close

Вход

Забыли?

вход по аккаунту

?

Ab initio study of conformations of biological molecules and carbon dioxide-laser/microwave-sideband spectroscopy

код для вставкиСкачать
Ab Initio Study of Conformations of Biological Molecules and
C 0 2-Laser/Microwave-Sideband Spectroscopy
by
Qiang Liu
B. Sc., Beijing Normal University, 1997
A Thesis Submitted in Partial Fulfillment of
the Requirements for the Degree of
Master of Science in Physics
in the Graduate Academic Unit of the Department of Physics
Supervisor(s):
Li-Hong Xu, Ph.D., Department of Physical Sciences/Microwave
and Infrared Spectroscopy
Examining Board:
Allan G. Adam, PhD., Department of Chemistry/Experimental
Physical Chemistry; Molecular Beams and Spectroscopy
William Ward, PhD., Department of Physics /Space and
Atmospheric Physics
This thesis is accepted.
Dean of Gil^Jiate Studies
THE ;NIVERSITY OF NEW BRUNSWICK
August, 2003 (of submission to Graduate School)
© Qiang Liu, 2003
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1*1
Library and
Archives Canada
Bibliotheque et
Archives Canada
Published Heritage
Branch
Direction du
Patrimoine de I'edition
395 W ellington S treet
Ottaw a ON K1A 0N4
C an ad a
395, rue Wellington
O ttaw a ON K1A 0N4
C an a d a
Your file Votre reference
ISBN: 0-612-98918-6
Our file Notre reference
ISBN: 0-612-98918-6
NOTICE:
The author has granted a non­
exclusive license allowing Library
and Archives Canada to reproduce,
publish, archive, preserve, conserve,
communicate to the public by
telecommunication or on the Internet,
loan, distribute and sell theses
worldwide, for commercial or non­
commercial purposes, in microform,
paper, electronic and/or any other
formats.
AVIS:
L'auteur a accorde une licence non exclusive
permettant a la Bibliotheque et Archives
Canada de reproduire, publier, archiver,
sauvegarder, conserver, transmettre au public
par telecommunication ou par I'lnternet, preter,
distribuer et vendre des theses partout dans
le monde, a des fins commerciales ou autres,
sur support microforme, papier, electronique
et/ou autres formats.
The author retains copyright
ownership and moral rights in
this thesis. Neither the thesis
nor substantial extracts from it
may be printed or otherwise
reproduced without the author's
permission.
L'auteur conserve la propriete du droit d'auteur
et des droits moraux qui protege cette these.
Ni la these ni des extraits substantiels de
celle-ci ne doivent etre imprimes ou autrement
reproduits sans son autorisation.
In compliance with the Canadian
Privacy Act some supporting
forms may have been removed
from this thesis.
Conformement a la loi canadienne
sur la protection de la vie privee,
quelques formulaires secondaires
ont ete enleves de cette these.
While these forms may be included
in the document page count,
their removal does not represent
any loss of content from the
thesis.
Bien que ces formulaires
aient inclus dans la pagination,
il n'y aura aucun contenu manquant.
i*i
Canada
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Abstract
This work basically consists of two parts, which respectively belong to two
important regimes of molecular spectroscopy, microwave and infrared. The first part
focuses more on theoretical calculations, while the second part involves more
experimental work.
In the first part, we have conducted extensive ab initio calculations for a series of
large molecules of biological interest, including the molecules
2
-(ethylthio)ethanol,
thiodiglycol, ethyldiethanolamine and methyldiethanolamine. The ab initio calculations
have produced good structural and dipole moment information which match with the
experimentally observed isomers identified by Fourier Transform Microwave (FTMW)
techniques at the National Institute of Standards and Technology (NIST). One of the
perplexing issues that remain is the failure to observe some of the ab initio calculated low
energy conformers for
2
-(ethylthio)ethanol and methyldiethanolamine, leaving an
unsolved question in this study. In addition to the detailed conformational studies, in this
thesis we also report some preliminary studies of a “diatomic”-twist approach for
anharmonic potential corrections to ab initio harmonic frequencies for large amplitude
torsions.
The second part of this thesis reports the dual-mode operation of a widely
tunable COa-laser/microwave-sideband spectrometer employing a Cheo waveguide
modulator and a CO2 laser that can operate both on 9 pm hot and sequence band lines
ii
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
as well as low-/ and high-/ regular band lines. The spectrometer has a wide-scan
mode at Doppler-limited resolution for spectral searching and assignment, and a
narrow-band sub-Doppler mode for precision measurements. The instrumental
performance is demonstrated via spectra of the C-O stretching fundamental vibrational
band of methanol (CH3 OH). Doppler-limited broad-band scans have been recorded in
the low-/ region of the 9.6 pm CO2 band, while narrow-band sub-Doppler scans have
permitted clean separation of very close-lying lines in the CH3 OH spectrum and
determination of small doublet splittings. The measurement precision is confirmed for
several CH3 OH transition systems through closure of combination loops. Our results
illustrate the wide spectral coverage and excellent resolution obtainable with CO2 sideband infrared laser radiation in a broadly tunable and convenient infrared source
with high potential for spectroscopic applications.
iii
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Acknowledgements
Firstly, I would like to express my gratitude to my advisor, Dr. Li-Hong Xu, who
gave me the chance to start my graduate study here. Also, I would like to thank her for
her continuous encouragement, guidance, patience and understanding both academically
and personally during the course of my research work.
I also wish to thank our colleagues in National Institute of Standards and
Technology (NIST) in Washington, US., who had done all the experimental work and
spectral assignments motivating the ab initio studies section of this thesis.
Many thanks to Dr. Ronald M. Lees, for his wonderful microwave course and
various interesting dialogues and discussions, especially for his patience in reading my
thesis, the valuable comments, and extra effort spent on correcting my language problems
in my thesis writing.
Deep thanks will be extended to Dr. Zhen-Dong Sun, who gave me the
opportunity to do experiments with him and allowed me to include the results in this
thesis. These first-hand, or at least first-eye, experimental experiences here will be of
special importance to my future study. His frequent personal help in my life here is also
greatly appreciated.
I am indebted to all my friends, classmates and colleagues both in North America
and in China. Their friendships are the most valuable treasure in my life.
Finally, and most importantly, I am deeply grateful to my dear family for
providing their love and support at each step on my life road. Here I would like to
dedicate this thesis to them, especially to my beloved parents. I love you so much!
iv
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table of Contents
Abstract
II
Acknowledgements
Iv
List of Tables
vii
List of Figures
Ix
Glossary of Terms
xii
Chapter 1 Introduction
1
Chapter 2 Ab Initio Conformation Studies of Molecules Relevant to Biological
Interest
12
12
2.1 Overview of Quantum Chemistry Calculation......................................
2.1.1 Chemistry Calculation...............................................................................
2.1.2 Methodology in Ab Initio Methods
12
.............................................
15
2.1.3 Hartree-Fock Theory..............................................................
2.1.4 Moller-Plesset Perturbation Theory.
...................................................
19
2.1.5 Quality of Ab Initio Results................................................
2.2 Ab Initio Studies of Conformations and Structures for 2(Ethylthio)ethanol.
....................................................
2.2.1 Experimental Aspects.
2.2.2 Theoretical Analysis
........................................................
23
........................................................
2 3 Ab Initio Conformation Study of Thiodiglycol
.....................
46
2.4 Ab Initio Conformation Study of Ethyldiethanolamine and
Methyldiethanolamine................................................................
2.5 Summary
..........................................................
Chapter 3 Vibrational Analysis for 2-(Ethylthio)ethanol
3 . 1 Identification of Vibrational Modes for 2-(Ethylthio)ethanol ....................
3.2 Frequency Calculation for Methyl Torsion Motions with Anharmonic Potential
Corrections................................................................
3.3 Suggestions for Future Study. ................................................
v
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
64
64
Chapter 4 Applications of a COi-Laser/Microwave Sideband System for Higfaresolution Spectroscopic Measurements
4.1 CCVLaser/Microwave Sideband System
4.1.1 CO2 Laser...
4.1.2 Sideband Generation
94
.............................
95
...............................................
............................................
4.2 Doppler-limited Broad Band Sideband Spectra in the C-O Stretching
Fundamental Band of CH3 OH
................................................
101
4.2.1 Experimental Details for Wide-scan Doppler-limited Operational Mode.
101
4.2.2 Spectral Coverage.............
104
4.2.3 Absorption Spectra of Methanol in the Wide-scan Mode.
.......................
107
4.2.4 Frequency Uncertainty of Present Doppler-limited Wide-scan Measurements. 111
4.3 Saturation-dip Measurements at Sub-MHz Resolution for CH3 OH
.........
115
4.3.1 Line Broadening Mechanisms...............................................
1
4.3.2 Doppler-free Spectroscopy......................................................
119
4.3.3 Lamb-dip Technique...........................
120
4.3.4 Experimental Details for Narrow-scan Sub-Doppler Operational Mode...........122
4.3.5 Recordings of Lamb-dip Saturated Signals of Methanol................................... 123
4.3.6 Observed Frequencies of Methanol Transitions............................
129
4.3.7 Asymmetry Splitting of Methanol..............................................
4.3.8 Observed Asymmetry Doublet lines of Methanol. ........................................
132
133
Chapter 5 Conclusions
136
References
140
vi
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
List of Tables
2.1
2.2
Rotational parameters for the low energy TG conformer (Conformer I) of
HOEES............................
29
Rotational parameters for the GG conformer (Conformer II) of HOEES
30
2.3 . Rotational parameters for the high energy TG conformer (Conformer ID) of
HOEES............................................
2.4
31
Calculated ab initio rotational constants (A, B, Q , inertial defects (A), relative
energies (Erei), and dihedral angles (D) for HOEES............................................... 3 9
2.5
Ab initio optimized non-bonded interatomic distances for HOEES confoimers... 4 5
2.6
Experimental rotational parameters for thiodiglycol isomers.................................47
2.7
Calculated ab initio (HF/6-31G*) rotational constants (A, B, C), relative
energies, and backbone dihedral angles for thiodiglycol...................................... .48
2.8
Experimentally determined rotational constants for ethyldiethanolamine
2.9
Calculated results for ethyldiethanolamine at different theory levels.
2.10 Comparison
of
theoretical
methyldiethanolamine
3.1
and
experimental
....... 54
.......
parameters
56
of
.......
60
Harmonic frequencies and eigenvectors for the 42 normal modes of Conformer I
for HOEES by diagonalization of the G.F matrix in internal coordinates
74
3.2
Ab initio calculation results for methanol along the methyl torsion reaction path.. 85
3.3
Polynomial coefficients for methanol with converted harmonic frequency and
anharmonic force constants with respect to the dimensionless normal
coordinate...............
86
3.4
Ab initio calculation results for ethane along the methyl torsion reaction path.....
88
3.5
Polynomial coefficients for ethane with converted harmonic frequency and
anharmonic force constants with respect to the dimensionless normal
coordinate.
3.6
3.7
...........
89
Ab initio, scaled, correction added and globally fitted frequency values for
methanol and ethane................
90
Ab initio results for HOEES along the methyl torsion reaction path .........
92
vii
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
3.8
Polynomial coefficients for HOEES with converted harmonic frequency and
anharmonic force constants with respect to the dimensionless normal
coordinate................................................. ........................................................
4.1
GRAMS32 Pick Picking frequencies for wide-scan spectra using 9P42 upper
114
sideband...................................
4.2
92
Observed saturation-dip frequencies for C-0 stretching transitions of CH3 OH.... 130
viii
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
List of Figures
2.1 Survey FTMW scans of HOEES
.........
2
2.2 Numbering of the heavy backbone atoms in the HOEES molecule...................... '
2.3
2
-D contour plots showing the potential energy of HOEES as a function of
dihedral angles....................
............
i
2.4 Hypothetical “3-D” view of the three dihedral angles D(l,2,3,4), D(2,3,4,5), and
D(3,4,5,6)........................................................
3
2.5 The lower energy conformational isomers of HOEES
................................... i
2.6 Molecular structure of HOEES’s NM1 with intramolecular hydrogen bonding
interactions indicated
...................................................
45
2.7
Numbering of the heavy backbone in the thiodiglycol molecule........................... 4 5
2.8
The lower energy conformational isomers of thiodiglycol molecule..................... 4 $
2.9
Molecular structure of ethyldiethanolamine with the heavy backbone atoms
labeled
.........
51
2.10 Survey FTMW scans of ethyldiethanolamine.........................................................5 3
2.11 The lower energy conformational isomers of ethyldiethanolamine
.......... 5 5
2.12 Molecular structure of methyldiethanolamine with the heavy backbone atoms
labeled.
...............................................
...5 8
2.13 The lower energy conformational isomers of methyldiethanolamine.................... 5 0
2.14 Survey FTMW scans of methyldiethanolamine.......................
53
3.1
Atom numbering for HOEES......................................
73
3.2
Low resolution solution spectrum of HOEES....................
79
3.3
Low resolution solution spectrum of 1-pentanol.
go
3.4
Methanol methyl torsion potential energy V(r), plotted as a function of torsional
angle x.
3.5
....................
.........
...84
Ethane methyl torsion potential energy V(x), plotted as a function of the
torsional angle x.
..................................
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
88
3.6 Methyl torsion potential energy V(r) of HOEES, plotted as a function of the
torsional angle r.
........................... ..................................... ........... .
4.1 Simplified vibrational energy level diagram of the CO2 and N2molecules.........
4.2 Observed output lines of the CO2 laser.
..........
97
^g
4.3 Block diagram of a Doppler-limited tunable C0 2 -laser/microwave-sideband
spectrometer
...
j qj
4.4 Observed regular, sequence (S) and hot (H) band CO2 laser lines from 1059.95
to 1069.63 cm'1.......................
jq^
4.5 Tunable windows of microwave sidebands of hot (.H), sequence (S), and regular
band CO2 laser lines from 1059.95 to 1069.63 cm' 1
......................................jQg
4.6 Broadband spectra of the C-0 stretching fundamental band of CH3OH recorded
in Doppler-limited mode using microwave sidebands of hot, sequence, and lowJ regular band CO2 laser lines
...................................
|Qg
4.7 Screen capture from GRAMS, with the frequencies determined by using the
Peak Picking command in GRAMS.................................................
|
4.8 (a) Velocity distribution along the laser propagation direction (b) Lamb-dip
experimental arrangement (c) "Hole burning" in the velocity distribution (d)
Detected absorption as a function of frequency...................................................... 1 2 1
4.9 Saturation-dip sub-Doppler spectra of the components of the CH3 OH P(5) K =
IA asymmetry doublet in the ot = 0 torsional ground state, observed with the
upper sideband of the 9P42 CO2 laser line
.............................................••••124
4.10 Saturation-dip sub-Doppler spectrum of the i?(19) K ~\E ot =0 transition of
CH3OH taken with the upper sideband of the 9HP12 CO2 laserline...................... 125
4.11 Doppler-limited wide-scan absorption spectrum of CH3 OH using the lower
microwave sideband of the 9P44 CO2 laser line.
..... ............ .
126
4.12 Saturation-dip sub-Doppler spectra of the P(7) K - 2A ot = 1 asymmetry doublet
and the nearby P(7) K = 4E ut = 1 transition of CH3 OH.........................................127
4.13 Saturation-dip sub-Doppler spectrum of the blended K = 4 E and 2A+ut - 1 P(8 )
transitions of CH3 OH. ...................................
X
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
128
4.14 CH 3 OH energy level and transition diagram for the K=IA+ o t = 0 system
illustrating closed transition combination loops for confirmation of the estimated
measurement precision
..........
131
4.15 CH 3 OH energy level and transition diagram for K = 3A o t = 0 asymmetry
doublet system illustrating closed transition combination loops for calculation of
the asymmetry doublet splitting AE.........................
xi
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
134
Glossary of Terms
1(2, 3Y:
1st (2nd, 3rd) derivative;
amu:
atomic mass unit;
B3LYP:
Becke-style 3-parameter Density Functional Theory (using the
Lee-Yang-Parr correlation functional);
cw CO2 Laser: continuous wavelength CO2 Laser;
fL:
CO2 laser carrier frequency;
fM:
Microwave frenquency;
FID:
Free Induction Decay
F-P:
Fabry-Perot;
FTIR:
Fourier Transform Infrared;
FTMW:
Fourier Transform Microwave;
FT-NMR:
Fourier Transform-Nuclear Magnetic Resonance;
FWHM:
Full Width at Half Maximum;
GG:
gauche gauche',
HF:
Hartree-Fock Theory;
HO:
Harmonic Oscillator;
HOEES:
2-(ethylthio)ethanol (Hydrpxyethyl Ethyl Sulphide,
CH3 CH2 SCH2 CH2 OH);
H, S:
Hot, Sequence band CO2 laser lines;
GPIB:
General Purpose Interface Bus;
MP2:
2nd order Moller-Plesset Perturbation Theory;
xii
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
MTE:
2-(methylthio)ethanol (CH3SCH2CH2OH);
MWSB:
Microwave Sideband;
NIST:
National Institute of Standard and Technology;
NM1(2):
conformer No Match 1 (2);
PAM:
Principal Axis Method;
PC:
Potential Curve;
PE:
Potential Energy;
PES:
Potential Energy Surface;
PZT:
piezo votage tuning element;
RMS:
Root-Mean-Square;
SB:
Sideband;
S/N:
Signal to Noise;
TDG:
Thiodiglycol (HOCH2 CH2 SCH2 CH2 OH);
TG:
trans gauche',
TT:
trans trans;
TWT(A):
Traveling-Wave-Tube (Amplifier);
ZPE:
Zero Point Energy;
xiii
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Chapter 1
Introduction
Microwave spectroscopy, which is associated with the transitions between the overall
rotational levels of molecules and is carried out in roughly the frequency range of 3-300
GHz [1], has for a long time played an important role in studies of molecular structural
properties. Due to the high resolution of microwave spectra, where line widths are much
less than 1 MHz, many small effects can be measured such as centrifugal distortion
constants, nuclear quadrupole hyperfme structures, internal rotation barriers, etc. [ 1 ].
From the application point of view, it has great potential in qualitative and quantitive
analysis of gases or vapours. Compared with infrared spectroscopy widely used for this
purpose, its high resolving power allows definite identification and more accurate
intensity measurements of close lying lines from different compounds [2 ],
Microwave spectroscopy techniques can be traced back to the 1933 experiment of
Cleeton and Williams in their study of the hindered inversion motion of ammonia gas [3].
In their historic experiment, they first observed the 1.1 cm wavelength inversion
absorption, corresponding to a frequency of -27 GHz, which had been previously
predicted by observation of small doublings in the infrared study of ammonia [3]. No
further papers on microwave spectroscopy appeared in the literature until 1946, when
mature microwave oscillators and techniques became available [2], The concentrated
research on microwave radar during World War II provided the necessary
instrumentation to permit rapid development in the initial period of microwave
1
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
spectroscopy immediately following the war period [4]. The work of Good in 1946
disclosed a definite hyperfine structure in the inversion spectrum of ammonia. The
observed satellite structure was later interpreted as being caused by the interaction of the
nuclear quadrupole moment of 14N with the molecular field. Around the same time,
Dakin, Good and Coles etc. observed the Stark and Zeeman effects in the presence of an
external electric or magnetic field [2], The Stark effect method has since then become an
important aid to identification of lines, and provides an accurate means of measuring
dipole moments of gases in excited as well as ground states [2]. In 1947, Hershberger and
Turkevitch detected a series of lines for CH3 OH, that were later further studied by Dailey
and by Coles with the Stark modulation method [2], Burkhard and Dennison interpreted
these lines as arising from hindered internal rotation of the -OH group. Since then, these
methods of microwave spectroscopy have been extensively employed to study hindered
internal rotation in molecules, which has been a subject of interest since the early 1930’s
[5]. During the first decade after 1946, with development of new microwave generation
and detection techniques, the measurable region was greatly extended throughout the
millimeter and into the submillimeter wavelengths, highlighted by the overlap with
infrared grating measurements in 1954 by the Gordy group [6 ],
Modem microwave spectroscopy addresses the challenge of studing “unusual
molecules” ranging from highly reactive free radicals and transient species to weakly
bound hydrogen bonded complexes and van der Waals complexes, as well as large
biological molecules. These species are normally characterized by either short lifetimes
or extremely complicated internal motions, and thus require experimental techniques with
2
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
very high sensitivity and resolution. One such new technique, called pulsed Fourier
Transform Microwave (FTMW) spectroscopy, was developed in the 1980’s, and is
widely considered to have revitalized the microwave spectroscopy field. This technique
was first successfully applied to observe weakly bonded molecular dimers in a supersonic
molecular beam by W.H. Flygare and his research group in May, 1979 [7]. Different
from the traditional method, in which a low pressure gas sample is placed in an evacuated
waveguide cell and the microwave frequency is swept to get the absorption line, the
FTMW technique employs a principle analogous to FT-NMR spectroscopy, involving a
microwave pulse excitation followed by time-domain signal recording and Fourier
transformation to the frequency domain. A description of this technique will be provided
in Chapter 2 of this thesis. The supersonic nozzle, a component incorporated in the
FTMW spectrometer, has been long considered an effective way to produce transient
species, and molecular complexes can be bound together relatively easily within the
beam if appropriate conditions are attained [8 ]. The supersonic expansion makes a nearly
collision-free environment, and thus even very reactive transient species, once produced
in the beam, can survive for a sufficiently long time to be detected [8 ].
As far as large molecule monomers are concerned, one of the current areas of '
active research in the FTMW field is related to carbon chain molecules of astrophysical
interest. Many of the polyatomic molecules that have been identified in molecular clouds
or in circumstellar shells are carbon chains [9]. More than seventy carbon chain
molecules have been studied using FTMW spectroscopy at the Harvard-Smithsonian
Center for Astrophysics, and six of them have already been detected in space based on
3
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
these data [9]. These extensive laboratory results are very helpful to searches for new
molecules in space. Another research interest for monomers concentrates on large
biological molecules. Some of these molecules contain functional groups important in
proteins, such as peptide bonds. Several molecules that contain one or two peptide bonds
have been investigated using FTMW spectroscopy as the main technique [10,11],
Detailed conformational information for the peptide molecules is required for further
study of the forces resisting rotation about the peptide bonds as well as the carbon bond
between two peptide linkages. This information will be of significance in clarifying
important problems of structural biology such as protein folding [ 1 1 ].
The FTMW and ab initio conformational studies for the series of biological
molecules described in this thesis are part of a collaboration with the Optical Technology
Division, Physics Laboratory at the National Institute of Standards and Technology
(NIST) in Gaithersburg, MD. All of the experimental measurements and spectral
assignments were carried out by our colleagues at NIST. The first NIST FTMW
instrument was constructed in 1985 and used to study van der Waals molecular
complexes as well as hydrogen bonded dimers and trimers. In 1987, the NIST group
published their FTMW measurements on OCS and rare gas complexes of OCS with Ne,
Ar, and Kr. This was the first time that four isotopic forms of Kr-OCS were reported, and
resulted in a refinement of the structure [12]. The early studies with this instrument also
included the rare gas-C0 2 complexes [13] and water-CSa [14] complexes, etc. In 1998, a
miniaturized version of the FTMW spectrometer was built to evaluate its feasibility as a
reliable and robust tool for quantitative field measurements of trace gases found in
4
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
automobile exhausts, factory emissions and chemical warfare [15,16]. More recently the
emphasis at NIST has shifted toward the analysis and characterization of larger organic
monomers with molecular weights in the 100 to 200 amu range. The challenge of such
experiments comes from the difficulty of sample vaporization and the possible
simultaneous existence of several conformers in the gas phase sample. Installing a
heated-reservoir nozzle on the spectrometer successfully solves the former problem [17].
As for the latter, a graphical user interface program, JB95, was used to aid the
conformational assignments [15]. This program includes features that enable real-time
refinement of rotational constants and band intensities through visual comparisons of the
experimental data with simulated spectra [15]. The capability to easily remove
experimental lines belonging to assigned conformers can dramatically simplify the
identification of sub-spectra from the remaining conformers by means of pattemrecognition strategies [15].
Our role in this project was to conduct ab initio computational searches for the
different low energy conformers. During recent years, as a result of the development of
efficient methodologies and powerful computers, ab initio quantum chemistry
calculations have provided us with impressive results. Thus one can nowadays carry out
ab initio calculations with high level theory for relatively large molecules [18]. The
theoretical predictions from ab
initio calculation can facilitate unambiguous
spectroscopic identifications and guide the experimental analysis. Conversely, agreement
with accurate experimental results represents unbiased verification of the significance of
ab initio calculations [19]. The application of this combined approach to microwave as
5
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
well as high-resolution infrared studies has shown that both experimental and theoretical
methods can benefit from this interplay. Over the past years, the NIST group has
successfully used FTMW spectroscopy together with ab initio calculations in the study of
a series of large biological molecules. These include diethyl sulphide [15], the parent of
the 2 -(ethylthio)ethanol molecule discussed in detail in the present study.
As well as the ab initio conformational studies, ab initio vibrational analysis also
has been carried out in this study, including a preliminary test of a “diatomic”-stretch
correction approach applied to large amplitude torsions. In common practice, raw
frequencies taken directly from ab initio calculation are usually scaled by an empirical
factor in order to account for anharmonic effects. However, these empirical scale factors
do not have any specific physical justification, and can not systematically produce
satisfactory corrected results for each vibrational mode of a molecule, especially for the
low frequencies belonging to torsional motions. The “diatomic”-stretch approach is well
established for correction of the highly excited stretching modes [20], This study
develops a parallel “-twist” method, working in a similar manner, for torsional
corrections. In this thesis, the results of an initial test for a methyl torsion correction are
given for the methanol, ethane and 2-(ethylthio)ethanol molecules. A description of the
results of these ab initio calculations is included in Chapter 3.
Following this chapter, results from work in infrared spectral region, another
important frequency region for molecular spectroscopy, are reported. The infrared can be
sub-divided into three spectral regions [2 1 ], the near-infrared, the mid-infrared and the
6
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
far-infrared. The mid-infrared region, with wavelengths ranging roughly from 3 to 30
jam, is of greatest practical use to chemists, physicists and industrialists. In this region,
most molecules, including a number of important pollutants, exhibit fundamental
vibrational transitions with strong absorption lines. Relative to the near-IR (-0.7 pm to 3
pm), where the overtone and combination bands occur, the line-strengths can be typically
two orders of magnitude stronger [22], thus making the mid-DR. the most appropriate
infrared region for pollutant monitoring. Further, because the well-known 8-13 pm
atmospheric window lies in the mid-IR, this region is also of great interest in research on
atmospheric spectra and in astrophysical exploration [23].
Considering the important role it plays in remote sensing applications, the
technological development of a continuously tunable mid-IR source has been a long­
term effort. Unlike semiconductor diode lasers at visible and near infrared wavelengths,
which are already established and relatively mature, the development of analogous
devices for the mid-IR has proven to be much more challenging. Traditionally, the most
widely used laser source is the lead-salt diode laser, which works at cryogenically cooled
low temperatures. During recent years, other semiconductor laser sources based on Sb
m -V diode lasers, sources based on difference frequency generation (DFG) and
distributed feedback (DFB) quantum cascade lasers have also been developed and
employed for atmospheric studies [24]. Each of these have provides unique advantages as
well as limitations [24].
