopy, supported with ab inito and Density Functional
Theory calculations, has been used to investigate gas phase acids and acid-base complexes in an
effort to further our understanding of the electronic and molecular interactions occurring in these
small reactive systems. The Stark effect has been measured on the In <— Ooo rotational transition
of the sulfuric acid monomer. The resulting dipole moment, 2.9643(67) D, represents an increase
of 0.24 D over the previously reported value and is supported by high-level theoretical
calculations. An examination of the CH3COOH-H20 spectrum shows an 18.6% lowering of the
three-fold methyl group internal rotation barrier with the addition of a single solvent water to the
acid. An argument has been made that suggests the lowering of the barrier in the acetic acid
monohydrate is consistent with the structural changes in the acetic acid moiety, and the degree of
proton transfer, determined from ab initio calculations, is similar to those calculated for other
protic acid hydrates. The rotational spectra for the HN03-(H20)3 and HN03-N(CH3)3 complexes
have also been observed. The experimental values of the 14N quadrupole coupling constants have
been used to determine the degree of proton transfer away from the acid, and comparisons have
been made to those determined from their optimized ab initio structures. The results show the
systems to be hydrogen-bound neutral pairs with a slightly higher degree of proton transfer than
similar HN0 3 complexes. The microwave spectrum of the (CH3)3CCN-S03 complex has been
observed and analysis of the data reveals a Lewis acid-base complex with intermolecular bonding
nearly halfway between the van der Waal's and chemically bound limits. The properties of the
complex are in good agreement with those predicted on the basis of the previously reported series
of complexes formed between S0 3 and a nitrogen-containing base.
i
Table of Contents
Title
Page
Abstract
i
List of Tables
iii - iv
List of Figures
v - vi
Introduction
1-6
Chapter 1
The Electric Dipole Moment of Sulfuric Acid from
Fourier Transform Microwave Spectroscopy
7-25
Chapter 2
The Microwave Spectrum and Theoretical Structure of
the Gas Phase Acetic Acid Monohydrate Complex
26-59
Chapter 3
The Microwave Spectrum and Theoretical Structure of
the Gas Phase Nitric Acid Trihydrate Complex
60 - 94
Chapter 4
The Microwave Spectrum and Theoretical Structure of
the Gas Phase Nitric Acid - Trimethylamine Complex
95-123
Chapter 5
A Microwave and Ab Initio Investigation of (CH3)3CCNSO3: Proton Affinity as a Measure of Interaction
Strength in Partially Bound Lewis Acid-Base Complexes
124 -148
Appendix to Chapter 1
149-164
Appendix to Chapter 2
165 - 174
Appendix to Chapter 3
175 -184
Appendix to Chapter 4
185 -193
Appendix to Chapter 5
194 - 202
References
203 - 224
ii
List of Tables
Description
Table
Table
Table
Table
Table
1.1
1.2
1.3
1.4
Table 2.1
Table 2.2
Table 2.3
Spectroscopic Constants of the H 2 S0 4 Monomer
Calibrated Spacings for the Stark Plates
Theoretical Dipole Moment of the H 2 S0 4 Monomer
Theoretical Dipole Moment of the H 2 S0 4 -H 2 0 Complex
14
16
18
21
Spectroscopic Constants for the CH3COOH-H20 Complex
35
35
37
40
41
44
47
48
52
13
Table 2.4
Spectroscopic Constants for the CH3COOH-H20 Complex
Spectroscopic Constants for the Acetic Acid Monomer
A Comparison of the Theoretical CH3COOH-H20 Results
Table 2.5
A Comparison of the Structural Parameters of (CH3COOH)2
Table 2.6
The Calculated Internal Rotation Barriers
A Comparison of the CH3COOH-H20 Conformers
A Comparison of the Carboxyl Group Geometry
Table 2.7
Table 2.8
Table 2.9
Table 3.1
Table 3.2
Table 3.3
Table 3.4
Page
A Comparison of the Theoretical and Experimental V3 Barriers
Spectroscopic Constants of the Nitric Acid Trihydrate Complex
Calculated Bond Lengths for Conformers 10A and 8A
Comparison Between Experimental Results and Theoretical
Predictions
The Calculated Angle Between the N-OH Bond and the a-axis
67
73
78
81
Table 4.1
Spectroscopic Constants of the (CH3)3N-HN03 Complex
Table 4.2
Table 4.3
Table 4.4
Binding Energies and Bond Lengths of the Amine Complexes
Bond Lengths of the Amine Cations
Comparison of the Experimental and Theoretical Results
Table 4.5
The Calculated Angle Between the N-OH Bond and the a-axis
Table 5.1
Table 5.2
The Physical Properties of the Previously Observed Base-S0 3
Complexes
Spectroscopic (CH3)3CCN-S03 Constants
132
Table 5.3
The Binding Energy and Physical Properties of (CH3)3CCN-S03
135
101
106
108
109
111
129
iii
List of Tables, continued
Table
Description
Page
150
Table A1.1
Rotational Transitions for the H 2 S0 4 Monomer
Table A1.2
Stark-Shifted Frequencies for the H 2 S0 4 Monomer
151-153
Table Al .3
Stark-Shifted Frequencies for the OCS Monomer
154-155
Table Al .4-5
Stark-Shifted Frequencies for the (CH^CCN Monomer
156-157
Tables A1.6-9
H 2 S0 4 Structural Parameters Calculated by Theory
159 -160
Tables Al.10-13
H 2 S0 4 -H 2 0 Structural Parameters Calculated by Theory
161-164
Table A2.1
Tables A2.2-4
Tables A2.5-10
Tables A2.11-15
Tables A2.16-21
Tables A2.22
Transition Frequencies for the CH3COOH Monomer
Transition Frequencies for the Acetic Acid Monohydrate Complex
Cartesian Coordinates of the CH3COOH-H20 Structure
Local Minimum CH3COOH-H20 Cartesian Coordinates
Cartesian Coordinates of the (CH3COOH)2 Structure
Calculated Energies at Internal Rotation Angles Between 180° - 300°
167-169
170
171
172 - 173
174
Tables A3.1 -4
Transition Frequencies of the Nitric Acid Trihydrate Complex
176-181
Tables A3.5-9
Cartesian Coordinates of the HN03-(H20)3 Conformers
182 -183
Tables A3.10-11
Tables A3.12-14
Cartesian Coordinates of the HN0 3 -H 2 0 and HN0 3 -(H 2 0) 2 Structures
Cartesian Coordinates of the HN0 3 , H 2 0, and H 3 0 + Structures
Table A4.1
Table A4.2
Tables A4.3-6
Tables A4.7-10
Table A4.11
Tables A4.12-16
Transition Frequencies of the (CH3)314N-H14N03 Complex
Transition Frequencies of the (CH3)315N-H14N03 Complex
Cartesian Coordinates of the NH3.„(CH3)„ Monomers
Cartesian Coordinates of the NH^CH;,)^ Ions
Cartesian Coordinates of the HN0 3 Monomer
Cartesian Coordinates of the (CH3)„H3.„N-HN03 Complexes
192 -193
Table A5.1
Tables A5.2-5
Tables A5.6-8
Tables A5.9-11
Table A5.12
Transition Frequencies of the (CH3)3CCN-S03 Complex
195 -197
Cartesian Coordinates of the Theoretical (CH3)3CCN-S03 Structure
198 -199
166
183
184
186-188
189
190
191
192
Cartesian Coordinates of the Theoretical Monomer Structures
200
Moments of Inertia for the S0 3 Monomer at Different Values of a
201
202
RNS Bond Length Calculated for Specific Values of a, %, and y
IV
List of Figures
Figure
Figure 1.1
Figure 1.2
Description
The 110«— Ooo transition of H2S04
Plots of AvSUak vs. e2 for the H2S04 monomer
Page
12
13
Figure 2.1
Figure 2.2
Figure 2.3
Figure 2.4
Figure 2.5
Figure 2.6
Figure 2.7
A Sample of the CH3COOH-H20 Spectrum
The Calculated Conformers of the CH3COOH-H20 Complex
The Calculated Structures for H20, CH3COOH, and (CH3COOH)2
The Potential Energy Surface for the Internal Rotation
Bond Length Variations Due to Internal Rotation
Bond Angle Variations Due to Internal Rotation
The Proton Transfer Parameters for Hydrated Acids
31
39
41
43
45
46
50
Figure 3.1
Figure 3.2
Figure 3.3
Figure 3.4
Figure 3.5
Figure 3.6
Figure 3.7
Figure 3.8
A Sample of the Nitric Acid Trihydrate Spectrum
10- and 8-Member Ring HN03-(H20)3 Conformers
Local Minimum Structures of the HN03-(H20)3 Complex
A Schematic of the 14N Quadrupole Tensor and Inertial Axis System
Plots of p and %„. vs the Number of Solvent Molecules
Global Minimum Structures of Other Nitric Acid Complexes
A Diagram of the Aqueous Nitrate Ion
A Plot of p vs i^ for a series of Nitric Acid Complexes
65
72
76
81
84
85
86
88
V
List of Figures, continued
Figure
Figure 4.1
Figure 4.2
Figure 4.3
Figure 4.4
Figure 4.5
Figure 4.6
Figure 4.7
Figure 4.8
Figure 4.9
Figure 4.10
Description
A Sample of the Nitric Acid - Trimethylamine Spectrum
The Global Minimum H3N-HN03 Structure
The Global Minimum (CH3)H2N-HN03 Structure
The Global and Local Minimum (CH-^HN-HNO-, Structure
The Global Minimum (CH3)3N-HN03 Structures
A Schematic of the 14N Quadrupole Tensor and Inertial Axis System
Plots of ppt vs the Number of Methyl Groups and Proton Affinity of the Amine
A Diagram of the Aqueous Nitrate Ion
Structures of the Nitric Acid Hydrates
APlotof p vsxccfora series of Nitric Acid Complexes
Page
99
104
104
105
107
111
114
116
117
119
Figure 5.1
Figure 5.2
Figure 5.3
Figure 5.4
Figure 5.5
Figure 5.6
Figure 5.7
Structures of the Previously Observed Base-S03 Complexes
The Proton Affinity of the Base vs the Physical Propertis oftiieComplex
A Partial Spectrum of the (CH3)3CCN-S03 Complex
The Theoretical Structure of the (CHj^CCN-SOj Complex
The Coordinate System of the (CH3)3CCN-S03 Complex
The Experimentally Determined Nitrogen - Sulfur Bond Length
The Proton Affinity of the Base vs the Physical Propertis of the Complex
126
128
130
133
136
141
144
Figure Al.l
Figure Al .2
Sulfuric Acid Monomer with Atom Labels
Sulfuric Acid Monohydrate with Atom Labels
158
158
vi
Introduction
Although the classifications used by the modern chemist owe much to Mendeleev's
work1 and the development of the electronic theory of matter, the study and
characterization of acids and bases, though crude, had already begun prior to their
inception.2
While many approaches for classifying acid - base systems have been
discarded, much of the earlier work has culminated into two methods for defining acids
and bases, with the difference lying in whether one defines the system as generating ions
(ionic method) or redistributing electrons (electronic method).
Although Arrhenius' definition of the ionic acid - base system persists, it is often more
useful to define the system using the formalism independently proposed by Bronsted,4
Lowry,5 and Lewis6 in which the acid donates an H* ion and the base acts as an H+ ion
acceptor. The utility of this definition for describing the acid - base interactions of
hydrogen bound systems and protic solutions is undeniable. However, an alternative
means of characterizing acids and bases is needed when discussing the interactions of
systems in which no ions are generated or redistributed. For such a generalized system,
Lewis defined a method of describing acids and bases where the acid is an electron
acceptor and the base is a substance that acts as an electron donor.6
While not always the case, much of the chemistry associated with the interaction between
an acid and a base happens in conjunction with significant changes in the molecular and
electronic structure of the system, and as such, the study of small reactive acid - base
complexes can yield information concerning how the chemical composition and structure
1
of a system affect the physical properties. While such information is of fundamental
importance to a complete chemical understanding, the very nature of the systems being
studied can often make collecting the relevant experimental data difficult.
However,
Fourier transform microwave spectroscopy has proven, since its development, to be an
excellent tool in the study of transient gas phase reactive systems. Utilizing this method,
the following work endeavors to add to our understanding of the molecular and electronic
structures of gas phase acids and acid - base complexes.
All of the experimental data presented in this thesis was collected using the University of
Minnesota's existing Fourier transform microwave spectrometer.
and Density Functional Theory calculations, performed
In addition, ab initio
on an IBM Power4
supercomputing cluster,9 have been included to supplement much of the spectroscopic
work.
The present study begins with a determination of the electric dipole moment of the
sulfuric acid monomer. Although an early determination of the H2SO4 dipole moment
can be found in the literature,10 it was observed, in a subsequent investigation of the
H2SO4-H2O complex,11 that the reported dipole moment of the monomer and those
determined by high level ab initio calculations were in poor agreement.
Given the
fundamental significance of the dipole moment as a measure of charge distribution within
the molecule and its proposed role in nucleation theory,12 additional experimental data
has been collected and a new determination of the dipole moment is reported.
2
One of the major issues addressed in the subsequent chapters of this work is the concept
of acid ionization upon complexation. Specifically, Chapters 2 - 4 discuss the proton
transfer of a Bransted acid - base system in the context of the incipient ionization of the
acid due to microsolvation and binding partner basicity. The study of microsolvation in
acid13 and base' 4 systems has been, and continues to be, an area of keen interest. The
investigation of the CH3COOH-H2O complex, presented in Chapter 2, offers the first step
in analyzing the acetic acid ionization in hydrated systems. The related study of the nitric
acid trihydrate, Chapter 3, was undertaken with the intent of extending the experimental
work available in the literature on the nitric acid hydrates136'15 and offers insight into how
the system evolves with the addition of the third solvent water molecule. In each case,
the ionization of the acid in these solvated systems was discussed using a strictly
structural argument similar to those presented in the microwave investigations of the
amine-hydrogen fluoride14 and nitric acid dihydrate13e systems.
In the discussion of the acetic acid monohydrate complex, it has been argued that the V3
barrier to internal rotation of the methyl group, deduced directly from the observed
spectrum, shows an inverse correlation to the degree of proton transfer in the system.
From this relationship, a qualitative understanding of the degree of acid ionization in
additional acetic acid systems may be obtained through a comparison of the measured
barrier to internal rotation in these complexes to those of the acetic acid monomer and
monohydrate. A second method of measuring the ionization in microsolvated nitric acid
systems has also been presented. In this case, the 14N quadrupole coupling constants of
the complex, obtained from the hyperfine structure of the spectrum, are used. As the
3
nitrate ion is one of the products in a fully proton transferred system, the present work
proposes that the difference between the quadrupole coupling constants in the complex
and those of the fully proton transferred nitrate ion can be used to quantify the degree of
nitric acid ionization in the system.
The concept of binding partner basicity and how it affects the ionization of the acid in
microsolvated systems remains one of fundamental interest. This question has been
thoroughly discussed in regards to the amine - hydrogen halide systems.16 However,
Chapter 4 of this work extends this discussion to include nitric acid complexes. In
particular, the first measurements of the (CHb^N-HNOa complex are presented, and the
ionization of this system, along with that of the previously observed H3N-HNO3
17
complex, is discussed using the methodology proposed for the nitric acid trihydrate.
Lastly, it has been observed, from a comparison of the gas phase structures of datively
bound Lewis acid - base complexes, that a wide range of bonding interactions can be
observed depending on the chemical constituency of the binding partners.18 The final
chapter of this thesis determines the physical properties attributed to the dative bond
formation in the Lewis acid - base (CH3)3CCN-S03 complex. These properties are then
related to those observed over a series of similar complexes using the proton affinity of
the base and the arguments originally discussed in the microwave analysis of the C5H5NS0 3 19 and HCCCN-SO320 systems.
4
U o t p r a n P AC
1) D. I. Mendeleyev, The Principles of Chemistry, 2 nd English Edition, American Home
Library, New York, NY, 1902.
2) W. B. Jensen, The Lewis Acid-Base Concepts, John Wiley & Sons, New York, NY,
1980
3) S. Arrhenius, Z. Phys. Chem. 1887, 1, 631; English translation in The Foundations of
the Theory of Dilute Solutions, Alembic Club Reprints, No. 19, Edinburgh, 1929.
4) J. N. Bransted, Reel. Trav. Chim. Pays-Bas 1923, 42, 718.
5) T. Lowry, Chem. Ind. (London) 1923,42,1048.
6) G. N. Lewis, Valence and the Structure of Atoms and Molecules, The Chemical
Catalog Co., New York, NY, 1923.
7) T. J. Balle, W. H. Flygare, Rev. Sci. Instrum. 1981, 52,1.
8) J. A. Phillips, M. Canagaratna, H. Goodfriend, A. Grushow, J. Almlof, K. R. Leopold,
J. Am. Chem. Soc. 1995, 117, 12549.
9) Computing resources were allocated as part of a University of Minnesota
Supercomputing
Institute
for
Advanced
Computational
Research
grant.
Information concerning the supercomputing institute, core hardware, and software
is available on the MSI website: www.msi.umn.edu
10) R. L. Kuczkowski, R. D. Suenram, F. J. Lovas, J. Am. Chem. Soc. 1981, 103, 2561.
11) C. S. Brauer, G. Sedo, K. R. Leopold, Geophys. Res. Lett. 2006, 33, L23805.
12) See for examples, (a) A. B. Nadykto, F. Yu, J. Geophys. Res. 2003, 108(D23), 4717.
(b) A. B. Nadykto, F. Yu, Phys. Rev. Lett. 2004, 93, 016101-1. (c) A.B. Nadykto,
A. Al Natsheh, F. Yu, K. V. Mikkelsen, J. Ruuskanen., Aerosol Sci. and Tech.
2004, 38, 349.
5
13) See for examples, (a) Z. Kisiel, E. Bialkowska-Jaworska, L. Pszczolkowski, A. Milet,
C. Struniewicz, R. Moszynski, J. Sadlej, J. Chem. Phys. 2000, 112, 5767-5776.
(b) D. Priem, T.-K. Ha, A. Bauder, J. Chem. Phys. 2000, 113(1), 169-175. (c) Z.
Kisiel, B. A. Pietrewicz, O. Desyatnyk, L. Pszczolkowski, I. Struniewicz, J.
Sadlej, J. Chem. Phys. 2003, 119, 5907-5917. (d) B. Ouyang, T. G. Starkey, B. J.
Howard, J. Phys. Chem. A 2007, 111, 6165-6175. (e) M. B. Craddock, C. S.
Brauer, K. R. Leopold, J. Phys. Chem. A 2008,112,488-496.
14) See for examples, (a) S. W. Hunt, K. J. Higgins, M. B. Craddock, C. S. Brauer, K. R.
Leopold, J. Am. Chem. Soc. 2003, 15, 13850-13860. (b) C. S. Brauer,
"Microsolvation of Reactive Systems in the Gas Phase via Fourier Transform
Microwave Spectroscopy," Chapter 2, PhD. Thesis, University of Minnesota,
2006.
15) M. Canagratna, J. A. Phillips, M. E. Ott, K. R. Leopold, J. Phys. Chem. A 1998, 102,
1489-1497.
16) (a) A. C. Legon, Chem. Soc. Rev. 1993, 153-163. (b) C. S. Brauer, M. B. Craddock, J.
Kilian, E. M. Grumstrup, M. C. Orilall, Y. Mo, J. Gao, K. R. Leopold, J. Phys.
Chem. A 2006, 110, 10025.
17) M. E. Ott, K. R. Leopold, J. Phys. Chem. A 1999, 103, 1322-1328.
18) See for examples, (a) K. R. Leopold, Advances in Molecular Structure Research,
Vol. 2, M. Hargittai, I. Hargittai, editors; JAI Pres, Greenwich, CT, 1996. (b) K.
R. Leopold, M. Canagaratna, J. A. Phillips, Ace. Chem. Res. 1997, 30, 57-64.
19) S. W. Hunt, K. R. Leopold, J. Phys. Chem. A 2001,105, 5498-5506.
20) S. W. Hunt, D. L. Fiacco, M. Craddock, K. R. Leopold, J. Mol. Spectrosc. 2002, 212,
213-218.
6
Chapter 1
The Electric Dipole Moment of Sulfuric Acid from Fourier
Transform Microwave Spectroscopy
Galen Sedo, Jane Schultz, and Kenneth R. Leopold
Department of Chemistry
University of Minnesota
207 Pleasant St., SE
Minneapolis, MN 55455
Parts of this work have been reprinted with permission from:
J. Mol. Spectrosc. 2008, 251, 4-8.
7
Abstract
The electric dipole moment of H2SO4 in the gas phase has been measured using pulsednozzle Fourier transform microwave spectroscopy. Ninety-one Stark-shifted frequencies
at a series of electric field strengths have been recorded for the 110 <— Ooo transition. The
total molecular dipole moment (jutot = l^c) was determined to be 2.9643(67) D. This is
approximately 0.24 D greater than the previous literature value obtained from similar
measurements on the 643 <— 533 transition. Both ab initio and Density Functional Theory
calculations using the Dunning's correlation consistent aug-cc-pVwZ (n = D,T,Q,Q+d)
basis sets have been performed and concur with the present result.
8
Introduction
Sulfuric acid is an important industrial compound and a key component in the chemistry
of the Earth's atmosphere.1 Its formation in the environment stems from both natural and
anthropogenic sources,1'2 and its high affinity for water has made its hydrates the subject
of much research.3 Aqueous sulfuric acid droplets exhibit a high propensity for uptake of
inorganic species4 and play an important role in the formation of atmospheric particles.
For this reason, the sulfuric acid - water system has long been an important, albeit
challenging, one for developing models of aerosol formation. Dissociation of H2SO4 via
multiphoton infrared absorption in the OH stretching region has also been recently
proposed to account for known stratospheric and mesospheric SO2 concentrations,
suggesting yet another role for the acid in the environment.5
The wide range of ambient conditions in the atmosphere gives rise to a number of viable
mechanisms for aerosol formation and growth.6 Among the many models that have been
explored for new particle production are ion-induced7 and ion-mediated8 nucleation, in
which small molecular clusters form around atmospheric ions. Indeed, the inclusion of
ion mechanisms into atmospheric models predicts particle formation in the middle
troposphere where classic binary nucleation theory does not.9 Recent modifications of
these models propose the inclusion of a charge-dipole interaction for small polar systems
with substantial dipole moments.85'10
In an effort to provide the dipole moment information necessary to accurately incorporate
the charge-dipole interaction into the co-nucleation of sulfuric acid and water, Brauer et
9
al.n measured the gas-phase dipole moment of sulfuric acid monohydrate, H2SO4-H2O.
Included in their analysis was a comparison between the experimental and theoretical
dipole moments for both H2SO4 and H 2 S0 4 -H 2 0. The authors found good agreement
between the experimental dipole moment of the monohydrate and those of MP2 level ab
initio calculations, whereas, previously available density functional calculations resulted
in poor agreement with experiment. However, when comparing the theoretical results
with the literature value for H2SO4 itself, the opposite was observed: The existing DFT
calculations were in good agreement with the experimental dipole moment of
Kuczkowski, Suenram, and Lovas,12 but MP2 results with larger basis sets were not.
The importance of sulfuric acid and its hydrates, and the somewhat irregular
discrepancies between the theoretical and experimental dipole moments, are the
motivation for the present work. In this paper, new observations of the Stark effect for
H2SO4 are presented using pulsed-nozzle Fourier transform microwave spectroscopy and
in doing so, a revised value of the experimental dipole moment is reported.
A
computational study employing a variety of methods and basis sets is also described and
should provide useful guidance for future calculations involving related species.
Experimental Methods and Results
Spectra were recorded using a pulsed-nozzle Fourier transform microwave spectrometer,
the details of which have been given elsewhere.13 This work employs an experimental
setup comparable to the previously reported injection source of Fiacco et al.u to form
sulfuric acid in situ. Argon carrier gas seeded with the vapor from a sample of solid,
10
polymerized S0 3 was expanded through a pulsed valve with a stagnation pressure of 2.3
atmospheres. H 2 0 vapor from a liquid sample, carried by 2.0 standard cubic centimeters
per minute (seem) flow of argon, was injected through a stainless steel needle (0.016"
inner diameter) situated below the pulsed source. The reaction between H2O and SO3
resulted in the formation of H2SO4 in the early parts of the supersonic expansion.
The spectrometer is equipped with a pair of aluminum Stark plates (30 cm x 40 cm),
mounted within the instrument cavity. Equal and opposite DC voltages are applied to the
plates, creating a uniform electric field perpendicular to both the molecular source and
the axis of the cavity. Rotation of the microwave antenna relative to the direction of the
electric field permits observation of both AM = 0 and AM = ±1 transitions. As in
previous work,15 with argon and SO3 already in the system, the effective spacing between
the two Stark plates was conveniently calibrated using the J = 4 <— 3, K = ±3 transition of
the Ar-S0 3 (11588.360 MHz15a, u=0.2676(3) D16) complex. Because accumulation of
diffusion pump oil on the plate surfaces can, at times, give rise to small changes in the
effective plate spacing, calibrations were performed both before and after data collection,
and data were included in the analysis only subject to agreement between the two
calibrations. A more detailed discussion of the calibration method is given in the next
section.
Stark effect measurements, at a series of electric field strengths (s), were performed on
the previously observed 1 10 «- 00o transition14 of the sulfuric acid monomer (10185.126
MHz at zero electric field). The spectra, at zero-field and 8 = 76.5 V/cm are shown in
11
Figure (1.1). Maximum Stark-shifts of 1.749 and 1.721 MHz were observed for the AM
= 0 and AM = ±1 cases respectively, with little spectral broadening. Plots of the electric
field squared (s2) vs. the observed shift in transition frequency (Av) for both the AM = 0
and the AM = ±1 spectra are shown in Figure (1.2). The dependence of Av on 8 was
found to be linear to within the experimental uncertainty, in accordance with the
expectation for an asymmetric molecule with no accidental near-degeneracies.
J
(a)
L
i
(b)
>*
(c)
1l,
10184.5
10185.0
10185.5
10186.0
10186.5
Frequency [WHz]
Figure 1.1 (a) The li 0 <— 0oo transition of H 2 S0 4 at
zero electric field, (b) The AM = ±1 component of the
same transition at 76.5 V/cm. (c) AM = 0
component s = 76.5 V/cm.
12
2.0-1
(a)
••
^
•
10-
•
>
<1 0J-
..•'*
y = 0.00012* - 0.00077
R 2 = 1.00000
^ ' "
4000
0
8000
2
12000
16000
2
e [Wan ]
10-|
(b)
•
I>
•<
•
.•*
as-
/
0
y
10000
..."
y = 0.00005x - 0.00059
R2 = 1.00000
20000
30000
40000
e2 [Wcm2]
Figure 1.2 Plots of frequency shift vs. the square of
the electric field strength for the 110 <— Ooo transition
of H 2 S0 4 . (a) the AM = 0 component, (b) the AM =
±1 component.
Analysis of the Stark-shifted frequencies was done using the QSTARK program
developed by Kisiel et al.11 This program performs a least squares fit via a direct
diagonalization of the full energy matrix, Equation (1.1), in the 1/ J K F M \ basis.
I '
H = Hr + HQ + Hl
'
'
'
Ft
(1.1)
Here, Hr is the rigid rotor Hamiltonian including centrifugal distortion, and HQ is the
nuclear quadrupole coupling term. For H 2 S0 4 , HQ = 0 due to the absence of quadrupolar
13
nuclei. The last term takes the form He = -u»e and accounts for changes in energy due to
the Stark effect.
Accurate rotational and distortion constants are needed for the calculation of the matrix
elements of Hr in Equation (1.1). Values for the rotational constants are readily available
in the original microwave work of Kuczkowski, Suenram, and Lovas.
However, their
treatment of the molecule's centrifugal distortion was done with the Txxxx distortion
constants of Kivelson and Wilson, which are incompatible with the Watson form of the
rotational Hamiltonian used by Q-STARK.
For this reason, the observed ho <— 00o
transition studied in this work was fit along with the 38 fully resolved transition
frequencies reported in the original paper of Kuczkowski et al. using Pickett's SPFIT
program. The resulting rotational and quartic centrifugal distortion constants can be
found in Table (1.1). The A, B, and C rotational constants agree with the previous
values12 to within the estimated uncertainties, but the centrifugal distortion has been cast
in different terms. A list of the fitted transitions and their residuals can be found in the
appendix of this chapter.
Table 1.1. Spectroscopic Constants of the H 2 S 0 4 Monomer."
A
B
C
5160.5951(57)
5024.5405(52)
4881.024(20)
Aj
0.002521(43)
AK
-0.00551(13)
AK
0.00521(11)
8j
-0.000412(27)
5K
0.00309(10)
u, [Debye]
2.9643(67)
(a) All values are in MHz unless otherwise stated.
14
The zero field frequency and the 91 observed Stark-shifted frequencies for the lio <— 00o
transition were used to fit the total dipole moment of H 2 S0 4 , which, by symmetry, is
oriented along the c- inertial axis (i.e., p.tot =
JLIC).
The result of this fit, included in Table
(1.1), is an experimental dipole moment of 2.9643(67) D. The reported error (A|atot) was
calculated using the following expression,
2
(
Opiate
&Mu* = Mb
V Mis J
(
+
A//cal
>2
(1.2)
\ Meal
where )j,is is the value of the dipole moment obtained from the least squares analysis done
by QSTARK, dpiate is the effective plate spacing, u<;ai is the dipole moment of the AX-SO3
complex used in the calibration, and the A's are the uncertainty associated with the
indicated values.
AJJ.IS was
taken as the standard error returned by the least squares fitting
routine of Q-Stark.
Calibration and Data Collection
Because of the approximately 9% discrepancy between the current and previously
measured values for the dipole moment of H2SO4, the calibration and data collection
procedures were carefully tested by measuring the Stark shifts of OCS and ( C I ^ C C N
on their J = 1 <— 0 transitions.
15
Specifically, the plate spacing calibration procedure was tested by using both Ar-S0 3 and
OCS [n = 0.2676(3) D16 and u = 0.715196(10) D19, respectively] to perform consecutive
calibrations. These calibrations, performed on September 9th, give plate spacings that
agree within the experimental uncertainty. In addition, using the plate spacing calculated
by the Ar-S0 3 calibration yields an OCS dipole moment of 0.7155(13) D, which is well
within the uncertainty of the accepted literature value. The plate spacing for all relevant
calibrations can be found in Table (1.2).
Table 1.2 Calibrated Spacings for the Stark Plates
H 2 S0 4
(CH3)3CCN
Plate Spacing3
Standard
Date
Plate Spacing3'1'
32.693(45)
Ar-S0 3
9/15/2006c
32.702(64)
32.710(45)
Ar-SOs
9/15/2006 d
32.682(46)
Ar-S0 3
9/19/2006 c
32.666(11)
OCS
9/19/2006 d
32.957(27)
OCS
8/8/2007 c
33.017(35)
(a) All Values are in centimeters
(b) Values used in the final fits
32.987(44)
OCS
8/8/2007 d
(c) Calibration before data collection
(d) Calibration after data collection
As a further test of our data collection method, two hyperfine components of the
(CH3)3CCN monomer's J = 1 <— 0 transition were Stark-shifted. In this case, using OCS
as the calibration species, a dipole moment of 4.0259(55) D was obtained. Agreement
with the literature value of 4.0129(30) D20 is reasonable, with the measured and literature
values differing by about 1.5 standard errors. It should be noted that this particular
experiment was performed during the month of August when cooling water for the
diffusion pump is warmer and back-streaming of diffusion pump oil is more significant.
Indeed, over the course of this test, the effective plate spacing drifted by about 0.2%
between the pre- and post-calibrations, causing them to agree only marginally within the
16
estimated uncertainties. It has previously been noted that Stark effect experiments in our
laboratory are more successful for this reason during cold weather,21 and this effect likely
accounts for the agreement with the literature value being slightly outside of la. Since
our goal was to eliminate the method of calibration as a source of the significant
discrepancy between experimental dipole moments for H2SO4, rather than a redetermination of the dipole moment of (CH3)3CCN, further testing was not pursued.
Measurements for H2SO4 and OCS were done during cooler weather and showed better
agreement between the pre- and post calibrations, as can be seen in Table (1.2). For
H2SO4, the pre- and post calibrations gave effective plate spacings that agreed to within
0.05%.
The frequencies for the September 19th OCS calibration and all of the
(CH3)3CCN frequencies can be found in Appendix 1.
Theoretical Methods and Results
Calculations of the electric dipole moment for the lowest energy (C2) conformer of
H2SO4 were performed using the Gaussian '03 (G03) program package.22
Four
theoretical methods were utilized: Hartree-Fock (HF), second-order Moller-Plesset
(MP2) perturbation theory, Becke three-parameter hybrid functional with Lee, Yang, and
Parr correlation (B3LYP), and Perdew-Wang 91 exchange and correlation (PW91PW91).
Dunning's augmented correlation consistent w-tuple C, basis sets, aug-cc-pVwZ (n = D, T,
Q), were employed. It has been shown, however, that the standard correlation consistent
basis sets give unacceptable errors when calculating the energy of molecules containing
second-row atoms.
Thus, in order to test our dipole-moment calculations for a
corresponding error, additional calculations were performed using an augmented
17
correlation consistent polarized split-valence basis set, aug-cc-pV(Q+d)Z, on the sulfur
atom and the standard basis set on the hydrogen and oxygen atoms. Dipole moments
were calculated using the population density corresponding to the theoretical method
employed.
All calculations were performed with fixed C2 symmetry during the structural
optimization. The resulting structures showed convergence with increased basis set and
good agreement was observed between the MP2, B3LYP, and PW91 calculations. The
HF calculations also show convergence with increased basis set size but were in more
limited agreement with both the experimental and the various other calculated structures.
Energies and important structural parameters for each of the methods and all basis sets
used are provided in Appendix 1.
Table 1.3 Theoretical Dipole Moment and Percent Error of the H 2 S0 4 Monomer
Miot*
% Errorb
Theory
Basis Set
3.4106
3.5190
3.5051
3.4937
15.1
18.7
18.2
17.9
B3LYP
aug-cc-pVDZ
aug-cc-pVTZ
aug-cc-pVQZ
aug-cc-pV(Q+d)Z
2.9056
3.0549
3.0757
3.0961
-2.0
3.1
3.8
4.4
aug-cc-pVDZ
-2.9
PW91
aug-cc-pVDZ
2.8793
aug-cc-pVTZ
2.8
aug-cc-pVTZ
3.0475
aug-cc-pVQZ
4.1
3.0854
aug-cc-pVQZ
aug-cc-pV(Q+d)Z
4.4
3.0947
aug-cc-pV(Q+d)Z
(a) All values are reported in Debye.
(b) Percent error is in relation to the experimental dipole moment of 2.9643(67) D.
2.7159
2.8915
2.9205
2.9520
-8.4
-2.5
-1.5
-0.4
Theory
HF
MP2
Basis Set
aug-cc-pVDZ
aug-cc-pVTZ
aug-cc-pVQZ
aug-cc-pV(Q+d)Z
iW
% Errorb
18
The theoretical dipole moments and their percent error relative to the newly measured
dipole moment are summarized in Table (1.3). The use of the split-valence basis set on
the sulfur atom does change the resulting dipole moment. However, for most of the
calculated dipole moments, this change is small when compared with the overall
difference with the experimental value. The PW91 calculations are the only case where
the change due to the split-valence basis set is larger than the ^exp - Utheo- However, this
is most likely due to the very good agreement achieved between the PW91 calculations
and the experimental value.
Discussion
The dipole moment of sulfuric acid measured in this work, 2.9643(67) D, represents an
increase of approximately 0.24 D over the previously reported experimental value of
2.725(15) D.
The quoted uncertainty in the new measurement incorporates the three
primary sources of experimental error, and is much too small to account for this change.
Moreover, our use of the ho <— Ooo transition makes mis-assignment of the M
components unlikely. The species studied is certainly the same conformer as that of
Kuczkowski et al, as the rotational constants in Table (1.1), derived primarily from the
frequencies of reference 12, were used to locate the ho «— Ooo transition to within
1 kHz.24
This discrepancy between experimental measurements is perplexing. We note, in this
regard, that the previous determination employed the Stark effect on the 643 <— 533
transition, while here, measurements were conducted with considerably lower rotational
19
energy. Thus, centrifugal distortion of the molecular dipole moment could, in principle,
account for such an effect, though we note that the magnitude would need to be unusually
large. An accidental near-degeneracy with a suitable level from an excited vibrational
state does not seem likely, as no vibrational frequency of H2SO4 appears low enough to
•ye
be close to the 643 or 533 rotational levels of the ground state.
Stark effect
measurements for other rotational transitions could prove useful but were not performed
in this work because the 110«— Ooo transition is the only sufficiently strong rotational line
of H2SO4 accessible to our spectrometer.