7
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
In the 10 pm mid-infrared region, the line-tunable CO2 laser (9-12 jam) is one of
the most important laser sources with high output power. The technique of sideband
generation by mixing CO2 laser and microwave radiation in an electro-optic modulator
gives an elegant solution to the tunability problem [23,25-29]. This technique is now used
by many groups throughout the world with either CO2 or CO lasers and has found a
number of applications [28].
Two kinds of modulators are currently in use within different groups. One of them
is the CdTe eletro-optic modulator, which was first realized by Magerl and co-workers in
the 1970’s. In this design, the CdTe crystal is mounted in a rectangular microwave
waveguide embedded between two AI2 O3 slabs that have roughly the same dielectric
constant as that of CdTe. It was first used to combine a CO2 laser with microwaves, and
was later adapted to the 5-6 pm region for use with a CO laser [30]. In 1998, Miirtz et al.
in Universitat Bonn extended this technique into the 3 pm region by using their newly
invented dc discharge CO overtone laser [30], Currently, sideband setups using this
modulator are in operation mainly in two groups, the Institut fur Angewandte Physik der
Universitat Bonn, Germany, and the Laboratoire de Spectroscopie Hertzienne, Universite
de Lille, France.
The second available modulator is a CdTe-buffered GaAs thin slab waveguide
modulator developed by Cheo [23,25]. This modulator is used in this study. A detailed
description of this modulator is provided in Chapter 4 of this thesis. Research groups, in
addition to our own infrared group, that have used or are currently using this type of
8
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
modulator include the Photonics Laboratory of the University of Connecticut, USA, the
Optical Technology Division of NIST, USA, and the Takagi Spectroscopy group in
Toyama University, Japan.
By using the Cheo waveguide modulator, the accessible tuning range can be
generally extended from 6.7 to 18.5 GHz on either side of each CO2 laser line. While this
coverage is good, there are still significant gaps when only the regular CO2 laser bands
are available, because the spacings between the adjacent regular CO2 lines vary from
about 70 GHz to 20 GHz going from the P to R branches across a band. However, by
special design of the mechanical and optical structures, notably with a ribbed discharge
tube and specially blazed grating, Evenson et al. developed a cw CO2 laser with
particularly high resolution that could operate with significant power on many of the lines
of the CO2 hot and sequence bands [31]. Since the hot and sequence band lines serve to
bridge many of the gaps between the regular band lines, considerable advantage would be
expected in spectral coverage if these additional CO2 laser lines could be used to generate
useful sidebands as well.
Recently, Sun et al, described the assembly of a CCVlaser/microwave-sideband
tunable infrared source [32] employing an Evenson laser and a Cheo waveguide
modulator, for application in spectroscopic measurements. In this thesis, we will describe
further extensions to this system and development of its capabilities as a dual-mode
precision computer-controlled spectrometer, working both in a Doppler-limited widescan mode and a sub-Doppler saturation-dip detection mode. As an application to
9
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
highlight the features and capabilities of this dual-mode spectrometer, we have recorded
spectra of the vibrational C-0 stretching fundamental band of methanol utilizing both of
the instrumental modes. Two spectral regions, the low-/ tuning range from 9P4 to 9R6
and the high-/ range from 9P42 to 9P56, were selected for this study. Full sideband scans
in the Doppler-limited regime were recorded in both regions, with an almost continuous
spectral coverage for the former, where prominent hot and sequence bands lines are
present. In both spectral regions, we then recorded narrow-band sub-Doppler scans for a
number of close-lying CH3 OH lines that are overlapped and unresolved in conventional
Fourier transform (FT) spectra. A clean separation is afforded by the Lamb-dip
observations with high accuracy of measurement. The measurement precision is
confirmed for several CH3 OH transition systems through closure of combination loops.
This thesis is structured as follows:
In Chapter 2, the principles of ab initio quantum chemistry calculation and
FTMW spectroscopy techniques are briefly reviewed, followed by a detailed
description of an ab initio conformational study of the 2-(ethylthio)ethanol (HOEES)
molecule. Initial ab initio calculations for the molecules thiodiglycol, Nethyldiethanolamine and N-methyldiethanolamine are also presented and discussed in
this chapter.
In Chapter 3, we start with a description of an internal coordinate method to
identify different vibrational modes for large molecules, for which the direct
identification from Cartesian displacements becomes extremely difficult. Then the
10
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
“diatomic’ -twist anharmonic correction approach for large amplitude torsions is
introduced, followed by its initial application to the methyl-top torsions of methanol
(CH3 OH), ethane (CH 3 CH 3 ) and HOEES (C4 H 10OS).
hi Chapter 4, the newly built UNB C0 2 -laser/microwave sideband system is
described, including its further development as a dual-mode spectrometer and its
application to methanol spectral recording using both operating modes. Precise
transition measurements in the saturation-dip detection mode, including several pairs
of asymmetry doublet components, will be given.
In the final chapter, general conclusions and suggestions for further studies are
presented.
11
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Chapter 2
Ab Initio Conformational Studies of Molecules
Relevant to Biological Interest
In collaboration with the National Institute of Standards and Technology (NIST) in
Gaithersburg, USA, a series of large molecules of biological interest is under
investigation by Fourier Transform Microwave (FTMW) techniques and ab initio
calculations in order to determine molecular structures, conformations and tunneling
paths. All the experimental data described in this thesis are from NIST, with the
assignments and spectral fits carried out by our collaborators there. Our main
contribution to this project is to conduct computational searches for the energy minima
corresponding to different conformers. By mapping the potential energy surfaces (PES)
over ranges of angular parameters, we can explore the tunneling paths for torsion about
different bonds and determine the molecular constants for different conformers which
might be observed experimentally. In this chapter, the molecules 2-(ethylthio)ethanol and
thiodiglycol, both of which are mustard gas hydrolysis products, as well as Nethyldiethanolamine and N-methyldiethanolamine are systematically investigated and
discussed.
2.1 Overview of Quantum Chemistry Calculations
2.1.1 Chemistry Calculation
12
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
In this section, a brief overview will be given of quantum chemistry calculations with
emphasis on ab initio methods. Much of the material is applicable to the Gaussian 98 ab
initio package [33], which was selected as the quantum chemistry calculation tool in our
study. No attempt will be made to provide a detailed description of this broad subject;
more detailed introductions are provided in Refs. [34] and [35],
Chemical physics calculations simulate chemical structures and reactions, based
in full or in part on the fundamental laws of physics. At the present time, this subject has
become relatively mature and the technology sufficiently stable, primarily because of the
explosive development in computer hardware and mathematical algorithms [34],
Theoretical chemists, as well as experimentalists, frequently use ab initio tools to guide
and improve experiments and to construct solutions to questions that are impossible to
examine experimentally. Computational chemical physics is therefore both an
independent research area and a vital adjunct to experimental studies.
There are two broad areas within computational chemical physics devoted to the
structure of molecules and their reactivity: molecular mechanics and electronic structure
methods [35]. Molecular mechanics simulation is principally a classical method with its
particular force field based on empirical results, averaged over a large number of
molecules. This type of calculation does not explicitly treat the electrons in a molecular
system, and thus is quite computationally inexpensive, allowing it to be used for very
large systems containing many thousands of atoms [35]. Overall, because of its extensive
averaging, this kind of empirical approach is useful for most standard systems, but there
13
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
are still many important questions in chemistry that can not be addressed. For properties
that depend directly on the electron density distribution, one has to resort to the more
fundamental and general approach - electronic structure methods [35].
Electronic structure methods are based on the postulates of Quantum Mechanics.
The properties of a molecular system can be derived from its wave-function after
successfully solving the Schrddinger equation: Hy(r,t) = E y ( r , t ) . In practice, the
Schrddinger equation can not be solved exactly, except for the smallest systems, without
a variety of approximations. Gaussian provides two types of electronic structure methods
which differ in the trade-off made between computational cost and accuracy of the result.
Semi-empirical methods use parameters derived from experimental data to
simplify the computation. They solve an approximate form of the Schrddinger equation
that depends on having appropriate parameters available for the type of chemical system
under investigation [35]. Different semi-empirical methods are largely characterized by
their differing parameter sets [35],
Ab initio methods, unlike either molecular mechanics or semi-empirical methods,
use no experimental parameters in their computations. Instead, the computations are
based solely on the laws of quantum mechanics and on the values of a small number of
physical constants [35]. In the next section, we will give a brief introduction to the
theoretical background of ab initio methods along with some of the terminology. All the
14
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
equations in the next section are consistent with Ref. [35], and the fundamental physical
constants have been removed by using atomic units [35].
2.1.2 Methodology in Ab Initio Methods
Because we are looking at states that are stationary in time, the time dependence can be
, leaving only the spatial part \\i(r). For a
separated from the full wave-function
molecular system, the Hamiltonian is made up of both kinetic and potential energy parts
[35]:
e le c tro n s n u c le i
e le c tro n s
n u c le i
[2.1]
The kinetic term is a summation of V2 over all the particles in the molecule. The three
potential energy terms correspond to electron-nuclear attraction, electron-electron
repulsion and nuclear-nuclear repulsion, respectively [35]. To simplify the solution of the
Schrddinger equation, the so-called Born-Oppenheimer approximation is introduced to
separate the motions of nuclei and electrons. The approximation is actually reasonable
considering that the electrons are so much lighter than the nuclei that their motions can
easily follow the nuclear motion. This situation can be pictured as the electrons moving
fast in a field of fixed nuclei. Under the Born-Oppenheimer approximation, the full
Hamiltonian [2.1] can then be rewritten as [35]:
u c l- e le c
H = T ekc(f) + T nucl(R) + V( r nnucl~
elec(R ,f) + Velec(r) + Vnud(R)
[2.2]
An electronic Hamiltonian can be constructed by neglecting the nuclear kinetic
energy term [35]:
15
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1
e le c tr o n s
ele c tr o n s n u c le i
7
e le c tr o n s
n u c le i
1
7
7
i y - 2 2 (i/4t)+ e E y ^r 3E S c # ^ )
/
|i? /
i
j{ i
i
7}
j
<i
ji? / — i ? j i
p-3]
This Hamiltonian is then used to set up the electronic Schrddinger equation describing
the motion o f electrons in the field of fixed nuclei [35].
[2.4]
ITefeV fec( f J ) = £ ^ ( j ? ) ¥ efcc(r , j?)
The effective electronic energy
here depends only on the nuclear coordinate and thus
defines the potential energy surface (PES) for the system [35].
will provide the
necessary information for optimizing the structure as well as predicting the vibrational
frequencies, etc.
From the above description, solving the electronic Schrddinger equation is the
most crucial step in the whole process. In the following section, we will focus on this
important question.
2.1.3 Hartree-Fock Theory
In the electronic Hamiltonian [2.3], the second potential energy term describes the pair­
wise electronic repulsion depending on the coordinates of two electrons at the same time.
It turns out that this term is the main bottleneck in practical computations, and can be
bypassed only for very small systems. To avoid this problem, the independent particle
approximation is introduced, in which the interaction of each electron with all the others
is treated in an average way [35].
i electron s
i t *
electron s n u c le i
7
e lectro n s
n u c le i
7
7
5*> 2- Ii E{np-q)+
Ii f r + Ei jE<i (#%
t)
i I-K/ rA
\Rl —iiyj
16
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
[2-5]
Under this approximation, the total electronic Hamiltonian [2.5] can be further sub
divided into a sum of separate components, expressed as H f ec’s, for each electron.
Separation of variables reduces the Schrddinger equation [2.4] into a set of oneelectron equations. Each is expressed as [35]:
[2 .6]
where the separated one-electron wave-function «jf ^ i r ^ R ) is often called a one-electron
orbital [35]. The whole electronic wave-function then can be expressed as
\|/efec = ^ dec(q, J?)<f>e/ec(r2,/?)•••§ekc(rn, R) , which is known as a Hartreeproduct.
Because for each electron the average potential due to all other electrons is
unknown, the equation [2.6] still can not be solved directly. In practice, <J>etec(i},J?) is
expressed as a combination of a pre-defined set of one-electron basis functions,
commonly known as the basis set [35].
[2.7]
These basis functions are usually centered on the atomic nuclei, and so bear some \
resemblance to atomic orbitals [35]. Thus, most ab initio packages, including Gaussian,
use a linear combination of gaussian-type atomic functions gp to form the one-electron
basis functions [35].
[2 .8]
P
where the dw coefficients are fixed constants within a given basis set [35].
17
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Gaussian offers a wide range of pre-defined internal basis sets, and larger ones
can be obtained from external basis set libraries and input to the Gaussian program. The
different basis sets are classified by the number and types of basis functions used to form
the electron orbitals [35]. For example, the 6-31G*, also termed as 6-31G(d), uses
6
gaussian functions to form the core orbitals, while the valence orbitals are described by
two sets of orbitals — one composed of three gaussian functions and the other containing
just one single gaussian function. The symbol *, or (d), indicates that polarization dfunctions are added to heavy atoms. This basis set is becoming very common for
calculations involving medium to large sized systems [35]. A more detailed description
of basis set nomenclature and relative performance is provided in the Gaussian user’s
reference [33].
At this point, solving the electronic Schrddinger equation reduces to the question
of how to determine the expansion coefficients in [2.7]. This can be realized by using the
common variational methods in quantum mechanics [35].
The electronic Schrddinger equation thus can be successfully solved by
introducing various approximations. Finally, it is worth pointing out that, instead of
expressing the wavefunction as a simple Hartree product, y/elec is in fact built as the
well-known Slater determinant, in order to satisfy the physical requirements for electron
(which are fermions) - under the Pauli principle.
18
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2.1.4 M0ller-PlessetPerturbation Theory
The limitation of the Hartree-Fock (HF) method described above in general lies in the
fact that, due to the independent particle approximation, the instantaneous correlation of
the motions of the electrons is neglected. Several approaches are known that try to
calculate the correlation energy after a Hartree-Fock calculation (post-HF methods).
Among them, the Moller-Plesset Perturbation Theory has become very popular in recent
years [35]. The basic idea is that the difference between the Hartree-Fock approximate
Hamiltonian [2.5] and the exact electronic Hamiltonian [2.3] can be treated as a
perturbation. Like many quantum mechanics problems, the 2nd order correction (keyword
MP2) can give a satisfactory result for the energy. Enormous practical advantages are that
MP2 is fast, rather reliable in its behaviour, and size consistent [36]. Subsequent MP3
and MP4 methods are more elaborate processes and much more time consuming [36].
The MP2 theory level, together with a 6-31G* or 6-311G** basis set, was used in most of
the calculations in this study.
2.1.5 Quality o f Ab Initio Results
Geometry Optimization-. The process of finding a minimum in the PES and then
predicting an equilibrium structure near the initially specified geometry is called
geometry optimization [36]. Gaussian determines convergence in such a search by
judging whether the following quantities are close enough to zero to satisfy the
predefined thresholds — all the forces, the root-mean-square (RMS) force, the calculated
displacement for the next step, and the root-mean-square displacement [35]. By default,
these threshold values are set to 0.00045, 0.0003, 0.0018 and 0.0012, respectively, where
19
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
each is given in atomic units (amu, Bohr and Hartree are used for mass, length and
energy units, respectively). To obtain improved results, the convergence criteria can be
tightened by specifying the Opt keyword in the route section as Opt=Tight or VeryTight.
These two options will set the RMS force criterion to IxlQ'5 and IxlO'6, respectively, and
scale the other three criteria accordingly. However, tighter convergence criteria will need
more computation time, of course, especially for large molecules. Under this
circumstance, the last two displacement criteria are difficult to satisfy on the rather flat
potential energy surface near the minimum that is common for large, floppy molecules
[35].
As far as equilibrium geometry is concerned, both HF and MP2 theory levels lead
to excellent results, even with modest basis sets. At present, HF/6-31G* or MP2/6-31G*
are considered good and reliable methods for the determination of the geometry of
organic molecules [36], A search for the possible existing conformers for relatively large
molecules can be started with a low theory level calculation, such as Hartree-Fock, to
give useful information while taking reasonable time. As well as the structural
information, the total energy (nuclear repulsion plus electronic energy) of the system will
also be given in the output of the geometry optimization job. The energy will be first >
computed at the HF level, and then be refined by more accurate procedures if a higher
level calculation is desired. However, the accurate computation of absolute or relative
energies still remains a major challenge for ab initio techniques [36]. Even
conformational energy differences and barriers are not reliably computed at the HF or
MP2 theory level if small basis sets are used [36]. The unreliability of ab initio energies
20
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
might be a possible explanation for an intriguing question about the failure to observe
some of the calculated lowest energy conformers in our study, as discussed in detail in
Sec. 2.2 below.
Vibrational Frequency. Vibrational frequencies depend on the second derivatives
of the energy with respect to the nuclear coordinates, which form a matrix called the
Hessian or the force constant matrix. The elements of the Hessian are defined as:
d 2E
H JJ = -----------, where Xj and Xj are the nuclear coordinates. In Gaussian 98, frequency
dXjdXj
calculations (keyword Freq) are done in the Cartesian system and the second derivatives
are calculated analytically for both Hartree-Fock and Moller-Plesset theory levels. The
diagonalization of the mass-weighted Hessian will give the harmonic frequencies. It turns
out that even the low theory level (HF) vibrational results, with a modest basis set, are
quite good [36]. However, the raw frequencies at the HF level are consistently
overestimated due to the neglect of correlation energy and anharmonicity. Therefore, it is
usual to scale a predicted frequency at HF level by an empirical factor of 0.89±0.01 for
comparisons with experiment. For higher theory level such as MP2, the scaling factors
are much closer to unity [36].
2.2 Ab Initio Studies of Conformations and Structures for 2 (Ethylthio)ethanol
This section describes the combination of an experimental jet-cooled Fourier transform
microwave (FTMW) study and ab initio conformational analysis of 2-(ethylthio)ethanol,
21
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
also known as ethyl 2-hydroxyethylsulphide or hydroxyethyl ethyl sulphide (HOEES).
This species is a hydrolysis/degradation product of mustard gas. Since HOEES is among
the family of compounds related to mustard gas chemical agents, it is therefore of interest
from both theoretical and practical viewpoints. The present study is part of an ongoing
effort aimed at setting up a microwave database for chemical agents and families of
related compounds (simulants, degradation products, hydrolysis and oxidation products).
These molecules are relatively large, and can exist in the gas phase as distinct
conformational isomers associated with internal torsional rotations about the bonds
joining the heavy atoms forming the molecular backbone. Typically these conformational
changes are hindered by substantial potential barriers, thus permitting the molecules to
exist as a variety of different conformers with differing energies. Tunneling between the
conformations is very slow on the timescale of the rotational motions, hence the different
conformers are quasi-stable in the FTMW experiments and appear as distinct isomeric
species with separate and well-defined spectra and molecular structures.
The internal potential energy of a molecule of this size is a complicated function
of the internal torsional degrees of freedom, for which current levels of chemical intuition >
cannot reliably predict the relative depths of the potential minima corresponding to the
stable conformations. Thus, to connect the different conformers observed experimentally
in the microwave spectrum to their corresponding conformational structures, ab initio
calculations can be of great assistance. By mapping the internal potential as a function of
a subset of the molecular internal coordinates, one can locate local minima in the
22
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
potential corresponding to stable conformers, calculate the conformer rotational constants
and dipole moment components, and then seek to match them against the experimental
results. With ab initio calculations, once the conformational isomers are matched,
estimates of the molecular structures are obtained without additional effort. This dual
approach has been used successfully in a previous study of the parent molecule, diethyl
sulphide [15].
In the present work, we report on observations and assignments in the jet-cooled
FTMW spectrum of HOEES and its 13C and 34S mono-substituted isotopomers. We
discuss the experimental identification of three distinct conformers, and then describe ab
initio calculations that have produced good structural matches for the three observed
conformers but which have also raised intriguing questions about the failure to observe
two other predicted low-lying species. At this stage, a manuscript on the HOEES work
has passed the internal evaluation of the NIST Washington Editorial Review Board
(NIST-WERB), was submitted to J. Mol. Spectrosc. in April, 2003, and was accepted for
publication in July, 2003.
2.2.1 Experimental Aspects
Introduction to Fourier-transform Microwave Spectroscopy Techniques
The technique of Fourier-transform Microwave (FTMW) spectroscopy was originally
developed by T.J. Balle and W.H. Flygare at the University of Illinois UrbanaChampaign in 1979 (see Ref. [37]), and was successfully applied to weakly bound
molecular dimers. Since then, many modifications and improvements have been
23
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
introduced based on their prototype in order to make this technique more sensitive and
also suitable for special applications. The 1990 design of the University of Kiel
introduced an automatic broadband scan facility to increase the efficiency [38].
Previously, all the adjustments had to be done manually, making it very tedious to scan a
wide region of the spectrum if unassigned species were to be measured. Most of the later
setups in other laboratories partly used the hardware and/or software supplied by the Kiel
group. It is estimated that today there are approximately 30 laboratories around the world
that have one or more FTMW instruments in use [16].
The traditional method for observing microwave spectra is to place a low pressure
gas sample in an evacuated waveguide cell and scan the microwave frequency to detect
where the sample absorbs [1]. However, FTMW spectroscopy involves a totally different
approach, in which pulses of microwave radiation are applied to gaseous samples, and the
resulting time domain emission signals are recorded. Fourier transformation of these
signals gives a frequency domain spectrum [1]. The principle of FTMW spectroscopy is
thus much more closely related to Fourier transform Nuclear Magnetic Resonance (FTNMR) spectroscopy than to the FTIR methods based on a Michelson interferometer [1],
The technique of impulse excitation was first introduced to NMR spectroscopy by ’■
Richard R. Ernst, laureate of the 1991 Nobel Prize for Chemistry, together with Weston
A. Anderson. This initiated a revolution in this field that still continues today [39].
24
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Fourier-transform Microwave Spectrometer
The heart of the Fourier-transform Microwave Spectrometer is a tunable Fabry-Perot (FP) microwave cavity in conjunction with a pulsed molecular beam valve and pulsed
microwave radiation. The following brief introduction will be mainly based on an
analytical prototype FTMW spectrometer at NIST. A more detailed description can be
found in Ref. [37].
The first NIST FTMW instrument was constmcted in 1985 and was used to study
a number of van der Waals complexes as well as hydrogen bonded dimers and trimers
[16]. More recently the emphasis at NIST has shifted toward the analysis and
characterization of larger organic monomers with molecular weights in the
100
to
200
amu range [16]. The 1 K temperature of the molecular beam greatly simplifies the spectra
of these compounds and permits their analysis. Over time, many changes have been made
in the instrument resulting in dramatic improvements in overall sensitivity of the
technique as well as greatly improved ease of use. In the early 1990's it became clear that
this technique could offer some advantages to the analytical chemistry community as a
new spectroscopic technique for trace gas analysis. In 1999, a miniaturized version of the
FTMW spectrometer was built up at NIST for use as an analytical instrument [37].
Although the F-P cavity had been reduced by a factor of 3 in diameter compared to most
apparatuses of this type, the overall sensitivity was not significantly affected [37]. This
instrument provides analytical chemists with a new tool that can unambiguously identify
trace amounts of large organic compounds in gas streams, such as automobile exhausts,
factory emissions, chemical warfare agents and their synthetic precursors. The instrument
25
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
can also permit real-time analysis, which should be useful for monitoring and
optimization of process gas streams [16].
The vacuum chamber is based on a commercially available multi-port sphere,
with two aluminum mirrors housed on two opposite ports to form the F-P microwave
cavity [37]. The sequence of events starts with the opening of the pulsed molecular beam
valve, lasting for several hundred microseconds, to admit a sample to the cavity. The
adiabatic expansion process cools the molecule in the supersonic beam to near IK [37].
An appropriate delay is given to allow the sample to emerge from the valve orifice into
the cavity and stabilize in this nearly collision-free environment. A microwave pulse
(typically 1-3 ps duration) is then applied to the sample. Since the microwave pulse lasts
for such a short time, the Fourier components of the pulse in the frequency domain can
extend over ~1 MHz. If the sample has transition(s) within this bandwidth, a coherent
macroscopic polarization will be induced in the ensemble of sample molecules [37].
After the microwave pulse is turned off, the sample begins to relax to equilibrium, and
the emission associated with the decay of the polarization with time (free induction decay
or FID) will be recorded by an antenna. This emission typically occurs for 100-500 ps
[37]. The time domain signal is stored, with signal averaging if necessary, and Fourier
transformation of the FED finally gives the frequency domain display of the spectrum. It
is necessary to point out that, since the cavity has a co-axial design of molecular beam
and microwave pulse for increased overlap and high sensitivity, two Doppler-split
components will appear in the frequency domain spectrum. The centre frequency is
obtained by directly averaging the two components.
26
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Experimental Conditions for the Study
A commercially-available sample of HOEES (CAS#110-77-0) was used at its stated
purity of 97%. Since the vapor pressure of HOEES is rather low (< lxl02 Pa), a small
sample of approximately
200
pi was transferred to a reservoir in the pulsed molecular
beam valve. The reservoir was then heated to between 40 C° and 70 C° in order to
increase the vapor pressure of the sample in the carrier gas. The mini FT spectrometer
described by Suenram et al. [37] was used to record survey scans from 10.5 GHz to 26
GHz. A composite of these scans is shown in Figure 2.1. Spectral assignments were
obtained using the JB95 spectral fitting program [15]. The most intense transitions in the
spectrum are a-type, i?-branch transitions that belong to two different conformers
(Conformers I and II). Both conformers are prolate rotors so these i?-branches occur at
intervals spaced by approximately the B+C values of the rotational constants. Computer
simulations of these are also shown in Figure 2.1 for the two conformers separately.
Other transitions in the spectrum arise through additional selection rules for the two
conformers, i.e., b- and c-type transitions. Weaker transitions in the spectrum result from
the 13C and 34S isotopomers of the two low energy conformers. Transitions of Conformer
HI with higher energy are relatively weak and were assigned only after the 13C and 34S
transitions of the other two conformers were assigned and subtracted from the spectrum.
It is believed that Conformer III lies at higher energy than the other two and thus has only
a minimal population in the 1 K molecular beam. The rotational parameters for the three
conformers are given in Tables 2.1 through 2.3.
27
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Experiment
1j aM | L
Jj-ius
Conformer I
Conformer II
m
11
1
i
i
|
i
i
i
i
15
j
20
i
i
i
i
j
i
25
Frequency in GHz
Figure 2.1. Survey FTMW scans of HOEES. The upper trace shows the experimental
spectrum. The lower two traces show simulations of only the prominent a-type, i?-branch
patterns for the two lowest energy conformers; Conformer I and Conformer II.
28
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 2.1. Rotational Parameters for the Low Energy TG Conformer (Conformer I) of
HOEES.