While numerous calculations on sulfuric acid have been reported,25"31 the emphasis has
been primarily on the relative stability of its conformers, with some additional interest in
vibrational frequencies, and structural and thermodynamic data for its hydrates.11'32"35
Much of the structural work on the monomer has recently been summarized and
expanded upon in a publication by Demaison and co-workers.31 The number of reported
dipole moment calculations, on the other hand, is fairly limited. Al Natsheh et al.25 give
values between 2.45 D and 2.94 D depending on method and basis set, whereas
Demaison and coworkers31 report 3.09 D for the C2 conformer. The values appearing in
Table (1.3) are in better agreement with the upper end of the range of literature values
and are closer to our experimental result than to that obtained from the 643 <— 533
transition.
It should be noted that our previous calculations11 employed the default
procedure for Gaussian, which utilizes the Hartree Fock density at the post-Hartree Fock
geometry. Here, however, we have explicitly used MP2 population densities in the MP2
calculations of the dipole moment, with clearly improved results, so that all of the non20
HF theoretical methods employed are now in reasonable agreement with the experimental
value. The PW91 exchange and correlation functionals perform the best, converging to
within 0.4% of experiment using the aug-cc-pV(Q+d)Z basis set.
For the H2SO4-H2O complex, we have calculated the dipole moments using the same
theoretical methods employed for the monomer, summarized in Table (1.4).
Interestingly, the MP2 results turn out to be in slightly worse agreement with the
experimental value, 3.052(17) D, than our previously published MP2 calculations using
the Hartree Fock density, but are within about 10% of the measured value and are still
superior to the DFT results for that system.
Table 1.4 Theoretical Dipole Moment and Percent Error of the H2S04-H20 Complex
% Errorb
Theory
Basis Set
B3LYP
aug-cc-pVDZ
aug-cc-pVTZ
aug-cc-pVQZ
2.5963
2.6996
3.4451
10.4
12.3
12.9
2.7493
2.7551
-9.9
-9.7
PW91
2.2860
2.4119
2.7544
-9.8
aug-cc-pVDZ
aug-cc-pVTZ
aug-cc-pVQZ
Theory
Basis Set
HF
aug-cc-pVDZ
aug-cc-pVTZ
aug-cc-pVQZc
3.3708
3.4284
aug-cc-pVDZ
aug-cc-pVTZ
aug-cc-pVQZ0
MP2
Utot"
Mtota
2.7060
2.4070
% Errorb
-14.9
-11.5
-11.3
-25.1
-21.0
-21.1
(a) All values are reported in Debye.
(b) Percent error is in relation to the experimental dipole moment of 3.052(17) D.
(c) Single-point calculation performed at the aug-cc-pVTZ geometry.
Acknowledgements
This work was supported by the National Science Foundation, the donors of the
Petroleum Research Fund, administered by the American Chemical Society, and the
Minnesota Supercomputer Institute.
We are grateful to Professor Chris Cramer for
helpful advice.
21
References
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Al Natsheh, F. Yu, K. V. Mikkelsen, J. Ruuskanen., Aerosol Sci. and Tech.
2004, 38, 349.
22
11) C. S. Brauer, G. Sedo, K. R. Leopold, Geophys. Res. Lett. 2006, 33, L23805.
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13) J. A. Phillips, M. Canagaratna, H. Goodfriend, A. Grushow, J. Almlof, K. R.
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L. Fiacco, A. Toro, K. R. Leopold, Inorg. Chem. 2000, 39, 37. (c) D.L. Fiacco, Y.
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16) K. H. Bowen, K. R. Leopold, K. V. Chance, W. Klemperer, J. Chem. Phys. 1980, 73,
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17) (a) Z. Kisiel, J. Kosarzewski, B. A. Pietrewicz, L. Pszczolkowski, Chem. Phys. Lett.
2000, 325, 523. (b) Program downloaded from the Programs for Rotational
SPEctroscopy (PROSPE) website (http://www.ifpan.edu.pl/~kisiel/prospe.htm).
18) (a) H. M. Pickett, J. Mol. Spec. 1991, 148, 371. (b) Program downloaded from the
Programs
for
Rotational
SPEctroscopy
(PROSPE)
website:
http://www.ifpan.edu.pl/~kisiel/prospe.htm
19) K. Tanaka, H. Ito, K. Harada, T. Tanaka, J. Chem. Phys. 1984, 80, 5893.
20) Z. Kisiel, E. Biaklkowska-Jaworska, O. Desyatnyk, B. A
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Gao, K. R. Leopold, J. Phys. Chem. A 2006, 110, 10025
23
22) Gaussian 03, Revision C.01, Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria,
G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, Jr., J. A.; Vreven, T.; Kudin,
K. N.; Burant, J. C ; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.;
Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.;
Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.;
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Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C ; Jaramillo, J.; Gomperts,
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Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.;
Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C ;
Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.;
Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.;
Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.;
Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.;
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A.; Gaussian, Inc., Wallingford CT, 2004.
23) T. H. Dunning, K. A. Peterson, A. K. Wilson, J. Chem. Phys. 2001, 114, 9244.
24) With our 110 <— 00o transition omitted from the fit, so that all the data is from the
previous microwave study, the predicted frequency is still within 5 kHz of that
observed.
25) A. Al Natsheh, A. B. Nadykto, K. V. Mikkelsen, F. Yu, J. Ruuskanen, J. Phys. Chem.
A 2004, 108, 8914.
24
26) T. S. Chen, P. L Moore Plummer, J. Phys. Chem. 1985, 89, 3689.
27) M. Hofinann, P. V. R. Schleyer, J. Am. Chem. Soc. 1994, 116,4947.
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35.
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25
Chapter 2
The Microwave Spectrum and Theoretical Structure of the Gas
Phase Acetic Acid Monohydrate Complex
Galen Sedo, Jamie L. Doran, Shenghai Wu, and Kenneth R. Leopold
Department of Chemistry
University of Minnesota
207 Pleasant St., SE
Minneapolis, MN 55455
26
Abstract
The gas phase acetic acid monohydrate, CH3COOH-H20, has been observed using
Fourier transform microwave spectroscopy.
A total of 14 A state and 13 E state
transitions have been analyzed, and the identity of the complex has been confirmed by
isotopic substitution. The resulting constants are consistent with a structure where the
carboxylic acid proton forms a hydrogen bond with the oxygen of the water moiety and
one of the water protons forms a second, longer, hydrogen bond to the carbonyl oxygen.
The barrier to internal rotation of the methyl group was determined to be 138.5 cm"1,
which represents a decrease of 18.6% when compared with that of the acetic acid
monomer. The rotational constants and three-fold barrier to internal rotation predicted by
second-order Medler-Plesset perturbation theory show quantitative agreement with the
experimentally determined values, and the changes in the optimized structure of the
acetic acid moiety upon complexation with water have been used to assess the degree of
proton transfer. The calculated binding energy and structure of the (CHaCOOtTh dimer
are also presented and compared with those predicted for the CH3COOH-H2O complex.
27
Introduction
The hydrogen bonding of protic solute - solvent systems plays an essential role
throughout the fields of chemistry and biology. Inter- and intramolecular hydrogen
bonds are known to influence the folding of biological systems,1'2 the formation of
1 A
O
crystalline structures,' and the reaction mechanisms in both the gas and liquid phase.
Spectroscopic and theoretical studies of small gas phase systems allow the formation and
evolution of hydrogen bonds to be studied in the absence of the perturbing influences
associated with the analogous bulk phase liquid4 and solid5 state experiments. For this
reason, the spectroscopic analysis of these systems continues to be a valuable source of
the information needed for a complete understanding of hydrogen bonding.
The ubiquitous nature of water as a solvent and its propensity to form hydrogen bonds
makes hydrated systems of fundamental interest. The large amplitude motion of the
hydrogen bound water dimer6"8 and the ability to observe larger water clusters9
experimentally has lead to thorough spectroscopic analysis of these prototypical systems.
In addition, the investigation of hydrated protic acids, such as the hydrogen halides,10"13
carboxyl acids,14"17 sulfuric acid,18 and nitric acid,19"21 have given insight into the types of
interactions that occur upon heterogeneous complexation with water.
The astrophysical significance ^ of the acetic acid monomer has lead to a concerted
effort to develop a spectroscopic database of its microwave transitions.24"26 However, the
relatively low barrier, -170 cm"1, to internal rotation of the methyl group hindered early
attempts to simultaneously fit the A and E internal rotor states of the acetic acid
28
monomer.27"31 The advent and availability of theoretical models that have proven their
utility over the entire range of potential barrier heights now makes it possible to not only
fit the observed monomer spectrum but also the spectra of hydrogen bound acetic acid
complexes.
This work offers the first spectroscopic investigation of the gas phase acetic acid
monohydrate complex. The spectra of two isotopologues have been observed, and their
analysis, along with the results of high level ab initio calculations, will be presented in
the context of microsolvation of the acid. Specifically, the changes in both the acetic acid
moiety's structure and its barrier to internal rotation upon complexation with a single
water molecule will be discussed.
Experimental Methods and Results
Rotational spectra have been observed for the CH3COOH, CH3COOH-H20 and
13
CH3COOH-H20 systems using the University of Minnesota's existing pulsed-nozzle
Fourier transform microwave spectrometer, details of which have been given elsewhere.32
The acetic acid monomer spectrum was observed by bubbling argon carrier gas through a
sample of glacial acetic acid. The resulting seeded gas was pulsed into the instrument
through a 0.8 mm pinhole, with a stagnation pressure of 2.5 atmospheres and a repetition
rate of 5 Hz. The spectrum of the CH3COOH-H2O complex was initially observed using
a continuous flow source similar to those employed in the microwave investigations of
the nitric acid hydrates.19"21 The parameters of the pulsed molecular source were the
same as those used to observe the acetic acid monomer spectrum.
However, the
29
monohydrate complex was formed in situ by introducing water vapor into the early part
of the super-sonic expansion, via a stainless steel needle (inner diameter = 0.016").
Although a number of monohydrate transitions were observed with this experimental
setup, the transition intensities were unusually low when compared to similar dimers
observed with this instrument. Upon further investigation, it was found that signal could
be increased33 by removing the continuous flow needle and bubbling the argon carrier gas
through a 60% sample of aqueous acetic acid prior to the expansion. For the
C-
substituted complex, the aqueous acid solution was made by diluting a sample of
commercially available 99% 13CH3COOH with water. The frequencies used in the final
analysis were averaged over 2,000 gas pulses (20,000 FID's) for the parent complex and
500 gas pulses (5,000 FID's) for the
13
CH3COOH-H20 isotopologue. A sample of the
parent complex's spectrum can be found in Figure (2.1).
Acetic Acid Monohydrate Fit
A total of 27 a- and b-type rotational transitions were observed for each of the acetic acid
monohydrate isotopologues studied. Of these, 14 belong to the ground internal rotor (A)
state and 13 belong to the doubly degenerate first excited internal rotor (E) state. The
frequency difference between the A and E states of the observed transitions ranged from
0.6 to 1515 MHz. In addition to the splitting from internal rotation of the methyl group,
15 of the 27 transitions were observed as doublets. Similar doubling has previously been
observed in the spectra of protic acid - water complexes containing cyclic hydrogen
bonding structures, and its occurrence has been attributed to the internal dynamics of the
water moiety.1 lbl2bl8b " 20
The frequency difference between the components of the
30
doublets was found to vary depending on the rotational transition, with splittings of up to
90 kHz observed for the transitions presented in this work. The A state 312 <— 2n
spectrum in Figure (2.1) has been included to illustrate the typical splitting and intensity
ratio of the observed doublets.
Estate
1
A State
I
1
J
9405.25
9405.75
9406.25
9406.75
A State
I
L State
14809.00
•
J
14809.50
*«
H State
14810.00
14810.50
Frequency [MHz]
Figure 2.1 A sample of the parent acetic acid
monohydrate spectrum.
The A/E labeling
corresponds to the states of the internal rotor, and the
L/H labeling is associated with the internal motion of
the H 2 0 moiety.
The analysis of the spectrum has been performed using two procedures to fit the doublets.
The first method treats each line of the doublet separately. As a result, two fits, one for
the lower frequency lines of the doublets (L state fit) and a second for the higher
frequency lines of the doublets (H state fit),34 are needed to account for all of the
observed data.
For the 12 transitions where a single line was observed, the same
31
transition frequency has been used in both fits. The second treatment of the observed
doublets fits the numerical average of the components. A number of the transitions,
especially the less intense b-type transitions that showed evidence of unresolved
hyperfine structure, required the components of each doublet to be weight averaged. In
these cases, the numerical average of the two weighted frequencies has been used in the
fit.
A list of the transition frequencies used in each of the L state, H state, and numerical
average fits has been included in the appendix to this chapter. From a comparison of the
RMS standard deviations, it can be shown that the numerical average fit, a = 7 kHz, best
reproduces the observed data, and as such, its constants should be used as the benchmark
values for the acetic acid monohydrate complex.
As previously noted, the doubling in
acetic acid monohydrate is consistent with that observed for other hydrated systems with
cyclic hydrogen bonding. It is possible, however, that this doubling is associated with
unanalyzed hyperfine structure. In which case, it is once again favorable to use the
numerical average fit, as this fit would than represent the line center of the observed
hyperfine structure.
In all of the fits presented in this work, a comprehensive analysis of the A and E internal
rotor states was achieved using the XIAM program of Hartwig and Dreizler,36 which has
demonstrated its ability to fit a wide range of three fold internal rotation barriers.37 This
program utilizes the extended internal axis method proposed by Woods38 and later
modified by Vacherand.39 The Hamiltonian used in the analysis has the form,
32
H = Hr+Hcd+H,+Hird
(2.1)
where Hr is the asymmetric rigid rotor Hamiltonian, Hca is the Watson A-reduced
Hamiltonian for centrifugal distortion,40 Hi is the Hamiltonian describing the internal
rotation, and H H is the internal rotation - overall rotation distortion Hamiltonian.41 The
matrix is expressed in the principle axis system (PAS) of the complex as a whole, making
it possible to compare the rotational and centrifugal distortion constants of Hr and Hca
with those of standard rigid rotor calculations. The program fits the rotational constants
in the form of the [A-54(B+C)], M>(B+C), and ^(B-C) linear combinations. However, to
aid in the comparison of the experimental CH3COOH-H2O results with those predicted
by theory, the values in Tables (2.1) and (2.2) have been given in terms of the A, B, and
C constants.
The internal rotation Hamiltonian of Equation (2.1) can be written,
H, = F ( P a - p p j +iF 3 (l-cos(3a))
(2.2)
where a and P a are the torsional angle and angular momentum of the internal rotor
relative to the framework of the complex. V3 is the three-fold potential barrier to internal
rotation of the top. p is a vector with components defined by Equation (2.3), and P p is
the projection of the total angular momentum along p.
I a and Ig correspond to the moment of inertia of the top and the moment of inertia of the
complex about its g* inertial axis, respectively. The values of Xg represent the direction
33
cosines relating the axis of the top to the g* inertial axis of the complex, and the F term
in Equation (2.2) is a rotational constant related to the moments of inertia for the complex
and the internal rotor's moment of inertia.
(
I 1
(
\
\
8
J
The second equality of Equation (2.4) expresses F in terms of the rotational constant of
the internal rotor, F0. For CH3COOH and CH3COOH-H20, the values of F 0 correspond
to the rotational constant of the methyl top and have been fit as part of the analysis.
Although XIAM expresses the total Hamiltonian of Equation (2.1) in the principle axis
system, the matrix elements of Hi are first calculated in the internal p-axis system of the
rotor and then transformed into the PAS of the complex. This transformation is done via
rotation about the two Euler angles, which relate the p-axis to the principle axes system.
As a result, the angle between the internal rotation axis and the a-axis of the complex,
labeled 8 in the program, is contained implicitly in the internal rotation Hamiltonian and
can be inferred from the observed spectrum. In addition, the experimental data and
theoretical predictions of the next section suggest a system with a very nearly planar
heavy atom structure, and as such, it was possible to fit the data without using the second
Euler angle, effectively fixing it to zero. A list of the parameters used to fit the internal
rotation of the acetic acid monohydrate complex and their experimentally determined
values can be found in Tables (2.1) and (2.2).42
34
Table 2.1 The Spectroscopic Constants of the CH3COOH-H20 Complex
L State*
Averageb
H Statec
Rotational and Centrifugal Distortion Parameters
A
[MHz]
11059.9085(49)
11059.935(12)
B
[MHz]
2584.5158(14)
2584.5230(21)
1059.9686(51)
2584.5239(14)
C
[MHz]
2127.4847(10)
2127.4809(17)
2127.4789(11)
Aj
[MHz]
[MHz]
0.001210(43)
0.001180(51)
0.001079(44)
0.00418(50)
0.00224(92)
0.00407(56)
AJK
Internal Rotation Parameters
v3
1
138.440(17)
157224(17)
138.514(30)
138.493(18)
F0
[cm" ]
[MHz]
157294(30)
A*2j
[MHz]
H
-0.0285(23)
2.91(10)
157278(18)
-0.0247(14)
6
Fd
-0.0238(13)
3.166(55)
169091
169165
0.0702
0.0702
d
P
[MHz]
[unitless]
3.029(65)
169147
0.0702
0.013
[MHz]
0.007
0.013
Values are taken from a fit of the (a) lower frequency lines, (b) the numerical average, and (c) the higher
frequency lines of the observed doublets, (d) Values are derived from the fit parameters.
CT(RMS)
Table 2.2 The Spectroscopic Constants of the '3CH3COOH-H20 Complex
L State0
Average0
H State"
Rotational and Centrifugal Distortion Parameters
A
B
C
[MHz]
[MHz]
[MHz]
11059.4731(58)
2523.3340(16)
2085.8602(11)
11059.502(13)
2523.3393(24)
2085.8579(17)
2523.3423(16)
2085.8581(11)
Aj
[MHz]
0.001105(44)
0.001087(52)
0.001066(42)
AJK
[MHz]
0.00397(69)
0.0030(10)
0.00384(58)
v3
F0
[cm 1 ]
[MHz]
138.492(24)
157222(23)
138.534(35)
157265(34)
138.544(21)
15276(20)
A*2j
[MHz]
8
Fd
[°]
[MHz]
[unitless]
-0.0208(18)
3.122(80)
169089
0.0702
-0.0230(26)
3.01(12)
169134
-0.0227(17)
3.001(74)
1105.5358(53)
Internal Rotation Parameters
P
d
0.0702
169145
0.0702
[MHz]
a (RMS)
0.009
0.005
0.012
Values are taken from a fit of the (a) lower frequency lines, (b) the numerical average, and (c) the higher
frequency lines of the observed doublets, (d) Values are derived from the fit parameters.
35
Acetic Acid Monomer Fit
Thirty-one low J transitions (J < 5) of the acetic acid monomer, spanning the 6 to 18 GHz
range, were collected as part of this work. Of these transitions, eight had not previously
been observed, while the other 23 were observed to within experimental resolution of
their previously published literature values.24"26
A complete list of the rotational
transitions and their frequencies has been given in the appendix to this chapter.
The present analysis is not meant as a substitute for the extensive reviews of the acetic
acid monomer available in the literature. However, the limited data set available for the
monohydrate complex made it essential to verify that a proper treatment of the system
could be achieved. For this reason, a fit of the observed monomer spectrum, once again
using the XIAM program, was performed to test the rigor of the method with a limited
data set and to aid in the choice of parameters.
Although the standard deviation of the monomer fit is slightly larger (a = 25 kHz) than
that typically achieved for a high resolution FTMW spectrum, it is consistent with the
experimental line widths, which were broadened due to partially resolved hyperfine
structure.
This structure had previously been observed in the microwave spectrum
collected at NIST and was left unanalyzed in the global fit of the acetic acid monomer.
Since the ultimate goal of this work is to present the analysis of the monohydrate
complex, the observed monomer hyperfine structure has once again been left untreated,
and the acetic acid monomer constants given in Table (2.3) are the result of fitting the
36
center of the hyperfine structure and imposing errors appropriate for the partially resolved
structure of each transition.
Table 2.3 Spectroscopic Constants for the Acetic Acid Monomer
Rotational and Centrifugal Distortion
Parameters
Internal Rotation
Parameters
A
11335.888(23)
V3 [cm"']
168.558(40)
B
9478.5678(37)
A*2j
C
Aj
5324.9820(31)
0.00511(13)
A*2K
0.3524(76)
-1.286(65)
A,K
AK
8j
0.01168(21)
-0.00223(46)
0.002141(30)
Fo
S[°]
Fc
A.2-
p c [unitless]
0.2054(28)
157778(41)
5.2192(77)
169974
0.0718
(a) All Values are in MHz, unless otherwise stated, (b) a(RMS) = 0.025 kHz.
(c) Values are derivedfromthe fit parameters.
As previously stated, the XIAM program utilizes the principle axis system, whereas, the
acetic acid monomer's global fit24"26 was performed in the rho axis system {i.e. a
nonprinciple axis system). The choice of axis system used in the analysis results in
rotational constants that are defined differently. As a result, the A, B, and C constants of
Table (2.3) do not agree with those of the global fit. Nonetheless, a comparison of the
constants determined in this work with those of Wlodarczak and Demaison,22 also
analyzed in the principle axis system, shows good agreement for all three rotational
constants.
Care must also be taken when comparing the internal rotation barrier determined for the
acetic acid monomer in this work with those available in the literature, which range from
168 to 170.2 cm"1. Although the present value falls within this range, the inclusion of a
V6 term in the analysis, through the addition of I / 2 V 6 (l-cos6a) to Equation (2.2), results
37
in changes to the experimentally determined value of the three-fold barrier. For the
acetic acid monomer, fixing V6 at the value determined for the global fit increases our
calculated value of V3 by approximately three wavenumbers.43 A similar change is
obtained for the CH3COOH-H2O complex when a V6 term is included and fixed at either
the monomer value or the theoretical value predicted for the complex in the next section.
As a result, a more conservative error of approximately 2-3 cm" could be associated with
the experimentally determined barriers of this work due to the use of only ground
torsional state data and the method of analysis.44
Theoretical Methods and Results
Ab initio calculations have been performed on the CH3COOH-H2O complex to predict
the equilibrium structure, binding energy, and the barrier to internal rotation of the
methyl group.
Similar calculations were preformed on the (CH3COOH)2 dimer to
determine the effect binding partner has on the binding energy and internal rotation
barrier. The Gaussian '03 (G03) program package45 and second-order Mtoller-Plesset
(MP2) perturbation theory were utilized, exclusively, throughout this work. Geometry
optimizations were performed using the aug-cc-pVDZ, 6-311++G(d,p), and 6311++G(2df,2pd) basis sets with and without employing the counterpoise correction.
The geometry optimizations of the CH3COOH-H2O complex were initiated with various
starting orientations. For each optimization, the complex converged to one of six low
energy conformers, which are in qualitative agreement with the predicted structures of
Rablen
and Gao.
The converged geometries of all six conformers, and their
38
corresponding energies, are shown in Figure (2.2). In addition, Cartesian coordinates for
each of the conformers have been included in the appendix to this chapter.
8 = 4.61°
t.
V-
= 71.02°
( A ) E = -305.0311 Hartree, AE„h<l = 9.09 kcal/mol ( D ) E = -305.0194 Hartree, A E ^ j = 7.08 kcal/mol
5 = 74.84°
( B ) E = -305.0255 Hartree, A E ^ = 5.61 kcal/mol ( E ) E = -305.0179 Hartree, AE^,, = 6.16 kcal/mol
8 = 9.71°
-^8 = 63.96°
x
„>.
( C ) E = -305.0224 Hartree, AE„ M = 3.63 kcal/mol ( F ) E = -305.0154 Hartree, A E ^ = 4.56 kcal/mol
Figure 2.2 The optimized structures of the CH3COOH-H20 complex, in order of increasing energy A
- F, calculated using the counterpoise correction and MP2/6-311-H-G(2df,2pd) level of theory/basis set.
In each of the acetic acid monohydrate conformers, the heavy atoms and the protons
involved in the hydrogen bonding optimized to a near planar configuration, with the
maximum displacement out of the a,b-plane predicted to be less than a few hundredths of
an Angstrom in all but conformer C. The global minimum structure (conformer A) is
calculated to have an amphiprotic hydrogen bond structure with the water moiety
accepting a hydrogen bond from the carboxylic acid proton and donating a hydrogen
bond to the carbonyl oxygen. The result is a near planar ring structure composed of six
atoms, four covalent bonds, and two hydrogen bonds. The oxygen-oxygen and oxygen39
hydrogen bond lengths associated with the two hydrogen bonds of the global minimum
CH3COOH-H2O structure have been given in Table (2.4) for each of the theoretical
methods employed.
Table 2.4 A Comparison of the Calculated Results for the Global Minimum CH3COOH-H20 Structurea
aug-cc -pVDZ
non-CPC
CPC
6-311++G(d,p)
non-CPC
CPC
6-311++G(2df,2pd)
non-CPC
CPC
10.6
9.0
10.4
8.1
10.7
9.1
10803
2611
10796
10953
10953
11027
11023
2544
2140
4.7
2095
4.5
2597
2134
2491
2062
2656
2177
2589
2132
5.0
4.6
5.8
4.6
[A]
0.990
0.987
0.982
0.978
0.984
0.981
Roo'[A]
2.738
2.799
2.745
2.842
2.717
2.769
[A]
1.795
1.858
1.809
1.908
1.783
1.835
-0.84
-0.90
-0.84
-0.94
-0.82
-0.87
[A]
0.978
0.977
0.969
0.967
0.972
0.969
Roo"[A]
2.780
2.823
2.791
2.862
2.750
2.799
[A]
1.965
2.016
2.041
2.117
1.936
2.004
-1.00
-1.05
-1.06
-1.14
-0.96
-1.03
AEbind [kcal/mol]
A [MHz]
B[MHz]
C[MHz]
8[°]
ROH
RH-O
Ppi [A]
ROH"
RH-O"
PP,"
[A]
(a) Labeling corresponds to the atoms in the primary (') and secondary ( " ) hydrogen bonds.
The equilibrium structure and binding energy have also been calculated for the acetic
acid dimer. The structural optimizations were initiated at a geometry consistent with that
of the experimentally determined gas-phase dimer46'47 and were performed with each of
the model chemistries used for the monohydrate complex. The equilibrium structures
calculated for H 2 0, CH3COOH, and the (CH3COOH)2 dimer are shown in Figure (2.3).
In addition, the calculated binding energies, rotational constants, and hydrogen bond
lengths of the global minimum dimer structure have been given in Table (2.5).
40
Figure 2.3 The global minimum structures calculated for the (a) water
monomer, (b) acetic acid monomer, and (c) acetic acid dimer.
Table 2.5 A Comparison of the Calculated Results for the Global Minimum (CH3COOH)2 Structure
aug-cc-pVDZ
6-311++G(d,p)
6-311++G(2df,2pd)
Experimental
non-CPC
CPC
non-CPC
CPC
non-CPC
CPC
AEbind [kcal/mol]
17.2
14.5
15.4
12.5
17.3
14.8
A [MHz]
5537
5531
5609
5603
5647
5643
5600"
B[MHz]
874
853
868
840
894
873
871.4b
C[MHz]
762
746
759
737
779
763
785.8b
1.002
0.997
0.991
0.985
0.999
0.992
2.670
2.727
2.696
2.779
2.632
2.690
2.680(10)°
R0102 [A]
1.669
1.731
1.705
1.794
1.633
1.697
RH-02 [A]
-0.72
-0.78
-0.74
-0.75
-0.83
-0.69
P«[A]
(a) Labeling corresponds to the atoms in a single ( ' ) hydrogen bond.
(b) Values determined from a femtosecond degenerate four-wave mixing experiment, reference [46].
(c) Gas phase electron diffraction values taken from reference [47].
Rom [A]
The barrier to internal rotation of the methyl group was calculated using z-matrix
representations of the CH3COOH, CH3COOH-H20, and (CH3COOH)2 systems, which
included the H1-C1-C2-01 dihedral angle as it is labeled in Figure (2.3). Starting with
the fully optimized global minimum geometry, this dihedral angle was increased in
41
increments of three degrees. At each new value, the angle was fixed while all other
structural parameters of the z-matrix were re-optimized, and the system's energy was
determined. Structural optimizations of the Ci symmetric CH3COOH-H20 complex were
performed over a full 360° rotation (120 points), and the acetic acid monomer and dimer,
which have Cs symmetry in their syn- and anti-configurations, were calculated over 180°
(61 points). For the acetic acid dimer, internal rotation of only one of the methyl groups
has been considered, and changes in the calculated potential barrier due to interactions
with the second rotor have been assumed to be minimal.
For each partial optimization, the methyl group geometry converged such that it lacked
C3 symmetry. However, a three-fold potential is obtained through the use of an effective
torsional angle (a e j) defined by,48
where oti, CLJ, and 0:3 are the torsional angles of the three methyl hydrogen atoms in
reference to the framework of the optimized structure, and aeff ranges from 0 to 360°.
The small step size of the calculations resulted in well-defined potential energy surfaces
for the methyl rotation.
However, the shear number of structural optimizations
performed necessitated limiting the calculations to the MP2/6-311++G(d,p) and
MP2/aug-cc-pVDZ level of theory and basis set. The energy calculated at each value of
oceff between 0 and 360° minus the energy of the global minimum structure, AE(oc), has
been plotted in Figure (2.4) for each of the systems.
42
E
9
<
175
—
1
i
150
125
100
75
50
A A
cm
cm
»
•
•
Q»
(b)
'
25
0
175
,_,
"g
150
125
•
Jt ioo
^
75
W
50
<
25
0
(C)
S
60
120
180
240
*
300
360
Figure 2.4 The theoretical energy difference at
torsional angles between 0 and 360° calculated using
MP2/6-311++G(d,p) [•] and MP2/aug-cc-pVDZ [o]
for (a) CH3COOH, (b) CH3COOH-H20, and (c)
(CH3COOH)2. The experimental value of V3 [—]
has been included for the available cases.
Although a rough comparison can be made between the experimentally determined
barrier, V3, and the maximum value of AE(cc) predicted by theory, a proper assessment
requires fitting the energy differences and effective torsional angles predicted by the ab
initio calculations to a series of three fold functions, as in Equation (2.6).
AE(a) = ±V3(l- cos 3a) + $V6(1- cos 6a) + ±Vg(l- cos 9a)...
(2.6)
A standard least squares analysis has been performed on each of the potential energy
surfaces shown in Figure (2.4). The inclusion of V9 or higher terms into the analysis
improved the standard deviation of the fit, slightly. However, the V3 and V6 terms were
found to be invariant with their inclusion. As a result, the calculated potential barriers
43
given in Table (2.6) are the product of fitting 120 torsional angles and their
corresponding energies to the first two terms of Equation (2.6).
Table 2.6 The Calculated Barriers to Internal Rotation of the Methyl Group a-c
CH3COQH
CH3COOH-H2O
(CH3COOH)2
6-311++G(d,p)
aug-cc-pVDZ
6-311++G(d,p)
aug-cc-pVDZ
6-311++G(d,p)
aug-cc-pVDZ
151.434
149.240
125.098
127.293
105.346
107.540
V3
153.5(2)
150.1(1)
127(1)
127.6(4)
106.6(1)
V6
-16.7(2)
-3.6(1)
-15(1)
-3.9(4)
-27.3(1)
_a
U
07
6
Z0
0/7
(a) The errors shown in parenthesis are those resulting from the least-squares analysis.
(b) All calculations were performed using the MP2 level of theory.
(c) Values are in cm"1.
106.2(2)
-8.5(2)
0.9
AECaU,
Because the structural parameters were re-optimized at each value of the torsional angle,
the calculations also determine the structural variations to the equilibrium geometry that
result from the internal rotation of the methyl group. Figure (2.5) illustrates the changes
in bond length predicted to occur during the internal rotation of the methyl group within
the CH3COOH and CH3COOH-H2O systems. The same qualitative changes to the acetic
acid moiety's bond lengths are predicted for each of the systems. However, it should be
noted that the largest overall change in bond length due to internal rotation is calculated
to be less than 0.005 A. Whereas, the change in the C-0 H bond upon complexation with
water is predicted to be 0.020 A. The predicted changes to the equilibrium bond lengths
of the acetic acid moiety upon complexation are larger than those due to internal rotation
for all but the C-C bond, which was predicted to be insensitive to both internal rotation
and complexation.
44
0.005 -|
0.003
(a)
V
'
0.0015 i
o 1.S08SA
• 1.5063 A
•-i
£
•J000000
0.001
u
30
-0.001 -
60
90
120
a
o 0.9737 A
• 0.9898 A
0.0005
30
4>.ooa
90
60
120
-0.0005 J
-0.00S
0.0005 -
«...
0.0000
<
o 13698 A
• 13499 A
(b)
30
60
90
0.005 i
.13.0
0*
• 1.7948 A
0.001
30
-0.001
• °
1
-0.0010 -0.0015 -
°:.
(e)
0.003
o
£ -0.0005 •<
(d)
0.0010
rt0000000n
.s°
60
90
.....
#«*
•
120
•
-4.003
-0.005 -
0.001S „
0.0010 Q
•<
0.0005 OJMOO
(c)
30
60
>
o 1.2202 A
1.2320 120
A
90•
-0.0005
••'»H-O
WToH
Figure 2.5 The change in bond length for effective torsional angles (a^) between 0 and 120°
calculated for CH3COOH [o] and CH3COOH-H20 [•] using MP2/aug-cc-pVDZ. The values in the
legend of each plot represent those of the equilibrium geometry.
The equilibrium bond angles of the acetic acid moiety also show variations due to the
internal rotation of the methyl group. These changes have been calculated and are plotted
versus the effective torsional angle in Figure (2.6) for the CH3COOH monomer and
CH3COOH-H2O complex. Once again, similar changes are predicted to occur in each of
the systems. However, all of the bond angles, except the CCOH angle, are predicted to
change very little due to the internal rotation when compared to the size of the changes
that occur upon the formation of the hydrogen bound complex.
45
0.25
0.15
0.05
3
:«a»
60
30
-0.05
0.25
o 12250"
• 12351°
(a)
3J 0.05
T»*»
o
^-0.05
3
-0.15
o 105.76°
• 107.39°
(c)
0.15
30
60
120
90
w*
'•">Sf:
CL*
-0.15
-0.25
-0.25
1.00 -I
-+90
-0.01
«
8
5™
0.75
1
8'
9 0.50
e
ft
%
»
*
o
<j
»
V
*
o*
u
«b
o 12639°
• 124.47°
"-0.61
^b»
•*
3
8
1
30
1
60
120
4>
O-041
0.25
0.00 »e?
J*
^-0-2!
1
90
**sf
120
-0.81
-1.01
(d)
"»««••
-"CCOH
Figure 2.6 The change in bond angle for effective torsional angles (ae^) between 0 and 120°
calculated for CH3COOH [o] and CH3COOH-H20 [•] using MP2/aug-cc-pVDZ. The values in the
legend of each plot represent those of the equilibrium geometry.
Discussion
The spectroscopic data presented in this work are not sufficient to determine a full
experimental structure. However, its analysis, in collaboration with the theoretical work
of the previous section, can be used to infer the overall geometry of the complex. A
comparison of the parent complex's rotational constants, along with the orientation of the
internal rotor axis obtained in the form of the angle 8, with those predicted by theory
shows good qualitative agreement between experiment and the values predicted for the
global minimum conformer, labeled A in Figure (2.2). In addition, the 13CH3COOH-H20
isotopologue was chosen to accentuate the differences in the predicted isotope shifts of
the conformers and has been used to unambiguously assign the experimental complex to
46
conformer A.
The rotational constants, orientation of the internal rotor axis, and
examples of the 13C isotope shifts for both a- and b- type transitions have been given in
Table (2.7).
Table 2.7 A Comparison of the Experimental Results to Those Predicted for the Theoretical Conformers
Rotational Constants a
Av A State:[MHz] b
5[°] a
<—
A [MHz]
BTMHzl
C[MHz]
11059.935(12)
2584.5230(21)
2127.4809(17)
2.91(10)
-204.035
-42.177
11023
2589
2132
4.61
-204.136
-41.996
Conformer B d
9571
2295
1873
74.84
-32.428
-347.898
Conformer C d
9118
2253
1863
63.96
-29.6653
-307.193
Conformer D d
9557
2224
1840
71.02
-34.090
-352.477
Conformer E
d
9678
2306
1884
74.22
-31.837
-349.745
Conformer F
d
10681
2040
1731
9.71
-143.236
-54.117
Experiment
c
Conformer A
d
2<>2 *~ l o i
In
Ooo
(a) Values are those determined for the parent complex.
(b) Isotope shifts for the 13C substitution on the methyl group.
(c) Values are taken from the numerical average fit.
(d) Calculated from the counterpoise corrected MP2/6-311++G(2df,2pd) structure.