Rotational
Parameters
Normal
Species
2-13C
3 - 13C
34s
5 - 13C
- Ca
6 13
A (MHz)
5513.9584(3)*’
5481.781(3)
5449.244(5)
5436.3208(5)
5484.168(3)
5489.576(4)
B (MHz)
1424.01194(7)
1408.672(1)
1418.882(2)
1420.6220(4)
1413.8472(9)
1392.818(1)
C (MHz)
1363.95091(7)
1350.884(1)
1357.392(2)
1359.1765(4)
1355.4039(8)
1333.883(1)
Aj (kHz)
0.8334(3)
0.810(2)
0.813(3)
0.824(1)
0.828(2)
0.797(3)
Ajk (kHz)
-8.000(2)
-7.75(3)
-7.68(3)
-7.87((1)
-7.92(2)
-7.84(3)
AK(kHz)
43.63(3)
44.2(7)
43.(1)
42.64(8)
43.6(6)
44.1(7)
Sj (kHz)
0.2086(1)
0.199(1)
0.206(2)
0.2065(6)
0.202(2)
0.197(2)
5k(kHz)
A / Ic- lb-la(UA2)
6.74(2)
6.8(6)
6.7(7)
7.0(1)
7.0(4)
6.6(7)
-76.026
-76.845
-76.608
-76.881
-76.740
-76.030
k/ (2B-A-C)/(A-C)
-0.971
-0.972
-0.970
-0.970
-0.972
-0.972
o(kHz)c
3.0
1.2
3.3
1.1
1.6
2.1
# lines fitd
113
18
31
25
25
21
a. See Figure 2.2 for atom numbering and Figure 2.5 for conformer geometry.
b. Numbers in parentheses are la standard deviations in the last digit.
c. Overall standard deviation of the fit.
d. j«a and
are active, with pic believed to be larger than jua. No jWb-type transitions have
been observed for this conformer.
29
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 2.2. Rotational Parameters for the GG Conformer (Conformer II) of HOEES.
k
Rotational
Parameters
Normal
Species
2-°Ca
3-°C
34s
5-13C
A (MHz)
4916.20067(27)'’
4876.74725(66)
4865.56173(76)
4824.15886(50)
4886.11485(91)
4881.51429(74)
B (MHz)
1574.72262(13)
1562.04733(41)
1567.80626(47)
1572.94379(28)
1560.75284(49)
1544.52850(37)
C (MHz)
1465.71477(13)
1451.32784(29)
1463.91760(43)
1456.13779(26)
1456.15525(52)
1436.44893(32)
A, (kHz)
3.7520(9)
3.697(2)
3.685(2)
3.673(2)
3.687(2)
3.714(2)
Ajk (kHz)
-44.297(4)
-43.37(1)
-43.33(2)
-42.95(1)
-43.48(2)
-44.75(1)
AK(kHz)
156.20(2)
151.92(75)
151.98(9)
151.15(5)
153.10(9)
158.97(9)
5j (kHz)
0.4954(5)
0.491(1)
0.458(1)
0.530(1)
0.479(1)
0.506(1)
8k (kHz)
-2.23(2)
-2.0(2)
-2.7(2)
-1.8(1)
-1.9(2)
-2.5(1)
A /I c -I t-U u A 2)
-78.930
-78.948
-80.993
-78.987
-80.172
-78.910
-0.937
-0.935
-0.939
-0.931
-0.939
-0.937
3.1
2.2
2.6
2.6
2.4
2.2
/ (2B-A-C)/(A-C)
o (kHzf
6
92
37
36
57
32
fid
a. See Figure 2.2 for atom numbering and Figure 2.5 for the conformer geometry.
# lines
b. The numbers in parentheses are la standard deviations in the last digit.
c. Overall standard deviation of the fit.
d. All three selection rules are active with fia «
» Me-
30
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
-13C
33
Table 2.3.
Rotational Parameters for the High Energy TG Conformer (Conformer HI)
of HOEES.
k
Rotational
Parameters
Normal
Species
A (MHz)
4769.3866(5)'
B (MHz)
1572.7320(4)
C (MHz)
1479.8687(4)
A; (kHz)
1.899(2)
Ajk (kHz)
-17.65(1)
AK(kHz)
62.63(7)
5, (kHz)
0.5723(9)
5k (kHz)
15.0(2)
A / Ic- lb -I, ( u A2)
-85.799
/ (2B-A-C)/(A-C)
-0.944
S(kHz)b
1.9
# lines fit5
43
a. Numbers in parentheses are lo standard deviations in the last digit.
b. Overall standard deviation of the fit.
e. All three selection rules are active with jua » juc» jih
At this point, three conformational isomers of HOEES had been assigned at NIST,
but even with the additional information available from the BC and 34S isotopomers it
was difficult to relate the assigned spectra to a particular conformational isomer. In order
to ameliorate the situation, a detailed ab initio search was carried out to locate the low
energy conformers of HOEES. The details of this work are discussed below.
31
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2.2.2 Theoretical Analysis
The quantum chemistry calculation tool selected for use in this work was the Gaussian 98
ab initio package [33], installed on the NIST SGI computers. The internal Z-matrix was
used to define the molecular configuration for all Gaussian calculations.
Limited-Dimension Potential Energy Mapping
For HOEES, there are 42 degrees of freedom; therefore, searching for all possible lower
energy conformers by means of a full potential energy (PE) scan is impractical. However,
each degree of freedom carries a different weight in its contribution to the overall energy
of the whole molecule. Clearly, in the case of HOEES the three backbone dihedral
angles, D (0 1-C2-C3-S4), £>(C2-C3-S4-C5), and £>(C3-S4-C5-C6), arising from the six
heavy atoms (O-C-C-S-C-C) of the molecule in Figure 2.2, should carry most of the
information for the whole molecule. Unfortunately, a full 3-D PES is also difficult in
practice if a relatively fine grid of points is desired in the searching process. Thus, we
chose to proceed with two separate 2-D PE scans, namely Z>(1,2,3,4) vs. £>(2,3,4,5) and
£>(3,4,5,6) vs. £>(2,3,4,5), at the MP2/6-31G* level as a starting point in the search for the
possible lower energy conformers of HOEES. With 10° grid steps and taking advantage \
of the C2 symmetry of the 2-D PES to reduce the coordinate ranges scanned, the number
of calculation points is 2x37x19 = 1406 which becomes a manageable task.
In each 2-D scan, the rest of the degrees of freedom were relaxed. In Figures 2.3a
and 2.3b, we show contour plots of the potential energy surfaces for possible
32
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
conformational isomerization. The MP2/6-31G* energies are plotted as a function of the
dihedral angles D(l,2,3,4) and D(2,3,4,5) in Figure 2.3a and D(3,4,5,6) and D{2,3,4,5) in
Figure 2.3b. In both scans, the energy was minimized with respect to the other internal
coordinates.
The contours are spaced by 399 cm"1, with the darker areas indicating
regions of lower energy. As seen from the two contour plots, lower energy valleys were
distributed around the -60°, 60° and 180° regions for each dihedral angle, which is
consistent with the three-fold-like molecular structure about each bond in the heavy-atom
backbone. This indicates that, in principle, one might be able to perform a full 3-D search
with three steps only for each backbone dihedral angle spaced by approximately 120°. In
practice, however, the ab initio program does not necessarily land on the desired
minimum if the starting point is some distance away, likely being diverted by numerous
unforeseen potential hills between the starting point and the desired minimum in the
complicated multi-dimensional potential space.
/I ;
'
.
M
Figure 2.2. Numbering from 1 to 6 of the heavy backbone atoms ( 0 1-C2-C3-S4-C5-C6)
in the 2-(ethylthio)ethanol molecule.
33
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
-IS C
-1 2 U
-6 0
0
6*1
ljr
-leo
130
0(2 J .4 5) / cleg.
- l- 'O
-6 0
0
60
1 -0
Ltfj
0'2.3.4,5) / deg
a
b
Figure 2.3. 2-D contour plots showing the potential energy of HOEES as a function of
dihedral angles for (a) D(l,2,3,4) vs. D(2,3,4,5), and (b) D(3,4,5,6) vs. D(2,3,4,5).
initio calculations at the MP2/6-31G* were used to generate the energies for the plot for
10° increments of the three dihedral angles.
For each fixed value of £>(1,2,3,4),
£>(2,3,4,5) and £>(3,4,5,6), the other structural parameters were relaxed to minimize the
energy. The contours are spaced by 399 cm'1, with the darker areas indicating regions of
lower energy.
The two 2-D PE scans, though limited in dimensionality, do provide good starting
point information about possible lower energy conformers. Structures from some of the
lowest energy points in each 2-D PES were first used as initial values for full structural
optimization at MP2=FULL/6-311G**. We thereby arrived at low energy Conformers I,
ITT, and NM1.
Guided by the two 2-D contour plots displayed in Figure 2.4 as a
hypothetical “3-D” view of the three dihedral angles D(1,2,3,4), D(2,3,4,5) and
D(3,4,5,6), several further 1-D scans were performed to ensure that further important
degrees of freedom were covered. The scan routes are: (i) starting at the Conformer III
34
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
and first along the D(3,4,5,6), (jj) making a 90° right turn at the Conformer NM1 to along
the 15(2,3,4,5), (iii) making another 90° right turn at the Conformer I to along the
Z5(3,4,5,6), and (iv) finally making another 90° right turn at the Conformer NM2 back to
the starting point to finish the “square walk”.
D ( 2,3,4,5) / deg.
D ( 3,4,5,6 )/d e g .
Figure 2.4. Hypothetical “3-15” view of the three dihedral angles 15(1,2,3,4), 15(2,3,4,5),
and 15(3,4,5,6). The conformer minima, I, II, HI, NMI and NMII, are indicated.
35
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Full Structural Ab Initio Optimization
Following the 2-D and 1-D PE scans in Figure 2.3 and Figure 2.4, full geometry
optimizations were performed at MP2=FULL/6-311G**. Altogether, five low energy
conformers, I, II, 1H, NM1 and NM2, were found as possible conformers for HOEES and
are shown in Figure 2.5. In order to establish the relative conformer energy ordering and
have some idea whether such energy ordering is dependent on the ab initio level theory,
we carried out full structural optimizations at B3LYP=FULL/6-311G* * and HF/6-31G*
levels of theory as well. In addition, we carried out harmonic frequency calculations for
each lower energy conformer at the HF/6-311G* and MP2=FULL/6-311G** level in
order to apply vibrational zero point energy corrections to the minimized electronic
energy for each conformer. The resulting relative energies (zero-point corrected),
rotational constants, inertial defects, backbone dihedral angles and dipole moments are
listed in Table 2.4. Their visualization structures are displayed in Figure 2.5. As seen in
Table 2.4, MP2 and B3LYP gave consistent conformer energy ordering as well as
approximately the same dihedral angle values and rotational constants, indicating that we
can rely to a reasonable extent on the structure determination at the current level of ab
initio theory.
All five low energy conformers show C; point group symmetry, with three
displaying relatively open and chain-like structures and the other two showing relatively
closed, folded structures with very different rotational constants. As seen in Table 2.4
and Figure 2.5, the values of the dihedral angle Z)(l,2,3,4) for the five low energy
36
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
confonners are all about -60° indicating that this half of the molecule favors a gaucheethanol-like structure. The dihedral angle D(3,4,5,6), on the other hand, is distributed
approximately evenly among angle values of -60°, 60° and 180°, consistent with a trans
or goMc/ie-ethane-like structure for the other half of the molecule. The dihedral angle
D(2,3,4,5) connecting the two halves of the molecule is either about -60° or about 120° in
order to bring the overall conformational energy for the molecule to a minimum value. In
all five conformational isomers, the hydroxyl hydrogen forms a hydrogen bond to one of
the lone pairs of electrons on the sulphur atom.
Coaformerl
CanfarmerJI
Conformer NM1
Conformer HI
Coaformer NM2
Figure 2.5. The lower energy conformational isomers of HOEES at the ah initio
MP2=FULL/6-311G* level. The FTMW spectra of the two conformers with relatively
closed structures (folding-like structures) were not experimentally identified in this study.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Ab Initio Dipole Moment in the Principal Axis System
The dipole moment information obtained from the ab initio frequency calculations is
presented in the Z-matrix orientation in which the first atom is at the origin, the second
atom is along the +Z axis, and the third atom is in the XZ plane. Thus, in order to be able
to compare the ab initio dipole moment information to the experimental intensity
information, we needed to rotate the Z-orientation dipole moments into the principal axis
system. For this, we could use the same transformation matrix obtained when rotating
the Z-orientation Cartesian coordinates to the principal axis system. The dipole moment
values in the principal axis system, together with the ab initio rotational constants and
atomic coordinates, form the three criteria used in our attempts to match the ab initio
conformers to the experimentally observed isomers as described in the next section.
General Comments on Conformational Comparisons
The five low energy conformers identified in the preceding theoretical section fall into
two groups, characterized by A values of about 3.5 GHz to 3.8 GHz and 4.5 GHz to 5.6
GHz. It should be pointed out that the energy surface is quite flat for four of the five
conformers and is calculated to lie within 104 cm'1 at the MP2=FULL/6-311G** level of '
theory and within 42 cm'1 at the B3LYP=FULL/6-311G** level of theory. Therefore,
reliable energy level ordering is probably not feasible. The fifth conformer NM2 GG’ is
always calculated to be higher in energy and thus may not be a viable candidate structure.
38
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 2.4. Calculated ab initio rotational constants (A, B, €), inertial defects (A), relative energies
(Eki), and dihedral angles (D) for HOEES.
Conformer No.
No Match 1
HF/6-31G*
A/MHz
3862
B/MHz
1936
C/MHz
1483
-51
A/p.A2 a
-64
D(l,2,3,4) /deg
D(2,3,4,5)/deg
118
-75
D(3,4,5,6) /deg
0.8
Ha /Debye b
0.3
Pb /Debye
1.0
fic / Debye
267
Erel(el) / c m 1
300
Erel(el+zpe) / cm1
MP2=FULL/6-311G**
A/MHz
3818
B/MHz
2044
1548
C/MHz
-53
A /p A2 °
-62
D(l,2,3,4) / deg
118
D(2,3,4,5) /deg
D(3,4,5,6) / deg
-73
fia /Debye b
-0.9
0.4
fib /Debye
1.1
fic / Debye
0
Erel(el) / c m 1
0
Erel(el+zpe) / cm1
B3LYP=FULL/6-311G**
3712
A/MHz
B/MHz
1998
C/MHz
1496
-51
A /p A2a
-60
D(l,2,3,4) / deg
113
D(2,3,4,5) /deg
-76
D(3,4,5,6) /deg
-0.7
fia / Debye b
0.3
fib / Debye
1.0
fic /Debye
0
Erel(el) / cm'1
Erel(el+zpe) / cm1c
2
n
I
5513
1443
1355
-69
-62
-79
-76
2.1
1.7
-0.4
145
138
5893
1339
1305
-76
-62
-79
-178
-1.7
-0.6
2.0
0
0
4622
1590
1459
-81
-59
99
79
0.6
0.0
0.6
234
250
3862
1814
1496
-72
-60
-73
100
-1.7
-0.4
2.0
492
476
4558
1673
1530
-83
-59
-66
-64
1.9
1.4
0.3
79
37
5656
1419
1364
-75
-60
-72
-171
-1.6
-0.5
1.8
144
88
4592
1645
1516
-84
-58
100
78
0.8
0.0
0.8
172
104
3545
2154
1649
-71
-56
-62
98
-1.2
0.0
1.8
124
150
5341
1453
1364
-72
-60
-78
-76
2.0
1.6
-0.2
58
18
5658
1350
1312
-78
-60
-78
-179
-1.6
-0.3
2.0
54
0
4466
1612
1468
-82
-57
96
80
0.6
0.0
0.7
108
42
3568
2003
1567
-72
-55
-65
97
-1.3
-0.1
1.9
277
305
...
m No Match 2
a. Inertial defect A is defined as 505379.047x(Ic.c-/aa-I6&) where Iaa is the moment o f inertia o f the molecule
about the a principal axis o f the inertia tensor.
b. PAM dipole moments obtained using transformation matrixes when structures from Z-matrix orientation
were rotated to PAM.
c. Zero point energy corrections are from MP2=FULL/6-311G**.
39
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
The conformers with the larger A values are those which are either trans gauche
(TG) or gauche gauche (GG) with the two ethyl type subunits on opposite sides of the
C3-S-C5 plane. The two conformers with the lower A values are gauche gauche with the
two ethyl subunits on the same side of the C3-S-C5 plane, hereafter referred to as “GG"’
conformers. The GG' conformer labeled as NM1 in Figure 2.5 is calculated to be one of
the lowest energy forms in both the MP2=FULL/6-311G** calculations and in the
B3LYP=FULL/6-311G** calculations whereas the GG' conformer labeled NM2 is
always calculated to be the highest energy of the five considered and thus is probably not
a likely candidate structure. It is interesting to note that in the previous work on diethyl
sulphide, the analogous GG' conformer was not observed either and it was always
calculated to be the highest energy of the four considered in that case [15]. Here we
believe that in reality the NM1 GG' conformer probably lies at somewhat higher energy
than one or more of the more prolate forms (larger A values) and gets cooled out in the
expansion process. This would imply that the barrier to conversion is < 400 cm'1. Ruoff
et al. have discussed this in detail in an earlier paper [40].
In Table 2.4, the TG Conformer I has the largest A value and we would tentatively \
map this to the experimental Conformer I. In addition, a comparison of the observed
transition strengths vs the calculated dipole moment components from the ab initio work
also agree well for this conformer. It is interesting that we actually get a better match
with the rotational constants for Conformer 3Hat the B3LYP=FULL/6-311G** level but,
relatively speaking, Conformer I retains the largest A value. Furthermore, the calculated
40
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
dipole moment components for Conformer H do not agree with the experimental data for
the experimental conformer with the largest A value.
For the second experimentally observed conformer with the intense spectrum, the
A value could be mapped to either Conformer II or Conformer HI of the ab initio results.
Here again, we can use the relative intensities of the a-type, b-Xype and c-type transitions
to aid in the selection process. Experimentally, for the observed conformer, we have
intense a-type and &-type transitions and very weak c-type transitions. This correlates
nicely with Conformer II from the ab initio work. Based on these general considerations
we can map the experimentally observed conformers with Conformers I and H of the ab
initio work.
As alluded to previously, the spectrum of the third experimentally observed
conformer was found only after the 13C species of Conformer II had been assigned. In
fact it was initially thought that this spectrum was a 13C isotopomer of Conformer II
based on the intensity of the spectrum and the similarity of the rotational constants.
However, after closely looking at the selection rule behavior and the relative intensities of
the transitions ( a-type, &-type and c-type) it was found that for this spectrum the a-type
and c-type transitions were equally intense whereas for conformer II the a-type and btype were the most intense and the c-types were quite weak. Based on these facts, we
mapped the carrier of this spectrum to that of Conformer HI of the ab initio work. Since
this spectrum is so weak, we were not able to observe any 13C or 34S isotopomers which
would help to elucidate the conformation. Experimentally, this conformer must lie at
41
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
higher energy than Conformers I and II and have a low barrier to interconversion as
discussed above [40].
One of the perplexing issues that remains is the failure to observe the no-match
GG' conformers. This is particularly true for the NM1 conformer which is predicted to
lie at very low energy at all levels of the ab initio calculations. A predicted spectrum for
the NM1 conformer can be generated using ab initio calculated rotational constants and
dipole moment values at the MP2=FULL/6-311G** level. Although the ab initio fi„ and
juc values for the no-match conformer are about half of the observed conformer I, they are
still sizable and transitions should be observable if the conformer were present.
To summarize, with the ab initio approach five lower energy conformers were
found. Three of them match well with the experimental findings both in rotational
constants and dipole moment information. However, the lowest and the fifth lowest
energy conformers found in the ab initio work at the MP2=FULL/6-311G** level of
calculation with “folded-liked” structures having very different A/B/C rotational
constants do not have experimental matches. The reason for this is most likely the fact
that four of the five conformers found at the highest level of theory (B3LYP=FULL/6311G**) are all calculated to lie within 42 cm' 1 of the lowest energy form. This is such a
small energy difference that theory cannot discern among the group as to which is the
lowest energy. Furthermore the NM1 GG' conformer must lie above Conformers I and II
and must have a low barrier to inter conversion (<400 cm'1) [40] down to Conformer I or
II in the molecular beam expansion.
42
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
It is interesting to compare the conformational geometries found here for HOEES
with the geometries found for the parent molecule, diethyl sulphide [15]. In that work,
three conformational isomers were also observed.
A trans trans (TT) form, a trans
gauche (TG) form and a gauche gauche (GG) form were identified with the TT form
estimated to be at higher energy than the latter two. The TG form corresponds directly to
the TG Conformer I form found here for HOEES. The GG form likewise corresponds to
the overall conformational geometry of Conformers II and III of HOEES. No analogue
of the TT form was found in this work and likewise no conformational form where the
terminal methyls are located on the same side of the C3 -S-C5 plane was found in either
case. For diethyl sulphide this GG' form was calculated to be at higher energy and was
not expected to be observable in the cold molecular beam. This is contrary to the case for
HOEES where the GG' Conformer labeled NM1 was always calculated to be one of the
lowest energy conformers.
Conformational Stabilization by Intramolecular Hydrogen Bond Interaction
The structures of isolated molecules are determined by a number of factors that include
intramolecular interactions.
The most
important
intramolecular
interaction is
intramolecular hydrogen bonding, which is well known to stabilize particular
conformations of many organic and biologically important molecules [41]. The
conformation of the molecules in which an intramolecular hydrogen bond is formed
between a hydroxyl hydrogen atom and a sulphur atom has been studied for several
compounds that contain the -SCH 2 CH2 OH group. Previous microwave spectroscopic
43
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
studies have shown that the molecules 2-mercaptoethanol (HSCH 2 CH 2 OH) [42] and 2(methylthio)ethanol (MTE) (CH3 SCH2 CH2 OH) [43] in the gas phase adopt the
conformation that is stabilized by an intramolecular -O H ...S hydrogen bond. This
characteristics is also confirmed by our HOEES (CH 3 CH 2 SCH 2 CH 2 OH) ab initio studies
above. In the cases of MTE [44] and HOEES, as well as the dominant hydrogen bonding
between the hydroxyl hydrogen atom and the sulphur atom (-O H ...S ), an additional C H ...0 intramolecular interaction between the methyl hydrogen and the hydroxyl
oxygen atom will also get involved for the ‘closed’ conformers, and their cooperative
effect may lead to high stability of particular conformations [44],
In their matrix-isolation infrared study, H. Yoshida et al. carried out both
experimental and theoretical investigations of the conformational stability of MTE [44],
From both experimental observations and ab initio calculations, they found that one of
the most stable conformers had both of the types of intramolecular hydrogen bond
involved resulting in a relatively ‘closed’ structure [44]. Our analysis of HOEES also
presents this interesting phenomenon. Both of the two No Match conformers, although
having no experimental partners in the molecular jet microwave spectrum in our current
observations, are always calculated to lie among the low energy group. Without
considering the additional hydrogen bonding between the methyl hydrogen atom and the
hydroxyl oxygen atom, it appeared difficult at first to understand the high stability of
these two folded structures, in which the methyl and hydroxyl ends come close to each
other, as shown in Figure 2.6. In Table 2.5, we list the optimized non-bonded -OH...S
and -C H .. .0 interatomic distances for the five low energy conformers of HOEES at MP2
44
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
level with a 6-3 11G** basis set. For conformers NM1 and NM2, the optimized -C H .. .0
distances are 2.64 A and 2.75 A respectively. Both of them are well within the typical
hydrogen bonding distance between the alcohol -OH and the hydrogen atom, which
normally ranges from 2.55 A to 2.96 A [45].
HOEES Conformer NM1
Figure 2.6. Molecular structure of HOEES’s NM1, one of the two conformers having the
folding-like structure. The dashed arrows indicate the intramolecular —OH...S and CH.. .0 hydrogen bonding interactions.
Table 2.5. ab initio optimized non-bonded interatomic distances (in A) for HOEES
conformers a.
MP2=FULL/6No Match I D
I
III
No Match 2
311G**
-OH...S b
2.64
2.55
2.57
2.63
2.50
-CH ...O b
2.64________—
—
— _______ 2.75
a. Structures of these conformers are shown in Figure 2.5.
b. See Figure 2.6 for intramolecular hydrogen bonding interactions.
45
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2.3 Ab Initio Conformation Study of Thiodiglycol
Thiodiglycol (TDG) with structural formula (HQCH2 CH2 SCH2 CH2 OH) is another
similar hydrolysis product found in the degradation of mustard gas. The only difference
between thiodiglycol and HOEES is that one of the methyl hydrogen atoms is replaced by
a hydroxyl group, as shown in Figure 2.7. The presence of two terminal hydroxyl groups
gives rise to interesting conformational phenomena due to the possible hydrogen bonding
interaction between them as well as to the central sulphur atom. Up to now, three
conformational isomers for thiodiglycol have been identified in the molecular beam
microwave spectrum. The experimental parameters are listed in Table 2.6. In this section,
the ab initio conformational analysis of thiodiglycol will be presented and compared with
experimental observations.
Figure 2.7. Numbering of the heavy backbone atoms (including two terminal hydroxyl
hydrogen atoms) in the thiodiglycol molecule.
46
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 2.6. Experimental rotational parameters for thiodiglycol isomers.a
Parameter
2hbGG’
2hbGG
lhbGG
A (MHz)
2543.0121(3)
4951.5310(6)
4474.6(6)
B (MHz)
1845.4959(3)
1006.7949(3)
1056.249(1)
C (MHz)
1259.2960(1)
974.6062(3)
1003.066(1)
A (uA2)
-71.27
-85.4865
-87.93
Dipole
Selection
Rules
/4>>/4
fic not yet
observed
ftb only,
and fic not
yet observed
/ 4 only
fib and fic not
yet observed
/4
a.Private communication from R.D.Suenram at NIST. Unpublished data.
Structure Determination o f Thiodiglycol
Considering the important role of the intramolecular hydrogen bonding and the structural
similarity between HOEES and TDG, it is reasonable to guess the possible conformers of
thiodiglycol by borrowing geometrical parameter information directly from HOEES.
Seven possible existing conformers can be constructed with the hydroxyl hydrogen
hydrogen-bonded to the central sulphur atom or to the oxygen on the other hydroxyl
group. Full structural optimizations for these seven starting conformers were then carried
out at the HF/6-31G* theory level. The principal axis system dipole moment was
obtained by the same procedure used in the preceding section for HOEES. The calculated
relative energies (zero-point corrected), rotational constants, and dipole moment values in
the principal axis system form the three criteria in our attempts to match the ab initio
conformers to the experimental observations.
47
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
&
2hbGG*
lhbGG
2hbGG
Figure. 2.8. The lower energy conformational isomers of thiodiglycol in the energy
ordering given at the ab initio HF/6-31G* level. The dashed arrows indicate the types of
intramolecular hydrogen bonding presented in 2hbGG’. The
/4
and fic dipole moments
are equal to zero for 2hbGG because of the symmetry.
Table 2.7. Calculated ab initio (HF/6-31G*) rotational constants (A, B, Q , relative
energies, and backbone dihedral angles for thiodiglycol.