Although the experimental spectra have been assigned to conformer A, the calculated
bond lengths of the predicted structure, given in Table (2.4) of the previous section, show
slight variations with the choice of theoretical method utilized in the geometry
optimization. The most quantitative agreement was observed between the experimental
CH3COOH-H20
rotational
constants
and
those predicted
using
the
MP2/6-
311++G(2df,2pd) level of theory and basis set, along with the counterpoise correction to
the basis set superposition error. Indeed, the agreement is such that, not only can the
experimental acetic acid monohydrate structure be assigned to conformer A, it can be
construed as having bond lengths and angles similar to those predicted by this
calculation. This level of theory was also able to reproduce, as an additional test, the
47
experimental structures of the acetic acid monomer and dimer, as evidenced by the
structural parameters in Table (2.8).
Table 2.8 AL Comparison of the Carboxyl Group Geometry Upon Complexation
CH3COOH
rCH [A]
c
rcc [A]
rco [A]
rCOH [A]
r0H [A]
Acco [°1
ACCOH [°]
ACOH n
d
CH3COOH
e
1.102(10) /1.090(4)
1.520(5)d/l .494(10)'
1.214(3)d/1.209(6)e
1.364(3)d/1.357(5)e
0.970(3)e
d
126.6(6) /126.2(7)
Experimental
Theoretical
Experimental
e
110.6(6)d/112.0(6)e
105.9(5)e
1.086
1.496
1.207
1.356
0.967
126.3
111.1
105.9
a
CH3COOH-H2Oa'b
(CH3COOH)2a,b
(CH3COOH)2
1.086
1.496
1.086
1.495
1.224
1.322
1.102(15)d
1.506(5)d
1.219
1.336
0.984
1.231(3)d
1.334(4)d
0.992
124.3
112.0
107.7
123.3
123.6(8)d
112.7
109.5
113.0(8)d
(a) Values are calculated using MP2/6-311++G(2df,2pd).
(b) Counterpoise correction was used throughout the structural optimization.
(c) Assumes a perfect C3 symmetric methyl group.
(d) Values are takenfromthe electron diffraction analysis of ref [46].
(e) Values are takenfromthe microwave analysis of ref [29].
With an acceptable CH3COOH-H20 structure established, it is now possible to
investigate the structural changes that occur upon complexation. A comparison of the
carboxylic acid group of the CH3COOH-H2O complex with the free gas phase acetic acid
monomer shows small but distinct structural changes.
Chief among these are an
elongation of the C=0 and O-H bonds and a shortening of the C-0 H bond, which are the
changes characteristic of an acetic acid system that is beginning the process of
relinquishing its acidic proton to form the CH3COO" ion.
The literature contains an assortment of methods for quantifying the degree of proton
transfer.
In the case of hydrated acids, the method of Kurnig and Scheiner49 has
previously been applied to nitric acid dihydrate20 as a means of determining the degree of
48
acid ionization. This method uses purely structural differences calculated in the form of
the proton transfer parameter (ppt),
_ (^complex _rfree\_
r
Ppt~\OH
OH )
[complex _ H30+ j
r
\H-0
OH )
/% <y\
V"'f
where r0H is the hydroxyl bond length of the acid, either as a free monomer or in the
complex. The value of rH...0 is the hydrogen bond length in the complex, and r"f* is the
covalent bond length of the free hydronium ion.50 Information is contained in both the
sign and magnitude of the proton transfer parameter. In hydrogen-bonded systems with
little monomer distortion, the first term of Equation (2.7) is near zero, and p is negative.
As the X-H bond of the donor acid elongates and the corresponding hydrogen bond
shortens, the magnitude of p decreases until it reaches zero. At this point, the system can
be thought of as sharing the proton equally between the donor acid and water acceptor.
Full proton transfer, i.e. ionization of the acid, is expressed by a positive value of the
proton transfer parameter.
Using the hydrogen bond length, 1.835 A, and the hydroxyl bond lengths found in Table
(2.8), the proton transfer parameter was calculated to be -0.870 A in the acetic acid
monohydrate complex. For comparison, the proton transfer parameters have also been
calculated for hydrated HBr,12 HC1,11 H 2 S0 4 , 18b HN03,19"21 CF3COOH,15 HCOOH,14 and
Q
H 2 0 systems.
Whenever possible the full experimental structure has been used in the
determination. However, for the cases where theoretical bond lengths had to be used,
structures that were in quantitative agreement with the experimentally determined
rotational constants were utilized. In addition, the experimentally determined hydronium
49
ion50 and free acid51"56 bond lengths were used in all cases. A plot of the resulting values
has been given in Figure (2.7). The acids of Figure (2.7) have been plotted in order of
increasing pKa as a means of organizing the available data. However, this choice was not
made in an attempt to draw a relation between the pKa of the acid and the degree of
proton transfer, as the pKa includes both entropy and enthalpy terms making such a
comparison difficult.
From the numerical value of p pt determined for the acetic acid monohydrate complex, it
is readily observable that the addition of one solvent water molecule to acetic acid is
insufficient to promote full ionization.
Nonetheless, the degree of proton transfer
calculated for the acetic acid monohydrate complex is similar to those of the other
available carboxylic acid monohydrates and surprisingly close to the value determined
for the nitric acid monohydrate.
Solute Protic Acid
-V.3 '
HCI
1
HBr
1
I^SO,
HNOj
HCOOH
Wfi
1
1
1
1
1
CFjCOOH
CHjCOOH
o
•
2z
-0.6 -0.7 -
1
3
o°
2
•
C
-0.9 -1.0 -
2
•
1
•
2
•
*
°
2
i
i
o
•
1
1
o
1
•
1
•
-1.1 -1
Figure 2.7 A plot of the proton transfer parameter calculated from the
experimental [•] or theoretical [o] structures of various hydrated acids,
where the integer signifies the number of solvent water molecules.
50
In addition to the structural changes upon complexation, the barrier to internal rotation of
the methyl group was determined to decrease significantly when acetic acid was solvated
by a single water molecule. Previous microwave analysis of weakly bound methanol
complexes had also reported a lowering of the barrier to internal rotation.
However,
further examination of these methanol complexes indicated that the cal
was due to the neglect of OH librational motions in the analysis.58 Because the value of F
in Equations (2.2) and (2.4) is directly related to the orientation of the internal rotor axis
to the inertial axis system, through the direction cosines (A-g), neglect of sigi
nt
vibrational motion would change the value of F to an effective rotational constant. In the
case of the previously studied, weakly bound, methanol complexes, this effective
rotational constant could vary from the value in free methanol (27.63 cm"1) to the value
for a methyl group bound to an infinite rigid frame (5.25 cm"1). Since the observed A/E
splittings are only sensitive to the ratio of V3 and F through the reduced barrier,
,=%•
9F
(2.8)
v
;
the use of an effective F constant to fit the observed spectrum results in an effective
barrier, which losses much of its physical meaning and may differ drastically form the
actual V3 barrier.
For acetic acid, the fitted value of F is approximately 5.6 cm"1, which is already close to
that of the rigid frame limit, making the available range of effective F values too small to
account for the observed decrease in the barrier. In addition, binding a water molecule to
the carboxylic acid gives the frame more mass, decreasing the possible range of an
51
effective F constant even further. Consequently, it is possible to assert that the lowering
the potential barrier in CH3COOH-H20 is not attributed to a neglect of vibrational
motion, but rather, is due to the structur
a comparable decrease in the three-fold potential barrier, as shown in Table (2.9).
Although a decrease in the V3 barrier of 18.6% is reported in Table (2.9), the possibility
of a 2-3 cm"1 error in both the monomer and monohydrate experimental barriers makes it
more reasonable to assume the decrease is on the order of 15 to 22 percent.
Table 2.9 The Change in the Internal Rotation Barrier Upon Complexation"
CH3COOH
CH3COOH-H2O
A Complexation
V3 experimental
170.17408(17)b
138.514(30)c
-31.7
[-18.6%]
d
V3 theoretical
150.1(1)
127.6(4)
-22.5
[-15.0 %]
1
(a) All values, except for the percentages, are in cm" .
(b) Value is takenfromthe microwave global fit of reference [24].
(c) Valuefromthe numerical average fit of this work.
(d) Calculated using the MP2/aug-cc-pVDZ level of theory and basis set.
From a comparison of the trends predicted for the monomer and monohydrate complex in
Figures (2.5) and (2.6), it is possible to conclude that it is the structural changes in the
acetic acid moiety upon complexation, and not an artifact of the internal rotation analysis,
that are the likely cause of the significant reduction in the V3 barrier. As previously
noted, the structural changes in the monohydrate complex, represented by the calculated
ppt value, are not sufficient to form the CH3COO" anion. However in the fully proton
transferred limit, the internal rotation axis would lie coincident with the C2 axis and
mirror plane of the ion. As a result, the internal rotation Hamiltonian, Equation (2.2),
would no longer contain a V3 term. In this limiting case, the first possible barrier would
52
be associated with V6.
The 18.6% reduction in the internal rotation barrier of the
monohydrate would be consistent with a system that has only begun the process of
ionization. This postulate could be tested with the examination of additional acetic acid
complexes, with various degrees of proton transfer.
Unfortunately, the lack of a
permanent dipole moment makes it impossible to determine the (CF^COOFfh dimer's
barrier to internal rotation using microwave spectroscopy. Nonetheless, a barrier of
97.2(15) cm"1 has been determined for the related CF3COOH-CH3COOH bimolecule.59
If the structural changes of the dimer, p pt ~ -0.74 A, are similar to those of the
bimolecule, the decrease of the V3 barrier observed in CF3COOH-CH3COOH is in
agreement with the present argument.
Acknowledgements
This work was supported by the National Science Foundation and the Minnesota
Supercomputer Institute. We greatly appreciate the insight provided by Ms. Ewa Papajak
of the University of Minnesota Chemistry Department.
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56
confusion between the A internal rotor state and the A state of the doublet, the
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57
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59
Chapter 3
The Microwave Spectrum and Theoretical Structure of the Gas
Phase Nitric Acid Trihydrate Complex
Galen Sedo, Jamie L. Doran, and Kenneth R. Leopold
Department of Chemistry
University of Minnesota
207 Pleasant St., SE
Minneapolis, MN 55455
60
Abstract
The gas phase nitric acid trihydrate, HN03-(H20)3, has been observed using microwave
spectroscopy. Rotational and nuclear quadrupole coupling constants have been obtained
and the identity of the species has been confirmed by isotopic substitution. The results
are consistent with a cyclic tetramer with co-planar heavy atoms and are in good
quantitative agreement with ab initio calculations.
The a-type spectra show some
evidence of internal motion, likely resulting from large amplitude motion of one or more
of the water sub-units. This system represents the third step in the sequential hydration of
HNO3, and the theoretical structure and experimental
14
N nuclear quadrupole coupling
constants have been used to track the degree of ionization of the acid.
61
Introduction
Nitric acid has a diverse and extensive role in the chemistry of the atmosphere.
Its
formation can create a temporary reservoir for atmospheric NO* or lead to its permanent
removal through deposition in the troposphere and denitrification in the stratosphere. '
The uptake of atmospheric HNO3 into sulfate aerosols to form liquid ternary aerosols
(LTA's)4"6 and the crystallization of nitric acid trihydrate (NAT)7'8 are responsible for
Polar Stratospheric Cloud (PSC) formation. All of these processes are known to play a
significant role in the atmospheric chlorine cycle and, consequently, the mechanism for
ozone depletion.
The mechanism for the formation of crystalline nitric acid trihydrate in the atmosphere is
still uncertain.9 Recent laboratory evidence suggests crystallization occurs at the gassolution interface between air and aqueous droplets.10
Although the homogeneous
nucleation rate of NAT under atmospheric conditions is small11 and nonequilibrium
behavior between the solid, liquid, and gas phases in PSC's is predicted,12 the presence of
stable molecular HNO3 on the surface of binary (HNO3-H2O) and ternary (HNO3-H2OH2SO4) solutions1 "16 makes understanding the interactions between nitric acid and a
limited number of solvent molecules important for a complete understanding of this gasliquid interface. Given their significance, an extensive body of work has been published
concerning the hydrates of nitric acid, with particular focus on the spectroscopic analysis
of crystalline NAT.17"23 However, spectroscopic data concerning the gas phase molecular
forms of the nitric acid hydrates is more limited.24,25
62
In addition, the ionization of nitric acid due to its "strongly acidic" nature remains a
question of fundamental chemical interest.
HN03 + H20{l)
->• NO-{aq)+H30+(aq)
(3.l)
From a comparison of the Raman intensities of alkali nitrates and aqueous HNO3
solutions, it is known that a bulk 1:10 stoichiometric ratio of nitric acid and water at 298
K results in 99.7% dissociation of the acid.26'27 Nonetheless, the exact number of solvent
water molecules and the types of intermolecular interactions needed to promote the
ionization of one nitric acid molecule remains unanswered.
The microwave
investigations of nitric acid mono-24 and dihydrate25 concluded that, although the process
of ionization has begun, both complexes were composed of hydrogen bonded neutral
monomers. This is in agreement with previous theoretical predictions and experimental
observations that estimate four or five water molecules are needed to promote ionization
in one nitric acid molecule. The present work endeavors, through a combination of
experiment and theory, to track how the nitric acid cluster evolves with the addition of a
third solvent water molecule.
Experimental Methods and Results
Rotational spectra were recorded using a pulsed-nozzle Fourier transform microwave
spectrometer, the details of which have been given elsewhere.29
The nitric acid
trihydrate, HN03-(H20)3, complex was formed using an experimental setup similar to
those employed in the investigation of both nitric acid mono-24 and dihydrate.25 Argon
carrier gas was passed through a sample of concentrated nitric acid and the resulting
63
vapor was pulsed, with a stagnation pressure of 2.5 atm, through a 0.8 mm pinhole. In
addition, ten standard cubic centimeters per minute (seem) of argon were bubbled
through a sample of liquid water and continuously introduced into the early parts of the
super-sonic expansion via a stainless steel needle (0.016" inner diameter).
It has
previously been noted that both nitric acid mono- and dihydrate can be observed without
incorporating a secondary water source.25 However, all four isotopic species of the
trihydrate presented in this work were observed only with the use of the continuous flow
source.
The transition intensities for the HN03-(H20)„, n = 0—>3, series were observed to drop,
on average, two orders of magnitude with the addition of each water moiety. This
decrease, although significant, was not prohibitive for the four isotopic species reported
in this work, given sufficient signal averaging. The frequencies employed in the final
analysis were collected using 1,000-2,000 gas pulses, with signal averaged over 6,00020,000 free induction decays. Sample spectra for both the parent and the 15N isotopically
substituted complexes are shown in Figure (3.1).
The spectra included in Figure (3.1) show splitting analogous to those observed for both
the mono- and dihydrated forms of nitric acid. In these previous works, two types of
spectral splitting were observed: 1) doubling associated with the internal motion of the
water sub-groups and 2) electric quadrupole hyperfine structure resulting from the I4N
nuclear spin.
64
HN03-(H20)3
4
^li*~322
04^"303
—I .il|
Cavity
Frequency
7274.00
7274.25
7274.50
7976.15
7976.65
7976.40
Frequency [MHz]
H15N03-(H20)3
4
423<—322
04*~^
-B State
TJL
A State
7246.75
T
7247.00
7247.25
7938.00
7938.25
7938.50
Frequency [MHz]
Figure 3.1 Sample spectra for the parent and 15N isotopically substituted Nitric Acid
Trihydrate complex.
In both the mono- and dihydrated complexes, each line of the doublet caused from the
internal water motion was fit separately, resulting in a fit of the lower frequency lines of
each doublet (A State fit) and a second fit of the higher frequency lines (B State fit). In
the case of nitric acid trihydrate, low transition intensities meant the less intense line of
the internal motion doublet was not observed for every transition.
When both
components of a doublet were observed, the less intense line was always located at a
lower frequency (A State) and the more intense line was always located at a higher
frequency (B State). As a result, only a fit of the more intense B state is presented here.
The size of the splitting between the A and B states, in the cases where both were
observed, was on the same order of magnitude as the 14N electric quadrupole hyperfine
structure. To avoid the possibility of initially assigning an A state line as one of the B
65
state hyperfine components, assignments were first completed on the transitions where no
A state was observed in the 15N isotopic species. This procedure was used for both the
parent and triple H2180 substituted complexes. However in the case of DNC>3-(H20)3, the
addition of the deuterium quadrupole made it necessary to fit the rotational transitions to
their approximate line centers, and errors equal to the width of the transition at half its
maximum intensity were imposed in the fit.
In all cases, the spectra were fit using the semi-rigid rotor Hamiltonian, as it is expressed
in Equation (3.1),30
H
= &(a+c)- A , J 2 ) J 2
+(A-±(B+C)-
AJKJ2 -AKJ2Z)J22
(3.1)
+ k ( * - C ) - 2 V 2 ) t e - J ^ K t e t e - j ; ) + f c - JJ)J2J
and the 14N hyperfine structure of the parent and triple H2180 substituted complexes were
fit with the addition of an electric quadrupole term containing the Xaa and (xwrXcc)
coupling constants.
Only hyperfine transitions where AF = +1 were observed for the parent and triple H2180
species. The splittings between these hyperfine components were observed to rapidly
decrease with increasing values of J. Inclusion of higher K_i rotational transitions (K_i <
4 and 3 for the parent and triple H2180 substituted species, respectively) where the
hyperfine splitting was more pronounced was necessary for an accurate determination of
both hyperfine constants. A complete list of the transition frequencies used to fit each of
the isotopic species can be found in Appendix 3, and the resulting constants are listed in
Table (3.1).
66
Table 3.1 Spectroscopic Constants of the Nitric Acid Tri-hydrate Complexa
HN0 3 -(H20)3
HN0 3 -(H 2 1 8 0)3
H 1 5 N0 3 -(H 2 0)3
DN0 3 -(H 2 0)3
A
B
C
2269.2958(33)
2090.7418(26)
2268.3900(55)
2246.4960(66)
1215.91165(47)
798.28664(29)
1150.91574(43)
748.13110(26)
1209.02260(65)
795.19691(39)
1210.2466(12)
792.93040(44)
Aj
0.0010561(43)
0.0009517(52)
0.0010550(90)
0.0010900(93)
AJK
-0.002266(25)
-0.001933(29)
-0.002340(76)
-0.002780(75)
5j
5k
0.0004094(27)
0.0003776(40)
0.0004100(62)
0.0004260(58)
0.000840(28)
0.000802(20)
0.000840(13)
0.000847(12)
-0.7993(67)
-0.7939(40)
0.387(12)
0.4004(76)
0.0048
0.0030
0.0021
0.0034
-0.4322
-0.4000
-0.4382
-0.4258
Xaa
V
V
Xbb'Xcc
a (RMS)
b
K
(a) All values, except for the asymmetry parameter (K), are in MHz
(b) Value was determinedfromthe A, B, and C constants of this table and Equation (3.2).
The inclusion of the higher K_i transitions also resulted in the need for four centrifugal
distortion parameters. The Aj, AJK, and 5j parameters were necessary to achieve adequate
residuals. However, similar results could be achieved when using either AK or 5k as the
fourth distortion constant.31 In the case of the H15N03 and DNO3 complexes where only
transitions with K-i < 2 were included, AK and 8k could be omitted completely from the fit
with the values of the other constants remaining unchanged to within their standard errors
and slight increases in the calculated residuals.
To maintain consistency from one
isotopologue to the next, the constants in Table (3.1) and the calculated frequencies in
Appendix 3 are the result of fitting 5k and omitting AK, effectively setting it to zero in
Equation (3.1).
67
Seventy-four a-type transitions were included in the analysis of the parent HN03-(H20)3
complex. A careful search for the corresponding b-type transitions was carried out, but
no transitions were observed. Given the low intensities of the observed a-type transitions
and a predicted b-type dipole moment that is approximately one fifth of the a-type
moment, our inability to observe the b-type transitions was not unforeseen. No attempt
was made to observe c-type transitions. This decision was based upon the absence of
rigid c-type transitions in HNO3-H2O, a detailed discussion of which can be found in the
work of Canagaratna et al.24
Although b- and/or c-type transitions are typically needed for an accurate determination
of the A rotational constant, it can be seen from the values in Table (3.1) that
uncertainties of 3-7 kHz were achieved for the A constant in all four isotopologues using
only a-type spectra. This outcome can be explained by looking at the asymmetry of the
HN03-(H20)3 complex. A simple way of conceptualizing the system's asymmetry is
through its value for the asymmetry parameter, K, 30
where A, B, and C are the rotational constants of the system. A value of K near -1 or +1
relates to a highly prolate or oblate asymmetric top, respectively. Between these two
limits, the asymmetry of the system increases as the value approaches zero. The values
of K calculated in Table (3.1) are closer to zero than the corresponding prolate limit. This
suggests the nitric acid trihydrate system is decidedly asymmetric, and consequently, its
a-type transitions show a significant dependence on the A rotational constant and allow
68
for an accurate determination of all three rotational constants for each of the
isotopologues.
The choice of which isotopically substituted forms of the HN03-(H20)3 complex to
investigate was given much consideration.
isotopically substituted
After locating the parent spectrum, the
15
N and deuterated forms of nitric acid were observed. Both
forms of nitric acid were synthesized "in house" from the reaction between the
appropriate isotopically substituted forms of NaNC>3 and H2SO4.32 Because the water
was later introduced to these species via a continuous flow source, the observed
transitions of these hydrated complexes did not show a noteworthy decline in intensity
from those of the parent.
Flowing 97% H2180 through the continuous flow needle
allowed for the observation of the triply substituted HNC>3-(H2180)3 species. However,
the HNC>3-(D20)3 species was not observed after switching the water source to 99.9%
D2O, likely owing to the addition of the six deuterium quadrupolar nuclei. Further
searches were undertaken to obtain the three singly substituted HN03-H2180-(H20)2
species by continuously flowing various mixtures of H2O and H2180. After an extensive
search, it is our belief that the lack of observed transitions was due to the lower
population density of these complexes in the molecular beam, resulting from the eight
possible H20/H 2 18 0 isotopologues. No attempt was made to find the mixed-deuterium
water species given the proton exchange between H2O and D2O would allow for 64
isotopologues. In addition, the deuterium spin of each isotopologue would have resulted
in spectral broadening due to extensive hyperfine structure and, in all likelihood, a loss of
peak intensity.
69
Theoretical Methods and Results
Theoretical studies of nitric acid trihydrate in its molecular23'28'33"35 and crystalline33"39
phases can be found in the literature. However, Herrero et al.40 have commented on the
care that must be taken when drawing comparisons between NAT in its molecular and
crystalline states. The present theoretical work was undertaken to expand on the previous
studies while limiting its discussion to the purely molecular conformers of the complex.
McCurdy et al.28 were the first to report a cyclic structure for the HN03-(H20)3 complex,
similar to that labeled 10A in Figure (3.2). Their structure, calculated using second-order
Ntoller-Plesset perturbation theory (MP2) and the aug-cc-pVDZ basis set, consists of a
primary hydrogen bond between the nitric acid proton and the oxygen of the first water
moiety. This water molecule then acts as a proton donor to the oxygen of the second
water. The motif of water as both a proton donor and acceptor continues until the third
water completes the cyclic structure through a fourth hydrogen bond to a second oxygen
on the nitric acid. The result is a cyclic structure that incorporates 10 atoms, 6 covalent
bonds, and 4 hydrogen bonds.
Later Density Functional Theory calculations performed by Escribano et al.23 found two
low energy structures using the Becke three-parameter hybrid functional with Lee, Yang,
and Parr correlation (B3LYP) and the aug-cc-pVTZ basis set.
The first structure
reproduces the previously calculated 10-member ring geometry of McCurdy, whereas,
the second conformer consists of the third water acting as a proton donor back to the
hydroxyl oxygen of the nitric acid, resulting in a cyclic structure that incorporates 8
70
atoms, 4 covalent bonds, and 4 hydrogen bonds. The energy difference between these
structures placed the 10-membered ring conformer -0.8 kcal/mol lower in energy. A
subsequent study by Scott et al.u found that this energy difference could be reversed
depending on the theoretical method employed.
In particular, the B3LYP/6-
311++G(2d,p) calculations performed by Scott showed qualitative agreement with those
of Escribano, placing the 10-member ring conformer -0.1 kcal/mol lower in energy.
However, their MP2 calculations with the same basis set resulted in an 8-member ring
structure that was ~0.4 kcal/mol lower in energy than the corresponding 10-member ring
conformer. For both methods employed, Scott and coworkers found that correcting for
the zero-point motion of the complex lowered the overall binding energy, but did not
result in a change to the calculated global minimum geometry (i.e. B3LYP calculated a
10-member global minimum and MP2 calculated an 8-member global minimum even
after correcting for the zero-point motion).
Given the very small energy differences and the agreement between the B3LYP
calculations of Scott and Escribano, this work presents a second look at the conformers
using the MP2 level of theory. The choice of basis set was made after considering both
the strong hydrogen bonding of the first water and the weaker interactions of the second
and third water units. A proper treatment of the strong hydrogen bond formed between
the acid and the first water moiety requires the inclusion of adequate polarizing functions,
and the inclusion of diffuse functions is necessary to accurately model the intermolecular
parameters associated with the weaker interactions of the second and third water units.
The 6-311++G(2df,2pd) basis set has both the necessary polarizing and diffuse functions
71
and has yielded good results for similar systems with reasonable computing time.
All
of the calculations presented in this work were performed using the Gaussian *03 (G03)
program package.42
Figure 3.2 Theoretical structures for the lowest energy 10-member and 8-member ring
nitric acid trihydrate conformers, optimized using the MP2/6-311-H-G(2df,2pd) level of
theory and basis set.
Figure (3.2) shows the structures of the lowest energy 10-member (10A) and 8-member
(8A) ring conformers of HN0 3 -(H 2 0) 3 , calculated using MP2/6-311++G(2df,2pd). The
global minimum structure is calculated to be 10A, with 8A lying 0.268 kcal/mol higher in
energy. This is in qualitative agreement with the previous B3LYP calculations. The use
of "A" in the labeling of the two conformers is not associated with the internal dynamics
of the water sub-units, which has been previously discussed in relation to the observed
spectrum, but rather is used to differentiate these conformers from those that will be
72
presented later. The Cartesian coordinates for these and all of the other optimized
geometries presented in this work can be found in Appendix 3.
Although the cyclic nature of the two conformers is distinctly different, they do show
similarities in their bonding. Table (3.2) lists the bond lengths of the intermolecular H--0
hydrogen bonds and the intramolecular O-H covalent bonds for both conformers. The
hydrogen bonds of Table (3.2) are listed according to the proton donor, i.e. the primary
hydrogen bond between the nitric acid and the first water is listed under nitric acid. The
Greek letters (a, p, and x) are used to differentiate between the individual water units and
have been labeled in Figure (3.2). The covalent O-H bonds within the ring of each
conformer are elongated from their corresponding values in the free monomers. This
increase is most pronounced in the nitric acid OH bond, which is elongated by 0.035 A in
conformer 10A, and is calculated to steadily decrease around the ring, with the OH bond
of the third (%) water remaining effectively unchanged from that of the free monomer for
both conformers.
Table 3.2 Calculated Bond Lengths of the 10-Member and 8-Member Ring Conformers of HNQ3-(H20)3i>
10A
8A
O-H (ring)
H--0
H—O
O-H (unbound)
O-H (ring)
O-H (unbound)
1.005
0.978
0.971
0.962
HN0 3
ccH 2 0
PH20
XH 2 0
0.957
0.957
0.957
Free HN0 3
Free H 2 0
0.970
0.961
Free H 2 N0 3 +
0.985
1.604
1.753
1.831
1.998
1.010
0.977
0.971
0.964
0.958
0.957
0.957
1.588
1.767
1.832
2.003
0.970
0.961
+
Free H 3 0
0.977
0.977
(a) Geometries calculated using MP2/6-311++G(2df,2pd) level of theory and basis set
73
The H--0 hydrogen bond lengths of the two conformers are also calculated to progress
along the ring structure. The primary hydrogen bond between the nitric acid proton and
the (a) water oxygen is calculated to be approximately 1.6 A in both conformers. This is
-0.4 A shorter than the weakest hydrogen bond, where the (x) water is acting as the
proton donor. In addition, all of the hydrogen bonds within the ring structures of both
conformers are calculated to be discernibly shorter than the corresponding hydrogen
bonds in the smaller hydrates. Specifically, the primary hydrogen bond of the trihydrate
is 0.13 and 0.05 A shorter than the primary hydrogen bonds of the theoretical mono- and
dihydrate structures, and the fourth hydrogen bond with the (%) water donating back to
the nitric acid is calculated to be 0.41 and 0.06 A shorter than the terminal hydrogen
bonds of the theoretical mono- and dihydrate ring structures.
As expected when going from a 10-membered ring to an 8-membered ring formation, the
bond angles of the two conformers are very different. Principal among these differences
are those describing the heavy atom planarity of the complex. The nitric acid monomer
has a calculated equilibrium structure with Cs symmetry, where the a,b-plane is also the
plane of symmetry. The addition of one or two solvent water molecules breaks this
symmetry and results in very slight distortions to the calculated HONO dihedral angle
(179.85° and 179.57° respectively). The corresponding HONO dihedral angle in the
trihydrate is calculated to be 178.7° and 169.6° for conformers 10A and 8A.
The dihedral angles of the heavy atom ring structures can also be expressed in terms of
the maximum displacement of the atoms out of the a,b-plane.
For the nitric acid
74
monohydrate complex the maximum out-of-plane displacement is calculated to be 0.08 A
on the water oxygen, and a similar 0.08 A out-of-plane distance is calculated for the p
water oxygen of the dihydrate complex. In the trihydrate, this maximum displacement
decreases to 0.03 A for the hydrogen bond accepting oxygen of the nitric acid in
conformer 10A and increases to 0.84 A for the hydroxyl oxygen of the nitric acid in
conformer 8A.
The structure of the 10-member ring previously reported by Escribano and coworkers had
a calculated HONO dihedral angle of 176.15 but showed significant out-of-plane
displacements on the (|3) and (%) water molecules, whereas, the heavy atom structure
calculated for conformer 10A in this work shows a much more "quasi"-planar structure
similar to those of the mono- and dihydrated complexes.
The light atom structures of both conformers 10A and 8A were calculated to prefer an
alternating up, down, up orientation of the free proton on each water sub-unit, in
reference to the ring plane. To explore how changes in this light atom orientation affect
the optimized geometry, the 10-member ring was re-optimized with different light atom
orientations. Allowing the three free protons to lie either above or below the heavy atom
plane results in eight possible orientations. However, the quasi-planar nature of the ring
means only four of these orientations are unique: (afPixTX (°4P?XTX (aTPTxJ-X
an
d
(ctTPTxTX where the Greek letters, once again, refer to the water moiety and the arrows
refer to the free proton's position lying above or below the ring plane.
These
configurations correspond to the starting geometries of the optimized global minimum
75
structure (10A) and three local minimum structures (shown in Figure (3.3) and labeled
10B, IOC and 10D), respectively.
Comparison of the structures in Figures (3.2) and (3.3) indicates that the bond lengths,
both the covalent and hydrogen bonds, remain effectively constant given changes in the
overall ring formation and light atom orientation. However, changes to either of these
structural characteristics results in optimized geometries with a range of out-of-plane
bending, with the global minimum structure showing the least amount of planar
distortion.
a
10B
(aiPtXt)
c
IOC
(aTPTxi)
a<
c
10D
(«TPTxT)
a
^
*
d
Figure 3.3 Local minimum structures for the 10-member ring nitric acid tri-hydrate
conformer calculated using MP2/6-311++G(2df,2pd).
76
Discussion
Although the four isotopologues studied in this work are not sufficient to determine a full
experimental structure, the data can be used to draw conclusions concerning the general
structure of the complex, and in collaboration with the theoretical work of the previous
section, the overall geometry of the complex can be inferred.
The differences in a system's effective moments of inertia, and consequently their
associated rotational constants, can be described in terms of the inertial defect,
h (\
A,n
=•
2
&r \C
1
O
A
B>y
J
AID,30
(3.3)
where A, B, and C are the system's rotational constants and h is Planck's constant. The
practicality of defining such a parameter lies in its capacity to convey the effective planar
nature of the system. The inertial defect for a rigid planar system will be zero in the
absence of vibrational effects, and distortion away from a planar structure will result in a
negative An> value. As the deviation from a planar geometry grows, the magnitude of the
inertial defect increases.
Using the rotational constants of Table (3.1), the inertial defect of the parent nitric acid
trihydrate is calculated to be -5.261 amu-A2. Comparable values, -0.380 and -1.822
amu-A , have been calculated for the experimental mono- and dihydrated forms of nitric
acid.43 Although the magnitude of the defect increases slightly from the mono- to the
trihydrate, a comparison of the Aro values in Table (3.3) suggests that the magnitude of
77
this change is consistent with the addition of out-of-plane hydrogen atoms and is smaller
than that expected for a trihydrate complex with out-of-plane heavy atoms.
Table 3.3 Comparison Between the Experimental Results and Theoretical8 Predictions
Experimental
10A
10B
IOC
10D
AE[kcal/mol]
0.000
0.245
8A
0.442
0.953
0.268
-15.559
5775.139
-18.916
5714.450
-54.182
6048.894
-20.636
5363.809
-56.089
5684.791
-18.923
5690.340
-54.189
6018.968
-18.941
5691.546
-55.139
6041.148
HN03-(H20)3
2
A ro [amuA ]
3 03 <- 202 [MHz]
-5.261
5670.400
-2.879
5668.684
-15.771
5816.296
HN0 3 -(H 2 18 0) 3
AnjtamuA2]
3 0 3 «- 2 02 [MHz]
-5.311
5319.160
-2.880
5313.547
-16.174
5455.488
-16.162
5414.482
H15N03-(H20)3
A, D [amuA 2 ]
3 0 3 «- 202 [MHz]
-5.259
5647.531
-2.879
5645.869
-15.785
5792.366
-15.559
5751.776
DN0 3 -(H 2 0) 3
2
A ro [amuA ]
303^202[MHz]
-5.191
5633.672
-2.879
5644.905
-15.804
5793.179
-15.559
5750.875
(a) All calculations were performed using MP2/6-311++G(2df,2pd) level of theory and basis set, and
the energies of the conformers are relative to that of 10A.
In addition, the changes in the inertial defects upon isotopic substitution can give insight
into the relative orientation of the substituted atoms. A small variation in the calculated
defects would be expected when an atom on the effective plane is isotopically substituted,
and as the distance between the substituted atom and the a,b-plane becomes larger, the
magnitude of the difference between the parent and isotopically substituted A© values
would increase.
The inertial defects for each of the NAT isotopologues, both
experimental and those calculated for the various theoretical conformers, can be found in
78
Table (3.3). The experimental values are small negative Aro values with minimal change
upon substitution, which strongly suggests an experimental structure with the proton and
nitrogen of the acid and all three oxygen atoms of the waters lying near the a,b-plane.
Further understanding of the nitric acid trihydrate structure can be inferred by a
comparison of the experimental rotational constants and those predicted by theory.
However, for ease of comparison, these rotational constants can once again be
represented in the form of the Am values found in Table (3.3). The experimental AID
values and those calculated for conformer 10A show good qualitative agreement in both
their magnitude and their change upon isotopic substitution. A similar comparison can be
made between the experimental transition frequencies and those predicted by theory. In
the case of conformer 10A, the predicted 3o3 «— 2o2 transition frequencies, found in Table
(3.3), are within 2-11 MHz of experiment; whereas, the frequencies predicted for the
higher energy conformers differ by as much as 400 MHz.
The orientation of the nitric acid in the trihydrate complex can be obtained from an
examination of its quadrupole coupling constants and an understanding of the
quadrupole coupling tensor in the free nitric acid monomer.
14
N
Given the nitric acid
trihydrate's near planar configuration, its c-axis deviates only slightly from an orientation
perpendicular to the heavy atom plane, and as a result, it can be considered coincident
with the c-axis of the free nitric acid monomer. Ott et al.44 used the measured quadrupole
coupling constants and the experimental structure of the nitric acid monomer to calculate
the two in-plane eigenvalues, xxx = 1.1468(34) MHz and
XYY=
-1.0675(34) MHz, of the
79
14
N quadrupole coupling tensor. These values can be related to the projections in the
complex, Xaa and XbtrXcc via the rotations expressed in Equations (3.4) and (3.5),
Xaa = Xxx c os 2 0 + Xn sin2 #
(3.4)
(xbb -Zcc) = Xxx(l + s^ 2 e)+ Xrr(l + cos2 O)
(3.5)
where 9 is the angle between the a- inertial axis and the X-axis of the 14N quadrupole
coupling tensor. In the absence of any electronic rearrangement around the nitrogen
nucleus, Equations (3.4) and (3.5) could be solved for an exact value of 0. However as
will be discussed in more detail later, the nitric acid trihydrate system does undergo
electronic redistribution, making 0 as it is determined from Equations (3.4) and (3.5) an
approximate value.