2hbGG'
HF/6-31G*
A /MHz
2549
B lMHz
1817
C/MHz
1241
D l 1874 /deg
-72
£>8743 /deg
115
71
<£141187 /deg
£7432 /deg
-57
£1714118/deg
-84
£4321 /deg
76
-0.7
/ 4 /Debye
1.3
fib /Debye
-0.4
Pc /Debye
-704.505040
£ eiec. /Hartree
ZPE /Hartree
0.156820
-704.348220
£eiec.+zPE/Hartree
£rel(elec.+zpe)/C m
0
2hbGG
lhbGG
5408
942
912
-81
-81
-62
-62
62
62
4472
1039
976
-97
-82
59
-62
-76
62
1.5
-0.4
-0 . 8
-704.501942
0.155706
-704.346236
435
0 .0
2 .0
0 .0
-704.502023
0.155587
-704.346436
392
a. Energies are converted to wavenumber using the conversion factor 1 Hartree =
219474.7 cm'1.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
The rotational constants of the three low energy conformers, together with their
dipole moments, agree well with the three experimental predictions. The ab initio results
are listed in Table 2.7, and their visualization structures are displayed in Figure 2.8. As
seen from Figure 2 .8 , the lowest energy conformer (2hbGG’) with the two hydroxyl ethyl
subunits on the same side of the C4-S 7-C 8 plane possesses a structure quite different from
the other two. In this conformer, one of the hydroxyl hydrogens forms a hydrogen bond
to one of the lone pairs of electrons on the sulphur atom, while the hydrogen on the
second hydroxyl end forms another type of hydrogen bond (-OH...O) with the oxygen
atom on the first hydroxyl group. Because thiodiglycol has a longer backbone chain
compared to HOEES and MTE [44], the -0 H ...0 interaction becomes much stronger,
which is indicated by the smaller - 0 H . . . 0 hydrogen bonding distance of
2 .0 1
A as
compared with the values in Table 2.5. This strong - 0 H ...0 hydrogen bonding
interaction is thought to explain why this “closed” structure lies at the lowest energy in
our current calculation (HF/6-31G*). Both of the other two conformers, 2hbGG and
lhbGG, have larger A values, which comes from the fact that the two hydroxyl ethyl
subunits hydrogen-bond to the central sulphide along opposite directions to the C4-S 7-C 8
plane. 2hbGG shows C2 point group symmetry, thus gives no //a,
dipole moment
components. The only conformational difference between 2hbGG and lhbGG is that one
of the hydroxyl methyl groups is rotated to its next staggered position by 120°. These two
open structure conformers are almost isoenergetic at current HF theory level. From their
visualization structures in Figure 2.8, we guess that the hydrogen bonding directions in
2hbGG are closer to the directions of the two non-bonding hybrid orbitals of the sulphur
49
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
atom. The skewed bonding direction of one of the hydrogen bonds in lhbGG leads to a
slight increase for its overall energy.
2.4 Ab Initio Conformation Studies o f N-ethyldiethanolamine and Nmethyldiethanolamine
N-ethyldiethanolamine (CH3CH2N(CH2 CH2 0 H)2 ) and N-methyldiethanolamine (CH3 N
(CH2 CH2 OH)2 )
are two nitrogen-containing species with subunits that resemble
biomimetic species. Three conformers of N-ethyldiethanolamine and two of Nmethyldiethanolamine have been identified in the molecular beam FTMW spectra [46].
In this section, preliminary ab initio studies of these two molecules will be described.
Ab Initio Conformational Study o f N-ethyldiethanolamine
N-ethyldiethanolamine, with the structural formula (CH3 CH2 N(CH2 CH2 OH)2 ), has three
subunits, one ethyl and two ethanol tops, connected by a central nitrogen atom, as shown
in Figure 2.9. The internal Z-matrix was used to define the molecular configuration and
for all Gaussian calculations. The Z-matrix specifies the atom locations using bond
lengths, bond angles, and dihedral (torsion) angles. Each atom in the molecule is
described on a separate input line within the Z-matrix, and the procedure for creating a Zmatrix can be found in Ref. [33]. The Z-matrix and the complete atom labeling for Nethyldiethanolamine are as follows:
50
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 2.9. Molecular structure of N-ethyldiethanolamine with the heavy backbone atoms
labeled.
H,
/
o6
Hl7
H,S
H,0
H,
H,
■C, H l2
I
H
\
C4 /
/
-Ns
\
\ C7/X
H/
H23
\ HW
I8
•H16
h 20
\
O9
\
H■24
51
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
c
c
N
C
C
0
C
c
0
H
H
H
H
H
H
H
H
H
H
H
H
H
1
2
3
4
5
3
7
8
1
1
1
2
2
4
4
5
5
6
7
7
8
rcc21
rnc32
rcn43
rec54
roc65
rcn73
rcc87
roc 9 8
rhclOl
rhclll
rhc!21
rhcl32
rhcl42
rhcl54
rhcl64
rhc175
rhcl85
rhol9 6
rhc2 07
rhc217
rhc228
1
2
3
4
2
3
7
2
2
2
1
1
3
3
4
4
5
3
3
7
a321
a432
a543
a654
a732
a873
a987
a!012
a!112
al212
a!321
al421
al543
al643
al754
al854
al965
a2073
a2173
a2287
1
2
3
1
2
3
3
3
3
10
10
2
2
3
3
4
2
2
3
d4321
<55432
<56543
<57321
<58732
<59873
<510123
<511123
<512123
<5132110
<5142110
<515432
<516432
<517543
<518543
<519654
<520732
<521732
<522873
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
The mini FT spectrometer described by Suenram et al. [37] was used to record
survey scans from about 10 GHz to 20 GHz. A composite of these scans is shown in
Figure 2.10. Spectral assignments were obtained using the JB95 spectral fitting program
[15]. Three conformers for N-ethyldiethanolamine, identified as I, II and HI, have been
assigned, and their rotational constants are shown in Table 2.8. Simulated spectra for
these three assigned conformers are also shown in Figure 2.10, and were generated by
using the experimental fitted parameters listed in Table 2.8. Conformer I gives the most
intense transitions in the spectra, with much weaker transitions coming from the other
two conformers. Their relative dipole components were estimated by trying to match the
simulated spectral patterns to the experimental trace.
52
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Conform or I
Conform orR
1
.
.j
.
Conformer Hi
. 5
i
..
I,
,
a
*
..............................
4 ^
a
.
.
ft
.
.
I
i
I .
.
I , .
s
I
I
i
i
t
11
13
15
17
19
Frequency (GHz )
Figure 2.10. Survey scan of N-ethyldiethanolamine. The upper trace shows the
experimental spectrum. The lower three traces show the simulated spectra from the three
assigned lowest energy conformers using the parameters in Table 2.8.
Instead of mapping a Ml- or limited-dimension potential energy surface, the
conformational structure searching was here carried out in a more direct way by using
chemical intuition. The initial geometrical parameters for our calculation were based on
other molecules having similar structures and/or functional groups, as obtained from the
Computational Chemistry Comparison and Benchmark DataBase (CCCBDB) at NIST, a
database containing comprehensive experimental and computational thermochemical data
for more than six hundred gas-phase molecules [47],
53
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table
2.8.
Experimentally
determined
rotational
constants
fo r. N-
ethyldiethanolamine.a
Experimental
Rotational
Conformer I Conformer II Conformer III
Constants
zf/MHz
1691.54
1610.55
1586.69
B /MHz
1315.86
1225.01
1246.96
C/MHz
845.77
910.75
924.63
a. Private communication from R.D.Suenram at NIST. Unpublished data.
The first geometry optimization started from an estimated possible low energy
conformer with an “open” structure. However it turned out that the calculated A/B/C
values were quite different from the experimental results. The calculated C value of
around 650 MHz was much smaller than the experimental observations, which range
from 840 to 925 MHz. This led us to think of trying a relatively “closed” structure with
one or both of the two ethanol tops folded to form intramolecular hydrogen bonds by
sharing the lone pair of electrons on the nitrogen atom. A low energy conformational
structure with two intramolecular -OH...N hydrogen bonding was then found, which
gave a good agreement with experimental Conformer I. Further, when we returned to the
spectrum and investigated the observed transition strengths, it turned out that the a-type
transitions should be very weak by comparing the simulated and experimental spectral
patterns, which was also consistent with our calculated dipole moment components in the
principal axis system. The structure of Conformer I was thus successfully determined.
We also found that the energy increases rapidly when one or both of these two —
OH...N intramolecular hydrogen bonds is broken, indicating that the other conformers
should also possess a similar double-hydrogen-bonded structure. These hydrogen-bonded
54
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
structures will make the molecular shape closer to spherical than linear, as indicated by
the almost equally-sized AIB/C values in Table 2.8. Based on this anticipation, the
conformer II was quickly arrived at by rotating the ethyl top around the C2 -N 3 bond to
another possible low energy position. The search for experimental Conformer III was less
easy. This conformer was not reached at first by only rotating the ethyl group. Later, we
realized that another type of intramolecular hydrogen bonding interaction, between the
hydroxyl hydrogen atom and the second hydroxyl oxygen atom, might also play an
important role in stabilization of the whole structure. By opening one -O H .. .N and then
forming the -OH ...O hydrogen bond, the experimental Conformer ID was finally found.
The mapping of Conformers II and HI between experimental and ab initio work also has
convincing support from dipole moment considerations. The calculated results for the
three conformers are listed in Table 2.9a, 2.9b and 2.9c, and their visualization structures
are displayed in Figure 2.11.
Conformer I
Conformer II
Conformer III
Figure 2.11. The lower energy conformational isomers of N-ethyldiethanolamine in the
energy ordering given at HF/6-31G* level. The structural difference between Conformers
I and II is the orientation of the ethyl group. In Conformer HI, there are two types of
intramolecular hydrogen bonding interaction present, as indicated by the dashed arrows.
55
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 2.9a. Calculated results for Conformer I at different theory levels.
HF/6-31G*
MP2/6-31G*
Diff.
Calc.
B3LYP/6-31G*
Exp.
Diff.
1634
1586.69
2.9%
1603
1586.69
1.0%
1239
1225.01
1.1%
1211
1225.01
-1.2%
924.63
3.3%
935
924.63
1.1%
Calc.
Exp.
A /MHz
1606
1586.69
1.2%
S /M H z
1216
1225.01
-0.8%
924.63
0.4%
956
Calc.
C /M Hz
928
£ de /Hartree
-440.072436
ZPE /Hartree
Ea +ZPE /Hartree
0.233650
0.222135
0.217612
-439.838786
-441.161939
-442.614022
-441.384074
Exp.
Diff.
-442.831634
fa/D ebye
0.48
—
0.25
fa /Debye
-2.56
—
-2.46
fa /Debye
2.36
—
2.38
Exp. Dipole Expectation: fa~fa>>fa
Table 2.9b. Calculated results for Conformer H at different theory levels.
HF/6-31G*
Calc.
1567
A /MHz
B !MHz
1266
841
C/M Hz
-440.071084
Ede /Hartree
0.233755
ZPE /Hartree
'dc+ZPE /Hartree -439.837329
-1.67
/ 4 /Debye
-2.87
fa /Debye
1.25
/it/Debye
MP2/6-31G*
Exp.
1610.55
1246.96
845.77
Diff.
-2.8%
1.5%
-0.6%
Calc.
1650
1244
862
-441.382571
0.222393
-441.160178
B3LYP/6-31G*
Exp.
1610.55
1246.96
845.77
Diff.
2.4%
-0.2%
1.9%
—
—
—
Calc.
Exp.
1548
1610.55
1246.96
1275
841
845.77
-442.830289
0.217765
-442.612524
-1.65
-2.92
1.24
D iff
-4.0%
2.2%
-0.5%
Exp. Dipole Expectation: fa is the biggest, fa~fa
Table 2.9c. Calculated results for Conformer III at different theory levels.
HF/6-31G*
A MHz
B/M H z
C/M Hz
Egie /Hartree
ZPE /Hartree
E^+ZPE /Hartree
fa /Debye
fa /Debye
fa /Debye
Calc.
1778
1294
927
-440.071271
0.234722
-439.836549
-3.43
1.58
1.35
MP2/6-31G*
Exp.
1691.54
1315.86
910.75
Diff.
4.8%
-1.7%
1.8%
Calc.
1840
1294
944
-441.386905
0.223642
-441.163263
—
—
—
B3LYP/6-31G*
Exp.
1691.54
1315.86
910.75
Diff.
8.1%
-1.7%
3.5%
Calc.
1831
1270
930
-442.834756
0.219149
-442.615607
-3.39
1.30
1.31
Exp. Dipole Expectation: fa is the biggest, fa~fa
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Exp.
1691.54
1315.86
910.75
D iff
7.6%
-3.6%
2.1%
Up to now, all of the calculations at different theory levels were carried out with a
small basis set (6-31G*), so we do not expect good energy information from the present
results. From our current calculation, the energy ordering of Conformers I and II is
always consistent for different theory levels, with Conformer II lying -300-400 cm' 1
higher than Conformer I. However, the energy of Conformer HI shifts from highest to the
lowest when post Hartree-Fock calculations are used. This indicates that the ab initio
energy calculations may become unreliable when dealing with H ...0 hydrogen bonding
interactions. If this is true, it might explain why the calculated low energy conformers
with the intramolecular -C H ...0 (NM1 and NM2 conformers for HOEES) or -OH...O
(No Match conformer for N-methyldiethanolamine, discussed in the next section)
hydrogen bonding are not observed experimentally.
Finally, it is interesting to note that the lower-level Hartree-Fock calculations
more closely approximate the experimental rotational constants than do the higher-level
calculations. This phenomena had been previously pointed out by R.D. Suenram et al. in
their FTMW and ab initio study of dimethyl methylphosphonate [17].
Ab Initio Conformational Study o f N-methyldiethanolamine
N-methyldiethanolamine (CH3 N(CH2 CH2 0 H)2 ) has a similar chemical constitution to Nethyldiethanolamine, with the only difference being that the ethyl subunit in the latter is
replaced by a methyl top, as shown in Figure 2.12. The internal Z-matrix was used to
define the molecular configuration and for all Gaussian calculations. The Z-matrix and
atom labeling are as follows:
57
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 2.12. Molecular structure of N-methyldiethanolamine with the heavy backbone
atoms labeled.
Hi,
O5
H l4
H,2
h6
h
I
/
I
\
\ Hi3
7 ----- c, — n 2
H8
H,
C9
/
\
/
H i9
Cjo
/
H;■20
\
On
<
\
H;•21
58
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
c
N
C
C
0
H
H
H
C
C
0
H
H
H
H
H
H
H
H
H
H
1
2
3
4
1
1
1
2
9
10
3
3
4
4
5
9
9
10
10
11
rnc21
rcn32
rcc43
roc 54
rhc61
rhcVl
rhc81
rcn92
rccl09
roclllO
rhcl23
rhcl33
rhcl44
rhcl54
rhol65
rhcl79
rhcl89
rhcl910
rhc2010
rho2111
1
2
3
2
2
2
1
2
9
2
2
3
3
4
2
2
9
9
10
a321
a432
a543
a612
a712
a812
a921
al092
alll09
al232
al332
al443
al543
al654
al792
al892
al9109
a20109
a211110
1
2
3
3
3
6
1
2
1
1
2
2
3
1
1
2
2
9
d4321
d5432
d6123
d7123
d8123
d9216
dl0912
dlll092
dl2321
dl3321
dl4432
dl5432
dl6543
dl7921
dl8921
dl91092
d2 01092
d211110 9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Anticipating the structural similarity, the geometrical parameters of Nethyldiethanolamine provide a convenient starting point for constructing the starting
geometries for N-methyldiethanolamine. The calculations for starting geometries
corresponding to conformers I, II and ID of N-ethyldiethanolamine quickly converged to
three geometries with two of them agreeing well with experiment for Nmethyldiethanolamine. In Table 2.10, the rotational constants and dipole moment
components in the principal axis system are compared with those observed
experimentally. Their visualization structures are displayed in Figure 2.13.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 2.10.
Comparison of Theoretical and Experimental Parameters of N-
methyldiethanolamine
No Match
Confromer II
Conformer I
Calc.
Calc.
Exp.a
Diff.
Calc.
■ Exp.a Diff.
HF/6-31g*
A /MHz
2152
2557
2567.7073 -0.4%
3063
3152.7972 -3.0%
1875
1349
1167
B /MHz
1342.2453 0.5%
1145.9656 1 .8 %
1173
1088
1014
C/MHz
1086.8715 0 .1 %
1016.8897 -0.3%
Eehc./Hartree
-401.039495 -401.037625
-401.037421
ZPE /Hartree
0.204291
0.203250
0.203308
Ee\sc+ZPE /Hartree -400.835204 -400.834375
-400.834113
0 .0 0
181.87
239.47
■fi'reI{elec.+ZPE)/cm
-1.78
-0.78
0 .0 0
/Debye
-2.90
-3.27
-3.66
//b/Debye
0.45
- 1 .0 0
0.05
/Debye
a. Experimental data are private communication from R.D.Suenram at NIST.
No Match
Conformer II
Conformer I
Figure 2.13. The lower energy conformational isomers of N-methyldiethanolamine.
Similar to conformer HI in Figure 2.10, here both -OH ...N and - 0 H ...0 types of
intramolecular hydrogen bonding interaction exist in conformer No Match. Conformer I
has a plane of symmetry, and gives no / 4 and juc dipole moment components.
In Figure 2.14, we display the observed spectrum along with the simulated ones
by using JB95 [15]. The second and third traces in Figure 2.14 are the simulated spectra
for the experimentally identified Conformers I and II. Both of them were generated by
60
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
using the experimental fitted rotational constants listed in Table 2.10. Their a-, 6 -, and ctype transition intensities were adjusted by pattern matching to the upper experiment
trace. From the pattern matching, for Conformer I, only intense 6 -type transitions are
observable. All three types of transition appear in the experimental observations for
Conformer n, and it was found for this conformer that a- and c-type are almost equally
intense and weaker than 6 -type transition. These experimental dipole data correlate nicely
with our calculated dipole moment components, as shown in Table 2.10.
The simulated spectra of Conformers I and II appeared together to reproduce the
overall features of the observed spectrum. Both conformers contribute strong transition
lines, indicating that both will hold a considerable percentage of the population in the
molecular beam. From the current lower-level Hartree-Fock calculations, Conformers I
and H are nearly isoenergetic, which is consistent with experimental expectation. In
Figure 2.14, we also generated the spectrum for conformer No Match by using its
calculated rotational constants and dipole moment components. Its intense
6
-type
transitions make it almost impossible to be overlooked in the spectral assignment if it has
any significant population in the experimental molecular beam. It is thought, like the
HOEES case, that this No Match conformer in fact lies above Conformers I and II and
must have a low barrier to interconversion down to Conformers I and/or II in the
molecular beam expansion. It is interesting to note that this No Match conformer also
possesses intramolecular -Q H ...0 hydrogen bonding, a similar situation to NM1 and
NM2 for HOEES, which have intramolecular -C H ...0 hydrogen bonding but do not
appear to have experimental partners.
61
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Conformer!
I
Conformer 9!
i.
1 . x ul
i
1 1, I 1
I
1 l ll l
.1
j 1
i
..at 4 J 1
n i
ll .L L.Mwli li1
I
i J ii
1
1
Ji
,i In .1...l.lil.,ji i s
No Match
|
[
.
a a
J J
j.
1! i
..i-
. .AL.-J lI . I, .
li ll
1
L
A1
1I ll i
_ JJL j
,-------------------------------------------- 1----------------------------------------- j---------------------------
,------------------------------------------ ,
12
18
14
16
20
Frequency (GHz)
Figure 2.14. Survey scan of N-methyldiethanolamine. The upper trace shows the
experimental spectrum. The lower three traces show the simulated spectra for the lowest
energy Confonners I, II and No Match. The rotational constants for the simulated spectra
of Conformers I and II are from their experimental values in Table 2.10. The a-, b-, and
c-type transition intensities for Conformers I and H were adjusted through pattern
matching to the experimental spectrum. The simulated spectrum for No Match was
generated by using the calculated rotational constants and dipole moment components.
2.5 Summary
In this chapter, we have carried out ab initio calculations for a series of large
molecules of biological interest. Generally speaking, all the calculations give satisfactory
results when compared with the FTMW predicted structural parameters. All the
62
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
experimentally observed conformational isomers were found to lie at low energies in our
ah initio calculations. However, in addition to the nicely matched conformers, there are
some with low calculated energies that do not have experimental partners. A possible
explanation for this issue lies in unreliability of current ah initio energy results when
dealing with nearly isoenergetic states of large molecules. It is also interesting to note
that this phenomenon seems always to appear along with intramolecular H .. .0 hydrogen
bonding, which is usually an important intramolecular interaction for organic and
biological molecules. This correlation might indicate that currently used ah initio
methodology is particularly unreliable when various hydrogen bonding interactions are
present in the system.
63
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Chapter 3
Vibrational Analysis for 2-(Ethylthio)ethanol
Most ah initio packages calculate vibration frequencies in the harmonic approximation.
In order to account for anharmonic effects, empirical scaling factors with no specific
physical origin are often used when ah initio results are compared to experimental
observations. It is well known that anharmonic effects become important in highly
excited stretching modes and can be corrected with a “diatomic”-stretch approach [2 0 ].
However, large amplitude torsions are very anharmonic even at their fundamental levels
due to their low barrier nature. In this chapter, we will describe our attempt to apply a
“diatomic”-twist approach for anharmonic potential corrections to ah initio harmonic
frequencies for some large amplitude torsions, initially on methyl torsion and ultimately
on backbone torsions in large bio-mimetic molecules. In this chapter, we will start with a
description of an internal coordinate method to identify different vibrational modes for 2 (Ethylthio)ethanol (HOEES), one of the molecules which we have studied extensively in
the previous chapter. The “diatomic”-twist approach will then be introduced followed by
its application to methyl torsion in methanol, ethane and HOEES.
3.1 Identification of Vibrational Modes for 2-(Ethylthio)ethanoi
In most ah initio molecular orbital packages, including Gaussian 98, the energy
derivatives are computed in Cartesian coordinates [48]. In addition to the frequencies and
intensities, Gaussian also gives the displacements, in Cartesian coordinates, of the nuclei
corresponding to each normal mode. This displacement information can be used to
64
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
associate normal modes with their corresponding internal vibrational motions. However,
this identification becomes increasingly difficult as the molecule gets bigger. One way to
simplify this process is to express the vibrational motions in terms of 3N-6 internal
coordinates, which are more appropriate for interpreting normal mode vibrations in terms
of bond stretches and angle bending. One such set of internal coordinates is made up of
the bond lengths, bond angles and dihedral angles. For the HOEES molecule, which has
42 degrees of freedom, we can define a set of internal coordinates consisting of 15 bond
lengths, 14 bond angles and 13 dihedral angles.
In order to obtain displacement information in terms of the above internal
coordinates, we have carried out Wilson GF matrix calculation [49] using Mathematica
with input force constants from the Gaussian frequency calculation output. This
calculation serves as a good exercise to become familiar with the GF matrix method as
well as coordinate transformations. The following paragraphs present a detailed
description of this procedure.
The force constant F matrix, more commonly known as the Hessian to chemists,
is output by Gaussian after a frequency (Freq keyword) job is successfully finished. The
Gaussian frequency output gives the Hessian in both internal and Cartesian coordinates,
with the latter being given to greater precision than the former. We therefore chose to use
the Cartesian Hessian for our GF matrix calculation.
65
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Because the F matrix is symmetric, only the elements in the lower triangle are
printed out in Gaussian output, and some effort is needed to re-arrange them into the
standard square form as follows:
x
X, ( &E
a p r,
&E
Y.
2l
dYpXx
tfE
Zx
azpxx
$E
x 2 dX2dXx
&E
r2 dY2aXx
$E
z 2 dL$Xx
Yi
Zi
&E
axxdYx
&E
dfpYx
&E
azf>Yx
&E
ax2dYx
$E
dY2dYx
$E
dZpYx
&E
dXplx
&E
a x ft
&E
dzpz,
$E
oXpZ,
&E
d¥2azx
&E
dzps^
h
&E
&E
dXxSX2 dXpY2
&E
&E
d%ax2 dYpYz
$E
$E
czpx2 8ZpY2
$E
&E
SX2dX2 SX2dY2
$E
$E
dYpX2 dYpY2
$E
$E
dZpX^ dZ2dY2
z2
tfE
axpz2
tfE
m pz2
&E
dzpz2
&E
dX2dZ2
&E
dY2az2
$E
dzpsz^
3e
&E
FXJYXv
tfE
tfE
dY^XN
$E
&E
dZ^XN a z ^
&E
fx^ zn
&E
SY^Zn
$E
azA
[3-1]
Here, consistent with the previous chapter, we use Xx, Yx and Z-x to indicate the three
Cartesian coordinates for each nucleus.
It is necessary to point out here that Gaussian prints out the F matrix in Z-matrix
orientation, used to specify the molecular orientation in Cartesian coordinates. In this
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
orientation, the origin atom is located at the origin point, the first bond is along the Zaxis, and the first angle is in the XY plane. Before we move on to the internal coordinates,
the Z-matrix orientation will first be transformed to the Principal Axis Method (PAM)
orientation, where the XYZ axes are set along the principal axes of inertia and the origin
point is located at the centre of mass of the molecule. The reason for this orientation
change in the Cartesian coordinates will be explained later.
It is of great advantage to set up the G matrix in Cartesian coordinates, because
the diagonal G matrix elements are simply defined as the inverse of the mass of each
atom, while the off-diagonal elements are all zero. Thus the Cartesian G matrix takes the
simple form:
1
ml
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
fflj
1
0
ml
1
■ o
0
0
0
0
0
0
0
0
0
0
0
0
m2
1
m2
0
0
1
m2
mN
m
N
J
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
At this stage, we have obtained both G and F matrices in Cartesian coordinates.
As a check for the G and F matrices built up above, their product is diagonalized in
Mathematica to get the eigenvalues, and the vibrational frequencies are then calculated as
JEigenvalue[G.F]
, ,
, _r .
.
.
v =--------------------- . Gaussian calculates the Hessian elements m atomic units, so it is
2 jz
necessary to convert the above ab initio derived frequencies (in units of
\ Hartree
L_ y to 0ther units for comparison to be made. A conversion factor of
VBohr.Bohr amu
5140.487 was used in order to convert the ab initio derived frequencies to units of cm'1, a
commonly used unit for vibrational frequencies. The Gaussian Freq job also gives
vibrational frequencies in wavenumber units, so they could be used directly to check the
Mathematica calculation. Our Mathematica calculated frequencies agree well with the
Gaussian results, with occasional differences occurring only in the fourth digit in units of
cm"1, which is thought to be due to insufficient significant digits for the F matrix
elements in the Gaussian printout. The eigenvectors of the GF matrix give the
displacements for each normal mode in Cartesian coordinates, similar to those given by
Gaussian directly.