Assuming for the moment that distortion to the nitric acid monomer is minimal upon
complexation, the angle between the N-0 H bond of nitric acid and the a-axis, (|>, can be
determined from Equation (3.6),
9 = y/ + <j>
(3.6)
where \\i is the angle between the X-axis of the 14N quadrupole coupling tensor and the
TJ
N-CT bond of the free HN0 3 monomer. A schematic diagram of the various angles and
axis systems can be found in Figure (3.4). The angle <>| has been calculated for the HNO3(H20)3 and the HNC>3-(H2180)3 complexes using both experimental quadrupole coupling
constants, and these values, along with the angle calculated for the theoretical structure of
conformer 10A, can be found in Table (3.4).
80
Figure 3.4 Schematic of the angles defining the
Quadrupole Coupling Tensor and the Inertial Axis of
the HNO3 monomer.
Table 3.4 The Calculated Angle between the N-OH Bond of the Nitric Acid Moiety
and the a-axis of HN03-(H20)3 Complex
HN0 3 -(H 2 0) 3
K [°]
ab
108.5 '
HN0 3 -(H 2 18 0) 3
10A
108.7*"
1010d
8 0
fob-cc [°1
126.1 (a) Determined using Equation (3.6) and the free monomer value of \|/ = 1.88°
(b) Values of 8 determined from the Xaa value in Table (3.1) and Equation (3.4)
(c) Values of 0 determined from the XNTXCC value in Table (3.1) and Equation (3.5)
(d) Value of <>| determined from the theoretical structure of conformer 10A.
Comparison of the angles in Table (3.4) shows experimental and theoretical results that
are in qualitative agreement. However, the resulting differences and the range of values
calculated by experiment may be the consequence of this method's assumptions that
HNO3 monomer distortion and electronic redistribution around the 14N atom are minimal
upon complexation. A further discussion of these two concepts, and how they pertain to
the ionization of nitric acid in the trihydrate, will be given later.
81
The arguments put fourth for a planar heavy atom structure and the good agreement
between the experimental data and that predicted by theory makes it possible to conclude
conformer 10A has the defining structural characteristics expected for the experimental
complex. With a resolution concerning the structure of the gas-phase trihydrate, it is now
possible to address the main goal of this discussion, assessing the degree of ionization in
the HN0 3 -(H 2 0) 3 complex.
The literature contains a variety of methods for quantifying the degree of ionization. In
the case of hydrogen bonded complexes, the method of Kurnig and Scheiner45 has
previously been applied to amine-hydrogen halide complexes '47 and nitric acid
dihydrate
as a means of determining the degree of proton transfer. This method uses
purely structural differences calculated in the form of the proton transfer parameter (p),
_ (complex _„free\_
I complex _rfree
r
y — \rOH
OH )
\rHO
'HO)
\
/ o 7"V
\D-')
where rOH is the "covalent" bond length of the proton donor in the complex and the free
monomer and rH...0 is the "hydrogen" bond length in the complex and the covalent bond
length of the free protonated acceptor ion. Information is contained in both the sign and
magnitude of the proton transfer parameter. In typical hydrogen bonded systems, the first
term of Equation (3.7) is near zero, and p is negative. As the covalent bond of the donor
elongates and the corresponding hydrogen bond shortens, the magnitude of p decreases
until it reaches zero, where the system can be thought of as sharing the proton equally
between the donor and acceptor. Ionization, i.e. full proton transfer, is expressed by a
positive value of the proton transfer parameter.
82
For the HN0 3 -(H20) 3 complex, rOH is the nitric acid O-H bond length in the complex and
free monomer, and rH...0 is the primary hydrogen bond length in the complex and the O-H
bond length in the free hydronium ion, H 3 0 + . 48 Using the bond lengths in Table (3.2), the
p value for the interaction between the nitric acid and the (a) water is calculated to be
-0.592 A. This value does represent a considerable change when compared to the -0.64 A
value reported for the dihydrate25 and the -0.79 A value calculated from the structure of
the monohydrate.24 Nevertheless, the negative value indicates that, although the degree
of proton transfer has progressed in the trihydrate, three solvent water molecules are
insufficient to completely ionize one nitric acid molecule.
A graphical representation of how the proton transfer parameter in hydrogen bonded
nitric acid complexes changes with the number and type of solvating molecules can be
found in Figure (3.5a), and the structures of the corresponding complexes can be found in
Figure (3.6). In both figures, the HN0 3 -NH 3 [ref. 49] and HN03-N(CH3)3 [ref. 50]
complexes have been included for comparison.
83
Number of Solvent Molecules
1
2
3
1
-02
1
1
HN03-N(CH3)3
-0.4
HNO3-NH3
*
HNO.f(H 2 0) 2
-0.6
-08
HN03-(H20)3
0
HN0 3 -H 2 0
(a)
0.7 - NO3 (aq)
m
OlS03 -
u
w
on -
7
HN03-N(CH3)3
•
HNO,-NH,
HN03-(H20)3
•
•
HNO»-H20 H N 0 3-(H 2 0) 2
-0.1 J HNO3
0
(b)
v
0.656 MHz
1
1
1
2
1
1
3
Number of Solvent Molecules
Figure 3.5 (a) The number of solvent molecules vs. proton transfer
using the p values calculated from the experimental [•] and theoretical
[o] structures (b) The number of solvent molecules vs. the experimental
value of Xcc-
84
H N
° ^ °
HNO^O),
- v^ v
HNO.-NH,
HN03-N(CH3)3
Figure 3.6 Experimental structures of HN0 3 -H 2 0, HN0 3 (H20>2, and HN03-NH3 and the theoretical structure of HN0 3 N(CH3)3 calculated using MP2/6-311++G(2df,2pd).
With the limited structural information determined from the experimental data, a second
means of assessing the degree of ionization, with a less stringent structural dependence,
has been perform and used to corroborate the previous conclusions. The method utilizes
the electron redistribution that occurs upon complexation and relies on the projected
quadrupole coupling constants as a means of measuring this change.
The hydration of HN0 3 with an infinite number of water molecules, as in Reaction (3.1),
results in an aqueous N0 3 " ion with D3h symmetry. Consequently, the 14N quadrupole
coupling tensor has only one unique projection, eqQ, which is coincident with the axis of
symmetry and perpendicular to the plane of the nitrate ion, as shown in Figure (3.7). The
value of eqQ for an aqueous nitrate ion in an infinite dilution at 25°C was determined to
be 0.656 MHz by Adachi et a/.51 using NMR relaxation times.
85
E>3h
eqQ = 0.656 MHz
Figure 3.7 Schematic of the symmetry axis and the unique
projection, eqQ, of the 14N electric quadrupole coupling in the
aqueous nitrate ion.
It is possible to compare the value of eqQ in the nitrate ion and the projection of the 14N
quadrupole coupling tensor perpendicular to the nitrate group in any nitric acid complex.
These two values quantitatively show how the electronic distribution around the
14
N
nucleus in the complex resembles that of the fully proton transferred limit, i.e. the N0 3 "
ion. In theory, the relation of the X-, Y-, and Z-axis of the
14
N quadrupole coupling
tensor to the a-, b-, and c-axis in the complex would have to be known in order to
determine the projection that lies perpendicular to the nitrate group in the complex.
However, the effective planar structures of the HN0 3 -(H 2 0)„ [n = 1-3] complexes, along
with the C5 symmetry of the HNO3-NH3 and HN03-N(CH3)3 complexes, simplify the
procedure by aligning the c-axis in each of these complexes with the symmetry axis of
the nitrate group, effectively making it possible to compare Xcc in the complex to eqQ in
the nitrate ion.
86
Because Laplace's equation holds true over the volume of the nuclei, the sum of a
complex's 14N quadrupole coupling constants must equal zero,
(3-8)
Xaa+Xbb+Xcc=^
and it is possible to express Xcc as a sum of the two experimentally determined coupling
constants.
Xcc =-l\Xaa+
iXbb ~ Xcc )]
( 39 )
Using the quadrupole coupling constants found in Table (3.1) and Equation (3.9), Xcc is
calculated to be 0.206(9) MHz for the HN03-(H20)3 complex. This value is roughly one
third that expected for the fully ionized system, reaffirming the conclusion that three
water molecules are insufficient to completely ionize one nitric acid molecule. A plot of
the Xcc values calculated from the experimental constants of all three nitric acid hydrates,
HNO3-NH3, and HN03-N(CH3)3 versus the number of solvent molecules is shown in
Figure (3.5b).
Although the two methods for determining the degree of proton transfer are
fundamentally different, they both give similar results for each of the nitric acid
complexes presented in this work, see Figure (3.5). Interestingly, a simple plot of p vs.
the experimental value of Xcc Figure (3.8), shows a linear relationship, and extrapolating
the available data to the Xcc fully proton transferred limit (foe = 0.656 MHz) leads to a
proton transfer parameter (p = 0.037 A) that more closely resembles proton sharing than
it does the fully transferred limit. Given the differences in the two methods, the linear
extrapolation of the relationship between p and Xcc may be misleading. Indeed while we
87
expect p to correlate with Xcc, there is no fundamental reason to expect a linear
relationship across the full range of relevant values. Therefore, a straight line determined
from the available neutral pair complexes need not extrapolate correctly to systems in the
fully proton transferred regime. However, it is important to note that the values of p and
Xcc are correlated over the range of systems investigated thus far.
N 0 3 (aq)
- 0.72
0.656 M H z
- 0.60
y = 0.71x + 0.63
R2 = 0.97
..o-
HN^-NCCH^
- 0.36 g^
U
- 0.24 **
™ ~ „m
o HN0 3 -(H 2 0) i
HNO,-NH, • .--•
' ^ "
7
•
•HNO,-(H20)J
- 0.12
HN0 3 -H,0
i
i
i
i
-0.8
-0.6
-0.4
-0.2
v.uu
0.0
P[A]
Figure 3.8 Proton Transfer vs. Quadrupole Coupling using the
experimental x^ values and the p value calculated from the
experimental [•] and theoretical [o] structures.
88
Conclusions
The gas-phase nitric acid trihydrate has been observed using Fourier transform
microwave spectroscopy.
The rotational and centrifugal distortion constants of four
isotopic species have been determined, along with the 14N quadrupole coupling constants
of the parent and triply H2180 substituted complexes. An analysis of the rotational
constants, in the form of the inertial defect, is consistent with a near planar structure with
the proton and nitrogen of the nitric acid monomer and the three oxygen nuclei of the
solvent water molecules lying near the a,b-plane. Ab initio calculations, using MP2/6311++G(2df,2pd), have been performed on the two lowest energy conformers,
confirming a 10-member ring global minimum structure with a near planar heavy atom
structure. The degree of proton transfer has been discussed using two methods: one that
assesses proton transfers from a purely structural standpoint and a second which analyzes
the electronic redistribution around the
14
N nuclei in the form of nuclear quadrupole
coupling constants. Both methods suggest that although the degree of proton transfer has
progressed, compared to the mono- and dihydrated forms of nitric acid, three water
molecules are insufficient to promote full ionization.
Acknowledgements
This work was supported by the National Science Foundation, the donors of the
Petroleum Research Fund, administered by the American Chemical Society, and the
Minnesota Supercomputer Institute.
89
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26) H. S. Harned, B. B. Own, The Physical Chemistry of Electrolytic Solutions, 3rd
Edition, Reinhold Publishing Co., New York, NY, 1958.
27) The determination of ref [6] found 98% dissociation at 278 K with a 1:20 ratio of
nitric acid to water.
28) P. R. McCurdy, W. P. Hess, S. S. Xantheas, J. Phys. Chem. A 2002,106, 7628.
29) J. A. Phillips, M. Canagaratna, H. Goodfriend, A. Grushow, J. Almlof, K. R.
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30) W. Gordy, R. L. Cook, Microwave Molecular Spectra, 3rd Edition, John Wiley &
Sons, New York, NY, 1984.
31) The rotational constants of both fits agreed to within the experimental uncertainties,
and the o values were 4.8 kHz and 7.3 kHz for the fits including 8k and AK,
respectively.
32) T. H. Chilton, Strong Water Nitric Acid: Sources, Methods of Manufacture, and
Uses, MIT Pres, Cambridge, MA, 1968, p 166.
33) J. Koller, D. Hadzi, J. Mol. Struct. 1991, 247, 225.
34) J. R. Scott, J. B. Wright, J. Phys. Chem. A 2004, 108, 10578.
35) A. Al Natsheh, K. V. Mikkelsen, J. Ruuskanen, Chem. Phys. 2006, 324, 210.
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37) Y. A. Mantz, F. M. Geiger, L. T. Molina, M. J. Molina, J. Phys. Chem. A 2002, 106,
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92
38) D. Fernandez, V. Botella, V. J. Herrero, R. Escribano, J. Phys. Chem. B 2003, 107,
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39) B. Martin-Llorente, Delia Fernandez-Torre, V. J. Herrero, I. K. Ortega, R. Escribano,
B. Mate, Chem. Phys. Lett. 2006, 427, 300.
40) V. J. Herrero, I. K. Ortega, B. Mate, B. Martin-Llorente, R. Excribano, H. Grothe,
Chem. Phys. 2006,331,186.
41) Specifically, this has been established for the HN0 3 -H 2 0 and HN0 3 -(H 2 0) 2
calculations of Appendix 3 and the work done on CH3COOH-H2O and HNO3N(CH3)3 as it is presented in Chapters 2 and 4.
42) Gaussian 03, Revision C.01, Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria,
G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, Jr., J. A.; Vreven, T.; Kudin,
K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.;
Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.;
Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.;
Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.;
Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C ; Jaramillo, J.; Gomperts,
R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C ;
Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.;
Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C ;
Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.;
Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.;
Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.;
93
Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.;
Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C ; and Pople, J.
A.; Gaussian, Inc., Wallingford CT, 2004.
43) These values were obtained using the experimental rotational constants of references
[24] and [25].
44) M. E. Ott, M. B. Craddock, K. R. Leopold, J. Mol. Spectrosc. 2005, 229, 286.
45) I. J. Kurnig, S. Scheiner, Int. J. Quantum Chem. Quantum Biol. Symp. 1987,14,47.
46) S. W. Hunt, K. J. Higgins, M. B. Craddock, C. S. Brauer, K. R. Leopold, J. Am.
Chem. Soc. 2003,125,13850.
47) C. S. Brauer, M. B. Craddock, J. Kilian, E. M. Grumstrup, M. C. Orilall, Y. Mo, J.
Gao, K. R. Leopold, J. Phys. Chem. A 2006,110, 10025.
48) (a) T. J. Sears, P. R. Bunker, P. B. Davies, S. A. Johnson, V. Spirko, J. Chem. Phys.
1985, 83(6), 2676-2685. (b) D.-J. Liu, T. Oka, T. J. Sears, J. Chem. Phys. 1986,
84(3), 1312-1316.
49) M. E. Ott, K. R. Leopold, J. Phys. Chem. A 1999,103,1322.
50) See chapter 4 of this work for a further discussion on the HN03-N(CH3)3 complex.
51) A. Adachi, H. Kiyoyama, M. Nakahara, Y. Masuda, H. Yamatera, A. Shimizu, Y.
Taniguchi, J. Chem. Phys. 1988, 90, 392.
94
Chapter 4
The Microwave Spectrum and Theoretical Structure of the Gas
Phase Nitric Acid - Trimethylamine Complex
95
Abstract
The microwave spectrum of the gas phase nitric acid - trimethylamine complex has been
observed using Fourier transform microwave spectroscopy. The experimental rotational
constants and (CH3)315N-HN03 isotope shift are consistent with a complex in which the
nitric acid proton is forming a hydrogen bond to the nitrogen of the amine, similar to the
experimentally determined H3N-HNO3 complex. Analysis of the hyperfine structure in
the parent and (CH3)3N-H15N03 spectra made it possible to determine, unambiguously,
the quadrupole coupling constants of the
14
N nuclei in both the nitric acid and
trimethylamine moieties. Ab initio calculations have been performed on the series of
complexes formed between an amine, (CH3)„H3.„N [n = 0 —* 3], and nitric acid. The
(CH3)3N-HN03 structure optimized using the MP2/6-31H-+G(2df,2pd) level of theory
and basis set is in quantitative agreement with the available experimental data. The
theoretical structures of the nitric acid - methylamine complexes optimized with this
method, along with the experimental structure of the H3N-HNO3 complex, have been
discussed in terms of the amine basicity and the degree of nitric acid ionization upon
complexation.
96
Introduction
Nitric acid is known to dissociate readily in the bulk phase to form the nitrate ion.
HN03 + H20
-+ H30++N03~
HN03 + NH3_n(CH3)n
->
(4.l)
NH4_n{CH3);
+
NO,
(4.2)
For the hydrated system of Reaction (4.1), it has been determined that upwards of 98% of
the acid will undergo dissociation,1'2 and there is both experimental3'4 and theoretical5'6
evidence that suggests much of the remaining molecular acid is located on the air-liquid
interface, not in solution. However, the formation of small hydrated nitric acid clusters,
consisting of 1-3 solvent water molecules, was determined to be insufficient to promote
•
7 Q
full ionization of the acid. "
•
This observation is in agreement with previous
predictions10'11 that 4-5 solvent water molecules may be needed to promote ionization and
reinforces the conclusions of the early IR matrix isolation work,12 which indicated the
formation and stabilization of the HsO^Oa" contact ion pair depends significantly on the
solvent effect.
The formation of FUN^NC^", which represents the simplest form of Reaction (4.2), was
found to occur in an argon matrix12 in the absence of aqueous solvent. However, the
microwave analysis of the complex formed between nitric acid and ammonia determined
the gas phase structure to consist of the hydrogen bound H3N-HNO3 molecular
complex.
Taken together, the matrix IR and microwave investigations of the complexes
formed between nitric acid and NH 3 /H 2 0, suggest that although ammonia is a better
97
proton acceptor than water14 neither is sufficient to stabilize a contact ion pair in the gas
phase.
From an investigation of the (CH3)„H3.„N-HX complexes, Legon was able to conclude
that the gas phase H3N-HX (X = Br, I) systems were best described as hydrogen-bonded
species, whereas, the complexes between trimethylamine (TMA) and the hydrogen
halides favored ion pair formation.15 With these conclusions in mind, the present work
endeavors, through a combination of experiment and theory, to track how the ionization
of the nitric acid evolves as the binding partner basicity is increased, from those of NH3
and H2O, to that of trimethylamine.
Experimental Results
Rotational spectra of two isotopologues of the nitric acid - trimethylamine complex were
recorded using a pulsed-nozzle Fourier transform microwave spectrometer, the details of
which have been given elsewhere.16 In order to limit mixing time and eliminate the
formation of solid HN(CH3)3N03, the gas phase nitric acid - trimethylamine complex
was formed in situ using a co-injection continuous flow source, similar to that employed
in the investigation of the H 3 N-HN0 3 complex.13 Specifically, gaseous trimethylamine,
Pvap = 100 kPa at 2.6°C,17 was diluted with argon until a 0.35% TMA mixture, by
pressure, was obtained. A sample of the resulting mixture was held at a stagnation
pressure of one atmosphere and pulsed into the instrument through a 0.8 mm pinhole with
a repetition rate of 5 Hz. In addition, the vapor from a liquid sample of 90% nitric acid,
Pvap = 10 kPa at 28.4 °C,17 was allowed to continuously flow into the early part of the
98
supersonic expansion, via a stainless steel needle with an inner diameter of 0.016 inches.
For the isotopically enriched (CH3)315N-H14N03 complex,
15
N-TMA was synthesized
using literature procedures18 and the appropriate isotopic reagents. All spectra were
recorded over 500 gas pulses with the resulting signal averaged over 3,000 FID's. The
observed 322 <— 22i transition of each isotopologue is shown in Figure (4.1).
(CHj)314N-H14N03
^22 *~ ^21
1
6083.5
\ «1
,,i
i
6084.0
6084.5
J i
i
I
i
6085.0
6085.5
6086.0
500 gas pulses
3001 FID's
(CH 3 ) 3 ^N-H»N0 3
^22 *~ ^21
i
ll
\
i
6059.25
i
6059.75
6060.25
Frequency [MHz]
Figure 4.1 The 3 22 -<— 221 transition of the nitric acid - trimethylamine complex.
A total of 111 and 37 a-type rotational transitions, including hyperfine components, were
observed for the parent and (CH3)315N-H14N03 complexes, respectively.
Upon
successfully analyzing the a-type spectra, attempts were made to observe the ho <— 00o
and 22i •*— ho b-type transitions, near their predicted frequencies.
No transitions,
however, were observed that could be positively attributed to these transitions, despite
significant effort.
Although the ultimate reason for the lack of observed b-type
99
transitions is open for debate, one possible explanation is the magnitude of the predicted
b-type dipole moment, which is less than lA that of the corresponding a-type moment.19
No attempt was made to observe the c-type transitions as the predicted Cs symmetry of
the complex, discussed in further detail later, results in a c-type dipole moment equal to
zero. Consequently, only a-type spectra were used in the final analysis of the nitric acid trimethylamine complex. A complete list of the rotational transitions observed for each
isotopologue has been included in the appendix to this chapter.
The observed rotational transitions were fit using the SPFIT program developed by
Pickett.20 The rotational part of the system was analyzed using an asymmetric rigid rotor
01 00
03
Hamiltonian ' and the Watson A-reduced Hamiltonian for centrifugal distortion.
As a
result, the hyperfine-free Hamiltonian used in the analysis of the system can be expressed
in the following form,
H = {A-±(B+C)-AJKJ2-AKJI)SI+{\(B
^(B-chis^ljl
-JI)-SK{J]{JI
C)-AJJ2)32
- J;) + (J> - i2yyz)
+
(4.1)
where A, B, and C are the system's rotational constants, and the values of A„ and 8,
correspond to the quartic centrifugal distortion constants. Rotational transitions with K-i
equal to 0, 1, and 2 were observed as part of this work, and although the observed
transitions make it possible to simultaneously fit Aj, AJK, and 5j, doing so led to slight
increases in the standard error determined for each constant with no discernable
improvement to the standard deviation of the fit.24 As a result, only Aj and AJK were fit in
the final analysis. The remaining quartic distortion constants were left out of the analysis
completely, effectively setting them equal to zero in Equation (4.1).
100
The 14N nuclear quadrupole coupling of the two isotopologues was treated using standard
91 99
methods appropriate for systems with either one or two quadrupolar nuclei. '
Consequently, the system was expressed in the | J, K, Fx, F) basis, where
J + I^F,
(4.2)
and
F1+I2=F
(4.3)
The values of// and h correspond to the two 14N nuclei of the complex, and subsequent
15
N(CH3>3 isotopic substitution made it possible to unambiguously assign the two spins to
the nitrogen nuclei of the nitric acid and trimethylamine, respectively.
For the
(CH3)315N-H14N03 isotopologue, the coupling scheme is expressed entirely by Equation
(4.2), with Fi representing the total angular momentum of the system.
The
experimentally determined constants of both nitric acid - trimethylamine isotopologues,
along with their standard errors, have been given in Table (4.1).
Table 4.1 Spectroscopic Constants of the Nitric Acid - Trimethylamine Complex *
A
B
C
Aj
AJK
X-CHNQ*//]
Xbb-XccfHNO,,/,]
Xa.[N(CH 3 ) 3 ,/J
Xbb-Xoo[N(CH3)3,/2]
a (RMS)
(CH3)314N-H14N03
(CH3)315N-H14N03
3654.80(17)
1048.85105(11)
979.41064(10)
0.0001996(47)
0.001273(24)
-0.3504(11)
-0.4036(28)
-3.28901(63)
-0.5810(16)
3653.53(23)
1044.39648(17)
975.52208(16)
0.0001491(52)
0.001428(39)
-0.3496(13)
-0.4142(36)
0.0025
0.0046
(a) All values are in MHz.
101
Theoretical Methods and Results
Ab initio calculations have been performed on the (CH3)„H3-„N-HN03 [n = 0 -*• 3] series
of complexes to determine their optimized global minimum structures and binding
energies. The Gaussian '03 (G03) program package25 and second-order IVMler-Plesset
perturbation theory (MP2)26,27 were utilized exclusively throughout this work. Structural
optimizations of the complexes were performed using the Pople extended 6-311++G(d,p)
and 6-311-H-G(2df,2pd) basis sets, both with and without correcting for the basis set
superposition error.
The structural optimizations of the complexes were initiated under multiple starting
conditions consisting of the amine oriented either in or above the plane of the nitric acid
moiety, with the nitric acid proton in each starting geometry forming a hydrogen bond to
the nitrogen of the amine. Upon obtaining a converged structure, the amine was rotated
2° about the hydrogen bond by changing one of the dihedral angles associated with the
amine orientation.
The chosen dihedral angle was than fixed and the remaining
structural parameters were re-optimized.
This procedure was repeated for one full
rotation of the amine in order to assure that the global minimum orientation of the amine
was achieved.
The equilibrium structures of the (CH3)„H3.„N-HN03 [n = 0 —> 3] complexes have been
given in Figures (4.2) through (4.5), along with a slice of the potential energy surface
associated with the orientation of the amine. In addition, Table (4.2) contains the binding
energies and selected bond lengths determined for each of the complexes. The global
102
minimum structure of the H3N-HNO3 complex determined in this work, Figure (4.2), was
found to agree with the previously published structure of Tao et al,
and is predicted to
have a three fold barrier to internal rotation of the amine. In contrast, the nitric acid monomethylamine complex is predicted to have Ci symmetry, with the methyl group
oriented approximately 72° out of the nitric acid plane.
Rotation of the
monomethylamine moiety about the hydrogen bond determined a single minimum
structure and an asymmetric two fold barrier. The nitric acid - dimethylamine complex,
Figure (4.4), is predicted to have two low-lying conformers associated with the
orientation of the amine. The global minimum structure, conformer S, converged such
that it has Cs symmetry with the nitric acid in the mirror plane and a methyl group above
and below the plane.
The second minimum, conformer A, was found to be
approximately 0.4 kcal/mol higher in energy, and consisted of a Ci symmetric complex
with the lone H-N covalent bond of the amine oriented 42° out of the nitric acid plane.
Lastly, the (CH3)3N-HN03 complex, Figure (4.5), was determined to have CS symmetry,
with the vector describing the N-C bond of the in plane methyl group oriented nearly
parallel to the N-0 H bond the nitric acid. Similar to the H3N-HNO3 complex, the nitric
acid - trimethylamine complex is predicted to have a three fold barrier to internal rotation
of the amine. Cartesian coordinates for each of the complexes, optimized at the MP2/6311-H-G(2df,2pd) level of theory and basis set, have been included in the appendix to this
chapter.
103
H3N-HN03
*£- r —- <
viewed along the c-axis
viewed along the b-axis
OJO -i
g
A
0.15 •
A
A
g OJOEs) 0.05 •
<
0
120
60
180
240
300
360
N-QH-N-H Dihedral Angle [°1
Figure 4.2 The global minimum structure of the H3N-HNO3 complex and a plot
of the change in energy as the ammonia moiety is rotated about the
intermolecular hydrogen bond. The difference between the energies calculated
at 180° and 607300° is due to the higher symmetry, Cs, of the complex at 180°.
(CH3)H2N-HN03
* / " 1 •-*- ^
viewed along the c-axis
viewed along the b-axis
0.7
^^
OJi -
1
OS •
©
«
.3
.-•"-.
.."•
•*,
.*••
0.4 •
03-
•
*•
/
*.
.*
."
.'
•.
".
*t
0.2 •
<
y •»"
'\
•
.
'
0.1 •
0.0 •
'^
1
,
^,
1
N-QH-N-C Dihedral Angle F°l
Figure 4.3 The global minimum structure of the (CH3)H2N-HN03 complex and
a plot of the change in energy as the amine is rotated about the intermolecular
hydrogen bond. The slightly lower energy calculated at 180° is due to the
changefromQ to Cs symmetry.
Conformer S
v
s>. -IK.
viewed along the c-axis
viewed along the b-axis
Conformer A
•f-f
c
•
^
<
- v. ^
viewed along the b-axis
viewed along the c-axis
=
1.0 -1
0.9 •
0.8-
^
3
0.60.5-
g °-7"
.--•*•.
*
s,
c£, 0.4y
<I
•
•
W
03 •
0.2 •
0.1 •
\
;
\s;
**
ft ft -
0
/-\
60
120
180
240
300
360
N-QH-N-H Dihedral Angle [°]
Figure 4.4 The global minimum (S) and local minimum (A)
conformers of the (CH3)2HN-HN03 complex and a plot of the change
in energy as the amine is rotated about the intermolecular hydrogen
bond.
Table 4.2 Binding Energies and Selected Bond Lengths of the (CH3)nH3.„N-HN03 Complexes
MP2/6-311++G(2df,2pd)
non-CPC
CPC
MP2/6-311++G(d,p)
CPC
non-CPC
H3N-HNO3
Ebmd [kcal/mol]
13.8
12.3
14.3
11.6
RH1-N2 [A]
1.668
1.707
1.684
1.757
ROI-HI [A]
1.016
1.011
1.013
1.006
RN1-N2 [A]
3.326
3.364
3.357
3.431
(CH3)H2N-HN03
Ebind [kcal/mol]
16.0
14.1
16.1
13.0
RH1-N2 [A]
1.595
1.639
1.614
1.694
ROI-HI [A]
1.034
1.026
1.030
1.018
RN1-N2 [A]
3.260
3.305
3.303
3.379
(CH3)2HN-HN03 Conformer S (C, symmetric)
Ebind [kcal/mol]
17.5
15.2
17.5
13.9
R«l-N2 [A]
1.550
1.604
1.568
1.661
ROI-HI [A]
1.050
1.038
1.045
1.027
RN1-N2 [A]
3.277
3.326
3.302
3.388
(CH3)2HN-HN03 Conformer A (local minimum)
Ebind [kcal/mol]
17.1
14.8
17.1
13.7
RH1-N2 [A]
1.535
1.593
1.556
1.652
ROI-HI [A]
1.054
1.039
1.047
1.028
RN1-N2 [A]
3.233
3.287
3.274
3.363
(CH3)3N-HN03
Ebiad [kcal/mol]
18.3
15.5
18.4
14.1
R-H1-N2 [A]
1.495
1.571
1.518
1.634
ROI-HI [A]
1.070
1.048
1.061
1.033
RNI-N2 [A]
3.259
3.319
3.287
3.388
(CH3)3N-HN03
**V
^4v
IT
viewed along the b-axis
viewed along the c-axis
120
180
240
300
N-QH-N-C Dihedral Angle [°1
Figure 4.5 The global minimum structure of the (CH3)3N-HN03 complex and a
plot of the change in energy as the amine is rotated about the intermolecular
hydrogen bond.
The global minimum structure of nitric acid and those of the free amines have been
optimized using the MP2 level of theory and both Pople extended basis sets. The
resulting energies were used to calculate the binding energies reported in Table (4.2). In
addition, the structure of each protonated amine cation, NH4.„(CH3)„+ [n = 0 —> 3], was
determined. The optimization of each ion was initiated at the global minimum geometry
of the free amine with the addition of a proton in the lone pair orbital of the nitrogen
atom.
The resulting optimized geometries were found to have varying levels of
molecular symmetry, and as a result of this symmetry, the N-H bond lengths within any
given ion were determined to be equivalent. The point group and RNH bond length
predicted for each amine cation are listed in Table (4.3), and the Cartesian coordinates of
the free neutral monomers and amine cations, calculated with the MP2/6-
107
311-H-G(2df,2pd) level of theory and basis set, have been given the appendix to this
chapter.
Table 4.3 Nitrogen - Hydrogen Bond Length in Amine Cations
RNH[A]
Point Group
NH/
NH3(CH3)
+
NH2(CH3)2
NH(CH3)3
+
+
6-311++G(d,p)
6-311++G(2df,2pd)
Td
1.025
1.025
C3v
1.024
1.021
C.2V
1.024
1.021
Civ
1.025
1.021
(a) Bond lengths were optimized using MP2 theory and the indicated basis set.
(b) Multiple N-H bonds, when present, were calculated to be equivalent due to the molecular symmetry.
Discussion
Arguments similar to those presented in the microwave analysis of the nitric acid
trihydrate, in which the available experimental data in collaboration with theory was
used to provide insight into the molecular structure and ionization of the acid, can be
made concerning the nitric acid - trimethylamine complex. From a comparison of the
experimental rotational constants and transition frequencies to those predicted by theory,
it has been determined that the structure optimized using the MP2/6-311++G(2df,2pd)
level of theory and basis set is in quantitative agreement with the observed gas phase
experimental data. A summary of these results has been included as Table (4.4).
108
Table 4.4 A Comparison of the Experimental and Theoretical Results a
Experiment
Theory b
Aexp.-theo
(CH 3 ) 3 14 N-H I4 N0 3
A
3654.80(17)
3704
-49
B
1048.85105(11)
1045
4
C
979.41064(10)
975
4
3 0 3 «- 202
6079.295
6054.080
25.215
A
(CH3)31SN-H14N03
3653.53(23)
3704
-50
B
1044.39648(17)
1040
4
C
975.52208(16)
971
5
3 03 <- 202
6054.360
6028.147
26.213
(a) All values are in MHz.
(b) Calculated from the MP2/6-311++G(2df,2pd) optimized structure.
In addition, the orientation of the nitric acid in the (CH3)3N-HNC>3 complex can be
obtained from an examination of its quadrupole coupling constants and an understanding
of the
N quadrupole coupling tensor in the free nitric acid monomer. Given the C5
symmetry predicted for the complex and the fact that the nitric acid lies in the mirror
plane, the c-axis of the complex is parallel to the c-axis of the free nitric acid monomer.
Ott et al.
used the measured quadrupole coupling constants and the experimental
structure of the nitric acid monomer to calculate the two in-plane eigenvalues of the 14N
quadrupole coupling tensor, xxx = 1.1468(34) MHz and XYY= -1.0675(34) MHz. These
values can be related to the projections of the 14N quadrupole coupling constants of the
nitric acid in the complex, &» and xwrXw, via the rotations expressed in Equations (4.4)
and (4.5),
109
Xaa = Xxx COS2 0 + Zrr s i n 2 °
^ - ^
e
(4-4)
) = ^ ( l + s i n 2 ^ ) + ^ ( l + cos 2 ^)
(4.5)
where 9 is the angle between the a- inertial axis and the X-axis of the 14N quadrupole
coupling tensor. In the absence of any electronic rearrangement around the nitrogen
nucleus of the nitric acid, Equations (4.4) and (4.5) can be solved for an exact value of 9.
However, as will be discussed in more detail later, a significant amount of electronic
redistribution is calculated to occur upon complexation of the acid with trimethylamine,
making 9 as it is determined from Equations (4.4) and (4.5) an approximate value.
Assuming for the moment that distortion to the nitric acid monomer is minimal upon
u
complexation, the angle between the N-O bond of nitric acid and the a-axis, if, can be
determined from Equation (4.6),
6 = y/ + </>
(4.6)
where \\i, 1.88°, is the angle between the X-axis of the 14N quadrupole coupling tensor
and the N-0 H bond of the free HNO3 monomer.30 A schematic diagram of the various
angles and axis systems can be found in Figure (4.6). The angle <)| has been calculated for
the (CH3)314N-H14N03 and the (CH3)315N-H14N03 isotopologues using both experimental
14
N quadrupole coupling constants of the nitric acid moiety, and these values, along with
the angle determined for the theoretical global minimum structure calculated using
MP2/6-311++G(2df,2pd), can be found in Table (4.5).
110
Figure 4.6 Schematic of the angles defining the
Quadrupole Coupling Tensor and the Inertial Axis of
the HN03 monomer.
Table 4.5 The angle between the N - O H bond of the nitric acid and the a-axis of the
nitric acid - trimethylamine complex
(CH3)314N-H14N03
(CH3)313N-H14N03
MP2/6-31 l++G(2df,2pd)
48.8
29.0 ^
^ A
28.7 ^
(a) Determined using Equation (4.6) and thefreemonomer value of \\i = 1.88°, ref [30].
(b) Values of 9 determinedfromthe XM value in Table (4.1) and Equation (4.4)
(c) Values of 6 determinedfromdie XwrXcc value in Table (4.1) and Equation (4.5)
Comparison of the angles in Table (4.5) shows a theoretical value of <>| that is in
qualitative agreement with the experimental angles determined using the Xaa quadrupole
coupling constants of each isotopologue. However, the resulting differences between
these values and those determined from the experimental Xbb-Xcc quadrupole coupling
constants may be the consequence of this method's assumptions that HNO3 monomer
111
distortion and electronic redistribution around the
14
N nucleus are minimal upon
complexation. A further discussion of these two concepts, and how they pertain to the
ionization of nitric acid in the (CFb^N-HNOs complex, will be given.
As previously stated, the experimental results and the values predicted from the MP2/6311++G(2df,2pd) optimized structure show good agreement, see Tables (4.4) and (4.5).