To obtain the internal coordinate G and F matrixes, the Wilson B matrix
transforming from Cartesian to internal coordinates needs to be constructed [49j. When
the Cartesian coordinates for each atom as well as the definition of a complete set of
internal coordinates are specified in the input file, the B matrix non-zero elements can be
calculated by the GMATPC program, a PC version of Schachtschneidef s GMAT
68
Reproduced with permission of the copyright owner. Further reproduction prohibited w ithout permission.
program [50]. The GMATPC program also gives the G matrix in the same defined
internal coordinate system. This should be identical to what we get by applying the B
transformation to the Cartesian G matrix [3.2], This comparison can be used as a road
map to check if the B matrix set-up is correct, which is quite convenient especially for
bigger molecules. The B matrix taken directly from the GMATPC program is a
rectangular matrix with 3N-6 rows and 3N columns, as shown below, which connects the
3N Cartesian with the 3N-6 internal coordinates:
X,
Yx
Zx ...
xN
Yn
Zn
>
rx rBn Ba B 13
B21 B22 B23
•
r3
*3, b 32 B
V2
33
a,
dx
dn
d
dB V
12
B 3 N -S .3 N -2
•®3A'-8,3Af-I
BzN-7,3N-2 B3 N - 7 , 3 N - X
B3 N - 6 . 3 N - 2 B 3 N - 6 . 3 N - X
B 3N-%,3N
B3 N - 1 , 3 N
B3N -6.3N ;
The n, a-%and d '%are those defined internal coordinates related to the bond lengths, bond
angles and dihedral angles, respectively. In order for the inverse to be defined, the B
matrix has to be square, and this is made so by adding 6 more rows to describe the
molecular translations along the three Cartesian directions and the molecular rotations
about the three principal axes of inertia [51]. In the principal axis method (PAM)
69
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
orientation, these
6
rows can be written out in a simple form. The B matrix elements
which relate to the internal coordinates for translations are :
T ’- 3/-----_ ?v/?u
OG
^ - 09V09
s i------9V
AX
4m
m
^
9
4m
_ „
m,
M.,
4m
„
TY : 0 , —jJ= ,0 ,0 , —j=^=,0 ,
4m
JOX-0
0j-----^
,0,—pM=,0;
4m
4m
Q Q m4
o p
m,N
yVjV/,
/ . ?■■■■■■ >^9^9
/
T
• v,V,
Q Q -3
X7 *
4m
4m
4m
where m; is the mass of the it/? atom and M is the molecular mass. The last three rows of
elements related to the internal coordinates for rotations are:
Y
. n
m i^ l0
‘ ^ 9
}-----------------
m 4 l0 ^
I
9
yfjx
J\y ..
” hZ lO
A
1--------
'Spz
9
2^20 A
,m
--------,
m i X lO
I
■ 'jjz
m 2^20
9
9
I
9------------- /-----------
* ftx
■\J^x
m 2X 20
4Y
m 2 X 20
9
I
f iz
m N ^N 0 .
m N ^N 0
9 ....................j ' - ' j -------------------/ --------
~^x
m iX w
9
a
/-----------
4B SB
m j w
’
I
-fix
■P4
m 2^20
m 2^20
9 ^ 9
........
^NO a
. 9.? m N,----
-
n
&
A
9 ^ 9 ................. 9
m N X NO
.---
4n
m N^N0
I
sf^z
9
4Y
m N X NO
.
9
a
{-
9
4h
where X®, Y® and Zjq are the equilibrium Cartesian coordinates of the ith atom in the
PAM orientation, and Ix, h and Iz are the moments of inertia about the three principal
axes. After adding these 6 rows, the B matrix is square and has the form:
70
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
f
i
Cl
Xi
Y\
Zi
B n
Bn
Bn
B
B 22
B 23
B
B
21
B 3i
32
xN
...
Yn
Zn
\
■■
33
j
d x
d u
d n
•
d x3
m l
Tx
0
0
B 3 N- i , 3 N - 2
B 3N-S.3N-1
B l f f - » , 3N
B 3N ~1,3N-2
B 3 N -7,3 N -I
B 3N- 1. 3N
B 3N- 6, 2N-2
m N
B 3 N- 6 , 3 N
sIW
Rz
,Z10
o
i=-&
m
I
0
Rx
,
VaT
0
Tz
Rr
m
0
z
0
m
4 m ~
m xY m
s/1x
4^7
0
m l X lo
4H
m I
X
m
0
m N
0
0
m N
0
VaT
0
0
IQ
0
m
4 IZ
4m
m
N
YftO
[3.4]
sjlx
Zjvo
n Y N0
m N
ff 0
m
m
0
4h
4^
B 3N-6. 3N
~
0
,
3 o
JN
o
r,
4
-1
m
M
X
NX
/CO
4*4
N0
0
4 h
J
Because the above three rotational conditions are written in the PAM orientation
Cartesian coordinates, in order to keep consistency within the
B
matrix elements, in the
GMATPC program input file the Cartesian coordinates for each atom should also be in
the PAM orientation. Thus the square B matrix we constructed here is the transformation
matrix from the PAM orientation Cartesian to internal coordinate. PAM Cartesian
coordinates, together with the transformation matrix coined
Z to P
in this study, can be
obtained from a moment program provided by F.J. Lovas at N IS T when the Z-matrix
71
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
orientation Cartesian coordinates (provided by Gaussian output directly) are given [52].
As mentioned earlier, the F matrix from Gaussian is printed out in Z-matrix orientation,
so before applying the above B matrix to get internal F [3.4], we first need to rotate the F
matrix to the PAM orientation. The transformation matrix ZtoP is used to make this
rotation. Finally the G and F matrices in terms of internal coordinates are obtained after
doing the multiplications B.G.B1\ and (.B'i).ZtoP,F.ZtoPr.(B'1) 1 where the superscript T
denotes the transpose of the matrix.
As mentioned earlier, in Gaussian the atomic unit system is used for the
calculations. The units of mass, length and energy are amu (atomic mass unit), Bohr and
Hartree, respectively. Since the length unit in GMATPC is angstrom while the masses are
in amu, unit conversion is needed in order to obtain a final consistent result. The unit
transformation is done by applying a matrix AtoB (which means from Angstrom to Bohr)
to transform the B matrix before doing the above multiplication.
Eigenvalues and eigenvectors in internal coordinates were then evaluated in
Mathemetica. The frequencies were obtained from the eigenvalues following the steps
described in page 68. Apart from some round-off errors, the results were essentially the \
same as the Cartesian values as well as those given by the Gaussian Freq job. The six
lowest frequencies, which correspond to three translations and three rotations, are quite
close to zero. These six frequencies, also printed out in Gaussian, can be used to judge
whether tighter convergence criteria are needed to improve the structure optimization.
We note that the internal coordinate eigenvectors could be obtained in a more direct way
72
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
by directly applying the B matrix to transform the Cartesian coordinate engenvectors
from the Gaussian frequency job output without setting up the internal F and G matrices.
However, the internal F matrix will give more information about the physical origins of
how the different vibrational modes are coupled, and this is often very useful for
vibrational analysis.
In Table 3.1, we list the 42 normal mode frequencies, not including the six “zero”
ones, and their associated eigenvectors in internal coordinates for Conformer I of
HOEES. It is necessary to note that the atom numbering here is somewhat different from
Figure 2.2 in the previous chapter where only the heavy atoms are numbered. A complete
atom numbering scheme is shown in Figure 3.1 below.
H r - Q r -
h5 h9
I I
C r- Q h6
h 10
S r
h 12 h 14
I I
- O r - C „ h I3
H I6
h ,5
Figure 3.1. Atom numbering for 2-(Ethylthio)ethanol (HOEES).
In the internal coordinate picture, the vibrational motions become clearer, and we
can identify them by considering the displacement magnitude associated with each
internal coordinate. The vibrational modes corresponding to bond stretching, with high
frequencies, are normally always well localized and thus very easy to identify. For
example, vj in Table 3.1 can easily be identified as the Q-H bond stretching, whose
motion is almost totally localized on r0h. The v2 and v3 modes are two -CH3 asymmetric
73
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 3.1. Harmonic frequencies and eigenvectors for the 42 normal modes of
cm'1
u, 3838.7774
u2 3185.6045
1)3 3177.1435
o4 3164.9096
o5 3151.6157
o6 3142.6263
i>7 3095.0538
Ug 3092.4694
u, 3087.7696
u 10 3055.1048
o „ 1537.0068
0 ,2 1520.4070
0,3 1509.9259
0,4 1503.1048
roh2i 9x32 r<x43
1.00 -0.02 0.00
0.00 0.00 0.00
0.00 0.00 0.00
0.00 0.00 0.00
0.00 0.00 0.00
-0.01 0.01 0.02
0.00 0.00 0.02
0.00 0.00 -0.03
0.00 0.00 0.00
0.01 -0.03 -0.03
0.00 -0.09 -0.07
0.00 0.01 0.00
0.00 0.00 0.00
0.00 0.00 0.00
a321 a432
0 , 3838.7774 0 00 001
o2 3185.6045 0.00 0.00
o3 3177.1435 0.00 0.00
o4 3164.9096 0.00 0.02
o s 3151.6157 0.00 0.00
o6 3142.6263 0.03 -0.01
o 7 3095.0538 0.00 0.01
o 8 3092.4694 0 00 -0 01
09 3087.7696 0.00 0.00
o,o 3055.1048 0.00 0.04
o,i 1537.0068 -0.04 0.09
u,2 1520.4070 0.00 -0.01
o 13 1509.9259 -0.01 0.00
o ,4 1503.1048 0.00 0.00
9*53 9*63
-0.01 -0.01
0.01 0.00
0.00 0.00
-0.11 0.12
-0.05 0.05
0.28 -0.93
0.04 0.10
0.09 -0 0 s
-0.01 0.00
0.95 0.28
0.05 0.03
0.00 0.00
0.00 0.00
0 00 0 00
9:s87
0.00
0.00
0.00
0.00
0.01
0.00
-0.03
-0 0?
0.00
0.00
-0.01
-0.06
0.01
0 05
9*94
0.00
0.02
-0.01
-0.56
0.03
-0.17
-0.48
0 65
-0.02
-0.06
-0.01
0.00
0.00
0 00
9*104 9x118
0.00 0.00
-0.01 0.00
0.01 0.00
0.80 0.00
-0.08 0.01
0.05 0.00
-0.33 -0.03
0 47 -0 0?
-0.01 -0.05
0.05 0.00
0.00 0.01
0.00 0.00
0.00 0.02
0.00 0 13
9*128
0.00
0.25
-0.03
-0.05
-0.74
-0.04
0.50
0 33
0.01
-0.09
0.00
0.01
-0.01
-0.04
9*138
0.00
-0.18
0.12
0.03
0.57
0.06
0.63
0.48
0.01
-0.05
0.00
0.01
0.00
-0.05
9*i4ii
0.00
-0.78
-0.17
-0.03
-0.23
-0.01
0.00
0.02
0.55
0.00
0.00
-0.02
-0.03
0.00
3532 a632 a743 a874 a943
0 00 -0.02 0.00 0 00 0 00
0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00
0.01 -0.01 0.00 -0.02 0.03
0.00 0.00 0.00 0.00 0.00
-0.04 0.04 0.02 0.00 -0.01
0.00 0.00 -0.02 0.01 0.00
-0.01 0.00 0 03 0 01 0 00
0.00 0.00 0.00 0.00 0.00
-0.03 0.02 0.00 0.00 0.02
0.35 0.37 -0.03 0.00 0.09
-0.02 -0.02 0.00 0.01 -0.01
-0.01 -0.01 0.00 -0.01 0.00
-0.01 0.00 0.00 -0.03 0.01
a1043
0 00
0.00
0.00
-0.03
0.01
-0.02
0.00
0 00
0.00
-0.02
-0.04
0.00
0.00
0.00
aU87 a1287
0 00 0 00
-0.01 -0.01
-0.03 0.00
0.00 0.00
-0.01 0.03
0.00 0.00
0.03 0.00
0 0? 0 00
0.00 0.00
0.00 0.00
0.00 0.03
0.00 0.13
-0.01 -0.05
-0.07 -0.27
a1387
0 00
0.01
0.00
0.00
-0.03
0.00
-0.01
0.00
0.00
0.00
0.01
0.14
-0.05
-0.29
a14118
0.00
0.03
0.01
0.00
0.04
0.00
0.00
0.00
0.02
0.00
-0.03
-0.22
-0.28
-0.04
a15118 a16118
0.00 0.00
-0.02 -0.01
0.03 -0.04
0.00 0.00
-0.04 0.00
0.00 0.00
-0.01 0.02
-0.01 0.01
0.02 0.02
0.00 0.00
0.00 0.02
-0.18 0.30
0.30 -0.01
-0.11 0.00
9*74
0.00
0.00
0.00
0.00
0.00
0.00
0.02
-0 03
0.00
0.00
0.00
0.00
0.00
0 00
<14321 ds321 ^6321 d7432 1*8743 d'3432 d,0432 D 11874 dl2874 d13874 dl41187 di5| 187 dl61187
0 , 3838.7774 -0.01 0.00 0.00 0.02 0.00 0.02 0.02 0.00 0.00 0.00 0.00 0.00 0.00
o 2 3185.6045 0.00 0.00 0.00 0.00 0.01 0.00 0.00 -0.02 -0.01 -0.01 0.00 0.03 -0.04
o3 3177.1435 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.00 0.00 -0.04 0.03 0.01
04 3164.9096 0.01 0.00 0.00 -0.04 0.04 0.03 0.02 -0.01 0.00 0.00 0.00 0.00 0.00
u5 3151.6157 -0.01 0.00 0.00 0.01 -0.03 0.00 0.00 -0.04 0.03 0.03 0.05 0.05 0.01
u6 3142.6263 0.04 -0.03 -0,01 -0.05 0.01 -0.03 -0.04 -0.01 0.00 0.00 0.00 0.00 0.00
o 7 3095.0538 -0.01 0.00 0.00 0.00 0.01 0.00 0.02 -0.01 0.01 -0.02 0.01 0.00 0.00
u8 3092.4694 0.02 0.00 0.00 -0.01 -0.01 0.01 -0.03 0.01 0.03 0.01 0.01 0.00 0.00
u9 3087.7696 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0,0 3055.1048 0.03 0.01 -0.02 -0.03 0.02 -0.01 -0.02 0.00 0.00 0.00 0.00 0.00 0.00
o „ 1537.0068 0.00 0.62 -0.56 -0.01 0.05 0.01 0.00 0.00 -0.03 0.00 -0.02 0.03 -0.01
o,2 1520.4070 0.00 -0.03 0.03 0.00 0.00 0.01 -0.02 0.00 0.12 -0.12 -0.59 0.64 -0.04
u ,3 1509.9259 0.00 -0.01 0.01 0.00 0.01 -0.01 0.01 -0.01 -0.15 0.04 0.38 0.35 -0.73
u,4 1503.1048 -0.01 -0.01 0.01 0.00 -0.01 -0.03 0.03 0.00 -0.62 0.59 -0.21 0.10 0.10
a. atom numbering is refered to Figure 3.1
74
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
9*,5h 9*,6ii
0.00 0.00
0.48 0.25
-0.61 0.76
0.03 0.00
0.21 0.00
0.01 -0.01
0.02 -0.06
0.03 -0.03
0.59 0.59
0.00 0.01
0.00 0.00
-0.02 0.03
0.03 0.00
-0.01 0.01
Table 3.1. Cont'd.
CIU
r0h21 rco32 ^cc43 fch53 ^c!i63 ^"CS74 ^"cs87
u ,5 1463.8627 0.02 0.08 -0.23 0.00 -0.01 -0.03 -0.01
o 16 1448.1632 0.02 0.09 -0.06 0.00 0.00 0.05 0.01
u 17 1432.4653 0.00 0.01 0.00 0.00 0.00 0.00 -0.02
u « 1410.4526 0.04 -0.14 0.12 0.02 -0.01 0.00 0.00
u ,9 1347.7338 -0.01 0.03 0.16 0.01 0.00 -0.17-0.12
Oa, 1335.5003 -0.01 0.04 0.07 0.01 0.00 -0.13 0.14
o2, 1290.8245 0.00 0.01 0.01 0.00 0.00 0.01 -0.02
u22 1244.9011 0.00 0.15 0.16 0.01 0.00 -0.03 0.05
023 1222.0747 0.02 -0.17 0.25 -0.01 0.01 -0.06 -0.01
u24 1131.7562 0.02 0.70 -0.43 -0.03 -0.01 0.07 -0.02
t>25 1115.6991 0.00 -0.07 -0.14 0.00 0.00 0.02 0.05
u26 1084.0030 0.00 0.02 0.07 0.00 0.00 -0.01 0.01
x>27 1057.8444 0.00 0.19 0.18 -0.01 0.00 -0.01 -0.08
t>28 1024.3109 0.00 -0.04 -0.02 0.00 0.00 -0.01 -0.27
7*94
0.01
-0.03
0.00
-0.01
0.01
0.01
0.00
0.02
0.01
0.00
0.00
0.01
0.00
0.00
Tchl04 rCcl,8
0.01 0.02
-0.02 -0.01
0.00 0.26
0.00 0.00
0.00 0.10
0.00 -0.14
0.00 0.04
0.00 0.02
0.01 -0.04
-0.01 -0.03
0.00 0.41
0.00 0.11
-0.01 0.36
0.00 0.50
Teh128
0.00
0.00
0.01
0.00
0.01
-0.02
-0.01
0.00
0.00
0.00
0.01
0.01
0.00
0.00
17*138
0.00
0.01
0.01
0.00
0.00
-0.01
0.01
0.00
0.00
0.00
0.01
0.00
0.01
0.00
0.00
0.00
-0.02
0.00
0.01
-0.01
-0.01
0.00
0.00
0.00
0.00
-0.01
0.00
0.01
a321 3*32 a532 %32 a743 a874 a943
u 15 1463.8627 -0.52 0.05 -0.15 -0.49 0.03 -0.01 0.15
u ,6 1448.1632 -0.33 0.05 -0.23 -0.34 -0.06 0.02 -0.28
u „ 1432.4653 0.03 0.00 -0.04 0.00 0.00 -0.01 -0.03
u 181410.4526-0.55 0.07 0.65 -0.06 -0.06 -0.01 0.16
0,9 1347.7338 0.12 -0.05 0.05 -0.15 0.05 -0.02 -0.42
o20 1335.5003 0.12 -0.03 -0.02 -0.13 0.04 0.04 -0.26
o21 1290.8245 -0.01 -0.01 0.03 0.02 -0.01 0.00 -0.05
U22 1244.9011 -0.09 -0.12 0.34 -0.05 -0.03 0.00 -0.57
Ub 1222.0747 -0.52 0.02 -0.34 0.53 -0.07 0.04 -0.25
u24 1131.7562 -0.38 -0.05 -0.14 0.22 0.12 -0.01 -0.09
u25 1115.6991 -0.08 0.10 -0.16 0.15 0.06 -0.15 0.03
V 26 1084.0030 0.00 -0.03 0.03 -0.02 -0.01 0.00 -0.02
o 27 1057.8444 0.04 -0.13 0.13 -0.17-0.08 0.01 0.04
u28 1024.3109 0.00 0.01 -0.02 0.03 0.01 -0.03 -0.03
31043
0.24
-0.14
0.01
-0.25
-0.44
-0.33
0.07
0.48
-0.21
-0.08
-0.10
-0.01
-0.06
0.05
aU87 a1287
0.00 0.02
0.00 0.01
0.01 0.08
0.00 -0.05
0.03 0.32
-0.03 -0.48
0.00 -0.26
-0.03 -0.04
0.02 -0.04
0.02 0.03
-0.18 0.04
-0.05 0.54
-0.09 -0.11
0.06 -0.10
31387
0.01
0.00
0.09
-0.02
0.29
-0.38
0.39
-0.04
-0.01
-0.04
0.20
-0.46
0.28
-0.22
aI4U8
-0.01
0.02
-0.55
-0.02
-0.05
0.07
0.37
-0.01
-0.02
-0.02
0.19
0.43
-0.01
-0.21
a15118 a16U8
-0.02 0.00
0.03 0.02
-0.55 -0.54
-0.03 -0.04
-0.02 0.17
0.00 -0.21
-0.37 .0.04
0.09 -0.06
-0.01 0.02
-0.05 0.07
0.31 -0.43
-0.26 -0.16
0.25 -0.22
-0.27 0.55
r chl4U Ic h lS ll Tchlfill
d4321 dj32, dfi32, d7432 D8743 d9432 d,0432D 11874 d,2874d,3874 d,41187 dl511S7 dl6U87
u 15 1463.8627 -0.02 0.27 -0.18 0.07 -0.03 0.37 -0.26 0.03 0.00 0.06 0.02 -0.02 0.00
u 16 1448.1632 -0.03 0.29 -0.16 0.06 -0.03 -0.44 0.54 -0.02 -0.02 -0.04 -0.01 0.00 0.01
0 ,7 1432.4653 0.01 0.01 0.00 0.00 0.00 -0.02 0.03 0.00 0.01 -0.01 0.07 -0.06 -0.01
o 18 1410.4526-0.07-0.30 0.12 0.03 0.06 -0.03 0.14 -0.01 0.02 -0.03 0.00 0.01 0.00
0,9 1347.7338 0.09 -0.10-0.15-0.06 0.01 0.19 -0.31 -0.02 -0.25 0.15 0.10 -0.13 0.01
oa, 1335.5003 0.06 -0.03 -0.20 -0.03 0.00 0.11 -0.29 -0.03 0.27 -0.21 -0.11 0.15 -0.03
o211290.8245 -0.01 0.01 0.00 0.01 -0.04 0.02 0.06 -0.13 0.32 0.44 0.26 0.22 -0.24
022 1244.9011 -0.12 -0.01 0.13 0.12 -0.07 0.33 0.25 0.00 -0.06 -0.07 -0.08 0.01 0.02
Ob 1222.0747 -0.03 0.10 0.24 0.01 0.03 0.15 -0.17 -0.04 -0.03 -0.07 0.01 -0.02 0.00
o 24 1131.7562 0.03 -0.14 -0.03 -0.01 -0.09 -0.06 -0.16 0.04 0.06 0.05 0.05 -0.02 -0.01
025 1115.6991 0.12 -0.17-0.20-0.18 0.12 0.18 0.11 0.04 -0.10 0.06 -0.28 0.20 0.03
o 26 1084.0030 -0.04 0.04 0.06 0.05 -0.10-0.03 -0.05 -0.12 0.10 0.14 0.13 0.30 -0.16
o 27 1057.8444 -0.15 0.33 0.34 0.22 -0.14-0.27-0.27 0.02 -0.11 -0.01 -0.19 0.04 0.06
o 28 1024.3109 0.01 -0.07 -0.08 -0.01 0.00 0.02 0.05 0.00 0.14 -0.12 0.28 -0.24 -0.01
75
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
0.00
0.00
-0.02
0.00
0.01
-0.01
0.01
0.00
0.00
0.00
0.00
0.01
0.00
0.01
0.00
0.00
-0.03
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.02
0.01
0.01
-0.01
Table 3.1. Cont'd.
cm 1 td ta i
u29 975.3061 -0.01
O30 857.8599 0.00
o 3, 809.5542 0.00
o32 735.5838 0.00
O33 693.2980 0.00
034 498.5867 0.00
u35 490.0786 -0.01
V)3« 372.1695 0.01
o37 290.8082 0.00
o38 268.3122 0.00
u39 196.4382 0.01
040 155.8642 -0.01
o4j 57.5128 0.00
042 46.4630 0.00
o 29 975.3061
o 30 857.8599
o 3i 809.5542
o 32 735.5838
o33 693.2980
034 498.5867
o 35 490.0786
036 372.1695
o37 290.8082
o38 268.3122
o39 196.4382
o 40 155.8642
o4i 57.5128
O42 46.4630
a32i
0.22
0.02
0.00
0.02
-0.03
0.00
0.02
-0.03
-0.01
0.00
-0.04
0.03
0.01
0.00
rco32 I«43 rch53
-0.17 -0.45 0.00
0.19 0.24 -0.01
0.01 0.02 0.00
-0.02 -0.09 0.00
0.00 0.08 0.00
0.01 0.01 0.00
0.00 0.00 0.00
0.00 -0.04 0.00
0.00 -0.04 0.00
0.00 0.00 0.00
-0.01 -0.01 0.00
0.01 0.00 -0.01
0.01 -0.01 0.00
0.00 0.00 0.00
Ich63
0.01
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
Ics74 rcs87
0.30 -0.02
0.06 0.06
0.00 0.03
-0.42 0.68
0.57 0.35
-0.02 0.03
-0.04 0.02
0.06 0.16
-0.05 -0.05
0.00 -0.01
-0.01 0.01
0.01 0.01
0.00 0.01
0.00 -0.01
rch94
0.00
0.00
0.00
0.00
0.00
0.00
0.00
-0.01
0.00
0.00
0.00
0.00
0.00
0.00
rchl04 *0:118
0.00 0.00
0.01 -0.02
0.00 0.01
0.00 0.07
0.00 0.04
0.00 0.01
0.00 0.01
0.00 0.08
0.00 -0.01
0.00 0.00
-0.01 -0.03
0.00 -0.01
0.00 0.00
0.00 0.00
*chl28
0.00
0.00
-0.01
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
*chl38
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
rchl4U
0.00
0.00
0.01
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
*<*1511 *chl61l
0.00 0.00
0.00 0 00
-0.01 0 00
0.00 0 00
0.00 0 00
0.00 0 00
0.00 0 00
0.00 0 01
0.00 0 00
0.00 0 00
0.00 0 00
0.00 0 00
0.00 0 00
0.00 0.00
a943
-0.12
0.35
0.03
-0.04
-0.01
-0.09
-0.01
0.16
0.08
0.02
0.08
-0.03
0.01
0.01
31043
-0.17
-0.33
-0.05
-0.10
0.13
0.15
0.04
-0.06
-0.02
0.00
0.02
-0.03
-0.02
-0.01
a1187 a1287
-0.01 0.00
-0.01 -0.05
-0.01 0.18
-0.13 -0.06
-0.17 0.00
0.01 0.00
0.03 0.00
0.32 -0.07
-0.25 0.08
-0.02 -0.02
0.16 -0.02
0.12 -0.03
0.01 0.02
-0.01 -0.01
a1387
0.00
-0.01
-0.19
-0.05
0.01
-0.01
0.00
-0.05
0.06
0.03
-0.10
-0.03
-0.03
0.01
a14U8
0.01
0.02
-0.35
-0.07
-0.06
0.00
0.00
0.07
-0.03
0.00
0.01
0.02
-0.01
0.01
3-15118
-0.03
-0.09
0.34
-0.12
-0.07
0.00
0.01
0.06
-0.04
-0.01
0.02
0.01
0.01
0.00
a16U8
0.01
0.08
0.02
0.22
0.14
-0.01
-0.01
-0.14
0.07
0.01
-0.03
-0.02
0.00
0.00
3-432 3532 3632 3743 3874
0.20 0.14 -0.17 -0.10 -0.04
0.09 -0.06 -0.12 -0.12 -0.07
0.01 0.00 -0.01 -0.01 -0.01
-0.02 0.03 0.00 0.14 -0.08
-0.03 -0.01 0.02 -0.12 -0.09
0.19 -0.05 -0.01 -0.11 0.03
0.06 -0.01 -0.03 -0.07 0.03
-0.19 0.03 0.03 -0.15 0.28
-0.10 0.01 0.00 -0.17 0.07
-0.02 0.00 0.00 -0.04 -0.02
-0.12 0.01 0.03 -0.21 -0.28
0.03 0.00 -0.03 0.05 -0.16
-0.01 0.00 -0.02 0.01 -0.01
-0.01 0.00 -0.01 0.00 0.00
d*321 ^3321 d«32i
o29 975.3061 -0.08 0.46 0.40
o30 857.8599 0.06 0.26 0.18
o3, 809.5542 0.00 0.04 0.03
u32 735.5838 0.13 0.26 0.30
U33 693.2980 -0.24 -0.38 -0.39
U34 498.5867 0.59 0.52 0.47
u35 490.0786 -0.56 -0.56 -0.59
U36 372.1695 0.20 0.11 0.17
u37 290.8082 -0.09 -0.13 -0.12
u38 268.3122 -0.03 -0.04 -0.04
U39 196.4382 0.15 0.09 0.12
u40 155.8642 -0.25 -0.18 -0.21
u41 57.5128 -0.27 -0.27 -0.27
U42 46.4630 -0.16 -0.15 -0.15
^7432
0.08
-0.11
-0.01
-0.07
0.01
-0.03
0.03
0.27
0.43
0.03
-0.29
0.51
0.23
0.05
DS743 (I9432 d10432 Dll874 dl2874 dl3874 dl4U87 dl51187 dl6lt87
0.04 0.26 0.16 0.03 0.01 0.02 0.01 -0.01 -0.02
0.15 0.45 0.44 -0.09 -0.15 -0.18 0.04 -0.03 -0.05
-0.04 0.08 0.07 -0.04 0.54 0.54 -0.05 -0.07 0.26
0.01 0.04 -0.10 0.04 0.01 0.00 0.10 -0.08 -0.01
-0.03 -0.25 -0.12 -0.02 -0.06 -0.01 0.05 -0.06 -0.01
0.06 -0.19 -0.14 -0.05 -0.05 -0.05 -0.02 -0.01 -0.01
0.02 -0.01 0.02 -0.03 -0.03 -0.04 0.00 0.01 0.01
-0.19 0.43 0.53 -0.02 0.03 -0.08 -0.08 0.04 -0.02
-0.24 0.42 0.50 -0.05 -0.12 0.00 0.25 0.18 0.21
0.05 0.02 0.03 0.04 0.02 0.03 -0.56 -0.57 -0.58
0.34 -0.40 -0.30 -0.20 -0.12 -0.21 ■0.25 0.28 0.27
-0.24 0.47 0.43 0.19 0.20 0.14 0.01 0.03 0.02
0.38 0.21 0.20 -0.43 -0.39 -0.40 -0.01 -0.01 -0.01
0.33 0.05 0.05 0.52 0.51 0.52 0.07 0.07 0.08
76
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
stretches, with a small frequency difference of
- 8
cm'1. These two stretching modes
would be degenerate in a free -CH 3 group or in a molecule in which the C3 symmetry is
maintained, and their small frequency difference here results from the removal of this
degeneracy. The next six modes, from V4 to vg and vio, are symmetric and asymmetric CH2 - stretching motions for the three methylene groups along the molecular backbone
and V9 is the -CH 3 symmetric stretch. By considering the components for the bond angles
and dihedral angles, the bond bending motions can also be clearly identified. These
bending mode frequencies range from -1500 cm' 1 to -500 cm'1, including the -CH 3
deformation, rocking and torsion motions as well as various scissoring, wagging, twisting
and rocking motions for -CH 2 - groups. The last several lowest frequency modes, below
500 cm'1, are mainly associated with backbone torsions, whose motions are generally
distributed among several dihedral angles, so are much less localized than bond stretches
and bendings.