Indeed, the agreement is such that it is possible to conclude that the theoretical geometry
has the defining structural characteristics of the gas phase nitric acid - trimethylamine
complex. Using this geometry as the benchmark for the structure, it is now possible to
address the structural changes that occur upon complexation of the nitric acid with a
strong base. Specifically, the degree of proton transfer from the nitric acid to the amine
binding partner will be discussed.
The literature contains a variety of methods for quantifying the degree of proton transfer.
In the case of hydrogen bonded complexes, the method of Kurnig and Scheiner31 has
previously been applied to amine-hydrogen halide complexes32'33 and a number of nitric
acid hydrates ' as a means of determining the degree of proton transfer and, therefore,
the extent of the nitric acid moiety's ionization. This method uses purely structural
differences calculated in the form of the proton transfer parameter (ppt),
— (-complex _rfree\_
r
yPt~\rAH
AH )
(complex _r.free\
r
\rH-B
HB+ J
(AI\
V*-'J
where /AH is the "covalent" bond length of the proton donating acid, rH...B is the
"hydrogen" bond length in the complex, and rHB+ is the covalent bond length of the free
protonated base cation. Information is contained in both the sign and magnitude of the
112
proton transfer parameter. In typical hydrogen bonded systems, the first term of Equation
(4.7) is near zero, and p pt is negative. As the covalent bond of the donor elongates and
the corresponding hydrogen bond shortens, the magnitude of p pt decreases until it reaches
zero, where the system can be thought of as sharing the proton equally between the donor
and acceptor. Ionization of the acid, i.e. full proton transfer, is expressed by a positive
value of the proton transfer parameter.
For the (CH3)„H3.„N-HN03 [n = 0 —• 3] series of complexes, rm is the nitric acid O-H
bond length in the complex and free monomer. rH...B is the hydrogen bond length in the
complex, and r
is the nitrogen - hydrogen bond length of the NH4-„(CH3)„+ [n = 0 —•
3] ion. Throughout this work, the N-H bond of the amine cations predicted by theory,
Table (4.3), have been used to determine the value of Ppt. Using the bond lengths in
Table (4.2) and the experimental nitric acid OH bond length of 0.964 A,34 the p pt value
for the interaction between the nitric acid and N(CH3)„H3_„ is -0.37 A, -0.44 A, and -0.51
A for values of n equal to 3, 2, and 1 respectively.
These values do represent
considerable changes when compared with the -0.67 A and -0.79 A calculated for the
experimental structures of the H3N-HNO313 and H2O-HNO37 complexes. The negative
value of ppt in the nitric acid - trimethylamine complex indicates that, although the
degree of proton transfer has progressed when compared to the complexes formed with a
single water or ammonia molecule, even a relatively strong base like TMA is insufficient
to completely ionize nitric acid in a gas phase 1:1 complex. In addition, the change in p pt
exhibits a nearly linear correlation, Figure (4.7), with the basicity of the amine when
113
expressed in terms of the base proton affinity.35 Although one expects the degree of
proton transfer to correlate with the basicity of the amine to some extent, there is no
fundamental reason to expect a linear relationship across the full range of relevant p pt
values given the relatively small data set that is available and the fact that only neutral
pair complexes are included.
r3
(a)
o
-2
o
1
•
-0.8
-1
1
1
1
-0.6
-0.4
-0.2
U
0.0
Ppt [A]
r260|
(b)
03
-245£
3 .---'"'
- 230 ••§
2 X
4
1 ..-"°
y = 77.16s + 255.36 - 2 1 5 ^
ao
R2 = 0.99
**
0
P
-0.8
'
_*-'
JS
CM
<>'''
1
'
1
-0.6
-0.4
-0.2
iUV
0.0
£
^
pp,[A]
Figure 4.7 The degree of proton transfer for the (CH3)„H3.„NHN03 series of complexes, calculated from the experimental
[•] and theoretical [o] structures, versus the (a) number of
amine CH3 functional groups, n, and (b) amine proton affinity,
where the value next to the point is the value of ». Theoretical
pp, values were calculated for the MP2/6-311++G(2df,2pd)
structures, without employing the counterpoise correction.
114
Nevertheless, if one assumes that the linear trend shown in Figure (4.7B) holds over the
entire neutral pair to fully proton transferred regime, it is predicted that a base with a
proton affinity of 255.36 kcal/mol would form a proton-sharing complex, and a base with
a proton affinity of -285 kcal/mol would be able to achieve full proton transfer of the
same magnitude, but opposite sign, as that determined for the nitric acid - trimethylamine
complex. Outside of the alkali and alkaline metal oxides, a searched revealed no possible
binding partners with the proton affinity necessary to form a fully proton transferred 1:1
complex.35 Eighteen possible nitrogen containing bases with proton affinities in the
proton sharing range of 250 to 260 kcal/mol were found. However, these bases consisted
of molecules, such as tetramethyldiaminobutane, with molecular masses in the 130 to 220
amu range. Observing the complex formed between nitric acid and such a base with
FTMW spectroscopy is unrealistic, and as a result, testing the trend exhibited in Figure
(4.7B) over the entire proton transfer range is not currently feasible.
Although the conclusions drawn from the previous argument reveal valuable insight, their
strong reliance on structural information obtained from theoretical calculations makes a
second means of assessing the degree of ionization, with a less stringent structural
dependence, desirable. A method utilizing the electron redistribution that occurs upon
complexation, in the form of the projected quadrupole coupling constants, has already
been proposed in the microwave analysis of the nitric acid trihydrate,9 and this
methodology has been utilized to analyze the nitric acid - trimethylamine data presented
in this work. A summary of the argument presented in the nitric acid trihydrate work
follows.
115
The hydration of HNO3 with an infinite number of water molecules, as in Reaction (4.1),
results in an aqueous NO3" ion with Dj/, symmetry. Consequently, the
N quadrupole
coupling tensor has only one unique projection, eqQ, which is coincident with the axis of
symmetry and perpendicular to the plane of the nitrate ion, as shown in Figure (4.8). The
value of eqQ for an aqueous nitrate ion in an infinite dilution at 25°C was determined to
be 0.656 MHz by Adachi et al.36 using NMR relaxation times.
D3„
eqQ = 0.656 MHz
w
/
..
Figure 4.8 Schematic of the symmetry axis and the unique
projection, eqQ, of the 14N electric quadrupole coupling in the
aqueous nitrate ion.
It is possible to compare the value of eqQ in the nitrate ion and the projection of the 14N
quadrupole coupling tensor perpendicular to the nitrate group in any nitric acid complex.
These two values quantitatively show how the electronic distribution around the
14
N
nucleus in the complex resembles that of the fully proton transferred limit, i.e. the NO3"
ion. In theory, the relation of the X-, Y-, and Z-axis of the
14
N quadrupole coupling
tensor to the a-, b-, and c-axis in the complex would have to be known in order to
determine the projection that lies perpendicular to the nitrate group in the complex.
116
However, the effective planar structures of the HN03-(H20)„ [n = 1-3] complexes,7"9
along with the C5 symmetry of the HNO3-NH313 and HN03-N(CH3)3 complexes, simplify
the procedure by aligning the c-axis in each of these complexes with the symmetry axis
of the nitrate group, effectively making it possible to compare Xcc in the complex to eqQ
in the nitrate ion. Although experimental data is not yet available for the (CH3)2HNHN0 3 complex, the theoretical calculations of the previous section predict a global
minimum structure with Cs symmetry, similar to the complexes formed with NH3 and
TMA.
If the experimental structure was found to agree with these predictions, the
present argument could be extended to include any (CH3)2HN-HN03 data collected in the
future.
Unfortunately, the predicted global minimum structure of the nitric acid -
monomethylamine complex has Ci symmetry.
As a result, the full
14
N quadrupole
coupling tensor would need to been known in relation to the nitrate group of the complex
for the present argument to be utilized.
-I V
V
HN03-H20
"- HNO,-<H,0),
HN03-(H20)2
Figure 4.9 The nitric acid mono- and dihydrate structures
determined from experiment, and the theoretical nitric acid
trihydrate structure optimized using the MP2 level of theory
and the 6-311++G(2df,2pd) basis set.
117
Because Laplace's equation holds true over the volume of the nuclei, the sum of a
complex's 14N quadrupole coupling constants must equal zero,
Za„+Z»+Zcc=0
(4-8)
and it is possible to express Xcc as a sum of the two experimentally determined
quadrupole coupling constants.
Zcc=-l\Zaa+
iXbb - Zee)]
(4-9)
Using the quadrupole coupling constants found in Table (4.1) and Equation (4.9), Xcc is
calculated to be 0.377(2) MHz for (CH3)314N-H14N03 complex, which is more than twice
the magnitude of the 0.174(7) MHz determined for the H3N-HNO3 complex
and
corresponds to roughly 60% of the value expected for a fully ionized system. This
conclusion reaffirms that, although the more basic TMA increases the degree of proton
transfer when compared to the complex formed with NH3, it is insufficient to completely
ionize one nitric acid molecule.
Although the two methods for determining the degree of proton transfer utilized in this
work are fundamentally different, they both give similar results for each of the nitric acid
complexes presented. Interestingly, a simple plot of p pt vs. the experimental value of %cc>
Figure (4.10), shows a linear relationship, and extrapolating the available data to the Xcc
fully proton transferred limit (xcc = 0.656 MHz) leads to a proton transfer parameter (ppt
= 0.037 A) that more closely resembles proton sharing than it does the fully transferred
limit.
Given the differences in the two methods, the linear extrapolation of the
relationship between p pt and %cc may be misleading. Indeed while we expect p pt to
118
correlate with Xcc, there is, once again, no fundamental reason to expect a linear
relationship across the full range of relevant values. Therefore, a straight line determined
from the available neutral pair complexes need not extrapolate correctly to systems in the
fully proton transferred regime. However, it is important to note that the values of p and
Xcc are correlated over the range of systems investigated thus far.
NO, (aq)
-0.72
0.656 MHz
- 0.60
j = 0.71 x +0.63
R2 = 0.97
>
HNO,-N(CH3)3
- 0.36
^
O
- 0.24 *"*
HN03-NH33
^ J
•
,
/
^
• HNO^O),,
«
- 0.12
HNOJ-HJO
l
l
1
l
-0.8
-0.6
-0.4
-0.2
VMV
0.0
PPt [A]
Figure 4.10 Proton Transfer vs. Quadrupole Coupling using the
experimental %« values and the p value calculated from the
experimental [•] and theoretical [o] structures.
Acknowledgements
This work was supported by the National Science Foundation, the donors of the
Petroleum Research Fund, administered by the American Chemical Society, and the
Minnesota Supercomputer Institute.
119
References
1) The following reference found 99.7% dissociation at 298 K with a 1:10 ratio of nitric
acid to water, (a) H. S. Harned, B. B. Own, The Physical Chemistry of
Electrolytic Solutions, 3rd Edition, Reinhold Publishing Co., New York, NY,
1958.
2) The following reference found 98% dissociation at 278 K with a 1:20 ratio of nitric
acid to water, (a) N. Minogue, E. Riordan, J. R. Sodeau, J. Phys. Chem. A 2003,
107,4436.
3) H. Yang, B. J. Finlayson-Pitts, J. Phys. Chem. A 2001,105,1890.
4) M. C. Kido Soule, P. G. Blower, G. L. Richmond, J. Phys. Chem. A 2007, 111, 3349.
5) E. S. Shamay, V. Buch, M. Parrinello, G. L. Richmond, J. Am. Chem. Soc. 2007, 129,
12910.
6) R. Bianco, S. Wang, J. T. Hynes, J. Phys. Chem. A 2007,111,11033.
7) M. Canagaratna, J. A. Phillips, M. E. Ott, K. R. Leopold, J. Phys. Chem. A 1998, 102,
1489-1497.
8) M. B. Craddock, C. S. Brauer, K. R. Leopold, J. Phys. Chem. A 2008, 112, 488-496.
9) see the investigation into the nitric acid trihydrate presented in Chapter 3 of this work.
10) X. Zhang, E. L. Mereand, A. W. Castleman Jr. J. Phys. Chem. 1994, 98, 3554.
11) P. R. McCurdy, W. P. Hess, S. S. Xantheas, J. Phys. Chem. A 2002,106, 7628.
12) G. Ritzhupt, J. P. Devlin, J. Phys. Chem. 1977, 81, 521-525.
13) M. E. Ott, K. R. Leopold, J. Phys. Chem. A 1999,103,1322-1328.
14) (a) B. S. Ault, G. C. Pimentel, J. Phys. Chem. 1973, 77, 57. (b) B. S. Ault, G. C.
Pimentel, J. Phys. Chem. 1973, 77,1649.
120
15) A. C. Legon, Chem. Soc. Rev. 1993,153-163.
16) J. A. Phillips, M. Canagaratna, H. Goodfriend, A. Grushow, J. Almlof, K. R.
Leopold, J. Am. Chem. Soc. 1995,117,12549.
17) CRC Handbook of Chemistry and Physics, 88th Edition (Internet Version 2008), D. R.
Lide, editor; CRC Press/Taylor and Francis, Boca Raton, FL.
18) (a) R. Adams, B. K. Brown, Organic Synthesis, 2nd Edition, H. Gilman, A. H. Blatt,
editors; Wiley, New York, NY, 1941. (b) P. H. Clippard, Ph.D. Thesis, The
University of Michigan, Ann Arbor, MI, 1969.
19) The MP2/6-311++G(2df,2pd) level of theory and basis set, with the Hartree-Fock
population densities, predicts an a-type dipole moment of 6.14 D and a b-type
dipole moment equal to 1.38 D.
Although 1.38 D seems sufficient for our
experiment, errors upwards of 25% are not unheard of using this theoretical
method, and it is not unreasonable to believe that the smaller b-type moment may
have been a major, if not the only, factor leading to our inability to observe b-type
transitions.
20) (a) H. M. Pickett, J. Mol. Spec. 1991,148, 371. (b) Program downloaded from the
Programs for ROtational SPEctroscopy (PROSPE) website
(http://www.ifpan.edu.pl/~kisiel/prospe.htm).
21) W. Gordy, R. L. Cook, Microwave Molecular Spectra, 3rd Edition, John Wiley &
Sons, New York, NY, 1984.
22) C. H. Townes, A. L. Schawlow, Microwave Spectroscopy, Dover Publications, New
York, NY, 1975.
121
23) J. K. G. Watson, J. Chem. Phys. 1967, 46, 1935-1949.
24) Fitting all three distortion constants resulted in a standard deviation of 0.0024 MHz
and a value of 5j close to zero, 0.000039(15) MHz.
25) Gaussian 03, Revision C.01, Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria,
G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, Jr., J. A.; Vreven, T.; Kudin,
K. N.; Burant, J. C ; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.;
Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.;
Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.;
Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.;
Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C ; Jaramillo, J.; Gomperts,
R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C ;
Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.;
Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C ;
Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.;
Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.;
Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.;
Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.;
Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C ; and Pople, J.
A.; Gaussian, Inc., Wallingford CT, 2004.
26) C. M0ller, M. S. Plesset, Phys. Rev. 1934, 46, 618.
27) J. S. Binkley, J. A. Pople, Int. J. Quantum Chem. 1975, 9, 229.
122
28) (a) The in plane
single
N-OH-N-H
N-OH-N-C
angle was used for the H3N-HNO3 complex, (b) The
angle was used for the (CH3)H2N-HN03 complex, (c) The
single N-0 H -N-H angle was used for the (CH3)2HN-HN03 complex, (d) the in
plane N-0 H -N-C angle was used for the (CH3)3N-HN03 complex.
29) (a) M.-T. Nguyen, A. J. Jamka, R. A. Cazar, F.-M. Tao, J. Chem Phys. 1997, 106,
8710. (b) F.-M. Tao, J. Chem. Phys. 1998, 108, 193. (c) R. A. Cazar, A. J. Jamka,
F.-M. Tao, J. Phys. Chem. A 1998,102, 5117.
30) M. E. Ott, M. B. Craddock, K. R. Leopold, J. Mol. Spectrosc. 2005,229, 286.
31) I. J. Kurnig, S. Scheiner, Int. J. Quantum Chem. Quantum Biol. Symp. 1987,14, 47.
32) S. W. Hunt, K. J. Higgins, M. B. Craddock, C. S. Brauer, K. R. Leopold, J. Am.
Chem. Soc. 2003,125,13850.
33) C. S. Brauer, M. B. Craddock, J. Kilian, E. M. Grumstrup, M. C. Orilall, Y. Mo, J.
Gao, K. R. Leopold, J. Phys. Chem. A 2006,110,10025.
34) A. P. Cox, J. M. Riveras, J. Chem. Phys. 1965, 42, 3106-3112.
35) NIST Chemistry WebBook, NIST Standard Reference Database, Number 69, P. J.
Linstrom, W. G. Mallard, editors; National Institute of Standards and Technology,
Gaithersburg MD, 2005. http://webbook.nist.gov
36) A. Adachi, H. Kiyoyama, M. Nakahara, Y. Masuda, H. Yamatera, A. Shimizu, Y.
Taniguchi, J. Chem. Phys. 1988, 90, 392.
123
Chapter 5
A Microwave and Ab Initio Investigation of (CH3)3CCN-S03:
Proton Affinity as a Measure of Interaction Strength in Partially
Bound Lewis Acid-Base Complexes
124
Abstract
The microwave spectrum of the partially bound (Cfb^CCN-SOs complex has been
recorded. The nitrogen - sulfur bond length is 2.391(23) A, which is almost half way
between the weakly bound N2-SO3 complex and the more strongly bound (CF^N-SOs
complex. A simple Townes and Dailey analysis of the 14N nuclear quadrupole coupling
constant gives a value of 0.18 e" transferred away from the nitrogen of the ( C I ^ C C N
moiety upon complexation. Ab initio calculations using the MP2/aug-cc-pVTZ level of
theory and basis set yield a binding energy of 11.0 kcal/mol for the complex, which is
only a fourth of the binding energy calculated for (CH3)3N-S03. As noted previously for
the HCCCN-SO3 complex, comparison of the nitrogen - sulfur bond length with those in
a series of SO3 adducts indicates that the proton affinity of the Lewis base is a good
predictor of the complex's properties. Indeed, the spectrum of the (CH3)3CCN-S03
complex was readily located from a simple analysis of the proton affinity of the
(CH3)3CCN monomer.
125
Introduction
The bonding interactions of donor - acceptor molecular complexes are of fundamental
importance to understanding a wide range of chemical phenomena.
Although our
understanding of these interactions in their chemically1'2 and weakly3'4 bound limits has
advanced dramatically over the course of the past century, comparatively less is known
concerning the "partially bound" systems that bridge these two extremes.5 Recently a
number of complexes formed between sulfur trioxide and a nitrogen containing Lewis
base have been investigated, and the interaction strengths observed over the entirety of
the series have provided valuable insight into the evolution of the sulfur - nitrogen dative
bond.6"12
van der Waals Limit
Chemically Bound Limit
Lower Base Proton Affinity
Higher Base Proton Affinity
;H
N 2 -S0 3 «
(CHJWJ-SO,
HCN-SOj
T
C^sN-SO,
HCCCN-S0 3 *
1
^CHJCN-SOJ
H 3 N-S0 3
Figure 5.1 The previously observed partially bound Base-S03 complexes in the
Lewis Acid-Base series.
126
Earlier work concerning the pyridine - sulfur trioxide complex observed a correlation
between the physical properties associated with the intermolecular interaction of the
complex and the energy gap between the donor and acceptor orbitals.
This, in effect,
made it possible to express the physical properties of the experimentally observed Base SO3 complexes in terms of the Lewis base's donor orbital energy, and consequentially, it
would be possible to predict the physical properties of additional systems for which this
energy is known. However, quantifying the energy of the nitrogen lone pair orbital can
often be difficult experimentally.
A subsequent investigation into the HCCCN-SO3
complex10 established it was possible to relate the properties of the complex to other
measures of relative basicity. Specifically, it was determined that the gas phase proton
affinity, for which experimental values are much more readily available,13 could be used.
Although the conclusions drawn in the investigation of the C5H5N-SO3 complex related a
number of physical properties to the orbital energy gap, the later HCCCN-SO3 work dealt
exclusively with the correlation between the base proton affinity and the nitrogen - sulfur
bond length. The data represented in Table (5.1) and Figure (5.2), however, make it
possible to relate the base proton affinity to five physical properties associated with the
strength of the intermolecular interaction of the complexes: (A) the nitrogen - sulfur
bond length, RNs, (B) the electrons transferred away from the nitrogen atom of the base
upon complexation, (C) the angular out-of-plane distortion of the S0 3 moiety, a, (D) the
binding energy of the complex, Ebind, and (E) the energy required to distort the free
monomers to their corresponding geometries in the complex, EdiSt.
In each case,
distinctive patterns are observed over the range of physical properties determined for the
127
available complexes, and furthermore, the observed patterns suggest the properties of the
system will drastically differ from those previously studied when a complex is formed
between S0 3 and a Lewis base with a proton affinity in the range of 185 to 205 kcal/mol.
Thus, the present work endeavors to test these predicted trends through the microwave
investigation of the complex formed between trimethylacetonitrile [(CH3)3CCN, proton
affinity =193.8 kcal/mol]13 and S0 3 .
Sum of the N and S van der Waals Radii
-^
S
°<
2
3
(A)
2.50 -
£
=f »1(D)
3.00 -
*•
I*
u
30
!*
20
6 7
2.00
2
Chemically Bound Limit
3
•a
1.50
110
«»,
0.75
£
0.60
i
0.45
^
0-JO
h
170
200
230
Proton Affinity of the Base [kcal/mol]
«:
110
==.
140
(B)
3
-6.0
S -9.0
100
W
3 <»
90
(Q
85
140
170
3 4
S3
105
2
230
S -3.0
3
I °-°°
95
200
170
0.0
2
2
0.15
110
140
200
230
Proton Affinity of the Base [kcal/mol]
(E)
-12.0
(1) N 2 - S 0 3
(5) H3N-SO3
(2) HCN-SOj
(6)H5CSN-S03
(3) HCCCN-SO,
(7) ( C H ^ N - S O ,
(4) HjCCN-SO,
Figure 5.2 The proton affinity of the base plotted against five physical properties of the Base-S0 3
series of complexes. All values, except E ^ for N 2 -S0 3 which was calculated as part of this work,
are taken from references [6] through [11].
128
Table 5.3 Physical Properties of the Base-SQ3 Series of Complexes
Electron
Base
RNS[A]
[kcal/mol]"
N(CH 3 ) 3
NC 5 H 5 d
NH 3 f
NCCH 3 g
e
NCCCH h
NCH g
N2
j
Transfer [e"]
b
a [deg]
Ebind
E
dist
[kcal/mol]
[kcal/mol]
226.8
222
1.912(20)
1.915(1)
0.58
0.54
100.1(2)
98.91(2)
40.0
28.4
-11.34
-9.18
204.0
186.2
1.957(23)
2.466(16)
0.36
97.6(4)
21.4
-6.22
0.16
92.0(7)
10.2
-0.77
179.5
170.4
2.567(13)
2.577(6)
2.934(12)
0.13
0.13
0.04
91.7(4)
8.5
8.2
-0.42
118.0
91.8(4)
90.40(4)
3.2
-0.37
-0.01 j
(a) Values takenfromthe "NIST Chemistry WebBook", reference [13].
(b) Determined from a Townes and Dailey analysis of the nuclear quadrupole coupling constants.
(c) Calculatedfromthe MP2/aug-cc-pVTZ energies of the complexes and their corresponding monomers.
(d) reference [9] (e) reference [8] (f) reference [6] (g) reference [7]
(h) reference [10] (i) reference [11] (j) Calculated as part of this work.
Experimental Results
The microwave spectrum of the (CH3)3CCN-S03 complex was recorded using a pulsednozzle Fourier transform microwave spectrometer, the details of which have been given
elsewhere.
An experimental configuration similar to those employed for the previous
Base-S0 3 complexes was utilized to introduce the nitrile and S0 3 separately into the
supersonic expansion, effectively limiting mixing times.6"11 Specifically, argon carrier
gas was passed over a sample of solid polymerized S0 3 . The resulting seeded gas was
held at a stagnation pressure of 2.2 atm and pulsed into the instrument through a 0.8 mm
pinhole, with a repetition rate of 5 Hz. In addition, the vapor from a liquid sample of
(CH3)3CCN [Pvap= 196 torr]13 was continually introduced into the early parts of the
expansion via a stainless steal needle with an inner diameter of 0.016 inches. The
(CH3)3CCN-S03 frequencies were collected with 500 to 1000 gas pulses, and signal was
averaged over 3000-6000 FID's.
129
The
experimental
B
rotational
constants
of
the
trioxide15'1
sulfur
and
trimethylacetonitrile17"19 monomers, along with the nitrogen - sulfur bond length
estimated from the trend shown in Figure (5.2A), were used to predict the J = 4 <— 3
transition frequency of the (CH3)3CCN-S03 complex, a partial spectrum of which has
been given in Figure (5.3). Successive transitions, up to J = 11«—10, were observed in
increments of 2B. In addition to the hyperfine structure resulting from the 14N nuclear
quadrupole moment, the observed transitions were split into multiple closely spaced K
states, characteristic of a symmetric top complex with freely rotating nitrile and S0 3
moieties.
1,'s—4
= 4«-3
|K|, F'«-F"
1,4—3
J
r
3579.825
° ' M l!
1,3—2
0,3—2
[LJ\
12,5—4
2,3-2
;
1
1
3579.950
3580.075
3580.200
Frequency [MHz]
Figure 5.3 The partial spectrum of the J = 4«-3 rotational transition of
(CH3)3CCN-S03 complex.
As a result of the internal rotation of the monomers, the projection of the system's total
angular momentum, K, is expressed as the sum of the projections of the SO3 and
(CH3)3CCN angular momenta, K = ma + nib. Because the oxygen atoms of the S0 3
130
moiety are spinless, the values of ma are limited to multiples of three, i.e. ma = 0, ±3.
However, values of mb equal to 0, ±1, and ±2 were observed for (CH3)3CCN.
Assignments of the K states in which ma is equal to zero, |K| = \mb\, were readily made
from the observed hyperfine splittings and transition peak intensities. Unambiguous
assignments of the less intense lines, where ma = ±3, could not be made due to the
overlap of key hyperfine components with those of the |K| = \ntb\ states. Consequentially,
the analysis incorporates eighty-one |K| = |/»j| lines corresponding to eight AJ = 1
transitions, spanning the 3.5 to 10 GHz frequency range.
Fitting of the observed transition frequencies was initially performed using an expression
similar to that employed in the microwave analysis of the CF3H-NH3 complex,
v = 2(j + liB-DJKK2
-DJmm2b - DJKn,b Kmb ) - 4D, (j +1)3 +AEQ
(5.l)
where the values of D^ are the quartic centrifugal distortion constants, and AEg is the
nuclear quadrupole coupling energy difference calculated for a 14N nucleus located on the
axis of symmetry.21 The lack of definitive assignments for the transitions in which ma
does not equal zero resulted in a high correlation of the DJK, DJm , and DJKm constants.
However, the sum of these three constants was found to be invariant regardless of their
specific values.
As a result, the transition frequencies were fit using an effective
distortion constant, which represents the sum of the three individual constants.
v = 2{J + lXi? - DeffK2)-
AD j (J +1)3 + AEQ
(5.2)
The transition frequencies used in the final analysis have been given in the appendix to
this chapter, and the resulting constants can be found in Table (5.2).
131
Table 5.2 Spectroscopic (CH3)3CCN-S03 Constants*
B
447.499218(65)
Dj
0.00004626(37)
0.001949(16)
eQq
-3.3596(26)
CT(RMS)
0.003
(a) All values are in MHz.
Theoretical Methods and Results
Ab initio calculations have previously been used to supplement the spectroscopic analysis
of the series of complexes formed between SO3 and a nitrogen containing Lewis
base.' '
For each complex and its corresponding free monomers, second-order IVfoller-
Plesset (MP2) perturbation theory and the Dunning's correlation consistent aug-cc-pVTZ
basis set were employed to determine the energy and optimized equilibrium geometry. In
order to draw accurate comparisons with these previous studies, calculations were carried
out on the (CH3)3CCN-S03 complex utilizing the same model chemistries and the
Gaussian '03 (G03) program package.22
Structural optimizations of the (CH3)3CCN-S03 complex predict a system in which the
monomers are interacting via an intermolecular nitrogen - sulfur bond, which is
consistent with the experimental results of the series. The structure of the complex was
found to converge with the oxygen atoms and methyl groups in a staggered, C3v
symmetric, configuration.
In addition, the complex was also optimized in the C3v
symmetric eclipsed configuration, and the energy difference, which to a good
approximation represents the barrier to internal rotation, is predicted to be effectively
132
zero, less than 0.002 kcal/mol.
The optimized geometries and energies of both
conformations have been given in Figure (5.4).
^-L. rf
f~*^^%
-i
(A) E =-873.2568354 hartree,
•
^ N S "=
jn#
^ w
2.402 A, a = 92.79°
C_.C
"1
rf
W-„^^^^s^^.^,
c
(B) E = -873.2568324 hartree ,
c
1*NS
w.
= 2.402 A, a = 92.79°
Figure 5.4 The structures of the (A) global minimum staggered and
(B) eclipsed (CI^CCN-SOs complex optimized using MP2/aug-ccpVTZ and viewed along the b- and z-axis.
Correcting for the basis set superposition error during the structural optimization resulted
in small changes in the calculated energy, intermolecular bond length (RNS), and N-S-O
bond angle (a) of the complex. It has also been noted that the standard correlation
consistent basis sets give unacceptable errors when calculating the energy of molecules
containing second-row atoms.23 For this reason, the optimizations of the S0 3 monomer
and the (CH3)3CCN-SC«3 complex were also performed using the corrected form of the
basis set, aug-cc-pV(T+d)Z, on the sulfur atom. The inclusion of the extra diffuse dorbital on the sulfur atom resulted in small changes in the calculated values of the energy,
RNS,
and a.
133
Although the energy of the system may be more accurately described with these
modifications to the standard correlation consistent basis set, the calculations were
performed with the intent of drawing conclusions concerning the relative changes in
energy and structure over the Base-S03 series of complexes. The qualitative information
obtained from the energies and the quantitative agreement between the experimental
structures and those calculated using the aug-cc-pVTZ basis set are more than sufficient
to meet this goal. Therefore, the structures and energies of the previously determined
Base-S03 complexes were not recalculated with the modified basis set on the sulfur atom
or corrected for the basis set superposition error. A list of the calculated energies and
physical properties of the (CEb^CCN-SCh complex has been given in Table (5.3), and
the Cartesian coordinates of the optimized equilibrium structures, both those of the
complex and those of the free monomers, have been given in the appendix to this chapter.
From the energies of the optimized (CH3)3CCN-SC>3 complex and the free monomers, the
binding energy of the system has been calculated using the following expression,
F
where Eg
and
_ Iffree
E^h
CCN
are
I J?free
_ pcomplex
^c ->\
th e MP2 energies of the SO3 and ( C t ^ C C N moieties at
their fully optimized free monomer geometries, and Ecomplex is the energy of the fully
optimized global minimum complex in the staggered configuration. Additionally, the
energy it takes to distort each of the free monomers to their corresponding geometry in
the complex, Edist, has been determined using Equation (5.4).
f
_ (Ffree _ pcomplex \
^dist -V^SO-,
^SOi
)
I j?free
\ (CH^CCN
+ n
^complex
\
^(CH,),CCN)
,~ A \
W^J
134
A comparison of the optimized free (CH3)3CCN monomer structure to its geometry in the
complex shows minimal changes upon complexation, which is consistent with the small
values calculated for Edist. The S0 3 monomer, on the other hand, shows minimal changes
in its Rso bond lengths, less than 0.003 A, upon complexation but significant changes in
its planarity, resulting in a calculated E^st value of approximately -1 kcal/mol.
Table 5.3 Calculated Energies and Physical Properties of the (CH3)3CCN-SO3 Comple>t a
Eclipsed
Staggered
aug-cc-pVTZ
aug-cc-pVTZ
aug -ccrpV(T+d)Z
aug-cc-pVTZ (CPC)
Ebmd [kcal/mol] b
11.5
11.0
9.7
11.0
Ejis, [kcal/mol]
c
-1.27
-0.99
-0.83
-0.99
(CH3)3CCN
d
0.05
0.04
0.04
0.04
1.22
0.95
0.79
0.95
454.249
2.350
3.1
446.553
2.402
2.8
439.977
2.448
2.5
446.553
2.402
2.8
so 3
d
B[MHz]
RNS
[A]
a[°]
(a) All calculations were performed using the MP2 level of theory.
(b) Calculated using the MP2 energies and Equation (5.3)
(c) Calculated using the MP2 energies and Equation (5.4)
(d) Ejjs, calculated for the acid and base independently, [kcal/mol].
Structure Analysis
A limited amount of structural information is available from an analysis of the parent
(CH3)3CCN-S03 spectrum alone. The nitrogen - sulfur bond distance has been obtained
from the complex's moment of inertia about its b-axis, which is related to the
experimentally determined B rotational constant via Ibb = hf/S^B.
As a first step in
calculating RNS, the distance between the monomers' centers of mass, Rcm, was
established using the expression for the complex's zero-point averaged moment of
inertia,
135
(5.5)
where Ms is the reduced mass of the complex, Ms = {m^m^^c^Kjn^
+ m^CH^CCN),
% and y are the excursion angles representing the large amplitude motion of the
monomers, and the values of Igg correspond to the moments of inertia of the designated
systems about their g* inertial axis. The coordinates used to describe the angles and
bond lengths of the (CH3)3CCN-S03 complex have been given in Figure (5.5).
Figure 5.5 Diagram of the angles (a, %, and y) and
lengths (R^) in the (CH3)3CCN-S03 complex.
136
The zero-point averaged Ibb value of the complex is dominated by the first term of
Equation (5.5), MJR^
\ , with the trigametric functions of x, and y accounting for small
corrections to the overall value. As such, it is possible to determine an accurate distance
between the monomers' centers of mass, Rem, using their moments of inertia and
estimated values of the excursion angles.
Given the limited structural changes that are predicted to occur in the ( C l ^ C C N
monomer upon complexation, the value of j ^ H ^ C C N is readily available from the free
monomer's B rotational constant,17"19 and j ^ H ^ C C N has been calculated using the gas
phase monomer structure of Nugent et al.17'2A Unlike the (CHa^CCN monomer, SO3 is
predicted, both theoretically and through the trends exhibited by the Base-SC>3 series, to
undergo structural changes in the form of out-of-plane distortion upon complexation. As
a result, the values of I^3 and 1^
used in Equation (5.5) are dependent upon the angle
a in the complex. The quantitative agreement between the experimentally determined B
rotational constant and that predicted by the MP2/aug-cc-pVTZ optimized geometry of
the complex make it reasonable to assume that the value of a in the experimental
structure will be similar to the predicted value. As a result, R^, has been determined
using the values of I^3 and I^3 calculated for the theoretical value of a, 92.8°. The
possibility of introducing error into the experimental bond length through the use of the
theoretical value of a has been addressed by determining similar R ^ distances with
values of a equal to 91.4° and 94.2°. These values are equal to ±50% of the theoretical
137
out-of-plane S0 3 distortion, and the small differences in Rcm associated with this range in
a has been incorporated into the experimental RNS error.
For the (CH3)3CCN-S03 complex, a range of possible S0 3 excursion angles, %, are
possible depending on the strength of the intermolecular interaction. In the case of a
strong nitrogen - sulfur bond, the S0 3 excursion angle would be effectively localized to
zero. Conversely, a weak intermolecular interaction could be assumed to have a S0 3
excursion angle similar to that of the Ar-S0 3 van der Waals complex, which has an
•ye
experimentally determined value of % equal to 15.6 degrees.
Although % in the
(CH3)3CCN-S03 complex is most likely between these limiting cases, the exact value
cannot be determined from the available spectroscopic data. Therefore, values of % equal
to 0°, 7.8°, and 15.6° have been used when determining the distance between the S0 3 and
(CH3)3CCN centers of mass. As previously mentioned, the trigonometric functions of %
only account for small corrections to the overall R<;m distance, and although a range of
values are used in determining the bond distance, the small differences that occur over
this estimated range have, once again, been included in the reported error.
Much like %, only an approximate value is needed for the (CH3)3CCN excursion angle, y.
In the case of weakly bond complexes, it is often possible to obtain such an estimate
utilizing the tensor projection formula,
eOff-** = eQq0 (P2 cos y) = \eQq0 (3(cos2 y) -1)
(5.6)
138
and the quadrupole coupling constants of the complex, eQqcomplex, and the free monomer,
eQq0. A value of y equal to 21.6° is calculated for the (CH3)3CCN-S03 complex using
this method. However, such a large excursion angle seems physically questionable given
the significant mass of the (CFb^CCN monomer and the predicted strength of the
bonding interaction.
In practice, the determination of y through the application of
Equation (5.6) is only valid for systems in which a trivial amount of electronic
redistribution occurs upon complexation.