Figure 3.2 shows the low resolution infrared solution spectrum of HOEES, as
commonly used for chemical analysis, obtained from an integrated spectral database
system for organic compounds founded by the National Institute of Advanced Industrial
Science and Technology of Japan [53]. It is necessary to note that our ab initio calculated
frequencies are gas phase results in the harmonic approximation and thus are not the
same as those in the solution spectrum shown in Figure 3.2, which is more commonly
used in chemistry. Even so, the gas phase calculations provide an excellent reference and
allow spectral assignments to be made for the observed peaks, a task which is often
77
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
difficult or impossible from the experimental data alone due to spectral overlap. It is
interesting that the experimental O-H stretching frequency in Figure 3.2, which is around
3400 cm*1, is much lower than the ab initio prediction of 3839 cm'1, even after
multiplying by the scaling factor. This phenomenon is thought to arise from the intermolecular hydrogen bonding effect. In the liquid the inter-molecular distances will be
much closer, so that in addition to the intra-molecular hydrogen bond interaction, intermolecular hydrogen bonding between the hydroxyl hydrogen and the oxygen atom from a
nearby molecule will further weaken the stretching force constant for the O-H bond and
thereby make the O-H stretching frequency red shifted. In chemical analysis of solution
spectra, a strong broad band between 3500 and 3200 cm*1 is an easily spotted signature of
the hydrogen-bonded O-H stretching mode of an alcohol or a phenol [54]. If the intermolecular hydrogen bonding is absent, as in the gas phase, the O-H stretching band is
expected to be much sharper and appear at a higher frequency.
Another interesting feature in Figure 3.2 is the prominent peaks in the range 13501150 cm*1. They are assigned to the wagging and twisting vibrational motions of series of
methylene groups. Normally these -CH 2- wagging and twisting infrared bands are quite
weak, unless an electronegative atom such as a halogen or sulphur is attached to the
same carbon in the methylene unit, which is the case for HOEES [54], This phenomenon
can be clearly seen by comparing the spectrum of HOEES with 1-pentanol
(HO(CH2 )4 CH3), whose spectrum is shown in Figure 3.3. The replacement of the sulphur
atom by a -CH2- group makes the line intensities in the 1350-1150 cm’ 1 region much
weaker compared with the same region in Figure 3.2.
78
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Finally, we note that the lower limit of most Fourier Transform Infrared (FTIR)
spectrometers is around 500 cm'1 to 300 cm'1, so that the frequencies corresponding to
the backbone torsions are normally not covered in the commonly used FTIR spectra.
Those frequencies below 500 cm'1 belong to the Far-IR region, and special detectors are
needed to record their spectra.
H I T - H D - 2 4 5 3 |5C0RE=
2 _ ( ETHYLTHI O) ETHRNOL
<
> ISOBS-NOMOQ3
| IR-NIDfl-16862
: LIQUID
FILfl
C4HjgQS
4900
3349
2 963
2927
2 972
2126
2232
2051
94
5
4
9
ea
94
84
1639
14S3
1425
1408
1379
1338
1220
79
IB
21
22
20
44
36
1266
1227
1168
I960
1044
1003
940
16
42
4*7
6
S
12
57
823
783
755
669
659
647
642
70
53
43
49
43
481
53
C H3 . - - C H ?
C.-------- 3 —
( C H 2 ^ —— OH
44
46
Figure 3.2. Low resolution solution spectrum of 2-(Ethylthio)ethanol(HOEES), from Ref.
[53]. The strong broad band near 3400 cm'1 corresponds to the hydrogen-bonded O-H
stretching mode of an alcohol or a phenol.
79
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
HIT-NQ=2622
jSCORE=
i
ijS0BS-N0=4321
jIR-NI0fl-02204
: LIQUID FILT?
i-PENTHHOL
c 5h 12o
im
50 -
150G
3000
4BOO
3346
3336
3325
2569
2932
2965
1468
10
IQ
10
6
4
S
20
1 300
1343
12*74
1236
1203
111*3
1077
34
52
6B
70
5B
53
26
3056
3017
1Q07
981
939
784
730
12
36
33
49
SQ
as
67
509
iOOO
500
77
CH3 —
(CH2)4 — OH
Figure 3.3. Low resolution solution spectrum of 1-pentanol, from Ref. [53]. The peaks in
the spectral range 1350 - 1150 cm'1 are relatively less prominent compared to the same
region in Figure 3.2.
3.2
Frequency Calculation for Methyl Torsional Motions w ith
Anharmonic Potential Corrections
The Hessian matrix obtained from Gaussian only contains the harmonic contributions,
which are the second derivatives of the potential energy surface. Hence, diagonalization
of the GF matrix gives the harmonic vibrational frequency for each normal mode.
80
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
However, we can obtain potential energies as a function of coordinates of interest with ab
initio calculation. This will allow us to obtain anharmonic components (higher order
terms) of the potential which are not given by Gaussian directly. In reality, of course, the
G matrix is structurally related as well, and the structure is also a function of the
coordinates of interest. Thus, the problem could be as simple as one-dimension or as
complicated as (3N-6)-dimensions. In this preliminary study, we will only consider the
one-dimensional potential energy higher order corrections.
In the case of stretching vibrations, the modes are all very localized. Correction
methods and related equations have been well established for diatomic molecules, and
also successfully applied to small polyatomic molecules, e.g. water (H2 O) [20].
Following is a brief description of this diatomic correction approach.
For a diatomic molecule, the potential function can be expanded in terms of a
polynomial series about the equilibrium bond length re :
[3.5]
where the fi’s are the usual quadratic and higher order force constants representing
successive derivatives of the potential energy V(r) with respective to (r-re) calculated at
the equilibrium bond length. For mathematical convenience, the above polynomials can
be re-expressed in terms of the dimensionless normal coordinate q, leading to the
vibrational Hamiltonian :
81
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Here, p =
dq
is the dimensionless conjugate momentum of q, and p and q satisfy the
usual commutation relation with each other. In the above expression, the first term
H0 = —°}{p +q ) is the well-known harmonic oscillator Hamiltonian which can be
00 1
solved exactly, while the summation term # ' = V —faq‘ represents the higher order
i- 3 *•
contributions. The fa’s are anharmonic force constants with respect to the dimensionless
normal coordinate q, and can be derived from the corresponding f force constants in
expression [3.5]. The necessary relations between the harmonic frequency &,
anharmonic force constants fa and their corresponding^ ’s are :
o
2m
2mm
t,
ng
5
x _
’
/3
3 /2
hca
,
^3
x _
’
^4
/a
2
hca
ro-7!
’
J
P-7]
where g is the reciprocal reduced mass of the two atoms.
As we can obtain an exact solution only for the harmonic oscillator Hamiltonian
H 0, the higher order term H ' will be treated by perturbation theory in this approach. In
the language of matrix quantum mechanics, this will be described as the whole
vibrational Hamiltonian matrix being set up in the harmonic oscillator (HO) basis set
followed by a diagonalization. The expectation values for the matrix elements of H are :
(
"
^
L
/= 3 *•
p
v ,v '
.
*
]
where the first term is the harmonic vibrational energy that only appears in the diagonal
elements. The required matrix elements for operators of the form q' can be evaluated
82
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
using generalized expressions for the one-dimensional harmonic oscillator [55]. The
whole vibrational Hamiltonian matrix constructed in this way can then be diagonalized to
get the approximate energies.
Temsamani et al. [56] have tested this method on Vi (O-H stretching mode) of
methanol (CH3OH), a medium-size polyatomic molecule. In their study, ab initio results
associated with the O-H stretch internal coordinate were used to evaluate the torsional
parameters(F3, F), E-A torsional splitting and infrared transition intensity ratio (Ia/Ib) as
they evolved with increasing excitation of the O-H stretching mode. Their ab initio
results successfully reproduced two interesting features reported in supersonic-jetinfrared-laser-assisted photofragment spectroscopy (IRLAPS) experimental studies,
indicating that the above diatomic stretch anharmonic correction approach is also valid
for localized stretching motions in medium-sized polyatomic molecules.
In this study, we wished to test if the above scheme could be transformed to
torsional motions, which are normally very anharmonic. For polyatomic molecules,
especially the large compounds, there are generally two kinds of torsional motions
involved, the three-fold methyl-top torsion and the backbone torsion. It is reasonable to
start from the first one, which is relatively easier to handle. Our initial test was done on
the methanol molecule. There are basically two considerations for this choice. First, this
medium-sized molecule is the smallest that has a methyl-top torsion present. Second, we
have considerable information available for its torsional energy levels, both from
observation and calculation, which can be used readily for comparison. Although the
83
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
methyl-top torsion is not localized to a single dihedral angle, it is almost localized to the
average of the three dihedral angles between the molecular frame (HOC) and the three
methyl C-H bonds. We can thus define a torsion angle rb y averaging the three dihedral
angles, and this torsion angle becomes the analogue to the bond length in the diatomic
case. At the same time, we can think of the masses of the two atoms in a diatomic
molecule as equivalent to the two moments of inertia in methanol where two parts are
twisting one against another. Therefore, all the above expressions for the diatomic stretch
might be applicable to the torsional motion case, and the only thing we need to pay
attention to is that the physical meaning of g will change to the reciprocal reduced
moment of inertia which, in fact, is the well-known torsional constant F for methanol.
-115.5568
-115.5570
'5? -115.5572
£
•e
«
-115.5574
'P
-115.5576
>> -115.5578
g>
Sj
-115.5580
-115.5586
-115.5588
- 1.0
Torsion Angle r (radian)
Figure 3.4. Methanol methyl torsion potential energy F(r), plotted as a function of
torsional angle r. The values corresponding to each point are listed in Table 3.2.
84
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 3.2. ab initio calculation results for methanol along the methyl torsion reaction path.®
Th (radian) Eeiec. (Hartree)
0.0000
0.0256
0.0511
0.0767
0.1023
0.1278
0.1534
0.1790
0.2045
0.2301
0.2556
0.2812
0.3068
0.3323
0.3579
0.3834
0.4090
0.4345
0.4601
0.4856
0.5112
-115.55865
-115.55865
-115.55865
-115.55863
-115.55862
-115.55860
-115.55857
-115.55854
-115.55851
-115.55847
-115.55843
-115.55839
-115.55834
-115.55829
-115.55824
-115.55818
-115.55812
-115.55806
-115.55800
-115.55794
-115.55788
r h (radian) Eelec. (Hartree)
0.5367
0.5622
0.5878
0.6133
0.6388
0.6644
0.6899
0.7154
0.7410
0.7665
0.7920
0.8175
0.8431
0.8686
0.8941
0.9196
0.9451
0.9706
0.9962
1.0217
1.0472
-115.55782
-115.55776
-115.55769
-115.55763
-115.55757
-115.55751
-115.55746
-115.55740
-115.55735
-115.55730
-115.55726
-115.55722
-115.55718
-115.55714
-115.55711
-115.55709
-115.55707
-115.55705
-115.55704
-115.55703
-115.55703
r b (radian) Eefec. (Hartree)
-1.0217
-115.55703
-0.9962
-115.55704
-0.9707
-115.55705
-0.9451
-115.55707
-0.9196
-115.55709
-0.8941
-115.55711
-115.55714
-0.8686
-0.8431
-115.55718
-0.8175
-115.55722
-0.7920
-115.55726
-115.55730
-0.7665
-0.7410
-115.55735
-0.7154
-115.55740
-115.55746
-0.6899
-0.6644
-115.55751
-0.6389
-115.55757
-0.6133
-115.55763
-115.55769
-0.5878
-0.5622
-115.55776
-0.5367
-115.55782
-0.5112
-115.55788
r b (radian)
-0.4856
-0.4601
-0.4345
-0.4090
-0.3834
-0.3579
-0.3323
-0.3068
-0.2812
-0.2556
-0.2301
-0.2045
-0.1790
-0.1534
-0.1278
-0.1023
-0.0767
-0.0511
-0.0256
0.0000
Eelec. (Hartree)
-115.55794
-115.55800
-115.55806
-115.55812
-115.55818
-115.55824
-115.55829
-115.55834
-115.55839
-115.55843
-115.55847
-115.55851
-115.55854
-115.55857
-115.55860
-115.55862
-115.55863
-115.55865
-115.55865
-115.55865
a. ab initio calculation was carried out at MP2 theory level with 6-311+G(3df,2p) basis
set.
b. Torsional angle is defined as the average of the three dihedral angles between the
molecular frame (HOC) and the three OCH planes of methanol.
The ab initio calculation for methanol was carried out at the second order of
Meller-Plesset perturbation theory with the 6-311+G(3df,2p) basis set. In a Gaussian
path job, when the reactant and product structures are specified, points along the mass
weighted reaction path will be optimized. The plot of the optimized energy as a function
of the torsional angle r(as defined above) is shown in Figure 3.4. The torsional potential
energy is well-known to be expressible as a Fourier series of the form
” V
^r_2«-(l_cos3/wr), in which the coefficients converge rapidly. To take advantage of
m=l 2
85
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
this structure, we first fitted the PEC to the Fourier series up to the 3rd order, then re­
expanded it as a polynomial series about equilibrium to ensure all the polynomial
coefficients were well-determined and least correlated. Because of the even symmetry of
the Fourier series, all the odd terms disappear in the polynomial expansion. In Table 3.3,
we list the polynomial expansion coefficients. These coefficients, together with the g
value, were then converted to get a and the $ anharmonic force constants by using
Eqs. [3.7]. It is necessary to point out here that the units were changed into cm’1 in this
step to make the final results directly comparable to experiment.
Table 3.3. Polynomial coefficients for methanol with converted harmonic frequency and
anharmonic force constants with respect to the dimensionless normal coordinate.
Polynomial coefficients
f2 /2!
(Hartree-radian'")3
0.003577
Harmonic frequency and anharmonic
>d
force constants (cm ) ’ ’
fi/4!
m \
fg/8 !
-0.002467 0.000411 0.000247
®
V 4!
294.7005 -19.0685
V 6!
4>s/8!
0.5957
0.0672
a. The potential energy curve was first fitted to a Fourier series with result
F(r)=Fo+0.00081345(l-cos3r)-4.1902xlO’6(l-cos6r)-1.9171xlO'7(l-cos9r), and then
re-expanded as a polynomial series to get the polynomial coefficients. Vo is the
energy at the equilibrium structure.
b. The harmonic frequency and anharmonic force constants are expressed with respect
to the dimensionless normal coordinate.
c. Eqs. [3.7] were used in obtaining these force constants from their corresponding
polynomial coefficients in the upper part of this table.
d. Torsional constant of methanol, F=27.65388 cm'1 [57], is used here to obtain
g=9.88967x!046 kg'1- m'2 for Eqs. [3.7],
86
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Construction and subsequent diagonalization of the vibrational Hamiltonian
matrix were done by using a Fortran program based on work of Ref. [56]. The energies
for the first eight levels are printed out in the output file after diagonalizing the
Hamiltonian matrix. Because the vt=2 torsional energy is already above the torsional
barrier, it is thought that the above correction approach might only be meaningful for the
fundamental torsion transition, which is from the ground level to the first excited level.
By using the converted harmonic frequency and anharmonic force constants in Table 3.3,
we find corrected energies for vt=0 and 1 of 131.57 and 362.54 cm'1, respectively, which
in turn leads to a corrected fundamental transition frequency of 230.97 cm'1. This result
gives almost perfect agreement, probably fortuitous, with the global fitted value of
231.34 cm'1 [57],
As another check of the validity of this approach, the above procedure was also
repeated for the ethane molecule (CH3CH3), which has a torsional motion with two
methyl tops twisting against each other. The reaction path along the torsional angle was
calculated at MP2=FULL theory level with 6-311G(d,f) basis set. The results are
summarized in Table 3.5, and the potential energy curve is plotted in Figure 3.4. The
fitted polynomial coefficients, as well as the converted force constants with respect to the
dimensionless normal coordinate, are listed in Table 3.5. For ethane, when the above
correction is added, the fundamental transition is calculated to be 304.97 cm'1, just 15.81
cm'1 higher than the global fitted value of 289.16 cm’1 [58].
87
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 3.4. ab initio calculation results for ethane along the methyl torsion reaction path®
r b(radian) Edec.(Hartree) r b(radian) E5iec.(Hartree)
-79.60348
0.4712
-79.60641
1.0472
0.9949
0.9425
0.8902
0.8378
0.7855
-79.60351
-79.60360
-79.60375
-79.60396
0.4189
-79.60680 .
0.3667
0.3143
-79.60717
-79.60752
0.2619
0.2096
-79.60421
-79.60783
-79.60809
-79.60831
r b (radian) E;lec.(Hartree)
0.0000
-0.0524
-79.60859
-79.60856
-79.60846
-0.1047
-0.1571
-0.2096
-0.2619
r b (radian) Eei<.c.(Hartree)
-0.5237
-79.60600
-79.60561
-0.5760
-0.6284
-79.60522
-79.60831
-0.6807
-79.60809
-79.60783
-79.60752
-0.7331
-0.7855
-79.60485
-79.60451
-0.8378
-79.60396
-79.60421
0.1571
0.1047
-79.60846
-0.3143
-0.3667
0.6284
-79.60451
-79.60485
-79.60522
0.0524
-79.60856
-0.4189
-79.60717
-79.60680
-0.8902
-0.9425
-79.60375
-79.60360
0.5760
-79.60561
0.0000
-79.60859
-0.4712
-79.60641
-0.9949
-79.60351
0.5237
-79.60600
0.7331
0.6807
a. ab initio calculation was carried out at MP2=FULL theory level with 6-311G(d,f)
basis set.
b. Torsional angle is defined as the average of the three dihedral angles for the methyl
top.
-79.603 -i
® -79.604
£rt
X
“p- -79.605 H
ST
'X
>>
£P -79.606
£
W
c
B
c£
°
°
—r~
-
1.0
-0.5
0.0
0.5
Torsion Angle z (radian)
Figure 3.5. Ethane methyl torsion potential energy F(r), plotted as a function of the
torsional angle t. The values corresponding to each point are listed in Table 3.4.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 3.5. Polynomial coefficients for ethane with converted harmonic frequency and
anharmonic force constants with respect to the dimensionless normal coordinate.
Polynomial coefficients
F2/2!
£j/4!
0.011722
-0.009136
o
<(>4/4!
<(>6/6!
<j>8/8!
332.3083
-8.3638
0.1661
0.0000e
(Hartree-radian"11)3
fc/6!
f8 / 8 !
0.002810 0.000002
Harmonic frequency and anharmonic
. . .
force constants (cm ) ,c’
a. The potential energy curve was first fitted to a Fourier series with result
F(r)=Fo+O.OQ25566(l-cos3r-)+O.OOOQ14176(l-cos6r)-9.4488xlO~7(l-co s9 4 and then
re-expanded as a polynomial series to get the polynomial coefficients. Fo is the
energy at the equilibrium structure.
b. The harmonic frequency and anharmonic force constants are expressed with respect
to the dimensionless normal coordinate.
c. Eqs. [3.7] were used in obtaining these force constant from their corresponding
coefficients in the upper part of this table.
d. g=3.83359x1046 kg’1- m ' 2 for Eqs. [3.7] is obtained from direct calculation at the
equilibrium structure.
e. The first non-zero number appears at the sixth digit.
Both of our tests on methanol and ethane have shown that the diatomic-twist
approach can give good correction results for the methyl torsion motion in a medium­
sized molecule. It is necessary to point out that great improvements have been achieved
by using this approach when compared with the commonly used practice of scaling the
harmonic predictions with an empirical factor which generally ranges from 0.8 to 1.0. We
used a high theory level together with a large basis set in our ab initio frequency
calculation, both for methanol and ethane, in which case the scale factor will be much
89
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
closer to 1.0. Suppose a scale factor of 0.94 [59] is used for both molecules. The scaled
vibrational frequencies will then be 277.17 cm'1 and 312.37 cm'1 for methanol and
ethane, respectively. Both of them are less satisfactory than the corrected results
produced by our approach. As a summary of the performance of this approach, we list in
Table 3.6 the four frequency values mentioned above, namely the ab initio harmonic,
scaled, corrected by our approach and globally fitted ones. It is necessary to point out
here that we used a different step size and different basis set in our calculation for the
PEC curves of methanol and ethane, thus the performance of our tests on these two
molecules can not be compared directly.
Table 3.6. ab initio, scaled, correction added and globally fitted frequency values for
methanol and ethane.3
ab initio
harmonic
Methanol
Ethane
294.70
332.31
—11
111■"
-
Scaled0
277.02
312.37
-—
—-—
Correction
Globally
added
fitted
230.97
231.34
304.97
289.16
—i—
a. The unit for all the frequencies in this table is c m ' .
b. MP2/6-311+G(3df,2p) and MP2=FULL/6-311G(d,f) were used for methanol and
ethane, respectively.
c. Scale factor used here is 0.94, from reference [59].
d. Globally fitted values come from references [57] and [58].
We also applied this approach to the methyl torsion for HOEES following a
similar procedure. The only difference from the above two small molecules was the g
value which was obtained through a backward calculation method, because a direct
calculation of the torsional parameter g becomes more difficult for large molecules like
90
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
HOEES. We used the harmonic frequency a>directly from the Gaussian output, together
with the second order force constant^ from the fitting of the PEC to a polynomial series,
r~T
to calculate g by using the equation co = - —- from Eqs. [3.7]. After adding the
2
jvc
correction, we finally got a frequency of 254.57 cm'1 for the methyl torsion of HOEES,
-14 cm'1 lower than the harmonic result of 268.31 cm"1. For HOEES, our corrected result
is a little bit higher than the directly scaled one, which is 252.21 cm'1, using a scaling
factor of 0.94. Our correction approach is assumed to be valid for localized vibration
motions, but HOEES’s methyl torsion is less localized compared to methanol and ethane.
Thus, it is expected that the correction for HOEES will be less satisfactory when
compared to those for smaller molecules. However, since we do not presently have an
experimental frequency for HOEES methyl torsion, it is not possible to do a comparison
and give further comment. In the following tables, we only list the data used in our
calculation.
-630.900 -
g -630.901 -
t:
'P'
ST
-630.904 -
-630.905 -
-630.906 -1.0
-0.5
0.0
0.5
1.0
Torsion Angle r (radian)
Figure 3.6. Methyl torsion potential energy V(r) of HOEES, plotted as a function of the
torsional angle r. The values corresponding to each point are listed in Table 3.7.
91
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 3.7. ab initio results for HOEES along the
methyl torsion reaction path.3________________
r b (radian) Eeiec.(Hartree) r h (radian) Eeiec.(Hartree)
0.0032
-630.90592
-630.90021
-0.9308
0.1127
-630.90576
-0.8067
-630.90078
-630.90164
0.2265
-630.90527
-0.6831
0.3409
-630.90268
-630.90449
-0.5602
-630.90375
0.4558
-630.90352
-0.4380
0.5712
-630.90470
-630.90249
-0.3162
-630.90542
0.6875
-630.90151
-0.1959
0.8044
-630.90072
-0.0789
-630.90581
-630.90592
0.9217
-630.90020
0.0032
1.0402
-630.90001
a. ab initio calculation was carried out at MP2=FULL theory level with 6311G(d,f) basis set.
b. Torsional angle is defined as the average of the three dihedral angles for
the methyl top.