For the (CH3)3CCN-S03 complex, the
observed trends of the Base-SC>3 series and the Townes and Dailey analysis of the
electron transfer, which will be discussed in detail shortly, suggest the system has
sufficient electronic redistribution to give erroneous values of y from the application of
Equation (5.6). For this reason, a second method of determining the nitrile excursion
angle has been employed.
Although the strength of the intermolecular bond changes significantly over the entire
Base-S03 series, it can reasonable be assumed that the RNS bending force constant would
be similar for systems in which the bonding does not drastically differ.
Such an
assumption makes it possible to determine an acceptable estimate of the (CH3)3CCN
excursion angle from the ratio,26
1
FiCH^CCN
( r(C//3)3CCW \J
—
(5 7)
\J-'J
Those
/base
V
*bb
J
where ybase and I*™e are the experimentally determined excursion angle and the free
base's moment of inertia for a Base-S0 3 system with bonding similar to that of the
139
(CH3)3CCN-S03 complex.
Using the experimentally determined value of the HCN
moment of inertia and the excursion angle in HCN-SO3, y = 8.3(±4.6)°, a (CH3)3CCN
excursion angle of 4.1 (±2.3)° has been predicted for the (CH3)3CCN-S03 complex. A
similar procedure was utilized in the microwave investigation of the HCCCN-S0 3 and
CH 3 CN-S0 3 complexes.7
With values for each of the parameters in Equation (5.5), it is now possible to calculate
the distance between the SO3 and (CH3)3CCN centers of mass, and subsequently, the RNS
bond length can be determined from,
D
_ Bcomplex
">NS ~ ^cm
pSOi _ Tf(CHl\CCN
R
cm
cm
R
(c
n\
\J-')
(CM \. CCN
where Rlm
3h
is the distance from the nitrogen atom to the center of mass in the free
(CH3)3CCN monomer,17 and R^
is the distance between the sulfur atom and the center
of mass in each of the S0 3 geometries in the complex (i.e. for a = 91.4, 92.8, and 94.2°).
A nitrogen - sulfur bond length of 2.391(23) A was obtained after averaging the bond
lengths determined using the range of a, %, and y values. The reported error represents
the largest deviation between the average RNs bond length and those calculated for
specific values of the angles. The particular RNs bond lengths used in the determination
are shown in Figure (5.6), and a list of the numerical values calculated for each value of
a, x, and y has been included in the appendix to this chapter.
140
2.450 -
2.425 O oO °° °
ooo
~ 2.400 0 0 0
2.375 -
2391(23)1
O Oo ° 0 O
Ooo
2.350 Figure 5.6 The nitrogen - sulfur bond lengths determined using all
combinations of the angles a (1.4,2.8,4.2), % (0, 7.8,15.6), and y (1.8,
4.1, 6.4). The x-axis is an arbitrary axis used to accentuate the small
differences in the calculated RNS due to the angles used.
Electron Redistribution
As previously mentioned, a non-trivial amount of electronic redistribution is predicted to
occur in the (CH3)3CCN-S03 system upon complexation.
In principle, the
14
N
quadrupole coupling constants contain information that is directly related to the amount
of electron transfer, and although it is only an approximation, the methodology of
Townes and Dailey21,27'28 has previously been used to quantify the electron transfer that is
occurring upon complexation in each of the Base-S0 3 complexes.
The quadrupole
coupling constant of the (CH3)3CCN-S03 complex and that of the free nitrile19 have been
used to perform a similar analysis on the present system.
141
Using the methodology of Townes and Daily, the quadrupole coupling constant of the
sp hybridized 14N nucleus in the free (CH3)3CCN monomer may be written,
eQq(WcN
= ( 2 f l 2 +b[l-ai]-.a)eQq2io
(5.8)
where eQq2io is the quadrupole coupling constant for a single 2pz electron in atomic
nitrogen, a and b are the populations of the % and sp orbitals involved in the C=N bond,
and a] is the amount of s character in each of the hybridized sp orbitals. For the
(CH3)3CCN-S03 complex, the wave function of the dative bond can be estimated as the
normalized linear combination of the donor and acceptor orbitals,
VDB=atN+Ms
(5.9)
where a and p are the populations of each orbital.
Utilizing Equation (5.9), an
expression similar to that for the free nitrile is obtained for the quadrupole coupling
constant of the nitrogen nucleus in the complex.
e&r*~
={2a2a] + b[\-a2s]-a)eQqm
(5.10)
Assuming the populations of the nitrogen bonding orbitals (a and b) in the free nitrile are
not significantly different from those in the complex, the change in the quadrupole
coupling constant due to complexation may be written
AeQq = (eQq™^ - eQq^CCN
) = 2a) (a2 - \)eQq2XQ
(5.11)
Using an atomic nitrogen quadrupole coupling constant of -9 MHz,28,29 and assuming a
system with pure sp hybrid orbitals {i.e. a) =\), a2 is calculated to be 0.91 e" for the
system.
By defining the amount of electron transfer as n = 2(1-a 2 ), the analysis
determines 0.18 e" are transferred away from the nitrogen upon complexation.
142
Discussion
Microwave spectroscopy and ab initio calculations have been used to investigate the gas
phase (CH3)3CCN-S03 complex. The analysis of the spectrum yielded physical data
concerning the molecular and electronic structure, while the ab initio calculations
determined the energy of the system and supplemented the experimental results. From
the zero-point averaged moment of inertia, the nitrogen - sulfur bond length of the
complex was calculated to be 2.391(23) A. A comparison of this value with those
obtained for a series of Base-S03 complexes, Figure (5.7A), shows that the bond length
of the (CH3)3CCN-SC>3 complex follows the trend predicted from the base proton affinity.
Additionally, the bond length was determined to be nearly halfway between the strongly
and weakly bound limits, 0.480 A longer than the corresponding (Ct^N-SOs bond and
0.542 A shorter than that of the N2-SO3 complex.
A Townes and Dailey analysis of the 14N quadrupole coupling constant determined 0.18
e" were transferred away from the nitrogen upon complexation. Once again, this follows
the qualitative trend established for the Base-SC>3 complexes, Figure (5.7B). However,
unlike the RNS bond length, which predicts the (CH3)3CCN-S03 complex to be roughly
half way between the bonding limits in terms of interaction strength, the amount of
electron transfer predicts the complex to be only a fourth of the way along the
progression from a weakly bound to a strongly bound complex.
The value of the N-S-0 angle (a) and the energies, predicted by the ab initio calculations,
show trends similar to that of the electron transfer. Considering the transfer of electrons
143
from the base to the S0 3 moiety is directly related to the evolution of the electronic
structure from a trigonal planar configuration to that of a tetrahedral, it is not surprising
that the properties would display some degree of correlation.
However, the trends
exhibited for each of the physical properties, taken over the entire series of complexes,
suggest that the molecular indicators of bonding strength (i.e. RNs bond length) and those
indicative of the electronic structure are fundamentally different means of describe the
interaction. Although such a conclusion should not come as a surprise, it bares reflection
upon when using intermolecular bond length as the only means of quantifying the
interaction strengths of the dative bond in gas phase complexes.
Sum of the N and S van der Waals Radii
3.50 -,
i—i
3.00 -
1
2
<a 2-50
3
4
• • • o
(A)
5
*** 2.00
Chemically Bound Limit
6 7
**
ST
©
50 -
s
*•
(D)
•
6
u
•*,
1
S
20
•
10
l
•
1.50 •
10
S
0.75 -
£
0.60 0.45 -
5
0.30
•
2
"3
(B)
000 A
105 -]
95
s
s
1
i-
•
i
(Q
90
110
' 1 0
•
• *
170
200
140
1
170
230
2
200
34#
S -3.0
140
Pi -oton Affinity
170
200
230
of the Base [kcal/mol]
« -9.0
•s
W
-12.0
230
°
5
SS
•
M. • " "
100
b
"
1 L0
3 « „
1 °" 15
£
140
*
Pi-oton Affinity of the Base [kcal/mol]
•
OB
g
u
*"*
B
7
6
•
(E)
7
•
(1) IVso,
(0) (CH^CCN-SOj
(2) IICN-SOj
(5) H3N-SO,
(3)B [CCCN-SO3
((OHJCSN-SOJ
(4) 1I J C C N - S O J
(7)
(CH^JN-SOJ
Figure 5.7 The proton affinity of the base plotted against the physical properties of the Base-S03
series of complexes. The values for the (CH3)3CCN-S03 complex [o] are taken from this work. All
other values [•] are takenfromtheir respective references.
144
Acknowledgements
This work was supported by the National Science Foundation, the donors of the
Petroleum Research Fund, administered by the American Chemical Society, and the
Minnesota Supercomputer Institute.
References
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Crystals: An Introduction to Modern Structural Chemistry, 3 rd Edition, Cornell
University Press, Ithaca, NY, 1960.
2) J. N. Murrell, The Chemical Bond, 2nd Edition, Wiley, New York, NY, 1985.
3) see for example, "Structure and Dynamics of Van der Waals Complexes," Faraday
Discussions 1994, No. 97.
4) see for example, (a) "van der Waals Molecules," Chem. Rev. 1988, No. 6. (b) "van der
Waals Molecules II," Chem. Rev. 1994, No. 7.
5) (a) K. R. Leopold, Advances in Molecular Structure Research, Vol. 2, M. Hargittai, I.
Hargittai, editors; JAI Pres, Greenwich, CT, 1996.
(b) K. R. Leopold, M.
Canagaratna, J. A. Phillips, Ace. Chem. Res. 1997, 30, 57-64.
6) M. Canagaratna, J. A. Phillips, H. Goodfriend, K. R. Leopold, J. Am. Chem. Soc. 1996,
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8) D. L. Fiacco, A. Toro, K. R. Leopold, Inorg. Chem. 2000, 39, 37-43.
145
9) S. W. Hunt, K. R. Leopold, J. Phys. Chem. A 2001,105, 5498-5506.
10) S. W. Hunt, D. L. Fiacco, M. Craddock, K. R. Leopold, J. Mol. Spectrosc. 2002, 212,
213-218.
11) M. B. Craddock, C. S. Brauer, K. J. Higgins, K. R. Leopold, J. Mol. Spectrosc. 2003,
222, 63-73.
12) C. S. Brauer, M. B. Craddock, K. J. Higgins, K. R. Leopold, Mol. Phys. 2007, 105,
613-625.
13) NIST Chemistry WebBook, NIST Standard Reference Database, Number 69, P. J.
Linstrom, W. G. Mallard, editors; National Institute of Standards and Technology,
Gaithersburg MD, 2005. http://webbook.nist.gov
14) J. A. Phillips, M. Canagaratna, H. Goodfriend, A. Grushow, J. Almlof, K. R.
Leopold, J. Am. Chem. Soc. 1995, 117, 12549.
15) V. Meyer, D. Hermann, H. Dreizler, Z. Naturforsch. 1991,46a, 710.
16) S. W. Sharpe, T. A. Blake, R. L. Sams, A. Maki, T. Masiello, J. Barber, N.
Vulpanovici, J. W. Nibler, A. Weber, J. Mol. Spectrosc. 2003,222,142.
17) L. J. Nugent, D. E. Mann, D. R. Lide, J. Chem. Phys. 1962, 36(4), 965.
18) Z. Kisiel, Chem. Phys. Lett. 1985,118(3), 334.
19) Z. Kisiel, E. Bialkowska-Jaworska, O. Desyatnyk, B. A. Pietrewicz, L.
Pszczolkowski, J. Mol. Spectrosc. 2001,208, 113.
20) G. T. Fraser, F. J. Lovas, R. D. Suenram, D. D. Nelson Jr., W. Klemperer, J. Chem.
Phys. 1986, 84(11), 5983.
146
21) C. H. Townes, A. L. Schawlow, Microwave Spectroscopy, Dover Publications, Inc.,
New York, 1975.
22) Gaussian 03, Revision C.01, Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria,
G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, Jr., J. A.; Vreven, T.; Kudin,
K. N.; Burant, J. C ; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.;
Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.;
Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.;
Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.;
Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C ; Jaramillo, J.; Gomperts,
R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C ;
Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.;
Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C ;
Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.;
Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.;
Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.;
Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.;
Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C ; and Pople, J.
A.; Gaussian, Inc., Wallingford CT, 2004.
23) T. H. Dunning, K. A. Peterson, A. K. Wilson, J. Chem. Phys. 2001, 114, 9244.
24) S. L. A. Adebayo, A. C. Legon, D. J. Millen, J. Chem. Soc. Faraday Trans. 1991,
87(3), 443-447.
147
25) D. L. Fiacco, B. Kirchner, W. A. Burns, K. R. Leopold, J. Mol. Spectrosc. 1998, 191,
389-391.
26) (a) W. G. Read, E. J. Campbell, G. Henderson, J. Chem. Phys. 1983, 78, 3501-3508.
(b) M. R. Keenan, L. W. Buxton, E. J. Campbell, A. C. Legon, W. H. Flygare, J.
Chem. Phys. 1981,74,2133-2137.
27) W. Gordy, R. L. Cook, Microwave Molecular Spectra, Wiley, New York, 1970.
28) E. A. C. Lucken, Nuclear Quadrupole Coupling Constants, Academic Pres, New
York, 1969.
29) The Townes and Dailey analysis of the previous Base-SC«3 complexes used the value
of eQq2io = -9.0 MHz estimated by Lucken for a three coordinate (sp2) nitrogen
atom.
It should be noted that Lucken estimated a value of -9.4 MHz for
molecular nitrogen using the quadrupole coupling constant of N2 available to him
at the time. However, incorporating this value into the present analysis changes
the number of electrons transferred by -4%, and given the approximations
inherent in the method, a value of -9.0 MHz was once again used to maintain as
much consistency as possible from one system to next.
30) Correcting the
14
N quadrupole coupling constant for the zero-point motion in the
complex, using Equation (5.6) and a value of y = 4.25°, resulted in minimal
changes in the calculated value of a 2 .
148
Appendix to Chapter 1
149
Table Al.l Rotational Transitions for the H2SQ4 Monomer.'
J'
K.,'
K+,1
r K.r K+r
0
0
0
1
0
3
5
2
3
3
2
5
2
3
4
5
5
1
0
5
4
4
5
2
3
5
1
5
2
5
3
4
5
3
3
5
4
1
5
1
5
4
2
5
2
7
5
3
5
2
7
4
3
5
3
7
5
4
5
3
9
4
5
5
5
4
9
6
4
5
4
9
6
6
3
9
4
6
5
6
3
9
2
7
7
7
4
7
9
3
9
5
6
5
5
9
1
9
0
9
7
9
6
3
3
7
4
9
4
6
2
9
2
8
7
8
9
3
3
7
10
1
9
1
9
6
5
10
5
5
5
6
10
4
6
4
10
7
7
3
5
7
10
4
7
7
4
10
4
6
6
10
6
6
5
3
10
8
2
8
4
8
10
3
8
1
10
10
0
10
7
5
10
6
5
8
3
10
7
3
8
4
10
4
7
10
1
10
9
1
10
11
1
1
10
All freqiuencies are in MHz.
Vobs
"calc
10185.127
10185.126
1
60668.65
60668.59
6
60861.43
60861.50
6
60934.87
60935.35
6
60939.80
60940.06
6
60945.72
60946.00
6
61060.32
61060.53
6
61317.72
61317.35
6
61353.12
61353.36
6
81056.47
81056.65
8
81066.92
81066.90
8
81212.24
81212.14
8
101080.21
101080.17
10
101267 JO
101267.42
10
101294.46
101294.00
10
101475.20
10147532
10
101480.71
10
101480.86
101503.07
101503.44
10
101574.71
10
101574.86
10
101594.99
101595.07
10
101775.30
101775.42
10
101852.61
101852.67
10
102221.46
10222132
10
102227.85
102227.76
10
103008.75
103008.82
11
111209.35
11120935
11
111267.94
111268.10
11
111533.90
111533.79
11
111612.31
111612.29
11
11161732
111617J21
11
111629.15
111629.04
11
111661.00
111660.40
11
111667.05
111667.42
11
111757.44
111757.51
11
111817.39
111817.21
11
112126.95
112126.89
11
112156.53
112156.62
11
112937.95
112938.13
11
113327.41
113327.29
(a)
(b) All transition assignments and frequencies, except the li 0 <— 0oo,
are those reported by Kuczkowski et al., Ref 12.
(c) Original vobs - v * values reported by Kuczkowski et al., Ref 12.
Vobs"^caIc
-0.001
-0.06
0.07
0.48
-0.26
0.28
-0.21
037
-0.24
0.18
-0.02
0.10
-0.04
-0.12
-0.46
-0.12
0.15
-037
-0.15
-0.08
-0.12
-0.06
0.14
0.09
-0.07
0.00
0.16
0.11
0.02
0.11
0.11
0.60
-0.37
-0.07
0.18
0.06
-0.09
-0.18
0.12
Assigned
Error
0.005
0.15
0.15
0.15
0.15
0.15
0.15
0.15
0.15
0.15
0.15
0.15
0.15
0.15
0.15
0.15
0.15
0.15
0.15
0.15
0.15
0.15
0.15
0.15
0.15
0.15
0.15
0.15
0.15
0.15
0.15
0.15
0.15
0.15
0.15
0.15
0.15
0.15
0.15
V0bs_vcal<
-0.06
0.06
0.47
-0.27
0.27
-0.22
0.34
-0.27
0.18
-0.02
0.09
-0.05
-0.11
-0.46
-0.12
0.15
-0.37
-0.16
-0.09
-0.12
-0.07
0.13
0.08
-0.09
0.00
0.16
0.12
0.02
0.12
0.10
0.61
-0.37
-0.05
0.18
0.07
-0.08
-0.20
0.12
i»
5 o
vobo^^tyNt^i^il/i*.
w u l o t o ^ b b J e x i b o b o ^ a a i ^ O i ^ ^ w k j
^OVOVOOOOOOO-J^J^l-JO
•— k--t— p p p p o o p p o p p p p o o o o o o o o o o o o o o
MMb«*»^^*b\uiui^^uuuk)k)k)Uh-MMbbbbbb
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1.3
Table A1.3
M'
—
0
0
0
0
0
0
0
0
0
0
M"
Stark-Shifted Frequencies for the 1 <— 0
Transition of the OCS Monomer, continued.
Vobs8
12162.979
12163.262
12163.270
12163.278
12163.286
12163.294
12163.302
12163.310
12163.319
12163.327
12163.338
12163.007
12163.013
12163.016
12163.020
12163.024
12163.028
12163.033
12163.037
12163.042
12163.047
12163.052
12163.057
12163.063
12163.068
12163.074
12163.080
12163.086
12163.093
12163.099
12163.106
12163.113
12163.120
12163.127
12163.136
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
(a) All frequencies are in MHz.
Vobs.-Vcdc'
Avobsa
—
-0.001
-0.001
-0.001
-0.001
-0.001
-0.001
-0.001
-0.001
-0.001
-0.001
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
-0.001
0.000
-0.001
-0.001
-0.001
-0.001
-0.001
-0.001
S(V/cm)
0.0
0.283
0.291
0.299
0.307
0.315
0.323
0.332
0.340
0.348
0.359
0.028
0.034
0.037
0.041
0.045
0.049
0.054
0.058
0.063
0.068
0.073
0.078
0.084
0.089
0.095
0.101
0.107
0.114
0.120
0.127
0.134
0.141
0.148
0.157
223.4
226.4
229.5
232.6
235.6
238.7
241.7
244.8
247.8
251.5
107.1
116.3
122.4
128.5
134.6
140.7
146.9
153.0
159.1
165.2
171.4
177.5
183.6
189.7
195.8
202.0
208.0
214.2
220.4
226.4
232.6
238.7
244.8
251.5
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Table A1.5
M'
M"
Stark-Shifted Frequencies for the J = 1 <— 0,
= 2 <- i Transition of the (CH3)3CCN Monomer.
F
Vobs a
5500.029
5500.071
5500.122
5500.133
5500.199
5500.219
5500.297
5500.323
5500.422
5500.451
5500.573
5500.593
5500.755
5500.967
5500.928
5501.202
5501.149
5501.477
5501.337
5501.781
5501.559
5502.118
5500.053
5500.130
5500.257
5500.437
5500.669
5500.949
5501.284
5501.671
5502.105
5502.594
5500.075
5500.197
5500.421
5500.449
5500.755
5501.132
(a) All frequencies are in MHz.
1
1
0
1
0
1
0
1
0
1
0
1
1
0
1
0
1
0
1
0
1
2
2
2
2
2
2
2
2
2
2
0
1
1
0
0
0
1
1
0
1
0
1
0
1
0
1
0
1
1
0
1
0
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
^obs.
^calc.
Avobsa
S (V/cm)
0.042
0.093
0.104
0.170
0.190
0.268
0.293
0.392
0.422
0.544
0.564
0.725
0.938
0.899
1.173
1.120
1.448
1.307
1.751
1.529
2.089
0.024
0.100
0.228
0.408
0.640
0.920
1.255
1.642
2.076
2.565
0.046
0.168
0.392
0.420
0.725
1.102
12.1
18.2
18.2
24.3
24.3
30.3
30.3
36.4
36.4
42.5
42.5
48.5
54.6
54.6
60.7
60.7
66.7
66.7
72.8
72.8
78.8
12.2
24.2
36.4
48.5
60.7
72.8
84.9
97.0
109.1
121.3
12.2
24.2
36.4
36.4
48.5
60.7
0.0
0.000
-0.003
-0.002
-0.002
0.002
-0.003
0.002
-0.003
0.005
-0.003
0.002
-0.001
0.003
-0.008
-0.002
0.018
0.002
-0.001
0.001
0.002
0.003
-0.001
-0.001
-0.002
-0.002
-0.001
-0.002
0.000
0.002
0.002
0.001
-0.001
-0.004
-0.003
0.003
0.000
0.000
Figure Al.l Sulfuric Acid Monomer with Atom Labels
l^NL
4
,-te
Figure A1.2 Sulfuric Acid Monohydrate with Atom Labels
158
Table A1.6 Calculated H2SQ4 Parameters using HF/aug-cc-pV«Z.
Experiment
«=D
-438068.8477 -438162.9200
E(HF) [kcal/mol]
» = (Q+d)
-438188.1809
-438197.3530
2.9643(67)
3.4106
3.5190
3.5051
3.4937
0.97(1)"
0.9502
0.9470
0.9458
0.9456
rs-oi [A]
1.574(10)"
1.5836
1.5529
1.5461
1.5421
TS-02 [A]
1.422(10)"
1.4295
1.4008
1.3931
1.3881
AS-oi-m [degree]
Aoi-s-02 [degree]
108.5(15)"
109.7383
108.2523
111.1045
108.4209
111.4238
108.3915
111.5915
108 4026
Aoi-s-or [degree]
101.3(10)"
101.8932
102.2766
102.3523
102.4055
Ao2-s-o2' [degree]
Aoi.s-02' [degree]
Dm-oi-s-02 [degree]
123.3(10)"
123.8135
106.2712
-24.5585
122.8900
106.4896
-24.6872
122.7884
106.5477
-24.6485
122.7413
106.5430
-24.6687
87.6895
-158.6068
87.6921
-158.5712
Utot [Debye]
roi-Hi [A]
-90.9(10)"
87.2162
87.5628
Dm-01-s-or [degree]
-158.7541
-159.5241
Dm-oi-s-02' [degree]
(a) Value taken from Kuczkowski, Suenram, and Lovas: Reference 12.
Table A1.7 Calculated H2SQ4 Parameters using MP2/aug-cc-pV/iZ.
Experiment
w=D
n=T
E(MP2) [kcal/mol]
« = (Q+d)
-438669.7736
-438892.4077
-438967.3446
-438976.6603
2.9643(67)
2.8793
3.0475
3.0854
3.0947
roi-m [A]
0.97(1)"
0.9758
0.9704
0.9676
0.9675
rs-01 [A]
1.574(10)'
1.6474
1.5998
1.5879
1.5821
rs-02 [A]
1.422(10)"
1.4670
1.4341
1.4237
1.4183
AS-OI-HI [degree]
108.5(15)"
106.2926
108.8262
107.6277
108.7215
108.1040
108.7289
108.3469
108.7196
Aoi-s-or [degree]
101.3(10)"
101.3932
101.9082
102.0851
102.1956
A02-S-02' [degree]
Aoi-s-02' [degree]
123.3(10)"
125.3881
104.9788
-27.9475
124.4330
105.4445
-26.8768
124.2154
105.4963
-26.8859
124.1258
105.5152
-26.9395
84.2819
-162.1326
84.2954
-162.0786
Htc [Debye]
Aoi-s-02 [degree]
DHI-OI-S-02 [degree]
-90.9(10)"
Dm-01-s-or [degree]
82.3724
84.1518
-164.3817
-162.3588
Dm-01-s-or [degree]
(a) Value taken from Kuczkowski, Suenram, and Lovas: Reference 12.
Table A1.8 Calculated H2SQ4 Parameters using B3LYP/aug-cc-pV»Z.
Experiment
« =D
«=T
E(RB+HF-LYP)
[kcal/mol]
Uto, [Debye]
roi-H. [A]
rs-o, [A]
AS^I-HI
[degree]
-439519.1433
-439544.8775
-439554.7631
2.9643(67)
2.9056
3.0549
3.0757
3.0961
0.97(1)»
0.9729
0.9691
0.9677
0.9675
a
1.6469
1.6102
1.6004
1.5928
a
1.422(10)
1.4660
1.4348
1.4255
1.4190
108.5(15)"
107.4179
109.0982
108.6515
109.4213
108.6798
108.5867
108.7053
108.6742
a
101.5445
101.8917
102.0256
102.1424
a
124.9832
105.3936
-25.4446
124.1212
105.6775
-25.8159
123.9927
105.7234
-25.8853
123.8928
105.7088
-26.0009
85.4814
-160.9611
85.4119
-160.9579
Aoi-s-02 [degree]
Aoi-s-or [degree]
Aoz-s-or [degree]
Aoi-s-or [degree]
DHI-OI-S-O2 [degree]
» = (Q+d)
-439432.7012
1.574(10)
rs.o2 [A]
»°Q
101.3(10)
123.3(10)
85.4482
Dm-oi-s-or [degree]
-90.9(10)a
85.3199
Dm-oi-s-or [degree]
—
161.4974
-161.0390
(a) Value taken from Kuczkowski, Suenram, and Lovas: Reference 12.
Table A1.9 Calculated H2SQ4 Parameters using PW91PW91/aug-cc-pV/iZ.
Experiment
" =Q
« =D
«=T
E(RPW91-PW91)
[kcal/mol]
n = (Q+d)
-439378.9427
-439461.7878
-439487.5392
-439497.3780
2.9643(67)
2.7159
2.8915
2.9205
2.9520
TOI-HI [A]
0.97(1 )a
0.9815
0.9774
0.9761
0.9758
rs-01 [A]
1.574(10)"
1.6701
1.6316
1.6211
1.6122
rs-02 [A]
1.422(10)"
1.4793
1.4481
1.4387
1.4317
ASOI-HI [degree]
108.5(15)'
105.9131
108.6986
107.1394
108.7896
107.5438
108.7691
107.9198
108.8016
Aoi-s-or [degree]
101.3(10)"
101.5818
101.9351
102.0763
102.2075
Ao2-s-02' [degree]
Aoi-s-or [degree]
123.3(10)'
125.5638
104.9323
-26.3516
124.6273
105.2552
-26.8531
124.4931
105.2998
-26.9186
124.3710
105.2890
-27.0341
84.0406
-162.4026
83.9833
-162.3767
Utot [Debye]
Aoi-s-02 [degree]
DHI-OI-S-02 [degree]
-90.9(10)a
83.9555
84.0007
-162.8818
-162.4910
(a) Value taken from Kuczkowski, Su<snram, and Lovas: Reference 12.
DHI-OI-S-OI' [degree]
DHIOI-S-02' [degree]
160
Table ALIO Calculated H 2 S04-H 2 0 Parameters using HF/aug-cc-pVwZ.
«=D
w=T
» = Qa
-485795.7472
-485901.6954
-485929.9376
3.052(17)b
3.3708
3.4284
3.4451
1.567(l)c
1.5664
1.5353
1.5353
r02-s [A]
c
1.578(3)
1.5857
1.5552
1.5552
T03-S [A]
1.464(1)°
1.4358
1.4072
1.4072
c
Experiment
E(HF) [kcal/mol]
^.[Debye]
roi-s [A]
ro4-s [A]
1.410(4)
1.4310
1.4028
1.4028
roi-m [A]
1.04(1)°
0.9658
0.9638
0.9638
T02-H2 [A]
0.95°
0.9498
0.9466
0.9466
IH3-05 [A]
0.98(1)°
0.9475
0.9449
0.9449
rH4-os [A]
0.98(1)°
0.9434
0.9412
0.9412
TH1-05 [A]
1.645(5)°
1.7980
1.7857
1.7857
T03-H3 [A]
2.05(1)°
2.3952
2.4489
2.4489
Ao3-H3-os [degree]
AHi-o5-H3 [degree]
AHi-o5-H4 [degree]
130.3(5)°
118.7455
100.3298
128.7629
116.2046
101.2404
127.9282
116.2046
101.2404
127.9282
[degree]
A05-H1-01 [degree]
107°
107.2229
165.0266
110.8999
107.6120
165.7408
111.4216
107.6120
165.7408
111.4216
AS-o2-H2 [degree]
108.5°
109.5881
110.9446
110.9446
AS-OI-HI [degree]
108.6°
110.2474
111.6062
111.6062
Aoi-s-02 [degree]
101.8(2)°
102.5735
102.8638
102.8638
Aoi.s.03 [degree]
106.71(6)°
109.0521
108.9523
108.9523
Aoi-s-o4 [degree]
106.7(4)°
107.1944
107.5225
107.5225
A02-S-03 [degree]
A02-S-04 [degree]
104.71(9)°
105.5864
108.0852
105.9208
108.1506
105.9208
108.1506
AH3-05-H4
AHS-OS-S [degree]
123.3°
A03-S-04 [degree]
122.5845
121.8362
121.8362
(a) Single-point calculation done at the aug-cc-pVTZ structure.
(b) Value taken from Brauer et al.
(c) Values taken from Fiacco et al. Those without reported errors were fixed in the final fit.
Table A l . l l Calculated H2SQ4-H2O Parameters using MP2/aug-cc-pV»Z.
w=D
«=T
" = Qa
^86536.9056
-486802.5909
-486891.5097
3.052(17) b
2.7493
2.7551
2.7544
roi-s [A]
1.567(1)°
1.6179
1.5717
1.5717
ro2-s [A]
1.578(3)°
1.6488
1.6017
1.6017
I03-S [A]
1.464(1)°
1.4767
1.4440
1.4440
T04-S [A]
1.410(4)°
1.4677
1.4352
1.4352
r0i-Hi [A]
1.04(1)°
1.0036
1.0020
1.0020
02-H2 [A]
0.95°
0.9755
0.9700
0.9700
TH3-05 [A]
0.98(1)°
0.9732
0.9699
0.9699
TH4-05 [A]
0.98(1)°
0.9665
0.9624
0.9624
TH1-05 [A]
1.645(5)°
1.6844
1.6530
1.6530
T03-H3 [A]
2.05(1)°
2.1559
2.1124
2.1124
A03-H3-05 [degree]
130.3(5)°
128.7248
95.1271
119.8713
128.5969
94.5314
120.7333
128.5969
94.5314
120.7333
107°
A05-H1-01 [degree]
105.3198
165.5747
A H 3 -03-S [degree]
108.4899
105.8258
165.0115
109.9230
105.8258
165.0115
109.9230
Experiment
E(MP2) [kcal/mol]
m„t Pebye]
r
AHI-OS-H3 [degree]
AHi-o5-H4 [degree]
AH3-05-H4 [degree]
AS4D2-H2 [degree]
108.5°
106.2592
107.5710
107.5710
As-01-m [degree]
108.6°
106.4062
107.8423
107.8423
Aoi-s-02 [degree]
101.8(2)°
102.3492
102.8404
102.8404
Aoi-s-03 [degree]
106.71(6)°
109.4962
109.2141
109.2141
Aoi-s-ot [degree]
106.7(4)°
106.8246
107.3967
107.3967
A02-S-03 [degree]
104.71(9)°
103.8985
108.7087
104.4234
108.5457
104.4234
108.5457
123.3°
123.5861
122.6785
122.6785
A02-S-04 [degree]
Ao3.s.Q4 [degree]
(a) Single-point calculation done at the aug-cc-pVTZ structure
(b) Value taken from Brauer et al.
(c) Values taken from Fiacco et al. Those without reported errors
•swere
were fixed
fixedin thefinalfit.
Table A1.12 Calculated H2SO4-H2O Parameters using B3LYP/aug-cc-pV«Z.
Experiment
« =D
«=T
E(RB+HF-LYP)
-487513.5396
-487413.5627
[kcal/mol]
_nZ^_
-487543
0455
^ t o / J*TJ .y*tjj
Uto, [Debye]
3.052(17)*
2.5963
2.6996
2.7060
roi-s [A]
1.567(1)"
1.6166
1.5804
1.5708
T02-S [A]
b
1.578(3)
1.6490
1.6123
1.6022
r03-s [A]
1.464(1)"
1.4773
1.4452
1.4359
ro4-s [A]
1.410(4)"
1.4674
1.4365
1.4274
roi-Hi [A]
1.04(1)"
1.0042
1.0015
0.9996
02-H2 [A]
0.95"
0.9723
0.9686
0.9671
TH3-OS [A]
0.98(1)"
0.9724
0.9691
0.9677
rH4-OS [A]
0.98(1)"
0.9650
0.9623
0.9611
TH1-05 [A]
1.645(5)"
1.6766
1.6730
1.6774
T03-H3 [A]
2.05(1)"
2.1461
2.1787
2.1860
Ao3-H3-05 [degree]
AHi-o5-H3 [degree]
AHI-OS-H4 [degree]
130.3(5)"
129.3722
94.8919
120.5642
127.1493
95.2880
120.3755
126.6570
95.3857
120.5721
[degree]
Aos-Hi-oi [degree]
AH3-o3-s [degree]
107"
106.2546
165.3401
109.5519
106.6491
165.5110
110.5066
106.6698
165.2948
10.8315
AS-02-H2 [degree]
108.5"
107.2890
108.5504
108.9634
ASOI-HI [degree]
108.6"
107.8550
109.1289
109.5149
Aoi-s-02 [degree]
101.8(2)"
102.5076
102.7879
102.8787
Aoi-s-03 [degree]
106.71(6)"
109.1948
109.0966
109.0772
Aoi.s-04 [degree]
106.7(4)"
107.3828
107.6745
107.6804
A02-S-03 [degree]
A02-S-04 [degree]
104.71(9)"
104.4589
108.2964
104.8314
108.3262
104.8713
108.3473
r
AH3-OS-H4
123.3"
A03-S-04 [degree]
123.1138
122.4060
122.3035
(a) Value taken from Brauer et al.
(b) Values taken from Fiacco et al. Those without reported errors were fixed in the final fit.
Table A1.13 Calculated H 2 S0 4 -H 2 0 Parameters using PW91Pw91/aug-cc-pVwZ.
Experiment
n=D
»=T
n= Q
E(RPW91-PW91)
-48734"? 9706
-487440 3658
-487470 0156
[kcal/mol]
3.052(17)a
2.2860
2.4119
2.4070
r0i-s [A]
1.567(1)"
1.6319
1.5943
1.5843
r02-s [A]
1.578(3)"
1.6719
1.6325
1.6223
ros-s [A]
1.464(1)"
1.4936
1.4615
1.4519
ib4-s[A]
1.410(4)"
1.4803
1.4498
1.4404
r0i-Hi [A]
1.04(1)"
1.0256
1.0225
1.0209
I"02-H2 [ A ]
0.95"
0.9810
0.9768
0.9754
TH3-05 [A]
0.98(1)"
0.9842
0.9804
0.9791
b
0.9731
0.9701
0.9689
H,ot [Debye]
rH4-05 [ A ]
0.98(l)
THl-OS [ A ]
1.645(5)"
1.6197
1.6185
1.6197
T03-H3 [A]
2.05(1)"
2.0224
2.0579
2.0588
A03-H3-05 [degree]
AHi-05-H3 [degree]
AHi-05-H4 [degree]
130.3(5)"
135.3149
91.6278
115.6868
132.6157
92.3374
115.2474
132.5010
92.0929
115.2439
AH3-o5-H4 [degree]
AOS-HI-OI [degree]
107"
105.3868
165.8595
108.3080
105.7854
165.7847
109.5229
105.8091
165.6869
109.7559
AS-02-H2 [degree]
108.5"
105.7831
107.0879
107.4500
AS-OI-HI [degree]
108.6"
106.2733
107.6263
107.9328
Aoi-s-02 [degree]
101.8(2)"
102.7183
102.9759
103.0740
Aoi-s-03 [degree]
106.71(6)"
109.2657
109.2343
109.1641
Aoi.s-04 [degree]
106.7(4)"
107.5660
107.8236
107.8535
A02-S-03 [degree]
A02-S-04 [degree]
104.71(9)"
103.8446
108.3533
104.2014
108.4306
104.2981
108.4238
AHS-03-S [degree]
123.3"
Aos-s-ot [degree]
123.2115
122.4638
122.3553
(a) Value taken from Brauer et al.