Table 3.8. Polynomial coefficients for HOEES with converted harmonic frequency and
anharmonic force constants with respect to the dimensionless normal coordinate.
m \
ft/4!
0.013127
-0.008579
©
<1*4/4!
268.3122
-4.0822
(Hartree-radian"n)a
Harmonic frequency and anharmonic
force constants (cnfl)b,c,d
fg/8!
-0.001055
-© -
Polynomial coefficients
-0.0234
0.005551
4»s/8!
0.0057
a. The potential energy curve was first fitted to a Fourier series with result
F(r)-F0+0.0029556(l-cos3r)+3.4164xlO'6 (l-cos6r)-5.7830><10'6(l-cos9r), and then
re-expanded as a polynomial series to get the polynomial coefficients.
Fq
is the
energy at the equilibrium structure.
b. The harmonic frequency and anharmonic force constants are expressed with respect
to the dimensionless normal coordinate.
92
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
c. Eqs. [3.7] were used to obtain the force constants from their corresponding
. coefficients in the upper part of this table.
d. g=2.23158* 1046 kg'1• m'2 for Eqs. [3.7] was obtained by using the ab initio harmonic
frequency co and second order force constant/) in this table.
3.3 Suggestions for Future Study
The next step is to extend the same approach to the backbone torsional motions for large
molecules in this study. For a certain backbone torsional motion, there are generally
several dihedral angles involved, each of them carrying different weights. The challenge
ahead might be how to relate these dihedral angles with a single torsional angle rin order
to localize the multi-dimensional motion into a one-dimensional case. The definition for
such a torsional angle is not clear so far. Once the potential energy curve (PEC) as a
function of r is ready, the converted anharmonic force constants <j)i ’s can be obtained in
the same manner as used for methyl top torsion. The corresponding g value, whose
physical meaning is not as obvious as for the methyl torsion cases, can be achieved
through a backward calculation process as demonstrated above for the methyl torsion in
HOEES.
The last thing to note is that our above approach assumes a deep potential well,
which means that the anharmonic effects are relatively small for the lower energy levels.
However, compared with the methyl top torsions, the backbone torsional barrier will be
lower, and even the ground level will experience more anharmonic influence. Whether
this approach will then give a useful correction result is yet to be determined.
93
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Chapter 4
Applications of a C02-Laser/Micro wave Sideband
System for High-resolution Spectroscopic
Measurements
A C0 2 -laser/microwave-sideband tunable infrared source system has recently been built
in our laboratory. The system employs a high-resolution CO2 laser of the Evenson design
that lases on a wide range of lines including hot and sequence band lines as well as high-/
lines of the regular 9.6 and 10.6 pm bands [32]. The CO2 laser carrier is mixed with
microwave radiation, which is generated by a microwave synthesizer and amplified by a
traveling-wave-tube (TWT) amplifier, in a Cheo waveguide modulator to generate upper
and lower sidebands. With this broadband precision tunable source, a spectrometer has
been developed which can work in dual modes, a wide-scan Doppler-limited mode and a
narrow-band sub-Doppler mode. In the wide-scan mode at Doppler-limited resolution,
almost continuous tunability is achieved from 1059.95 to 1069.63 cm"1 using 9.6 pm hot,
sequence and low-/regular band CO2 laser lines, with the 6.7-18.5 GHz window for each
sideband being covered in a single sweep. In the second operational mode, sub-Doppler
saturation dip spectra are obtained at sub-MHz resolution with absolute measurement
accuracy of the order of 200 kHz. The instrumental performance is demonstrated via
sample spectra of the C-0 stretching fundamental vibrational band of methanol
(CH3OH). Doppler-limited scans have been recorded over a broad range with good
signal-to-noise ratio, while narrow band sub-Doppler scans have permitted clean
94
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
separation of very close-lying lines in the methanol spectra. Our results show that
achieving both wide tunability and very high resolution is possible with C0 2 -sideband
infrared laser radiation, and this broadly tunable and convenient infrared source has high
potential for spectroscopic applications.
The 10 pm region, where the CO2 laser operates, is rich with vibration-rotational
lines of many molecules, associated with the fundamental stretching mode involving two
heavy atoms. Also, because the
10 pm region lies in the well-known 8-13 pm
atmospheric window, the CO2 -laser/microwave sideband system will be valuable for
research on atmospheric remote sensing and astrophysical exploration [23],
4.1. C 02-Lasei7Microwave Sideband System
4.1.1 CO1 Laser
The CO2 laser is one of the most useful radiation sources in the important mid-infrared
region. In fundamental scientific research, it has improved high-resolution and saturation
spectroscopy, contributed to laser-induced fusion and nonlinear optics, and is even used
for the optical pumping which has made newer types of lasers possible (e.g. far-infrared)
[60]. The C 0 2 laser can operate with an efficiency of up to 30%, compared to only -0.010.14% for He-Ne laser, and can produce high power radiation [61]. For a commercially
available TEA (Transverse Electrical discharge at Atmospheric pressure) C 0 2 laser, the
typical operating power can be several hundred watts to a few kilowatts. All these facts
have made it currently the most frequently used laser in industrial cutting, and in surgical,
environmental and communications applications.
95
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
The C 0 2 laser used in this study was built by K.M. Evenson at the Time and
Frequency Division of the National Institute of Standards and Technology (NIST) in
Boulder. Because of the use of a high-resolution specially blazed grating and a ribbed
laser tube with double electrodes, both the mode structure and the effective resolution
have been greatly improved [31], The higher resolution permits weaker lines to lase that
are otherwise in competition with the regular lines, and also leads to a considerable
extension of the customary operating range [62].
The premixed gas used in this laser (Air Liquide, Inc.) consists of 16.2% N2 , 12%
CO2 and the balance He. A simplified vibrational energy level diagram for C0 2 and N2 is
shown in Figure 4.1. The C 0 2 vibrational modes are denoted by (viv 2 'v3), where vi, v2',
and v3 are the quantum numbers associated with symmetric stretching, degenerate
bending, and asymmetric stretching, respectively. The upper levels of the regular and
sequence bands are the successive excited states of the asymmetric stretching mode.
These are in near resonance with the successive N2 vibrational excited states, populating
the upper laser levels by resonant energy transfer through collision. The lower laser levels
are the mixed [10°v3, 02°v3] doublets formed from Fermi resonance between the first
excited symmetric stretch and second excited bending states, with successive quanta of
the asymmetric stretch added in [62]. The 00°1->[10°0, 02°0] transitions are the most
important, allowing the strong emission of the 10.4 pm and 9.4 pm regular lines. The
00°2—>[10°1, 02° 1] and 00°3-»[10°2, 02°2] transitions give the first and second sequence
bands [31]. The hot band transition, 01°1—>[1110, 03*0], differs from the above regular
96
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
band in having one additional quantum of bending for both the upper and lower lasing
levels [62].
00°3
V=3
10.5 jam,
9.5 pm
V= 2
10.4
.4 pm
/
/
V=1
10.8 pm
9.3 pm
10.4 pi
9.4 pm
oro
V=0
00°0
N,
Figure 4.1. Simplified vibrational energy level diagram of the CO2 and N2 molecules. The
dotted line is the 4.3 pm fluorescence emission used to lock the regular band laser lines to
their line centers. For the hot and sequence band laser lines, their lower power output is
currently insufficient for Lamb-dip locking. The dashed lines represent possible
excitation paths for populating the hot band lasing levels. (From Ref. [31])
97
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
890
910
930
950
970
990
lOl'O
1030
1050
1070
1090
Wavenumber (cm'1)
Figure 4.2. Observed output lines of the CO2 laser. The vertical scale is relative output
power for each observed CO2 laser line, and the horizontal scale is the corresponding
oscillation frequency. The output power of the laser lines was measured by a powermeter after tuning to the peak of the gain curve. The accurate frequency for each line
comes from Ref. [63], (From Ref. [32])
Figure 4.2 illustrates the observed spectral output of the laser versus its oscillation
frequency. The laser is scanned through its output lines by rotating the grating through a
tuning micrometer. Between the lines of the strong regular bands, transitions of the
sequence and hot bands are also clearly visible. As seen in Figure 4.2, the hot and
sequence band lines are more prominent in the high J 10-pm P-branch region as well as
98
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
around low J in the 9-pm region. Currently, the typical output powers are 10 W for
regular band lines, and 2-4 W for hot and sequence band lines.
The frequency of the microwave synthesizer is known to much better than 1 kHz,
hence the fundamental accuracy limitation of the CO2 microwave sideband source is the
frequency stability of the CO2 laser. In our system, the laser is locked to the zero-crossing
of the 4.3 pm CO2 fluorescence Lamb-dip signal from an external CO2 cell (with -5.3 Pa
pressure). The traditional first derivative servo technique is used, with a 1 kHz signal
applied to the laser piezo voltage tuning element (PZT) in order to modulate the cavity
length and the laser frequency. Currently, only the regular band lines, whose output
power is large enough to generate a usable Lamb-dip signal, can be precisely set to the
line centre through this technique. The accuracies of these regular lines are estimated to
be of the order of ±100 kHz [32], For the hot and sequence band laser lines, the current
lower power output is insufficient for Lamb-dip locking, hence the laser is simply
adjusted to the peak of the gain curve in the free-running state during spectral recording.
We estimate this unlocked state will give an uncertainty of about ±5 MHz in a typical
-10 GHz broad scan.
4.1.2 Sideband Generation
In optical waveguides, extremely intense optical and microwave fields can be established,
provided that special techniques are used to couple the light and microwaves efficiently
into the device. If these two waves are properly synchronized with nearly the same phase
velocity, very efficient and broad-band modulation can be achieved. Phase modulation of
99
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
a CO2 .laser beam at microwave frequencies with linear polarization will generate both
the upper and the lower sideband frequencies, which can be well resolved from the laser
carrier frequency fy. By varying the microwave frequency fu, it is possible to tune the
sidebands over a significant range [25],
In this study, efficient sideband generation was accomplished by mixing the
infrared laser carrier with a traveling microwave in an integrated Cheo-type electro-optic
CdTe-buffered GaAs waveguide modulator (PC Photonics). The structure, design
parameters and fabrication procedures for this kind of GaAs waveguide modulator have
been described in detail previously by Cheo [23, 25, 64]. The waveguide in this
modulator operates in the X and Ku bands (about 8-12 and 12-18 GHz), giving a sideband
tunable range up to ~11 GHz, from 6.7 to 18.5 GHz. The whole modulator unit is
mounted on a 5-dimensional kinematic stage for precise positioning and angular
alignment. The microwaves are provided by amplifying a low power signal from a
synthesized sweeper (Hewlett Packard, 83630A, 10 MHz - 26.5 GHz) through a high
power broad-band traveling-wave tube amplifier operating in the X and Ku bands (CPI
Model ZM-6991K4ADI) [32], Typically, with 10 W laser and 15 W microwave powers
as the inputs, output power of about 10 mW in a single sideband can be obtained.
CO2 laser microwave sideband generation provides one of the best available
widely tunable sources in the 10 pm mid-infrared region. It is a very convenient and
reliable tunable coherent infrared radiation that can operate at room temperature with
high output power and resolution [64]. Once the sideband is obtained, its frequency can
100
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
be easily determined by adding or subtracting the microwave synthesizer frequency from
the corresponding CO2 laser carrier which is precisely known. In the mid-infrared region,
the lead-salt diode laser is another class of commonly used tunable source. Compared
with the CO2 laser microwave sideband system, the diode laser technology has several
drawbacks of its own such as low output power, requirement for cryogenic cooling,
limited lifetime due to thermal cycling, and the need for frequency references for
calibration [64]. The CO2 laser microwave sideband system thus has proven itself to be
of great potential for use in spectroscopic studies in the important mid-infrared region.
4.2. Doppler-limited Broad Band Sideband Spectra in the C-O
Stretching Fundamental Band of CH3OH
To test the performance of the wide-scan mode of the CO2 -laser/microwave sideband
spectrometer at Doppler-limited resolution, methanol (CH3 OH) was selected as the
sample gas, in view of its strong C-0 stretching fundamental band centred at 10 pm
(1033.5 cm'1). Although methanol is a relatively light molecule, the vibrational spectra
are highly congested due to asymmetry splitting, torsional tunneling splitting, hot bands,
and interactions between different vibrational bands [65]. The richness of the various
spectral features thus make it an ideal sample molecule to test the instrumental
performance, both for the sensitivity and resolution.
4.2.1 Experimental Details for Widescan Doppler-limited Operational Mode
In the first operational mode of the spectrometer, involving wide scans at Doppler-limited
resolution, we employed both regular band CO2 laser lines from 9P4 to 9R6 and the hot
101
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
and sequence lines lying among the regular lines. Since the hot and sequence band lines
serve to bridge many of the gaps between the regular band lines, the spectral coverage is
greatly improved. The range from 9P4 to 9R6 represents -1/10 of the normal
12
C 160 2
laser lasing range from 9P58 (1007.77 cm'1) to 9R58 (1098.15 cm'1).
A schematic diagram of the spectrometer as set up for the wide-scan mode is
shown in Figure 4.3. As described in the preceding section, the laser (frequency fL) is
locked to the Lamb-dip in the 4.3 pm fluorescence for the regular band laser lines [32]
and is manually set to the power peak in the free-running state for hot and sequence band
laser lines. After passing through a two-mirror polarization rotator, the beam is focused
into the modulator with a ZnSe lens of 10 cm focal length. The microwave radiation of
-15 W (frequency fM) in the range 6.7 - 18.5 GHz is coupled into the modulator where
nonlinear mixing takes place, yielding laser sidebands. The radiation from the exit
window of the modulator then contains the laser carrier ft and two sidebands at
frequencies ft ± fM. They are then separated from each other by a tunable Fabry-Perot (FP) etalon, controlled by a ramp generator, to select the desired upper or lower sideband as
the probing infrared radiation for the sample gas. Typical transmission efficiencies of the
modulator and F-P etalon are -25% (carrier and sideband power from the output divided
by input) and -30%, respectively. After the F-P etalon, the sideband power is of the order
of 1-5 mW depending on the power of the laser carrier.
102
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Servo
System
oo
C 02 Laser
BS1
jiSb Detector
M5,
M4
M2
CO2 Cell
Detector
M12;
Block
Oscillator &
Phase Shifter
Microwave
Synthesizer
TWTA
Ramp Generator
L2
M 7,
_ Chopper
F-P Etalon
M6
^ 0 J g C d T e Detector 1
M9,
______ Multipass Cell
M8
Lock-in
Amplifier 1
BS2
Mlof{
Detector 2
M il
Lock-in
Amplifier 2
A/D Card
Computer
Figure 4.3. Block diagram of a Doppler-limited tunable CCVlaser/microwave-sideband
spectrometer. BS, beam splitter; LI, L2, ZnSe lenses; M1-M12, plane and concave
mirrors; TWTA, traveling wave tube amplifier; F-P, Fabry-Perot interferometer. The
spectrum analyzer is used for confirmation of the selected CO2 line.
A White-type multi-pass cell (Model 35-V, Infrared Analysis, Inc.), which is a
cylinder of borosilicate glass 60-cm long with two ZnSe windows and three mirrors
coated with protected gold, was used as a sample cell. The selected CO2 laser sideband
103
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
was amplitude modulated by a mechanical chopper (Stanford Research Systems SR540)
at a frequency of 1 kHz before being split into a signal beam and a reference beam in a
7:3 ratio. The multi-pass cell was set at eight transits, and the path was further doubled by
a retro-reflecting plane end mirror M10 to give a total optical path length up to -9 .6 m.
Two liquid nitrogen cooled HgCdTe detectors simultaneously detected the reference
beam and the signal beam after the sample cell. These detected signals were then
demodulated by two identical lock-in amplifiers (Stanford Research Systems SR510)
operating in 1/mode and sent via an A/D card to the computer where the ratio of sample
signal to reference signal was calculated. The ratioing procedure greatly improves the
signal-to-noise (S/N) ratio of the molecular absorption signals and gives a relatively flat
background over the 6.7-18.5 GHz range of a scan. The procedure effectively
compensates for fluctuations in the laser sideband power as a function of frequency due
principally, we believe, to standing waves in the microwave circuitry. In implementing
the sideband sweeps, the frequency of the microwave synthesizer, the tuning of the F-P
etalon by the ramp generator voltage, and data acquisition from the lock-in amplifiers
were all computer controlled via a program written in the Visual
programming
language by V. Dorovskikh, a visiting researcher in our laboratory.
4.2.2 Spectral Coverage
The accessible tuning range on either side of each CO2 laser line extends from 6.7 to 18.5
GHz for our sideband system. While this coverage is good, there are still significant gaps
when only the regular CO2 laser band lines are used to generate sidebands, because the
spacings between the regular CO2 lines vary from about 70 GHz to 20 GHz going from P
104
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
to R branch across a band. Since the hot (B) and sequence (S) band lines serve to bridge
many of the gaps between the regular band lines, there is considerable advantage in
spectral coverage if these additional CO2 laser lines can be used to generate useful
sidebands as well. Our trials were carried out in the region of the low-/ CO2 laser lines,
where the hot and sequence band lines are relatively more prominent, as shown in Figure
4.2. This region is also considered important because it plays the role of a bridge to link
the 9P and 9R branches.
1 0 -,
o
if)
8
9R6
9P4
9R4
(0
9R2
fl
1
9P2
O
o
I
o
Q.
zs
&■
Z3
o
4-
I
is
p
isi
2-
->SR9
■
JSR7
1
Ilf
i
I
tv’
9HP
9R0 9SR5
9 H P I1
21.5
21.6
■
9 H P 10
21.7
21.8
21.9
22.0
22.1
22.2
Microm eter Reading o f C 0 2 Laser (cm)
Figure 4.4. Observed regular, sequence (S) and hot (H) band CO2 laser lines from
1059.95 to 1069.63 cm'1.
Within the region of the six low-/ CO2 laser lines from 9P4 to 9R6 in the centre
of the 9.6 pm band, we could observe three hot band and three sequence band lines
105
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
interspersed among the regular lines. We assigned them in the frequency increasing
direction as 9P4, 9HPY2, 9P2, 9HPW, 9HPIQ, 9RQ, 9SR5, 9R2, 9SR1, 9R4, 9SR9, and
9R6. All of them are drawn in Figure 4.4 according to the observed output power
measured by a power meter. The typical output power of the H and S lines was ~2 W, as
compared to a typical output power of ~ 6 W for the regular lines in this region. By using
each of the
12
laser lines to generate sidebands, we were able to cover most of the gaps
between the regular band lines and obtain near-continuous spectral coverage from
1059.95 cm' 1 (9P4 - 18.5 GHz) up to 1069.63 cm*1 (9R6 + 18.5 GHz), a range of almost
10 cm'1. The frequency tunable sideband windows are drawn in Figure 4.5 as calculated
from the CO2 laser line frequencies listed by Maki et al. [63],
9Z?6
9SR9
9R4
9SR1
9R2
— • 9SR5
---- 9R0
9 HPI Q
•—
9HPU
9P2
9HPX2
9 P4
t " -1* ' '
1060
t
1062
I------'1
*-
1064
1066
C O , sideband laser frequency
<
1068
«--------—
1-1070
(c m '1)
Figure 4.5. Tunable windows of microwave sidebands of hot (H), sequence (S), and
regular band CO2 laser lines from 1059.95 to 1069.63 cm'1.
106
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
4.2.3 Absorption Spectra o f Methanol in the Wide-scan Mode
The C-0 stretching fundamental band of methanol has been studied by many researchers
because it is of spectroscopic interest and has practical interest related to opticallypumped far- infrared lasers. This band has been studied by infrared Fourier transform
(FT) spectroscopy and the data given in Ref. [6 6 ] are now widely used. In contrast to the
FT technique, in our experiment, the upper and lower sideband of each COa laser line
was swept across the microwave frequency range from 6.7 to 18.5 GHz in one scan to
obtain a piece of the broad band spectrum.
Figure 4.6 depicts the 24 segments, corresponding to the upper and lower sidebands
of the 12 CO2 lines from 9P4 to 9R6, of our broad band scan for the C-0 stretching band
of CH3 OH. The top axes give the microwave sideband frequencies (GHz) and the bottom
axes show the absolute wavenumbers (cm'1). The remarkable near-continuous spectral
coverage in these broadband scans is evident. They were recorded at a typical pressure of
80 mTorr with a lock-in time constant of 0.3 ms, sensitivity of 500 mV, and an
absorption path of 9.6 m. Each of these scans represents a broadband sweep of
microwave frequency over a full sideband from 6.7 to 18.5 GHz. The step size for the
sweeps was 2 MHz per point, and the minimum time interval between two adjacent
points was 80 ms, limited by the speed of the GPIB bus. When controlling the microwave
synthesizer in a sweep, the computer can pause the microwave sweeping process after
each frequency interval of 300 MHz, in order to adjust the F-P etalon bias voltage for
optimum resonance. Altogether, the sweep time for each scan totaled approximately 14
min. It is seen from Figure 4.6 that all of the CO2 laser sidebands, even the sequence and
107
Reproduced with permission of the copyright owner. Further reproduction prohibited w ithout permission.
hot band C 0 2 lines with lower laser power, gave very nice spectra for methanol in the
fundamental C -0 stretching band.
-185
-16.3
-145
-125
-105
-85
-6.5
6.5
«5
105
125
145
165
0
-
1050.95
1060.05
1060.15
8060.25
1C60J5
1060.79
8060.89
1060.99
65
9HM Z-SB
-185
145
-16.5
-14.5
106126
-12.5
1061.36
-10.5
-85
1061.19
16.5
SHP12+SB
-
0
1061.16
-
1061.09
12.5
0
1063.06
385
1061.46
1061.90
-65
<5
1062.00
8.5
1062.10
105
1062.20
125
145
165
306230
185
yyffrrn'1TTwnnnr
9F2-SB
106U 5
-1 8 3
1061.65
-16.5
-143
1061.75
-12.5
1061*5
-105
9P2+SB
1061.95
-Z.5
1062.48
*5
65
9HPI1-SB
,l>s
*-s
1
1062-58
1062.68
125
,4 J
145
1062.7*
**-5
TTF B
1
9HP1H5B
0
1061.98
1062.08
1062.18
1062.28
1062.38
1062.52,
1062.92
1063.02
1063.12
1063.22
Figure 4.6. Broadband spectra of the C-0 stretching fundamental band of CH3OH
recorded in Doppler-limited mode using microwave sidebands of hot, sequence, and lowJ regular band CO2 laser lines. Each segment represents a continuous scan over a full
microwave sideband from 6.7-18.5 GHz. The bars with numbers indicate regions of
spectral overlap in which the same lines can be seen.
108
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
-SSLS
i
-J63
-14.5
-SIS
-103
r
%
-S3
-63
63
83
M3
SIS
143
S6.5
n
n
^
SH TJM B
106X78
106X88
-183
-463
106X98
-14.5
-1X5
2063.08
-103
o
n
p
T
f
9HFMH-SB
1063.18
-83
-63
^
3063.72
30 3^1
63
83
1053.81
103
S23
S063.SS
343
9R0-SB
G>—
1063.89
2063.99
-163
1064.09
-M3
-1X5
1064.19
-103
2064X9 1064.73
-S3
-43
1064.83
63
83
1064.93
103
i t T
1X5
9SR5-SB
r y
1064.47
-163
1065.42
S064.57
-34.5
143
W
1065.13
165
f
f
J8.5
f
5SRS+SB
-123
1064.67
____ (5)---------
-103
-8.5
1064.77
*q65.2S
-63
65
106531
83
1065.41
103
1X5
S0S53S
143
SB65.6S
16.5
183
r j
f
—
106533
t !
__________ _______
-1X5
f l J
9R0FSB
v
l i f
306437
183
n
—
-183
*064.01
163
f l f l T
u
W
o —
................................................. —
r
SIS
f
T
H
h
t
f
9KZ-SB
9K2+SB
f
m
n
106445
106635
p
l
®106532
1065.62
1065.72
1065.62
1066.25
S066.3S
1066.65
Figure 4.6. Cont’d.
109
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
•18.5
-16.5
-143
-12.5
-303
-S3
-6.5
5.5
83
103
323
14.5
363
183
9SR7+SB
3055.82
-1S3
106532
-16.5
-1 4 3
1066.02
-523
1066.32
-1 0 3
-8 3
3966.22
1066.65
-6 3
63
1066.75
S3
1066.85
103
32 5
1666.95
143
1067.05
163
1S3
163
1*3
9 R 4 -S B
1067.02
-S S 3
-163
106724
-183
-1 4 3
106734
-163
443
106S.06
1067.22
-1 2 3
-1 0 3
1067.44
-12.5
-S 3
106734
-1 0 3
-S 3
-6.5
63
1067.64
106807
-6.5
6.5
83
10.5
1068.17
83
103
123
143
1968.27
123
196837
143
1068.47
163
183
9R6+SB
1068.40
106*30
IO 6I.60
1068.70
1068.50
3069.23
1969.33
1069.43
106933
1069.63
Figure 4.6. Cont’d.
It may be noted that sometimes the same spectral lines appear more than once in the
upper or lower sideband range of different CO2 laser lines as shown by the numbered
bars in Figure 4.6. For example, the 9HPII - (18.5 - 9.0) GHz sideband (number 2 in
110
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 4,6) has a region of overlap approximately with 9HP 12 + (9.0 - 18.5) GHz, while
9R2 - (18.5 - 12.9) GHz overlaps approximately with 9SR5 + (12.9 - 18.5) GHz (number
5 in Figure 4.6). The spectra in these overlapping regions display the same lines in Figure
4.6 (although with slight differences in relative intensity at the edges of the sidebands).
This confirms that the hot and sequence band CO2 laser lines have indeed been correctly
identified, and confirms the good performance of the system even with these weaker CO2
lines.
Compared with a FT spectrometer, this COa-laser/microwave sideband spectrometer
is convenient to operate. It has intrinsically high absolute measurement accuracy, without
the need for frequency calibration against known reference spectra. This system also has
the advantage, with a tunable monochromatic source, that we can focus on any particular
scanning range or spectral feature of particular interest and monitor the effects of
changing experimental conditions essentially in real time for that specific signal. When
the construction expense is taken into consideration, this spectrometer is much less
expensive than a FT spectrometer system. However, the CCh-laser/microwave sideband
system also has its own drawbacks, such as the spectral coverage, which is limited by the
CO2 laser carriers.