(b) Values taken from Fiacco et al. Those without reported errors were fixed in the final fit.
Appendix to Chapter 2
165
Table A2.1 Transition Frequencies for the CH3COOH Monomer *-b
A State
v
lie »•* loi
22cf*~2i,
32i « - 3 1 2
33c(* 321
2„*""2o2
431 <-4 2 2
541- 5 3 2
In ^-Ooo
EState
obs
Apb!is-calc
Vobs
^\)bs-calc
AA-i
6088.810°
8560.601
12398.377
12983.555°
12989.907
13381.244
16539.474
16741.492
0.008
0.003
0.013
-0.018
0.034
-0.001
-0.011
0.031
6175.165°
9031.240
12508.430
14075.372
13025.271
13616.999
17137.626
16418.448
8683.799°
9542.824°
17173.064
-0.013
0.004
-0.023
-0.019
0.004
-0.007
-0.023
0.013
0.024
-0.002
-0.007
-86.355
-470.639
-110.053
-1091.817
-35.364
-235.755
-598.152
9944.026
12453.867
14803.997
17144.973
0.003
0.030
0.024
-0.035
10519.360
12591.666
14802.617
17904.238
8534.613
11639.023°
15152.875°
17606.669°
-0.020
-0.018
-0.026
0.038
0.009
0.002
-0.005
-0.007
-575.334
-137.799
1.380
-759.265
331«-3 2 ,
542,<—532
221«-2, 2
321<—322
2„- 2 I 2
loi —Ooo
532- 5 3 3
4 3 i •"-432
4,4 .«-32,
3,3 •
221
<—
<—
22o
2o2
(a) All frequencies are in MHz
323.044
(b)CT= 0.025 MHz
(c) Not observed as part of the global fit, reference [24].
166
Table A2.2 L State Transition Frequencies for the Acetic Acid Monohydrate Complexa
A State
EState
Vobs
^\>bs-calc
"obs
AA-E
^\>bs-cal<
CH3COOH-H20 (CT = 0.01297)
2l2«-lll
8967.221
-0.005
9294.865
0.002
-327.644
<—
9406.286
0.001
9405.580
0.012
0.706
211*— lio
9880.767
0.021
9552.921
0.017
327.846
3l3 "* 2i2
13439.899
0.001
13747.632
-0.010
-307.733
3o3 *— 2Q2
14065.226
-0.011
14062.941
0.002
2.285
3n*— 2u
14809.744
-0.005
14501.183
0.006
308.561
At A <
^14
1 / ^\J\J.\J*T
17900 0471
0.013
9055.872
0.003
10193.897
-0.003
-1138.025
2 n — 202
9530.344
0.014
10341.240
0.005
-810.896
3l2"*— 3o3
10274.858
0.016
10779.483
0.009
-504.625
404^-313
11137.470
0.000
12001.990
-0.014
-864.520
2o2
loi
J
3 n
13
lio*— loi
<
4l3*-4o4
11327.148
-0.011
11617.242
-0.007
-290.094
1 ii •* Ooo
13311.107
-0.018
11802.823
-0.002
1508.284
2 1 2 * - loi
17566.305
-0.030
16385.760
-0.024
1180.545
13
CH3COOH-H20 (CT = 0.00903)
2 l 2 * ~ 111
8781.153
-0.008
9099.482
-0.001
-318.329
<—
loi
9202.251
0.002
9201.608
0.008
0.643
2ii — lio
9655.600
0.012
9337.102
0.018
318.498
3l3<—2j2
13161.766
0.001
13466.844
-0.018
-305.078
3o3 *~ 2o2
13763.093
-0.006
13761.018
-0.001
2.075
<
3i2 -2„
14473.031
-0.003
14167.196
0.003
305.835
4 K «—
M4
3ii
-M3
17530 919
0.007
lie*
loi
9096.953
-0.003
10242.049
0.001
-1145.096
202
9550.304
0.009
10377.532
0.000
-827.228
3i2*— 3 0 3
10260.235
0.006
10783.711
0.005
-523.476
404^3,3
10639.149
0.005
11523.131
-0.037
-883.982
4l3 *~ 4o4
11261.280
-0.019
11567.188
-0.003
-305.908
I n * - Ooo
13268.951
0.001
11753.908
-0.004
1515.043
2 l 2 < — loi
17440.899
-0.003
16244.273
-0.014
1196.626
2o2
<
2a*
-
(a) All values are in MHz.
167
Table A2.3 Numerical Average Transition Frequencies for the Acetic Acid Monohydrate Complex'
A State
EState
v
2l2
<—
2o2
<—
111
Id
<
2n — lio
3l3 "*
2n
3 03 *— 2o2
3i2^— 2 U
4l4—3i3
lio'*
loi
2 n •*— 2o2
3l2*~~ 3o3
4o4<-313
4i3<-404
-
I n * Ooo
212*- I d
obs
8967.221
9406.286
9880.767
13439.899
14065.226
14809.768
17900.047
9055.893
9530.369
10274.886
11137.470
11327.197
13311.128
17566.331
^\)bs-calc
CH3COOH-H20 (o == 0.00727)
-0.006
9294.865
0.000
9405.580
0.004
9552.921
-0.002
13747.632
14062.941
-0.013
-0.008
14501.205
0.006
0.014
10193.935
0.012
10341.279
-0.008
10779.526
0.001
12002.012
-0.050
11617.289
0.000
11802.858
-0.007
16385.794
13
2 , 2 ^ 111
202*
-
loi
-
2 a * lio
3l3 ^
2i2
3o3 •— 2o2
3i2 •*— 2 n
4tA
•<— 3i^>
^14
-M3
lio "*— loi
2n < — 2o2
3l2 •* 3o3
4o4<-3i3
4l3 «~ 4o4
I n « - Ooo
2 1 2 * - loi
8781.167
9202.251
9655.614
13161.766
13763.105
14473.053
17530
919
I / J J U i / 1 7
9096.977
9550.327
10260.265
10639.149
11261.323
13268.951
17440.899
(a) All values are in MHz.
Vobs
CH3COOH-H20 (CJ = 0.00539)
0.005
9099.482
-0.002
9201.608
0.011
9337.102
-0.001
13466.856
0.001
13761.018
-0.003
14167.216
0.002
0.009
10242.083
0.009
10377.570
-0.004
10783.756
-0.001
11523.153
-0.040
11567.231
-0.007
11753.950
-0.011
16244.319
^obs-calc
A A -E
0.004
-327.644
0.003
0.706
0.012
327.846
-0.004
-307.733
-0.007
2.285
0.012
308.563
0.003
-1138.042
0.015
-810.910
0.017
-504.640
0.001
-864.542
-0.019
-290.092
0.001
1508.270
-0.014
1180.537
-0.001
-318.315
0.002
0.643
0.011
318.512
-0.004
-305.090
-0.009
2.087
0.006
305.837
0.005
-1145.106
0.008
-827.243
0.011
-523.491
0.000
-884.004
-0.020
-305.908
-0.005
1515.001
-0.008
1196.580
Table A2.4 H State Transition Frequencies for the Acetic Acid Monohydrate Complex'
A State
EState
Vobs
-
111
—
loi
212*
2o2'*
<
2ii — lio
3l3"— 2 j 2
3 03 < — 2o2
3u«-2„
4i4<-313
lio — loi
2n
<—
2o2
312 < — 3o3
4o4 < — 3 n
4i3<-404
I n —Ooo
2i2 < — loi
8967.221
9406.286
9880.767
13439.899
14065.226
14809.793
17900.047
9055.916
9530.394
10274.915
11137.470
11327.241
13311.147
17566.357
^obs-calc
V 0 bs
CH3COOH-H20 (CJ == 0.01305)
0.002
9294.865
-0.004
9405.580
0.003
9552.921
0.004
13747.632
-0.023
14062.941
0.010
14501.226
0.002
0.005
10193.972
0.009
10341.317
-0.004
10779.568
-0.023
12002.034
-0.027
11617.335
-0.008
11802.893
0.000
16385.827
^obs-calc
AA-E
0.002
-0.002
0.005
-0.011
-0.022
0.014
-327.644
0.706
327.846
-307.733
2.285
308.567
0.002
0.013
0.015
0.013
-0.020
0.002
-0.016
-1138.056
-810.923
-504.653
-864.564
-290.094
1508.254
1180.530
-0.005
-0.007
0.005
0.003
-0.022
0.015
-318.302
0.643
318.525
-305.102
2.098
305.838
0.001
0.009
0.013
0.018
-0.009
0.004
0.005
-1145.117
-827.257
-523.498
-884.025
-305.908
1514.959
1196.535
13
8781.180
9202.251
2o2*~ loi
9655.627
2 n < — lio
<—
3i3 212
13161.766
13763.116
3 03 < — 2 0 2
14473.074
3i2*~ 2 U
4 i ^ •<— 3»->
17530.919
^14
13
9097.000
l i o * loi
9550.350
2,1-202
10260.294
312 — 3o3
404—3,3
10639.149
11261.366
4 n — 4o4
13268.951
I n "* Ooo
17440.899
2 l 2 < — loi
(a) All values are in MHz.
2l2
<—
111
J
CH3COOH-H20 (a = 0.01185)
0.017
9099.482
-0.008
9201.608
0.018
9337.102
-0.004
13466.868
0.001
13761.018
0.008
14167.236
-0.004
0.007
10242.117
0.007
10377.607
0.000
10783.792
-0.008
11523.174
-0.021
11567.274
-0.033
11753.992
-0.034
16244.364
Table A2.5 Cartesian Coordinates of the
Global Minimum CH3COOH-H2Q Complex"
H
-0.893774
-0.962593
-0.009602
O
0.076906
-1.108436
-0.016564
O
0.056836
1.151762
-0.011150
C
0.668567
0.095635
-0.010163
C
2.168024
-0.020017
0.006286
H
2.613800
0.971145
-0.052842
H
2.479483
-0.516227
0.928653
H
2.498621
-0.637848
-0.831373
O
-2.456544
-0.057569
0.088962
H
-1.946571
0.763191
0.022138
H
-3.188681
0.042571
-0.523701
(a) Optimized with MP2/6-311++G(d,p)
Table A2.7 Cartesian Coordinates of the
Global Minimum CH3COOH-H2O Complex'
H
0.903002
-0.963939
0.010917
O
-0.070070
-1.107777
0.012151
O
-0.043213
1.144803
0.006585
C
-0.070070
-1.107777
0.012151
C
-0.657973
0.091673
0.006984
H
-2.150037
-0.014641
-0.001523
H
-2.590379
0.974534
0.018582
H
-2.467426
-0.548451
-0.894230
O
-2.478631
-0.592580
0.858747
H
2.431201
-0.050975
-0.092973
H
1.845399
0.721333
-0.025412
(a) Optimized with MP2/6-311 ++G(2df,2pd)
Table A2.6 Cartesian Coordinates of the Global
Minimum CH3COOH-H2Q Complex a'b
-0.010938
H
-0.860444
-0.980657
0.108614
-1.114605
-0.015789
O
-0.010256
O
0.067866
1.145147
-0.009967
0.689814
0.097101
C
0.005995
C
-0.009037
2.189997
-0.052023
H
2.628646
0.985292
H
-0.504182
0.927528
2.505535
-0.832792
H
2.524352
-0.623178
O
-2.527128
-0.057706
0.087650
-2.013264
0.758354
0.022202
H
H
-3.258504
0.053303
-0.522980
(a) Optimized with MP2/6-311++G(d,p)
(b) Optimized with the counterpoise correction
Table A2.8 Cartesian Coordinates of the Global
Minimum CH3COOH-H20 Complex *-b
H
0.886368
-0.968199
0.011977
O
-0.084860
-1.108111
0.012807
O
-0.055567
1.144396
0.007606
C
-0.671536
0.093978
0.007135
C
-2.163564
-0.014002
-0.002661
H
-2.604640
0.974863
0.016341
H
-2.480376
-0.895094
-0.548590
H
-2.492960
-0.591216
0.857790
O
2.472282
-0.052106
-0.093003
H
1.905224
0.730633
-0.022098
H
3.142144
0.049219
0.584959
(a) Optimized with MP2/6-311++G(2df,2pd)
(b) Optimized with the counterpoise correction
Table A2.9 Cartesian Coordinates of the
Global Minimum CH3COOH-H2O Complex'
Table A2.10 Cartesian Coordinates of the
Global Minimum CH3COOH-H20 Complex "•b
-0.962392
0.005762
H
0.911237
O
-0.066647
-1.115983
0.008248
O
-0.047093
1.158953
0.003584
C
-0.665630
0.093619
0.005059
C
-2.167637
-0.020060
0.002113
H
-2.612972
0.980803
0.010992
H
-2.488443
-0.573887
-0.892470
H
-2.492532
-0.593056
0.882946
O
2.453698
-0.050521
-0.093610
H
1.870889
0.731769
-0.022155
H
3.091760
0.035812
0.626112
(a) Optimized with MP2/aug-cc-pVDZ
H
O
O
C
C
H
H
H
O
H
H
0.889459
-0.086996
-0.053654
-0.678748
-2.181395
-2.622213
-2.502519
-2.511225
2.497201
1.917059
3.137891
-0.976366
-1.120419
1.154821
0.094812
-0.012766
0.990166
-0.562767
-0.586335
0.009099
0.010458
0.005833
0.006203
-0.000553
0.009503
-0.897464
0.878116
-0.095249
-0.050394
-0.023487
0.73182
0.621992
0.039151
(a) Optimized with MP2/aug-cc-pVDZ
(b) Optimized with the counterpoise correction
170
-0.002563
C
0.764327
-0.097280
-0.005083
C
0.392754
1.348903
0.007678
-0.269803
O
2.101998
-0.008209
-1.037577
O
-0.001935
0.009762
H
2.251788
-1.225787
-0.020658
1.458603
H
-0.684838
0.879101
H
0.808756
1.826123
-0.874151
H
0.835006
1.830263
0.022994
0.011872
O
-2.699402
H
-3.441542
-0.580164
-0.038770
H
-1.916932
-0.000135
-0.543682
(a) Optimized with MP2/6-311 ++G(2df,2pd)
(b) Optimized with the counterpoise correction
Table A2.12 Cartesian Coordinates of a Local
Minimum (C) CH3COOH-H20 Complex a'b
0.006911
-0.019948
-0.987387
C
0.128351
1.327773
-0.357204
C
0.239129
-1.016495
O
-0.081203
-0.253351
-0.262280
-2.138981
O
-0.096804
2.089887
H
-1.092730
1.459393
1.139023
H
0.022481
1.403325
-0.543558
H
0.494229
0.144588
-1.844405
H
-0.573065
-0.163830
O
2.690978
0.040602
0.007217
-0.568419
H
1.965913
-0.481341
-0.037623
H
3.484369
(a) Optimized with MP2/6-311++G(2df,2pd)
(b) Optimized with the counterpoise correction
Table A2.13 Cartesian Coordinates of a Local
Minimum (D) CH3COOH-H20 Complex a'b
C
-0.557563
1.337833
-0.000082
C
-1.012593
-0.099031
-0.000018
O
-0.019934
0.000671
-1.015161
O
-2.166397
-0.445753
-0.000264
H
0.848017
-0.579103
0.000476
H
-1.423413
-0.002293
1.988830
H
0.051858
1.539387
0.878797
H
0.055875
1.538415
-0.876362
O
2.632745
-0.000545
0.028793
H
3.158542
-0.228712
0.759956
H
3.158746
-0.234660
-0.758868
(a) Optimized with MP2/6-311 ++G(2df,2pd)
(b) Optimized with the counterpoise correction
Table A2.14 Cartesian Coordinates of a Local
Minimum (E) CH3COOH-H20 Complex *•"
C
-0.149271
-0.001965
0.755456
C
0.395498
1.309798
-0.004218
O
2.081979
-0.421982
0.005258
O
-0.032537
-1.062705
-0.005130
H
-0.681606
1.428447
-0.019281
H
0.801649
1.789800
0.885057
H
0.827654
-0.878234
1.795011
H
2.578450
0.402609
0.006650
O
-2.683260
0.066996
0.009533
H
-3.443360
-0.513724
-0.036565
H
-1.917963
-0.523783
0.002188
(a) Optimized with MP2/6-311++G(2df,2pd)
(b) Optimized with the counterpoise correction
Table A2.ll Cartesian Coordinates of a Local
Table A2.15 Cartesian Coordinates of a Local
Minimum (F) CH3COOH-H20 Complex "•b
C
0.745033
-0.081678
-0.001775
C
2.228272
-0.319797
0.004796
O
0.361806
1.220491
-0.002890
O
-0.091705
-0.947394
-0.005953
H
2.422336
-1.385258
0.004957
H
2.683830
0.132075
-0.874892
H
2.675732
0.130828
0.889271
H
1.138183
1.789475
0.001080
O
-2.994373
-0.105507
0.004206
H
-2.091412
-0.443859
-0.000267
H
-2.874331
0.844864
-0.001173
(a) Optimized with MP2/6-311++G(2df,2pd)
(b) Optimized with the counterpoise correction
171
Table A2.16 Cartesian Coordinates of the
Global Minimum (H3COOH)2 Complex *
H
H
H
C
C
O
O
H
H
O
O
C
C
H
H
H
2.533397
0.882302
2.883613
2.533397
-0.882302
2.883613
1.238046
0.000000
3.748183
2.876392
1.889408
0.000000
1.061076
1.622731
0.000000
-0.166212
0.000000
1.622731
0.520654
1.801045
0.000000
1.199027
-0.266192
0.000000
-1.199027
0.266192
0.000000
-0.520654
-1.801045
0.000000
-1.622731
0.166212
0.000000
-1.061076
-1.622731
0.000000
-2.876392
-1.889408
0.000000
-1.238046
-3.748183
0.000000
-2.533397
-2.883613
-0.882302
-2.883613
-2.533397
0.882302
(a) Optimized with MP2/6-311++G(d,p)
Table A2.18 Cartesian Coordinates of the
Global Minimum (H3COOH)2 Complex *
2.881384
2.468668
0.876515
H
H
2.881384
2.468668
-0.876515
H
3.737277
1.175889
0.000000
C
2.870508
1.825121
0.000000
C
1.617222
1.009658
0.000000
O
1.617222
-0.217212
0.000000
O
0.524207
1.747181
0.000000
H
-0.280416
1.155475
0.000000
H
0.280416
-1.155475
0.000000
O
-0.524207
-1.747181
0.000000
O
-1.617222
0.217212
0.000000
C
-1.617222
-1.009658
0.000000
-2.870508
C
-1.825121
0.000000
H
-3.737277
-1.175889
0.000000
H
-2.881384
-2.468668
-0.876515
-2.881384
H
-2.468668
0.876515
(a) Optimized with MP2/6-311++G(2df,2pd)
Table A2.ll Cartesian Coordinates of the
Global Minimum (H3COOH)2 Complex '' b
0.882064
2.894346
2.584998
H
-0.882064
2.894346
2.584998
H
0.000000
3.766894
1.295688
H
0.000000
1.940679
C
2.890438
0.000000
1.642144
1.103744
C
0.000000
1.642144
-0.120273
O
1.845714
0.000000
0.536233
O
0.000000
1.245239
H
-0.244619
0.000000
H
0.244619
-1.245239
0.000000
-0.536233
-1.845714
O
-1.642144
0.000000
O
0.120273
0.000000
-1.642144
-1.103744
C
0.000000
C
-2.890438
-1.940679
H
-3.766894
0.000000
-1.295688
-0.882064
H
-2.894346
-2.584998
H
0.882064
-2.894346
-2.584998
(a) Optimized with MP2/6-311++G(d,p)
(b) Optimized with the counterpoise correction
Table A2.19 Cartesian Coordinates of the
Global Minimum (H3COOH)2 Complex "-b
H
H
H
C
C
O
O
H
H
O
O
C
C
H
H
H
2.893470
2.499166
0.876431
2.893470
-0.876431
2.499166
3.754534
1.210104
0.000000
2.884984
1.855499
0.000000
1.635921
1.033540
0.000000
1.635921
-0.190803
0.000000
0.539447
1.772497
0.000000
-0.257728
1.181408
0.000000
0.257728
-1.181408
0.000000
-0.539447
-1.772497
0.000000
-1.635921
0.190803
0.000000
-1.635921
-1.033540
0.000000
-2.884984
-1.855499
0.000000
-3.754534
-1.210104
0.000000
-2.893470
-2.499166
-0.876431
-2.893470
-2.499166
0.876431
(a) Optimized with MP2/6-311-H-G(2df,2pd)
(b) Optimized with the counterpoise correction
172
Table A2.20 Cartesian Coordinates of the
Global Minimum (H3COOH)2 Complex a
Table A2.21 Cartesian Coordinates of the
Global Minimum (H3COOH)2 Complex *-b
H
H
H
C
C
O
O
H
H
O
O
C
C
H
H
H
H
H
H
C
C
O
O
H
H
O
O
C
C
H
H
H
0.887435
2.904428
2.501522
2.904428
2.501522 -0.887435
0.000000
3.772155
1.193805
0.000000
2.896664
1.851866
0.000000
1.637639
1.026652
1.637639
0.000000
-0.211937
0.530251
0.000000
1.769948
0.000000
-0.269131
1.166560
0.000000
0.269131
-1.166560
0.000000
-0.530251
-1.769948
-1.637639
0.000000
0.211937
-1.637639
-1.026652
0.000000
-2.896664
0.000000
-1.851866
-3.772155
0.000000
-1.193805
-2.904428
-2.501522 -0.887435
-2.904428
-2.501522
0.887435
(a) Optimized with MP2/aug-cc-pVDZ
2.535423
0.887620
2.913681
2.535423
-0.887620
2.913681
1.230955
0.000000
3.786359
1.885886
0.000000
2.908366
1.653224
1.054713
0.000000
-0.182132
1.653224
0.000000
1.799389
0.000000
0.542716
1.196491
0.000000
-0.250853
-1.196491
0.000000
0.250853
-1.799389
0.000000
-0.542716
0.182132
-1.653224
0.000000
-1.653224
-1.054713
0.000000
-1.885886
-2.908366
0.000000
-3.786359
-1.230955
0.000000
-2.913681
-2.535423
-0.887620
-2.535423
-2.913681
0.887620
(a) Optimized with MP2/aug-cc-pVDZ
(b) Optimized with the counterpoise correction
173
Table A2.22 Ab Initio Determination of the Barrier to Internal Rotation of the Methyl Group'
AEC
AEd
180
183
186
189
192
195
198
201
204
207
210
213
216
219
222
225
228
231
234
237
240
243
246
249
252
255
258
261
264
267
270
273
276
279
282
285
288
291
294
297
300
0.000
0.000
2.195
4.389
8.779
15.363
21.947
30.726
41.700
52.674
65.842
79.011
92.179
105.348
118.516
129.490
138.269
144.853
149.243
151.438
151.438
149.243
144.853
138.269
129.490
118.516
107.543
94.374
83.400
70.232
57.063
46.090
37.311
26.337
19.753
13.168
8.779
4.389
2.195
0.000
0.000
0.000
0.000
4.389
8.779
13.168
21.947
30.726
41.700
52.674
63.648
76.816
89.985
100.958
111.932
122.906
131.685
138.269
142.659
147.048
149.243
149.243
147.048
142.659
138.269
131.685
122.906
114.127
103.153
92.179
81.206
70.232
57.063
48.284
37.311
28.532
19.753
13.168
8.779
4.389
0.000
0.000
e
(CH3COOH)2
CH3COOH-H20
CH3COOH
b
0b
180
183
186
189
192
195
198
201
204
207
210
213
216
219
222
225
228
231
234
237
240
243
246
249
252
255
258
261
264
267
270
273
276
279
282
285
288
291
294
297
300
AEC
AEd
e
b
AEC
AEd
2.195
2.195
4.389
6.584
10.974
15.363
21.947
30.726
39.505
48.284
59.258
70.232
81.206
92.179
100.958
109.737
118.516
122.906
127.295
127.295
127.295
125.101
118.516
111.932
105.348
94.374
85.595
74.621
63.648
52.674
43.895
32.921
26.337
17.558
13.168
8.779
4.389
2.195
2.195
0.000
2.195
0.000
2.195
4.389
8.779
13.168
21.947
28.532
37.311
46.090
57.063
68.037
76.816
87.790
96.569
105.348
111.932
118.516
122.906
127.295
127.295
127.295
125.101
120.711
116.322
109.737
103.153
94.374
85.595
74.621
65.842
54.869
46.090
37.311
30.726
21.947
15.363
10.974
6.584
4.389
2.195
0.000
180
183
186
189
192
195
198
201
204
207
210
213
216
219
222
225
228
231
234
237
240
243
246
249
252
255
258
261
264
267
270
273
276
279
282
285
288
291
294
297
300
0.000
0.000
0.000
0.000
0.000
2.195
4.389
8.779
13.168
21.947
30.726
39.505
50.479
61.453
72.427
81.206
89.985
98.764
103.153
105.348
105.348
103.153
98.764
89.985
81.206
72.427
61.453
52.674
41.700
32.921
24.142
17.558
10.974
6.584
4.389
2.195
0.000
0.000
0.000
0.000
0.000
0.000
2.195
4.389
6.584
10.974
13.168
19.753
24.142
32.921
39.505
48.284
57.063
65.842
74.621
83.400
89.985
96.569
100.958
105.348
107.543
105.348
105.348
100.958
96.569
89.985
83.400
76.816
68.037
59.258
52.674
43.895
37.311
28.532
24.142
17.558
13.168
8.779
4.389
2.195
2.195
0.000
(a) 9 is in degrees and AE is reported in cm"1
(b) Value of the H-C-C-OH dihedral angle in the acetic acid moiety
(c) The energy at angle 9 minus the Global Minimum energy calculated using MP2/6-311++G(d,p)
(d) The energy at angle 0 minus the Global Minimum energy calculated using MP2/aug-cc-pVDZ
Appendix to Chapter 3
175
Table A3.1 Rotational Transitions for the HN03-(H20)3 Complex."
J-l.l' <— J-i.i"
F'
F"
3 2
4 3
2 1
2 1
4 3
3 2
3
2
•>22 "
4 3
2 1
3 2
'20
4 3
2 1
3 2
2 1
4 3
4 3
5 4
3 2
303
5 4
4 3
4 3
+23 <— J 22
5 4
3 2
4 3
+32 ' • 3 i
5 4
3 2
4 3
43,
'30
5 4
3 2
3 2
4l3
4 3
5 4
5 4
6 5
4
3
+22 '
5 4
3 2
(a) Allfrequenciesare in MHz.
3
Vpbs
Vcalc
AVpbs-calc
5358.741
5358.787
5358.800
5670.343
5670.402
5670.425
6042.338
6042.596
6042.737
6414.393
6414.687
6414.834
6595.519
6595.556
6595.580
7057.362
7057.386
7274.238
7274.261
7274.282
7976.370
7976.473
7976.496
8220.527
8220.777
8220.872
8312.486
8312.751
8312.848
8635.665
8635.677
8635.694
8713.710
8713.720
8756.534
8756.660
8756.678
5358.740
5358.801
5358.809
5670.344
5670.400
5670.427
6042.335
6042.592
6042.735
6414.390
6414.683
6414.832
6595.518
6595.562
6595.579
7057.364
7057.384
7274.236
7274.261
7274.283
7976.368
7976.470
7976.496
8220.525
8220.773
8220.866
8312.487
8312.748
8312.844
8635.668
8635.678
8635.689
8713.712
8713.718
8756.530
8756.659
8756.686
0.001
-0.014
-0.009
-0.001
0.002
-0.002
0.003
0.004
0.002
0.003
0.004
0.002
0.001
-0.006
0.001
-0.002
0.002
0.002
0.000
-0.001
0.002
0.003
0.000
0.002
0.004
0.006
-0.001
0.003
0.004
-0.003
-0.001
0.005
-0.002
0.002
0.004
0.001
-0.008
Table A3.1 Rotational Transitions for the HNQ3-(H20)3 Complex, continued."
F F"
A*obs-calc
Vcalc
Vobs
I-Ll'-I-Ll"
4 3
6 5
5 4
5 4
5 2 4 *— 423
6 5
5 4
5 33 <— 4 3 2
6 5
4 3
5 4
5 42 <— 44i
6 5
4 3
54i <— 44o
5 4
6 5
4 3
6 5
6 l 6 < — 515
7 6
606 •— 5o5
5, 4 <-4 13
4 3
6 5
5 4
5 4
532 *~ 431
6 5
4 3
5 4
523 *— 4 2 2
6 5
6^ «— 5 24
6 5
7 6
7
6
7|7 "«— 6i6
8 7
7o7 <— 6()6
7
6
615 < — 5 1 4
6 5
634 *— 533
7 6
5 4
633 « — 53 2
6 5
7 6
5 4
8 7
7 2 6 <— 625
9 8
8ig < — 7i7
(a) All frequencies are in MHz.
5o5 *— 4()4
8831.029
8831.043
8831.059
9846.041
9846.085
10285.806
10285.937
10285.958
10295.143
10295.370
10295.437
10311.327
10311.562
10311.626
10340.961
10395.198
10508.581
10508.602
10508.625
10578.359
10578.509
10578.530
11069.255
11069.315
11645.269
11645.300
11951.487
11974.309
12190.491
12315.380
12315.448
12315.457
12968.480
12968.570
12968.594
13377.606
13553.677
8831.030
8831.042
8831.054
9846.036
9846.082
10285.810
10285.936
10285.966
10295.144
10295.371
10295.437
10311.328
10311.557
10311.624
10340.965
10395.191
10508.587
10508.604
10508.618
10578.359
10578.507
10578.541
11069.262
11069.321
11645.272
11645.293
11951.488
11974.308
12190.489
12315.387
12315.456
12315.466
12968.475
12968.571
12968.585
13377.594
13553.679
-0.001
0.001
0.005
0.005
0.003
-0.004
0.001
-0.008
-0.001
-0.001
0.000
-0.001
0.005
0.002
-0.004
0.007
-0.006
-0.002
0.007
0.000
0.002
-0.011
-0.007
-0.006
-0.003
0.007
-0.001
0.001
0.002
-0.007
-0.008
-0.009
0.005
-0.001
0.009
0.012
-0.002
Table A3.2 Rotational Transitions for the HNQ3-(H2'80)3 Complex."
J-1,1 •*— J-1,1
F
F
3 2
4 3
2 1
2 1
4 3
3 2
3 2
->22
4 3
2 1
3 2
4 3
2 1
3 2
•2„
2 1
4 3
4 3
5 4
3 2
5 4
4 3
4 3
+23 *— J>22
5 4
3 2
4 3
5 4
3 2
(a) Allfrequenciesare in MHz.
V0bs
Vcalc
AVobs-caic
5034.369
5034.428
5034.436
5319.106
5319.161
5319.189
5696.885
5697.142
5697.282
6074.738
6075.030
6075.176
6225.087
6225.117
6225.146
6624.275
6624.298
6813.330
6813.358
6813.380
7513.529
7513.629
7513.657
7762.099
7762.344
7762.440
5034.368
5034.428
5034.435
5319.103
5319.159
5319.188
5696.886
5697.141
5697.283
6074.735
6075.029
6075.177
6225.085
6225.126
6225.144
6624.278
6624.297
6813.332
6813.356
6813.379
7513.530
7513.630
7513.656
7762.100
7762.347
7762.440
0.000
0.000
0.001
0.003
0.001
0.001
-0.001
0.001
-0.001
0.003
0.001
-0.001
0.003
-0.009
0.002
-0.003
0.001
-0.002
0.001
0.001
-0.001
-0.001
0.001
-0.001
-0.003
0.000
Table A3.2 Rotational Transitions for the HNQ3-(H2180)3 Complex, continued."
J-l.l' *~ J-1.1
F
F
4 3
5 4
3 2
3 2
4l3<-3i2
5 4
5 4
5i5<-414
6 5
4 3
5o5 *~ 4()4
6 5
5 4
4 3
4 2 2 <— 32i
5 4
3 2
5 4
524 < - 4 2 3
6 5
7 6
6l6 «— 5i5
5 4
533 « - 4 3 2
6 5
4 3
7 6
606 *— 5os
(
5i4- -4 1 3
4 3
6 5
5 4
5 4
532 *- 43i
6 5
(a) Allfrequenciesare in MHz.
431 « — 330
Vpbs
7862.331
7862.593
7862.685
8134.967
8134.991
8173.428
8173.437
8270.659
8270.673
8270.686
8293.659
8293.784
8293.826
9264.626
9264.667
9695.685
9708.843
9708.967
9709.003
9738.513
9872.222
9872.241
9872.260
10023.247
10023.391
v
calc
AVpbs-calc
7862.327
7862.588
7862.685
8134.969
8134.991
8173.430
8173.437
8270.660
8270.672
8270.683
8293.660
8293.788
8293.814
9264.622
9264.666
9695.687
9708.844
9708.969
9708.998
9738.510
9872.224
9872.241
9872.258
10023.239
10023.390
0.004
0.005
0.001
-0.002
0.000
-0.002
0.000
-0.001
0.001
0.003
-0.001
-0.003
0.012
0.004
0.001
-0.003
-0.001
-0.002
0.005
0.002
-0.002
0.000
0.002
0.008
0.001
Table A3.3 Rotational Transitions for the H15NQ3-(H20)3 Complex."
r-u'«-J-i.r
2
U
«-ll,
2o2 "*— loi
2 n •*— lio
313<—212
3o3 *— 2o2
3 2 2 •*— 221
3i2 "*— 2 n
4l4^313
4o4 <— 3o3
4 2 3 <— 3 22
4i3<-312
4 2 2 <— 3 2 i
5o5 < — 4()4
524 < - 4 2 3
6i6*-515
606 *~ 5o5
5i4<-413
625 <— 524
v
obs
3594.602
3908.937
4422.221
5335.686
5647.531
6012.601
6561.594
7028.100
7247.048
7938.227
8594.168
8705.801
8798.238
9800.823
10300.193
10355.957
10463.266
11594.180
(a) Allfrequenciesare in MHz.
v
calc
^^obs-calc
3594.605
3908.938
4422.224
5335.685
5647.531
6012.601
6561.593
7028.100
7247.049
7938.226
8594.163
8705.801
8798.235
9800.825
10300.193
10355.961
10463.269
11594.179
-0.003
-0.001
-0.003
0.001
0.000
0.000
0.001
0.000
-0.001
0.001
0.005
0.000
0.003
-0.002
0.000
-0.004
-0.003
0.001
Table A3.4 Rotational Transitions for the DNQ3-(H20)3 Complex.'
J-Ll'-J-U"
V0bs
3 03 <— 2 0 2
5633.672
7224.833
8656.952
8770.738
9788.337
10272.692
10324.784
10443.974
11016.128
11574.385
11872.011
11893.733
12109.189
13195.921
13293.417
13463.222
13471.770
13645.545
4o4 <— 3o3
5is<-4 1 4
5o5 * - 4()4
524 *~ 423
6i6 •«— 5i5
606 *~ 5o5
514 <~ 4 B
523 <— 422
625 <— 5 2 4
7l7 <— 616
7<)7 <— 606
615 *— 5]4
624 <— 523
^26 «— 625
8ig <— 7n
808 <— 7o7
7l6 «~ 615
(a) Allfrequenciesare in MHz.
(b) Fits were done to line centers.
v
calc
AVobs-caic
5633.672
7224.835
8656.954
8770.736
9788.336
10272.695
10324.779
10443.968
11016.132
11574.382
11872.011
11893.731
12109.184
13195.921
13293.414
13463.228
13471.769
13645.551
0.000
-0.002
-0.002
0.002
0.001
-0.003
0.005
0.006
-0.004
0.003
0.000
0.002
0.005
0.000
0.003
-0.006
0.001
-0.006
Table A3.5 Cartesian Coordinates for the 10A
Conformer of Nitric Acid Trihydrate"
O
N
O
H
O
H
O
H
O
H
O
H
H
H
-2.592889
-1.622961
-1.881374
-0.978418
0.392397
1.195007
2.656656
2.511907
2.048388
1.086794
-0.440947
0.531628
3.271112
2.284845
-1.095485
-0.373220
0.961445
1.403247
2.236065
1.676766
0.709773
-0.250447
-2.020927
-1.989237
-0.701886
2.881569
0.844829
-2.666068
-0.007343
-0.016096
-0.013498
-0.000087
-0.004823
-0.005849
0.004006
0.030032
-0.016553
-0.006090
-0.027431
0.687353
-0.716659
0.649106
Table A3.6 Cartesian Coordinates for the 10B
Conformer of Nitric Acid Trihydrate8
O
N
O
H
O
H
O
H
O
H
O
H
H
H
-2.620930
-1.628261
-1.760831
-0.838805
0.577744
1.348196
2.750467
2.527273
1.758474
0.848568
-0.524484
0.795125
3.273716
2.000225
-0.947821
-0.272269
1.044075
1.432733
2.174123
1.573621
0.524079
-0.412494
-2.053182
-1.944631
-0.635579
2.808230
0.551380
-2.948516
-0.053704
0.091091
-0.216184
-0.115084
-0.026806
0.024575
0.074598
-0.048277
-0.332448
-0.037519
0.488659
-0.709599
0.874814
-0.099476
(a) Geometry optimization performed
using MP2/6-311++G(2df,2pd)
(a) Geometry optimization performed
using MP2/6-311++G(2df,2pd)
Table A3.7 Cartesian Coordinates for the 10C
Conformer of Nitric Acid Trihydrate"
Table A3.8 Cartesian Coordinates for the 10D
Conformer of Nitric Acid Trihydrate"
O
N
O
H
O
H
O
H
O
H
O
H
H
H
-2.568731
-1.616592
-1.820196
-0.933872
0.450424
1.251482
2.664825
2.493170
1.956802
1.009810
-0.497093
0.620967
3.118097
2.268240
-1.053881
-0.342754
0.989493
1.417246
2.174868
1.658459
0.655826
-0.292896
-2.033192
-1.953984
-0.678975
3.066431
0.712872
-2.641971
0.225778
0.002743
0.186093
-0.010740
-0.316369
-0.101245
0.244793
0.123081
-0.003342
-0.156883
-0.370725
-0.015818
1.085086
-0.672505
(a) Geometry optimization performed
using MP2/6-311++G(2df,2pd)
O
N
O
H
O
H
O
H
O
H
O
H
H
H
-2.618124
-1.635921
-1.864721
-0.959694
0.450301
1.246822
2.657727
2.552250
2.047569
1.090594
-0.466706
0.621808
2.892878
2.358415
-1.050780
-0.356552
0.983909
1.395944
2.114979
1.637559
0.698064
-0.233872
-1.936557
-1.968707
-0.715193
3.044260
0.673578
-2.808269
0.193455
0.066154
0.018967
-0.113015
-0.390691
-0.086814
0.399358
0.149868
-0.342572
-0.256596
-0.020240
-0.246665
1.326023
-0.102097
(a) Geometry optimization performed
using MP2/6-311++G(2df,2pd)
182
Table A3.9 Cartesian Coordinates for the 8A
Conformer of Nitric Acid Trihydrate*
O
N
O
H
O
O
H
O
H
O
H
H
H
H
(a)
1.867769
-1.066975
-0.647497
1.722241
-0.007031
-0.067968
0.679801
0.067263
0.840610
0.137481
-0.770732
0.689795
2.370093
1.010798
-0.168049
-0.967456
-1.882638
0.434936
-1.737241
-1.408669
0.063733
-2.876354
-0.190179
-0.517940
-2.451711
0.671282
-0.372296
-1.325818
2.032752
0.112877
-0.514160
1.623241
0.434281
-0.688324
-2.504432
-0.237963
-3.747432
-0.110151
-0.131015
-1.038573
2.780496
-0.410245
Geometry optimization performed
using MP2/6-311++G(2df,2pd)
Table A3.10 Cartesian Coordinates for the
Global Minimum Structure of HN03-H2Oa
Table A3.11 Cartesian Coordinates for the
Global Minimum Structure of HN0 3 -(H 2 0) 2 a
o 2.053884 -0.104398 0.017078
N
0.861235
0.079186
0.002473
O
-1.073421
0.101038
-0.009317
H
-0.829558
-0.746532
-0.017930
O
0.254105
1.140049
-0.003217
O
-2.404048
-0.027421
-0.078895
H
-2.138879
0.888620
0.033526
H
-3.100049
-0.174862
0.561908
(a) Geometry optimization performed
using MP2/6-311++G(2df,2pd)
O
2.532736
-0.440409
0.015656
N
1.348885
-0.199285
0.001051
O
1.028308
1.127467
-0.029611
H
0.031188
1.171585
-0.031338
O
0.422613
-1.001936
0.008875
O
-1.585419
1.480177
-0.077229
H
-2.088854
0.649206
-0.031499
H
-1.959593
2.050438
0.593840
O
-2.504890 -1.098629
0.083066
H
-1.595345 -1.407983
0.036181
H
-2.976379 -1.601611
-0.580597
(a) Geometry optimization performed
using MP2/6-311++G(2df,2pd)
183
Table A3.12 Cartesian Coordinates for the HNQ3 Monomer with Cs Symmetry"
o
0.000000
1.171534
0.460732
0.151754
0.000000
0.000000
0.000000
-0.988067
0.832927
-1.226327
0.000000
-0.262506
H
0.632319
-1.600932
0.000000
(a) Geometry optimization performed using MP2/6-311++G(2df,2pd)
N
O
o
Table A3.13 Cartesian Coordinates for the H2Q Monomer with C2v Symmetry"
O
0.000000
0.000000
0.118225
H
0.000000
0.758141
-0.472899
H
0.000000
-0.758141
-0.472899
(a) Geometry optimization performed using MP2/6-311++G(2df,2pd)
Table A3.14 Cartesian Coordinates for the H3Q+ Ion with C3v Symmetry"
O
0.000000
0.000000
0.077800
H
0.000000
0.934113
-0.207466
H
0.808966
-0.467057
-0.207466
H
-0.808966
-0.467057
-0.207466
(a) Geometry optimization performed using MP2/6-311-H-G(2df,2pd)
Appendix to Chapter 4
185
3
U.
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Table A4.1 (CH3)3l4N-H1'tN03 Transition Frequencies, continued.
F — F"
F,'
F,"
Vobs
1-0
3—2
1 —1
2—1
2— 2
3— 3
2<-2
3—2
4— 3
3— 3
2—1
2— 1
1<-1
3—4
3— 3
4— 4
4— 3
3—3
3—2
4— 3
2—1
2—1
4— 3
5— 4
1—1
2—1
2— 3
2— 2
3—3
1—2
(a) All Frequencies are in MHz.
1
3
1
2
3
3
3
2
3
2
1
3
2
3
3
4
4
3
3
4
2
3
3
4
2
3
3
3
4
2
1
2
1
1
1
2
2
1
2
2
0
2
2
3
2
3
2
3
2
3
1
2
2
3
2
1
3
2
3
2
4125.032
4125.117
4125.151
4125.159
4125.648
4125.729
4125.796
4126.090
4126.162
4126.183
4126.216
4127.267
4127.275
5978.800
5978.905
5978.922
5979.029
5979.442
5979.506
5979.557
5979.570
5979.768
5979.812
5979.853
5979.949
5980.655
5980.685
5980.750
5980.802
5980.928
*^calc
^^obs-calc
4125.033
4125.115
4125.155
4125.161
4125.648
4125.729
4125.793
4126.090
4126.163
4126.170
4126.218
4127.267
4127.271
5978.801
5978.906
5978.920
5979.025
5979.439
5979.504
5979.558
5979.568
5979.766
5979.812
5979.851
5979.948
5980.655
5980.684
5980.748
5980.801
5980.931
-0.001
0.002
-0.004
-0.002
0.000
0.000
0.003
0.000
-0.001
0.013
-0.002
0.000
0.004
-0.001
-0.001
0.002
0.004
0.003
0.002
-0.001
0.002
0.002
0.000
0.002
0.001
0.000
0.001
0.002
0.001
-0.003
(b) a = 2.5 kHz
187
Table A4.1 (CH3>j14N-H14N03 Transition Frequencies, continued.
J-i.i' -^ J-i.i"
F' <- F"
2- -2
4 -4
3- - 3
4^ - 3
2- - 2
2- - 1
3- - 2
3' -2
4 -3
4^ - 3
5' -4
2- - 2
2' -2
3' -3
-2
3'22'
^21
4- - 3
2- - 1
4- - 3
5- - 4
3- - 2
2< -1
3- - 2
1< -0
3< -2
3< - 2
4< -3
2< - 1
4< -3
5< -4
3< -2
2< -1
3< -2
1< -0
3 - -3
2„
4< -4
2< -2
3< -2
4« -3
4* • 3
2< 1
5* 4
3* • 2
2* • 2
3* •3
\* 1
(a) All Frequencies are in MHz.
•>03
'02
Vote
2
4
3
4
3
3
4
3
4
3
4
2
3
4
3
4
2
3
4
2
3
4
2
4
3
4
3
3
4
2
2
4
2
3
4
2
3
4
3
3
4
4
3
4
2
l
3
2
2
3
2
3
2
3
2
3
2
2
3
2
3
1
2
3
1
2
3
1
2
2
3
1
2
3
1
2
3
1
2
3
1
2
3
2
2
3
3
2
3
1
6078.215
6078.224
6078.235
6078.326
6079.045
6079.094
6079.138
6079.268
6079.298
6079.322
6079.337
6079.381
6080.754
6080.787
6083.865
6083.921
6083.951
6084.893
6084.993
6085.029
6085.515
6085.564
6085.643
6089.331
6089.343
6089.398
6089.429
6090.369
6090.465
6090.501
6090.989
6091.037
6091.116
6187.391
6187.416
6187.425
6187.825
6187.851
6188.113
6188.129
6188.143
6188.154
6188.808
6188.831
6188.844
^calc
Av,obs-calc
-0.002
6078.217
0.000
6078.224
0.003
6078.232
6078.325
0.001
-0.001
6079.046
-0.003
6079.097
0.000
6079.138
0.003
6079.265
0.000
6079.298
0.000
6079.322
0.002
6079.335
-0.007
6079.388
0.002
6080.752
0.002
6080.785
0.002
6083.863
6083.922
-0.001
6083.951
0.000
6084.894
-0.001
0.000
6084.993
6085.030
-0.001
0.000
6085.515
-0.002
6085.566
6085.643
0.000
6089.331
0.000
6089.342
0.001
6089.398
0.000
6089.427
0.002
6090.369
0.000
6090.465
0.000
6090.502
-0.001
6090.989
0.000
6091.037
0.000
6091.114
0.002
6187.393
-0.002
6187.417
-0.001
6187.425
0.000
6187.831
-0.006
6187.851
0.000
-0.004
6188.117
6188.133
-0.004
6188.144
-0.001
6188.153
0.001
6188.811
-0.003
6188.831
0.000
6188.842
0.002
(b) a = 2.5kHz
188
Table A4.2 (CH3)31SN-H14N03 Transition Frequencies. a-b
J-l.l' *— J-l.l"
F' — F "
2— 2
2—1
V00s
3970.839
3970.866
3—2
3970.980
1-0
3971.029
1—1
3971.051
2— 2
4038.377
1—0
4038.400
2—1
4038.486
3—2
4038.496
1—1
4038.664
1
—
1
4108.601
2„
4108.614
2—1
3—2
4108.718
2— 2
4108.747
1-0
4108.881
3— 3
5955.444
3l3
3—2
5955.564
2—1
5955.585
4— 3
5955.601
2— 2
5955.770
3— 3
6054.242
3 03 — A>2
2— 1
6054.341
4— 3
6054.367
2— 2
6054.521
3—2
6059.618
322
4— 3
6059.731
2—1
6059.793
3— 2
6064.998
4— 3
6065.109
2—1
6065.169
•2„
3—2
6162.168
4— 3
6162.198
2—1
6162.212
4— 4
8066.084
+04 '
4— 3
8066.208
8066.217
5—4
3— 3
8066.368
(a) All Frequencies are in MHz.
2i2 *~ 111
Vdic
3970.855
3970.865
3970.978
3971.032
3971.056
4038.381
4038.401
4038.485
4038.495
4038.663
4108.598
4108.614
4108.718
4108.728
4108.884
5955.441
5955.564
5955.585
5955.598
5955.776
6054.244
6054.344
6054.365
6054.522
6059.618
6059.730
6059.793
6064.999
6065.109
6065.171
6162.171
6162.200
6162.213
8066.087
8066.208
8066.214
8066.368
( b ) a = 4.6kHz
Av0bs-calc
-0.016
0.001
0.002
-0.003
-0.005
-0.004
-0.001
0.001
0.001
0.001
0.003
0.000
0.000
0.019
-0.003
0.003
0.000
0.000
0.003
-0.006
-0.002
-0.003
0.002
-0.001
0.000
0.001
0.000
-0.001
0.000
-0.002
-0.003
-0.002
-0.001
-0.003
0.000
0.003
0.000
Table A4.3 The Cartesian Coordinates of the
Global Minimum N(CH3)3 Monomer *
0.402386
0.000000
0.000000
N
-0.064860
0.000000
1.373202
C
-0.064860
1.189227
-0.686601
C
-0.064860
-1.189227
-0.686601
C
0.307597
-0.882954
1.889175
H
-1.164932
0.000000
1.437681
H
0.307597
0.882954
H
1.889175
0.307597
1.194596
-1.709248
H
0.307597
H
2.077551
-0.179927
-0.718841
-1.164932
H
1.245068
0.307597
H
-1.194596
-1.709248
-1.245068
-0.718841
-1.164932
H
0.307597
H
-2.077551
-0.179927
(a) Optimized at the MP2/6-311++G(2df,2pd)
level of theory and basis set.
Table A4.4 The Cartesian Coordinates of the
Global Minimum NH(CH3)2 Monomer'
0.000000
-0.027082
0.591951
N
1.190470
0.000000
0.787707
H
-0.224464
1.202237
-0.027082
C
-0.224464
-1.202237
-0.027082
C
-0.776153
1.255532
-0.964847
H
0.410870
2.082551
H
0.036383
-0.954996
0.791894
1.237740
H
-0.776153
-1.255532
-0.964847
H
-0.954996
H
0.791894
-1.237740
0.410870
-2.082551
H
0.036383
(a) Optimized at the MP2/6-311++G(2df,2pd)
level of theory and basis set.
Table A4.5 The Cartesian Coordinates of the
Global Minimum NH2CH3 Monomer'
Table A4.6 The Cartesian Coordinates of the
Global Minimum NH3 Monomera
N
0.049797
-0.756716
0.000000
0.049797
C
0.705021
0.000000
-0.440944
H
0.809572
-1.110462
H
-0.440944
-1.110462
-0.809572
H
-0.940756
1.167257
0.000000
H
0.587643
1.060275
-0.875496
H
0.587643
1.060275
0.875496
(a) Optimized at the MP2/6-31H HG(2df,2pd)
level of theory and basis set.
N
0.000000
0.000000
0.112104
H
0.000000
0.938653
-0.261576
H
0.812897
-0.469326
-0.261576
H
-0.812897
-0.469326
-0.261576
(a) Optimized at the MP2/6-311++G(2df,2pd)
level of theory and basis set.
190
Table A4.7 The Cartesian Coordinates of the
Global Minimum HN(CH3)3+ Ion
1.368175
0.000000
0.000000
H
0.347214
0.000000
0.000000
N
-0.104132
1.422102
0.000000
C
-0.104132
1.231577
-0.711051
C
c -1.231577 -0.711051 -0.104132
0.274159
-0.891380
1.911543
H
-1.189747
H
0.000000
1.426378
0.274159
0.891380
1.911543
H
0.274159
H
1.209755
-1.727729
-0.183814
0.274159
H
2.101135
-1.189747
H
1.235280
-0.713189
-1.209755
0.274159
H
-1.727729
-1.235280
-1.189747
H
-0.713189
-0.183814
0.274159
H
-2.101135
(a) Optimized at the MP2/6-311++G(2df,2pd)
level of theory and basis set.
Table A4.8 The Cartesian Coordinates of the
Global Minimum NH2(CH3)2+ Ion*
0.544695
0.000000
N
0.000000
1.159685
0.000000
H
0.814492
1.159685
H
-0.814492
0.000000
-0.276619
1.249238
C
0.000000
-0.276619
-1.249238
C
0.000000
-0.895990
1.246107
H
0.890003
-0.895990
H
-1.246107
0.890003
-0.895990
-1.246107
H
-0.890003
-0.895990
1.246107
H
-0.890003
0.385581
H
0.000000
-2.107957
H
2.107957
0.385581
0.000000
(a) Optimized at the MP2/6-311++G(2df,2pd)
level of theoryand basis set.
Table A4.9 The Cartesian Coordinates of the
Global Minimum NH3CH3+ Ion a
Table A4.10 The Cartesian Coordinates of the
Global Minimum N H / Ion'
N
C
H
H
H
H
H
H
N
H
H
H
H
0.000000
0.000000
0.705987
0.000000
0.000000
-0.796223
0.000000
0.949951
1.078795
-0.822682
-0.474976
1.078795
0.822682
-0.474976
1.078795
0.000000
-1.029099
-1.133651
0.891226
0.514549
-1.133651
-0.891226
0.514549
-1.133651
(a) Optimized at the MP2/6-311++G(2df,2pd)
level of theory and basis set.
0.000000
0.000000
0.000000
0.591551
0.591551
0.591551
-0.591551
-0.591551
0.591551
0.591551
-0.591551
-0.591551
-0.591551
0.591551
-0.591551
(a) Optimized at the MP2/6-311 ++G(2df,2pd)
level of theoryand basis set.
191
Table A4.ll The Cartesian Coordinates of the Global
Minimum HNQ3 Monomer"
0.460732
0.000000
1.171534
0.151754
0.000000
0.000000
0.832927
0
-0.988067
0.000000
-0.262506
-1.226327
0.000000
H
-1.600932
0.632319
0.000000
(a) Optimized at the MP2/6-311++G(2df,2pd)
level of theory and basis set.
o
N
o
Table A4.12 The Cartesian Coordinates of the Global
Minimum (CH3)3N-HN03 Complex"
o
o
N
0
H
N
C
C
c
H
H
H
H
H
H
H
H
H
(a)
-2.923814
1.048504
0.000000
-1.684633
-0.749281
0.000000
-1.861877
0.464856
0.000000
-0.760241
1.243217
0.000000
0.070841
0.568874
0.000000
1.316113
-0.257545
0.000000
2.463506
0.647375
0.000000
1.316113
-1.091771
1.200732
1.316113
-1.091771
-1.200732
3.407497
0.092135
0.000000
2.425917
1.279490
-0.884562
2.425917
1.279490
0.884562
0.434840
-1.727365
1.190733
0.434840
-1.727365
-1.190733
1.282019
-0.454865
2.082230
1.282019
-0.454865
-2.082230
2.215790
-1.714613
1.247112
2.215790
-1.714613
-1.247112
Optimized at the MP2/6-311++G(2df,2pd)
level of theory and basis set.
Table A4.13 The Cartesian Coordinates for
Conformer S of the (CH3)2HN-HN03 Complex *
Table A4.14 The Cartesian Coordinates for
Conformer A of the (CH3)2HN-HNO3 Complex'
1.163148
0.000000
-2.567876
O
0.000000
-0.628598
-1.319530
O
0.000000
0.582855
N
-1.505301
0.000000
-0.406132
1.370696
O
0.000000
0.715895
H
0.415225
0.000000
0.415394
2.505517
H
1.682194
-0.998741
1.212340
C
1.682194
-0.998741
-1.212340
C
0.754932
1.239658
-1.565331
H
-1.565331
-1.239658
0.754932
H
1.722328
-0.357244
2.089133
H
-2.089133
1.722328
-0.357244
H
2.524233
-1.694360
1.238846
H
-1.238846
H
2.524233
-1.694360
(a) Optimized at the MP2/6-31 l+4G(2df,2pd)
level of theory and basis set.
-0.676417
0.933143
1.302373
O
-0.286841
0.209335
2.881851
O
-0.044964
1.726842
-0.028218
N
0.425919
-0.905064
0.810683
O
0.113387
-0.524251
H
-0.120785
0.030343
-0.281416
H
-1.496699
-0.242909
-0.949566
C
-2.581353
1.187687
0.574598
-1.763015
C
0.766232
H
-1.349426
-2.655368
-2.359498
-1.769278
-0.921105
H
H
-0.513255
-0.512459
-3.546078
0.352722
-1.232562
H
-1.357513
0.851732
1.608360
H
-1.814533
0.323151
H
-2.704489
1.681205
(a) Optimized at the MP2/6-311++G(2df,2pd)
level of theory and basis set.
Table A4.15 The Cartesian Coordinates of the
Global Minimum (CH3)H2N-HN03 Complex *
1.064981
-0.414615
o 0.70839
2.489538
-0.001047
0.26414
o
N
1.315704
0.079644
-0.015921
-1.063495
0.13569
o 0.599815
H
-0.364163
-0.820189
-0.148564
N
-1.866463
-0.426594
-0.513442
C
-2.39242
0.409783
0.575434
H
-2.460138
-0.189514
1.479037
H
-3.37295
0.832558
0.36116
H
-1.690609
1.218849
0.754644
H
-1.788644
0.119171
-1.363127
H
-2.495608
-1.194444
-0.711933
(a) Optimized at the MP2/6-311++G(2df,2pd)
level of theory and basis set.
Table A4.16 The Cartesian Coordinates of the
Global Minimum H3N-HNQ3 Complexa
O
0.352749
2.048440
0.000000
O
-1.140616
0.454819
0.000000
N
0.000000
0.892932
0.000000
O
1.012394
-0.020051
0.000000
H
0.554243
-0.926410
0.000000
N
-0.170587
-2.428924
0.000000
H
-0.002233
-3.004227
0.814807
H
-1.151880
-2.178851
0.000000
H
-0.002233
-3.004227
-0.814807
(a) Optimized at the MP2/6-311++G(2df,2pd)
level of theory and basis set.
193
Appendix to Chapter 5
194
Table A5.1 Transition Frequencies for the (CI^CCN-SC^ Complex."
J' — J"
4— 3
| K | = \mi,\
0
1
2
5—4
0
1
2
F'—F"
V0bs
Vgaic
Apbs-calc
3—2
4<-3
5<-4
3—3
4— 4
3—2
4— 3
5— 4
3— 3
4—4
3—2
4— 3
5—4
3— 3
4— 4
4— 3
5<-4
6— 5
4— 4
5*-5
4— 3
5—4
6— 5
4— 4
5— 5
4— 3
5<-4
6— 5
4— 4
5— 5
3579.910
3579.983
3580.005
3581.423
3578.860
3579.969
3579.879
3580.015
3581.106
3579.040
3580.160
3579.583
3580.040
3580.160
3579.583
4474.938
4474.978
4475.000
4476.369
4473.821
4474.946
4474.906
4474.987
4476.166
4473.930
4474.987
4474.722
4474.959
4475.562
4474.263
3579.910
3579.982
3580.007
3581.422
3578.862
3579.972
3579.882
3580.016
3581.106
3579.042
3580.159
3579.584
3580.042
3580.159
3579.584
4474.929
4474.969
4474.987
4476.369
4473.824
4474.944
4474.908
4474.981
4476.167
4473.934
4474.987
4474.723
4474.963
4475.563
4474.265
0.000
0.001
-0.002
0.001
-0.002
-0.003
-0.003
-0.001
0.000
-0.002
0.001
-0.001
-0.002
0.001
-0.001
0.009
0.009
0.013
0.000
-0.003
0.002
-0.002
0.006
-0.001
-0.004
0.000
-0.001
-0.004
-0.001
-0.002
(a) All frequencies are in M H z .
195
H .
l/l
SO
~J
tO
»
M
Ul
NO
^„ b
00
M
to
t
ON
S£2
O
O
o
o
O
°
O
O
o
O
o
O
o
C
>
o o o o P o o o o
I
o o
oo
to
o
ON
to
NO NO NO
NO NO NO
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Table A5.2 Cartesian Coordinates for the Staggered (CH3)3CCN-S03 Complex *
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
-1.453648
0.000000
c
0.726824
1.258896
c
0.726824
-1.258896
c
-1.459615
0.000000
H
1.264064
0.729808
H
-1.264064
0.729808
H
-1.981842
-0.885170
H
-1.981842
0.885170
H
1.273741
1.757501
H
2.158911
0.224341
H
-2.158911
0.224341
H
-1.273741
H
1.757501
0.000000
0.000000
S
0.000000
1.440663
O
-1.247651
-0.720332
O
1.247651
-0.720332
O
(a) Geometry optimization performed using MP2/aug-cc-pVTZ
N
C
C
0.120625
-1.047787
-2.512542
-2.996624
-2.996624
-2.996624
-4.086848
-4.086848
^1.086848
-2.644436
-2.644436
-2.644436
-2.644436
-2.644436
-2.644436
2.522536
2.592642
2.592642
2.592642
Table A5.3 Cartesian Coordinates for the Staggered (CH3)3CCN-S03 Complex
0.000000
0.000000
N
0.101243
C
0.000000
0.000000
-1.067652
C
0.000000
0.000000
-2.532214
0.000000
-1.453240
-3.017419
c
1.258543
0.726620
-3.017419
c
-1.258543
0.726620
-3.017419
c
H
0.000000
-1.458496
-4.107653
H
1.263095
0.729248
-4.107653
H
-1.263095
0.729248
-4.107653
H
-0.885056
-1.981897
-2.665716
H
0.885056
-1.981897
-2.665716
H
1.273845
1.757429
-2.665716
H
2.158901
0.224467
-2.665716
H
-2.158901
0.224467
-2.665716
H
-1.273845
1.757429
-2.665716
0.000000
S
0.000000
2.549613
O
0.000000
1.441116
2.613645
O
-1.248043
-0.720558
2.613645
O
1.248043
-0.720558
2.613645
(a) Geometry optimization performed using MP2/aug-cc-pVTZ
(b) Geometry optimization performed with the counterpoise correction
Table A5.4 Cartesian Coordinates for the Staggered (CH3)3CCN-SQ3 Complex
0.142123
0.000000
0.000000
N
-1.025768
0.000000
0.000000
C
-2.490316
0.000000
0.000000
C
-2.973852
-1.453886
0.000000
c
-2.973852
0.726943
1.259102
c
-2.973852
0.726943
-1.259102
c
-4.064035
-1.459775
0.000000
H
-4.064035
0.729888
1.264202
H
-4.064035
0.729888
-1.264202
H
-2.621721
-0.885206
-1.981989
H
-2.621721
H
0.885206
-1.981989
-2.621721
1.757606
H
1.273850
-2.621721
0.224384
H
2.159056
0.224384
-2.621721
H
-2.159056
-2.621721
H
-1.273850
1.757606
0.000000
0.000000
2.492510
S
O
0.000000
1.429302
2.569718
-1.237812
O
-0.714651
2.569718
1.237812
O
-0.714651
2.569718
(a) Geometry optimization performed using MP2 theory, the aug-cc-pV(T+d)Z
basis set on the sulfur atom, and the aug-cc-pVTZ basis set on all other atoms.
Table A5.5 Cartesian Coordinates for the Eclipsed (CH3)3CCN-SQ3 Complex a
N
C
C
0.000000
0.000000
0.000000
0.000000
c
-1.258896
c
1.258896
c
H
0.000000
H
-1.264064
H
1.264064
H
0.885170
H
-0.885170
H
-1.273741
H
-2.158911
H
2.158911
H
1.273741
S
0.000000
O
0.000000
O
-1.247651
O
1.247651
(a) Geometry optimization performed using
0.000000
0.000000
0.000000
1.453648
-0.726824
-0.726824
1.459615
-0.729808
-0.729808
1.981842
1.981842
-1.757501
-0.224341
-0.224341
-1.757501
0.000000
1.440663
-0.720332
-0.720332
MP2/aug-cc-pVTZ
0.120625
-1.047787
-2.512542
-2.996624
-2.996624
-2.996624
-4.086848
-4.086848
-4.086848
-2.644436
-2.644436
-2.644436
-2.644436
-2.644436
-2.644436
2.522536
2.592642
2.592642
2.592642
Table A5.6 Cartesian Coordinates for the (CH3)3CCN Monomer with C3v Symmetry'
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
1.450883
0.000000
-0.725442
-1.256502
c
-0.725442
1.256502
c
1.458339
H
0.000000
-0.729170
H
-1.262959
-0.729170
H
1.262959
1.980151
H
0.884396
H
1.980151
-0.884396
-1.755985
H
-1.272663
-0.224166
H
-2.157059
H
-0.224166
2.157059
H
-1.755985
1.272663
(a) Geometry optimization performed using MP2/aug-cc-pVTZ
N
C
C
C
2.359860
1.187569
-0.279924
-0.770682
-0.770682
-0.770682
-1.861193
-1.861193
-1.861193
-0.418171
-0.418171
-0.418171
-0.418171
-0.418171
-0.418171
Table A5.7 Cartesian Coordinates for the SQ3 Monomer with D3h Symmetry8
S
0.000000
0.000000
O
0.000000
1.445057
O
1.251456
-0.722529
O
-1.251456
-0.722529
(a) Geometry optimization performed using MP2/aug-cc-pVTZ
0.000000
0.000000
0.000000
0.000000
Table A5.8 Cartesian Coordinates for the SQ3 Monomer with D3h Symmetry8
S
0.000000
0.000000
0.000000
O
0.000000
1.433799
0.000000
O
1.241707
-0.716900
0.000000
O
-1.241707
-0.716900
0.000000
(a) Geometry optimization performed using MP2 theory, the aug-cc-pV(T+d)Z basis
set on the sulfur atom, and the aug-cc-pVTZ basis set on the oxygen atoms.
Table A5.9 Cartesian Coordinates and Moments of Inertia for SQ3 with a = 1.4°"
c
b
a
s
o
o
o
0.0000000
0.0000000
1.2292330
-1.2292330
0.0000000
1.4193960
-0.7096980
-0.7096980
0.0208180
-0.0138710
-0.0138710
-0.0138710
48.360
96.674
I,i [amu-A2]
48.360
(a) The molecule has fixed C3v symmetry and Rso values of 1.4198199 A.
Table A5.10 Cartesian Coordinates and Moments of Inertia for S0 3 with a = 2.8°"
a
b
c
s
o
o
o
0.0000000
0.0000000
1.2281320
-1.2281320
0.0000000
1.4181250
-0.7090620
-0.7090620
0.0416240
-0.0277340
-0.0277340
-0.0277340
I,, [amuA 2 ]
48.343
48.343
96.501
(a) The molecule has fixed C3v symmetry and Rso values of 1.4198199 A.
Table A5.ll Cartesian Coordinates and Moments of Inertia for SQ3 with a = 4.2°*
a
b
c
0.0000000
0.0000000
s
0.0624050
0.0000000
1.4160070
-0.0415800
o
1.2262980
-0.7080030
-0.0415800
o
-1.2262980
-0.7080030
-0.0415800
o
I/, [amu-A2]
48.314
48.314
96.213
(a) The molecule has fixed C3v symmetry and Rso values of 1.4198199 A.
to
o
(O
c
O-
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I
o
o
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a
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References
Introduction
1) D. I. Mendeleyev, The Principles of Chemistry, 2nd English Edition, American Home
Library, New York, NY, 1902.
2) W. B. Jensen, The Lewis Acid-Base Concepts, John Wiley & Sons, New York, NY,
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11)C. S. Brauer, G. Sedo, K. R. Leopold, Geophys. Res. Lett. 2006, 33, L23805.
12) See for examples, (a) A. B. Nadykto, F. Yu, J. Geophys. Res. 2003, 108(D23), 4717.
(b) A. B. Nadykto, F. Yu, Phys. Rev. Lett. 2004, 93,016101-1. (c) A.B. Nadykto,
A. Al Natsheh, F. Yu, K. V. Mikkelsen, J. Ruuskanen., Aerosol Sci. and Tech.
2004, 38, 349.
13) See for examples, (a) Z. Kisiel, E. Bialkowska-Jaworska, L. Pszczolkowski, A. Milet,
C. Struniewicz, R. Moszynski, J. Sadlej, J. Chem. Phys. 2000, 112, 5767-5776.
(b) D. Priem, T.-K. Ha, A. Bauder, J. Chem. Phys. 2000, 113(1), 169-175. (c) Z.
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Kisiel, B. A. Pietrewicz, O. Desyatnyk, L. Pszczolkowski, I. Struniewicz, J.
Sadlej, J. Chem. Phys. 2003, 119, 5907-5917. (d) B. Ouyang, T. G. Starkey, B. J.
Howard, J. Phys. Chem. A 2007, 111, 6165-6175. (e) M. B. Craddock, C. S.
Brauer, K. R. Leopold, J. Phys. Chem. A 2008,112,488-496.
14) See for examples, (a) S. W. Hunt, K. J. Higgins, M. B. Craddock, C. S. Brauer, K. R.
Leopold, J. Am. Chem. Soc. 2003, 15, 13850-13860. (b) C. S. Brauer,
"Microsolvation of Reactive Systems in the Gas Phase via Fourier Transform
Microwave Spectroscopy," Chapter 2, Ph.D. Thesis, University of Minnesota,
2006.
15) M. Canagratna, J. A. Phillips, M. E. Ott, K. R. Leopold, J. Phys. Chem. A 1998, 102,
1489-1497.
16) (a) A. C. Legon, Chem. Soc. Rev. 1993, 153-163. (b) C. S. Brauer, M. B. Craddock, J.
Kilian, E. M. Grumstrup, M. C. Orilall, Y. Mo, J. Gao, K. R. Leopold, J. Phys.
Chem. A 2006,110,10025.
17)M. E. Ott, K. R. Leopold, J. Phys. Chem. A 1999, 103,1322-1328.
18) See for examples, (a) K. R. Leopold, Advances in Molecular Structure Research, Vol.
2, M. Hargittai, I. Hargittai, editors; JAI Pres, Greenwich, CT, 1996. (b) K. R.
Leopold, M. Canagaratna, J. A. Phillips, Ace. Chem. Res. 1997, 30, 57-64.
19) S. W. Hunt, K. R. Leopold, J. Phys. Chem. A 2001, 105, 5498-5506.
20) S. W. Hunt, D. L. Fiacco, M. Craddock, K. R. Leopold, J. Mol. Spectrosc. 2002, 212,
213-218.
204
Chapter 1
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Theory, Experiments, and Applications, 2000, Academic Press, New York, and
references therein.
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K. Quinn, E. S. Saltzman, W. J. De Bruyn, J. Geophys. Res. 2000, 105(D20),
24689. (b) R. A. Cox., Phil. Trans. R. Soc. Lond. 1997, B 352, 251.
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218.
4) K. S. Carslaw, B. P. Luo, S. L. Clegg, T. Peter, P. Brimblecombe, P. J. Crutzen,
Geophys. Res. Lett. 1994,21,2479.
5) V. Vaida, H. G. Kjaergaard, P. E. Hintze, D. J. Donaldson, Science 2003,299, 1566.
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Processes in the Environment, K. R. Spumy, editor: Lewis Publishers, Boca
Raton, FL 2000, and the references therein.
7) (a) F. Raes, A. Janssesns, J. Aerosol Sci. 1986, 17, 715. (b) L. Laakso, J. M. Makela,
L. Pirjola, M. Kulmala, J. Geophys Res. 2002,107(D20), 4427.
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Yu, J. Geophys. Res. 2003,108(D23), 4717.
9) E. R. Lovejoy, J. Curtius, K. D. Froyd, J. Geophys. Res. 2004,109, D08204.
10)(a) A. B. Nadykto, F. Yu, Phys. Rev. Lett. 2004, 93, 016101-1. (b) A.B. Nadykto, A.
Al Natsheh, F. Yu, K. V. Mikkelsen, J. Ruuskanen., Aerosol Sci. and Tech.
2004, 38, 349.
205
11)C. S. Brauer, G. Sedo, K. R. Leopold, Geophys. Res. Lett. 2006, 33, L23805.
12) R. L. Kuczkowski, R. D. Suenram, F. J. Lovas, J. Am. Chem. Soc. 1981,103,2561.
13) J. A. Phillips, M. Canagaratna, H. Goodfriend, A. Grushow, J. Almlof, K. R.
Leopold, J. Am. Chem. Soc. 1995,117, 12549.
14) D. L. Fiacco, S. W. Hunt, K. R. Leopold, J. Am. Chem. Soc. 2002,124,4504.
15)(a) M. Canagaratna, M. E. Ott, K.R. Leopold, Chem. Phys. Lett. 1997, 281, 63. (b) D.
L. Fiacco, A. Toro, K. R. Leopold, Inorg. Chem. 2000, 39, 37. (c) D.L. Fiacco, Y.
Mo, S. W. Hunt, M. E. Ott, A. Roberts, K. R. Leopold, J. Phys. Chem. A 2001,
105,484.
16) K. H. Bowen, K. R. Leopold, K. V. Chance, W. Klemperer, J. Chem. Phys. 1980, 73,
137.
17) (a) Z. Kisiel, J. Kosarzewski, B. A. Pietrewicz, L. Pszczolkowski, Chem. Phys. Lett.
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SPEctroscopy (PROSPE) website (http://www.ifpan.edu.pl/~kisiel/prospe.htm).
18) (a) H. M. Pickett, J. Mol. Spec. 1991, 148, 371. (b) Program downloaded from the
Programs
for
ROtational
SPEctroscopy
(PROSPE)
website:
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