4.2.4 Frequency Uncertainty o f Present Doppler-limited Wide-scan Measurements
For the broadband scan spectra, centre frequencies for the spectral lines can be obtained
by using the Peak Picking command in the commercial spectrum analysis software
GRAMS32. Without fitting to any spectral line function, this command determines the
111
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
line centre by considering the first derivative of line profiles, which is a much more
efficient way but loses some accuracy. Figure 4.7 is a screen capture of the Peak Picking
result from GRAMS32 for a section of broadband scan spectrum recorded by using the
upper sideband of the 9P42 CO2 line. It was recorded at a pressure of 80 mTorr with a
lock-in time constant of 0.3 s. The step size for the sweep was 2 MHz per point. The
determined frequencies of some strong lines were then compared with the literature
Lamb-dip measurements by Sun et al. [67], as shown in Table 4.1. In Table 4.1, we list
our experimental frequencies for six measurements, three in the laser-locked condition
and three in the laser-unlocked condition. The frequencies are given in terms of the
microwave offset from the 9P42 CO2 line. All our frequencies are consistently up-shifted
compared to the Lamb-dip results, which is mainly due to computer GPEB HPMicrowave synthesizer scan speed limitations. This frequency shift can be significantly
reduced if greater delay times for the HP-Microwave synthesizer are introduced. This
problem can also be circumvented by averaging up and down measurements or adding an
empirical shift correction in order to get comparable frequencies. In Table 4.1, we list the
frequency differences Av between consecutive lines, which should be independent of the
frequency shifts. Compared with the Lamb-dip measurements, the differences are
typically less than
6
MHz. It is interesting to point out that the differences for the laser-
unlocked condition are comparable with, or in some cases even some better than, the
laser-locked values.
112
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
O'
8
10
12
-14
16
18
Figure 4.7. Screen capture from GRAMS. The frequencies marked for each spectral line
were obtained by using the Peak Picking command in GRAMS. Horizontal scale is the
microwave frequency (in GHz) with respect to the 9PA2 CO2 line.
When accurate measurements for individual lines are desired, a narrow band scan
for a single line with smaller step size can be performed, sweeping in both up and down
directions. The recorded line shapes are fitted to a Voigt profile using commercial linefitting software (such as GRAMS 32 or Origin). The pairs of up/down scan centre
frequencies are then averaged to remove the frequency shift effect. In the laser locked
condition, we can achieve an overall absolute measurement accuracy of around ± 0.5
MHz, verified by checking against earlier precise measurements. For the hot and
sequence band CO2 lines, the uncertainty in the free-running CO2 laser frequency is the
dominant factor, giving an overall estimated uncertainty of ±5 MHz. In the first
113
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
operational mode, further accuracy improvement is mainly limited by the Doppler line
width, which causes a large uncertainty in determining the line centre. To achieve better
accuracy, as well as higher resolution, a sub-Doppler technique is necessary, such as the
saturation-dip measurement in our second operational mode. For the narrow-band,
saturation-dip mode at high-resolution, our measurement accuracy can be judged from
the residual frequency defects in closure relations for transition loops containing our
observed lines together with known infrared and millimetre-wave transitions. The
transition loop results indicate an absolute experimental uncertainty for the Lamb-dip
measurements of somewhat better than ±200 kHz. Detailed descriptions of the second
mode are given in the next section.
Table 4.1. GRAMS32 Pick Picking frequencies for wide-scan spectra using 9P42 upper
sideband.
Lamb-dip
measurement2’1’
A vc
Scan 1
Scan 2
Scan 3
Average
1.60723
2.23941
3.77355
0.14315
9.07410
10.68815
12.91978
16.69011
16.83639
9.07288
10.68469
12.91852
16.68954
16.83528
9.07121
10.68312
12.91838
16.68926
16.83558
9.07136
10.67936
12.92115
16.69321
Laser Unlocked
9.07376
9.07259
10.68114 10.68008
12.92130 12.92115
16.69521 16.69387
16.84219 16.84054
A vc
Diff.
1.61259
2.23357
3.77074
0.14611
0.00536
-0.00584
-0.00281
0.00296
1.60749
2.24107
3.77272
0.14668
0.00026
0.00166
-0.00083
0.00353
Laser locked
9.04574
10.65297
12.89238
16.66593
16.80908
9.04574
10.65297
12.89238
16.66593
16.80908
1.60723
2.23941
3.77355
0.14315
9.07265
10.67973
12.92099
16.69318
16.83968
16.83976
9.07273
10.68532
12.91889
16.68964
16.83575
a. The microwave frequencies are in GHz;
b. Literature frequencies of sub-Doppler measurements, Sun et al. (From Ref. [67]);
c. Av is defined as the frequency difference between two consecutive lines;
d. Diff. is defined as the Av in this study minus Av of literature measurements.
114
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
4.3. Saturation-dip Measurements at Sub-MHz Resolution for CH3OH
The C-0 stretching band is one of the most crowded spectral regions for methanol, and
blended lines are often observed in the FT spectrum, whose spectral resolution is limited
by the Doppler width of 60 MHz (FWHM), giving an accuracy of several megahertz [6 8 ],
Considering the importance of methanol in both practical and theoretical studies, the subDoppler technique is useful for application to the many blended features. In this section,
the second operational mode of our CCb-laser/microwave spectrometer, a narrow-band
sub-Doppler mode for precision measurements, will be described.
4.3.1 Line Broadening Mechanisms
Observed spectral lines are always broadened due to intrinsic physical causes. The
variety of broadening mechanisms can be divided into two main categories,
homogeneous and inhomogeneous broadening.
Homogeneous broadening: A spectral line is homogeneously broadened when every
molecule affects the line width in the same manner. In this case, all the molecules are
assumed to be independent of the particular behaviour of others. Examples in this
category include lifetime broadening, transit-time broadening, etc. Pressure broadening is
not strictly homogeneous, but can often be approximately represented by a Lorentzian
function, which is a common mathematical expression for most homogeneous broadening
effects [69].
115
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Lifetime broadening: Lifetime broadening arises from the energy uncertainty due
to the finite lifetime of the states involved in the transition. For an exponentially decaying
oscillator, Fourier transformation into the frequency domain gives a Lorentzian line
profile with FWHM equal to 2/x, where x is the lifetime [69]. For most stable molecules
in the ground electronic state, the radiative lifetime in a given rovibrational state will be
on the order of 1 ms [70] or more which gives a line width of about 2 kHz or less. This is
negligible when compared with other broadening effects.
Transit-time broadening: The finite size of the laser beam gives a finite
interaction time with the moving molecule, which causes transit-time broadening. This
situation can be modeled as an undamped oscillator in the time domain truncated by a
square wave with duration T. When Fourier transformed, the frequency domain profile
has a pattern similar to that for single slit diffraction. This gives a FWHM of 0.89IT [69].
Suppose the width of the laser beam is 0.5 cm, and the average thermal speed of
molecules is 200 m/s. Then the interaction time would be 2.5xl0 ' 5 s. This gives a line
width of -40 kHz. In reality, both the molecular velocity and the laser beam intensity are
not distributed uniformly, and in that case the integration of the line shape will be much
more complicated. Further discussion about transit-time broadening can be found in Ref.
[69].
Pressure broadening: Pressure broadening, also known as collisional broadening,
originates from interactions between molecules. As one molecule approaches another,
both of them experience transient induced dipole moments, which will skew the energy
116
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
levels. It is the most import source of broadening when the pressure is high. As discussed
in Ref. [69], in a simple treatment, the pressure broadening line shape can be
approximated as a Lorentzian, [71] i.e.,
. .
2A
w
y(y) = y 0+----% 4 ( v - v 0) +w
r . ...
[4.1]
where yo is the baseline offset, A is the total area under the curve from the baseline, Vo is
the line peak centre and w is the full width of the peak at half maximum (FWHM). w is
related to the pressure P by the pressure broadening coefficient c, w=cP. Experimental
values for the pressure broadening coefficient are found in the range from
2
to 60
MHz/Torr depending on the kind of molecule and the temperature [69]. Generally, for
molecules with a large dipole moment, the pressure broadening coefficients will be
bigger. For Methanol, the coefficient is -40 MHz/Torr. Thus, for pressure on the order of
lOmTorr, the pressure broadening line width (FWHM) is estimated to be -400 kHz.
Inhomogeneous broadening
When the transition frequencies of different molecules in the ensemble are different, the
spectral line is apparently broadened. Stark and Zeeman effects of molecules in an
inhomogeneous field are obvious examples of inhomogeneous broadening. In the absence v
of any inhomogeneous external field, the spectral line is mainly inhomogeneously
broadened by the Doppler effect due to the molecular velocities [69].
Doppler broadening: As the result of the Doppler effect, a molecule traveling
with velocity component vx along the propagation axis of the laser beam will experience
a light frequency shift of Av=v-vo=-v0(vx/c), where v0 is the frequency experienced by
117
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
the stationary molecule. This shift is expressed by a classical treatment, since the thermal
velocities are non-relativistic, where the classical mechanics works well. Considering the
one-dimensional Boltzmann velocity distribution, the resulting line shape will take the
form of a Gaussian function [71]:
2
{v-Vq)2
[4.2]
where y$ is the baseline offset, A is the total area under the curve from the baseline, Vo is
the line peak centre and w is approximately 0.849 times the full width of the peak at half
maximum (FWHM) [71], The Doppler broadened FWHM can be estimated by the
expression 7.162x10~7v(T/M)m [70],
where v is the transition frequency, T is the
absolute temperature of the gas, and M is the molecular mass in amu (atomic mass unit).
In the 10 pm region, the Doppler width for methanol is thus estimated to be about 60
MHz, which is often the dominant factor for the total line width at room temperature.
In many cases, both of the Doppler and pressure broadening are comparable. In
this case, provided these two effects are statistically independent, the line shape is more
accurately defined by a Voigt profile, which is a convolution of the Gaussian and
Lorentzian. However, the Voigt function is not analytical, so there is no good closedform expression. In most line-fitting software, all three of these popular line shape
functions, Lorentzian, Gaussian and Voigt, are built in.
118
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
4.3.2 Dovvler-free Spectroscopy
As discussed in the previous section, Doppler broadening is the
d om inant
broadening
mechanism for gases at low pressure. For example, for a Methanol C-0 stretching
transition at 10 pm at 10 mTorr, the Doppler broadened FWHM is about 60 MHz,
compared with pressure broadening of only ~400 kHz. The Doppler broadening is
therefore the bottle neck to the discovery and measurement of the fine structures of the
spectral transitions. To remove this limitation, quite a number of experimental methods
have been developed to observe Doppler-free spectral lines [723. One way to achieve this
is to use a supersonic molecular beam, in which the translational velocity distribution can
be made to resemble a delta function along the beam direction, while the velocity
distribution transverse to the beam is characterized by low temperature (typically T<20
K) [73]. At such a low temperature, the absorption line width will be far narrower than
that observed at room temperature [73], Some other Doppler-free techniques, such as
two-photon absorption and saturation spectroscopy, became possible after the advent of
the laser in 1960. In the two-photon absorption technique, a transition is achieved by
absorption of two photons traveling in counter propagating directions. The Doppler width
can thus be eliminated due to the canceling of their velocity dependence. Detailed
descriptions of two-photon absorption spectroscopy can be found in Refs. [69, 73] The
second technique, saturation-dip or Lamb-dip spectroscopy was employed in our study to
obtain high resolution and accurate measurement. The principle of this technique will be
briefly introduced in the next section.
119
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
4.3.3 Lamb-dip Technique
At thermal equilibrium, all directions are equi-probable, that is, the velocity distribution
of the molecules is isotropic [72]. Therefore, the projection of the molecular velocity
along the laser propagation direction, say vx, takes the form of a Maxwell function. When
plotted as a function of vx, the number of molecules yields a Maxwellian distribution
centered at vx=0. (Figure 4.8(a))
When counter-propagating laser beams, respectively called pump and probe, are
applied to the sample (Figure 4.8(b)), the radiation field at a frequency v interacts with
the two groups of molecules with velocity vx„res which comply with one of the resonance
conditions: vx.res-±(vo-v)c/vo, where c is the speed of light, v is the frequency of the laser
radiation, and vo is the centre frequency for a stationary molecule (which is the frequency
we want to measure precisely). These two groups of molecules suffer depopulation due to
promotion of molecules into their excited states and thus the laser “bums” holes in the
ground level velocity distribution curve. This phenomena is called “hole burning” in the
velocity distribution. The two holes occupy symmetric positions about the centre where
vx=0, as shown in Figure 4.8(c). The detected absorption intensity at frequency v will be
proportional to the total area of these two holes. As the laser frequency v is timed to the
centre frequency vo, the two holes will get closer together and then coincide. At this
point, the two counter beams interact with only one group of molecules, which are
moving perpendicular to the beam direction. When the intensities of the two counter
beams, or at least one of them, are high enough to saturate the transitions, the hole area at
120
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
vx=0 will be much smaller than the sum of the two at vx slightly off the centre. Thus, in
the frequency picture, the overall observed absorption will decrease in the centre of the
Doppler-broadened line, as shown in Figure 4.8(d).
Sample cdl
Laser
Detector
Figure 4.8. (a) Velocity distribution along the laser propagation direction; (b)
Experimental arrangement, in which the intense laser beam is reflected back into the
sample cell to form a counter propagating probe; (c) “Hole burning” in the velocity
distribution; (d) Detected absorption as a function of frequency, the narrow dip in the
center is the Lamb-dip. (From Ref. [69])
This phenomenon, often termed the “Lamb-dip”, was first considered by Lamb in
his gas-laser theory. Experimental observations of this effect were first reported in 1963
[72]. Because the typical width of a Lamb-dip signal is only about, or less than, 1 MHz,
this technique soon gained wide use in spectroscopy to separate very close-lying lines as
well as provide precise measurements.
121
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
4.3.4 Experimental Details for Narrow-scan Sub-Doppler Operational Mode
The second mode of operation of the spectrometer involves narrow-band scans at subDoppler resolution in order both to record standard reference spectra at high accuracy and
to resolve very close lines that are blended in traditional Doppler-limited spectra. Two
main modifications were made to the optical arrangement of Figure 4.3 in order to
observe saturation-dip signals. First, mirror M10 was reoriented to act as a retroreflector
in order to return the radiation incident on the cell back along exactly the same path. This
gives the counter-propagating overlapping beams inside the cell that are a prerequisite for
observation of Lamb-dips. When the signal radiation reemerges from the cell, it is
reflected off beam splitter BS2 onto mirror M il. Secondly, the F-P etalon was relocated
from its position in front of the absorption cell and placed between mirror M il and
detector 2. This allows the full sideband output from the modulator to pass through the
cell. (However, since the radiation reflected off the front surface of BS2 now contains
both carrier and sideband, we can no longer monitor the background sideband power via
detector 1, so mirror M9 is replaced by a beam block.) For spectral observations, we
could take advantage of the 1 kHz modulation of the CO2 laser frequency already
provided by the laser-locking system. However, now having just a single detection
channel and no longer being able to ratio out the background, we needed to switch to a
digital lock-in amplifier (Stanford Research Systems SR830) to have the capability for
operating in either 2 / or 3 / mode to detect the infrared spectral signals. We found that 3 /
detection was effective in giving a reasonably flat baseline for scans over a few tens of
MHz with just a single detector.
122
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
4.3.5 Recordings o f Lamb-dip Saturated Signals o f Methanol
In carrying out a measurement, we first set the microwave power level according to the
measured gain curve of the microwave synthesizer at the centre frequency for the scan
and then maximized the sideband laser power by tuning the bias voltage of the F-P etalon
using the computer. For a single line sweep, the span was set to 3 MHz with a step size of
10 kHz. The sample pressure for each individual scan was typically -10 mTorr. For
CH3 OH, the Lamb-dip signals generally began to appear at a pressure of -15 mTorr and
to disappear when the pressure dropped below -5 mTorr. The transition centre frequency
was determined by fitting each Lamb-dip spectral line to a second or third derivative
Gaussian line profile (equation [4.2]) using Origin 6.0 commercial software [71],
In this section, the notation (ot Ts K, J)v will be used for the CH3 OH energy
levels, where o t is the torsional quantum number, Ts is the torsional A or E symmetry, K
is the axial projection of rotational angular momentum J, and v is the vibrational mode.
We denote the excited C-O stretching state as v = co, and the ground state by v = gr. An
alternate notation is used in the figures where transitions are labeled as ot, K, Ts, P/R(J),
with P and R denoting P-branch (AJ—-1) and P-branch ((AJ=+1) transitions.
In Figure 4.9, the saturated absorption Lamb-dip signals are illustrated for the two
components of the P(5) K = 1A asymmetry doublet of CH3 OH in the ut = 0 torsional
ground state, recorded using the 9P42 CO2 laser line. Figure 4.9(a) was recorded in the 2 /
mode of the lock-in amplifier, and Figure 4.9(b) in the 3 / mode. The open circles
represent
123
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
0.4
02
3° O
0.0
coQ-
OD -0 .2 -
-0.4 1—
9.044
9.045
9.046
9.047
Microwave frequency (GHz)
w
-4
00
12.892
12.893
12.894
Microwave frequency (GHz)
Figure 4.9. Saturation-dip sub-Doppler spectra of the components of the CH3 OH P(5) K
= IA asymmetry doublet in the ut = 0 torsional ground state, observed with the upper
sideband of the 9P42 CO2 laser line. Trace (a) is the K — \A+component recorded using
the 2 / mode of the lock-in amplifier; trace (b) is the K - 1A~ component recorded in 3 /
mode. Open circles are the data points for the individual scan steps; solid lines are least
squares fits of the appropriate derivatives of a Gaussian profile to the observed data.
124
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
the data points for the individual scan steps, and the solid lines are second- or thirdderivative Gaussian profiles fitted to the observed data. It is interesting that Gaussian
profiles were found to give a better representation of the observed Lamb-dip line shapes
for both the 2 / second-derivative and 3/ third-derivative signals. One would have
assumed that a Lorentzian profile would be more appropriate for the collisional, powerbroadening and transit-time effects contributing to the widths of the Lamb-dips, but this
does not seem to be the case.
0.12
0.08
-e
cS
"X
0.04
rt
G
W
> 0.00
-0.04
13.973
13.974
13.976
13.975
13.977
Microwave frequency (GHz)
Figure 4.10. Saturation-dip sub-Doppler spectrum of the f?(19) K=IE ot —0 transition of
C H 3O H
taken with the upper sideband of the 9HPY2 C O 2 laser line. The spectrum was
recorded using 2 /detection, with a lock-in time constant of 30 ms and methanol pressure
of 8 mTorr. The solid curve is a least-squares fit of a second-derivative Gaussian profile
to the experimental data points (open circles).
With careful system alignment and tuning, we were also able to obtain saturationdip signals with the weak hot band lines. A recording is shown in Figure 4.10 of a Lamb-
125
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
dip observed using the upper sideband of the 9HP 12 CO2 laser line. Because the lower
output power currently does not permit locking to fluorescence Lamb-dip signals, we
have not carried out systematic sub-Doppler measurements using the hot and sequence
band laser lines. However, although the laser is not locked for hot and Sequence band
lines, the narrow-band scan time is short, therefore the expected laser drift would be
small.
-19
-18
-17
-16
-15
-14
-13
-12
-11
10
-9
-8
-7
-6
9P44 - SB
Figure 4.11. Doppler-limited wide-scan absorption spectrum of CH3OH using the lower
microwave sideband of the 9P44 CO2 laser line.
The great advantage of the saturation-dip mode of the spectrometer is the ability
to resolve very close lines in the spectrum. Taking the feature marked in Figure 4.11 by
an asterisk in the 9P44 -SB spectrum as an example, we see that it is actually three lines
overlapped together. Figure 4.12 shows the sub-Doppler observation for this blended
feature in which the components of the P(7) K - 2 A asymmetry doublet in the excited u t
=
1
torsional state as well as the nearby P(7) K = 4E v t - I line are all clearly resolved.
126
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Here, it can be seen that the use o f the 3 / mode in Figure 4.12(b) effectively removes the
significant background slope still present for the 2f mode in Figure 4 . 1 2(a).
0.6
0.4
0.2
o.25?
- 0 . 2 >----------•----------1--------- «--------- 1______ *______ I______ i______ \_________
-10.485
-10.480
-10.475
-10.470
-10.465
I___>______ L_____ l. _____1.........
-10.460
-10.455
-10.450
-10.455
-10.450
Microwave frequency (GHz)
0.4
-0.4
-10.485
-10.480
-10.475
-10.470
-10.465
-10.460
Microwave frequency (GHz)
Figure 4.12. Saturation-dip sub-Doppler spectra of the P{1) K = 2A ot = 1 asymmetry
doublet and the nearby P(7) K = 4 E v t = 1 transition of CH3 OH, recorded with the lower
sideband of the 9P44 CO2 laser line using (a) 2 / mode and (b) 3 / mode of the lock-in
amplifier.
127
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
The approach to the limiting resolution of the spectrometer is illustrated in Figure
4.13 for the very close P( 8 ) lines of the K - 4 E and 2A+i>t = 1 transitions, recorded in 3/
mode using the 9P48 CO2 line. The two lines are only 0.85 MHz apart, and their profiles
overlap in Figure 4.13, but it is unmistakable that there is more than one transition
present. The present resolution of our spectrometer in the narrow-scan Lamb-dip mode is
estimated as follows. The peak-to-peak linewidth of the saturation dip in Figure 4.9(b) is
-0.6 MHz, and was obtained with a modulation amplitude of 0.6 V on the laser piezo
tuner and a cell pressure of 10 mTonr. By reducing the modulation to 0.4 V and lowering
the pressure to 7 mTorr, we were able to reduce the dip width to 0.4 MHz without
significantly degrading the S/N ratio. Thus, we believe that we can resolve blended
features down to a frequency separation of 0.4 MHz.
0.10
^
°-05
-0.05
- 0.10
-0.15
-
0.20 *—
12.885
12,887
12.886
12.888
Microwave frequency (GHz)
Figure 4.13. Saturation-dip sub-Doppler spectrum of the blended K - 4 E and 2A+ut = 1
P(8 ) transitions of CH3 OH, recorded in 3/mode using the upper sideband of the 9P48
CO2 laser line. Solid line is a least squares fit of a third-derivative Gaussian profile to the
experimental data points (open circles).
128
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
4.3.6 O bserved Frequencies o f Methanol Transitions
In this work, we have observed twenty spectral lines for C-O stretching transitions of
CH3OH by using the microwave sidebands of high-J CO2 laser lines from 9P44 to 9P50.
The assignments and measured transition frequencies are summarized in Table 4.2. The
transition frequencies were calculated from the CO2 laser frequencies listed by A.G. Maki
et al. [63] plus or minus the microwave frequencies, and then converted to wavenumbers
(cm'1).
In least-squares fitting each of the observed Lamb-dip signals to a second- or
third-derivative Gaussian profile, the accuracy of determination of the transition peak
frequencies is about several tens of kHz. Coupled with the ±100 kHz uncertainty in the
frequency of the locked laser, this gives a total estimated measurement uncertainty for the
Lamb-dip observations of less than ±200 kHz. This estimate can be supported by
applying the Ritz combination principle to closed loops of transitions with the use of
known ground-state millimeter-wave [74] and Lamb-dip infrared [26] data, the CO2 laser
frequencies given by A.G. Maki et al. [63], and the results observed here in Table 4.2.
129
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 4.2. Observed saturation-dip frequencies for C -0 stretching transitions o f CH3 OH.
Transition
c o 2 Laser Sideband
Vobs
(0 , T SK ,J)'" * - (u, Ts K, I f
(MHz)
(cm-1)
(0 A 2', 5)’ <- (0 A 2', 6)°
9P44
+9133.67
1023.494040
(0 A 2+, 5)1 <- (0 A 2 \ 6)°
+9060.24
1023.491591
(0 E -3, 5)' <- (0 E -3,6)°
+9037.35
1023.490828
(1 E 4, 6)' <- (1 E4, 7)°
-10455.47
1022.840617
(1 A 2 \ 6 ) 1 <- (1 A 2+, 7)°
-10465.39
1022.840286
(1 A T , 6)' ^— (1 A 2", 7)°
-10475.98
1022.839933
-7475.84
1020.807544
(0 A 3+, 7)' <- (0 A 3+, 8)°
9P46
(0 A 3', I ) 1
<-
(0 A 3', 8)°
-7480.27
1020.807396
(0 E -2, 7)'
<-
(0 E -2, 8)°
-10930.11
1020.692322
(0 E -4, 7)1 +- (0 E -4, 8)°
-10947.69
1020.691735
(0 A 1+, 7)1 <- (0 A 1+, 8)°
-13549.56
1020.604946
-13554.03
1020.604797
+12887.21
1019.330564
(I E 4, 8)' <- (1 E 4, 9)°
+12886.36
1019.330536
(1 A T , 8)1 <- (1 A 2', 9)°
+12863.57
1019.329776
(0 E -5, 7)1 <- (0 E -5, 8)°
+12205.44
1019.307823
(0 A 2 ',8 )‘ <- (0 A 2', 9)°
-18141.74
1018.29555
(0 A 2+, 8)’
-18377.92
1018.287672
+16708.87
1017.278290
+16695.28
1017.277837
(1 E 5, 7)‘
(1 E 5, 8)°
(1 A 2 \ 8)‘ <- (1 A 2+, 9)°
—
(0 A 2 \ 9)°
(0 A 3+, 9)1
4
—
(0 A 3+, 10)°
(0 A 3', 9)1
4
-
(OAT, 10)°
9P48
9P50
a. Frequencies were converted to wavenumber using the conversion factor 29979.2458
MHz/cm'1; CO2 laser wavenumbers are from Ref. [63].
130
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
%=;0 A species
Figure 4.14. CH3 OH energy level and transition diagram for the K=1A+ ot = 0 system
illustrating closed transition combination loops for confirmation of the estimated
measurement precision. The line frequencies (in MHz) are: a = 9P46 - 13549.56, b =
9P22 - 12935.23, fi = 383477.880, f2 = 335582.005. C0 2 laser wavenumbers (in cm'1)
are: 9P46 = 1021.056912, 9P22 — 1045.021670. Frequency a is from Table 4.2; b is
from Ref. [26]; ground-state millimeter-wave frequencies fi and f2 are from Ref. [74];
laser wavenumbers are from Ref. [63] and converted to MHz using the factor 29979.2458
MHz/cm'1.
An example of an energy level and transition system for A-species transitions is
illustrated here in Figure 4.14. By using the frequencies given in the caption, we find the
loop residual frequency defect to be:
(b-a-fr f2) = [9P22 - 12935.23] - [9P46 - 13549.56] - 383477.880 - 335582.005 =
(1045.021670 - 1021.056912) x 29979.2458 - 12935.23 + 13549.56 - 383477.880 335582.005 = -0.18 MHz, which is quite consistent with the estimated frequency
uncertainty.
131
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
4.3.7 Asymmetry Splitting o f Methanol
Methanol (CH3 OH) is one of the simplest slightly asymmetric molecules capable of
hindered internal rotation. As well as the Bom-Oppenheimer approximation, which
separates the rotational and vibrational degree of freedom, the internal rotation can be
further separated from the other small-amplitude vibrational modes because of the
different orders of magnitude. Thus, at zeroth order approximation, the Hamiltonian can
be considered as the sum of a rotational Hamiltonian ffrot°, a torsional Hamiltonian H j
and a vibrational Hamiltonian Hvjb°. In practice, it is convenient to reduce the importance
of coupling between the small-amplitude vibrational modes and use a different
for each given vibrational state, Haefi =
“effective” torsion-rotation Hamiltonian
HTOt° + Hj° + perturbation.
When dealing with the rotational component, since that methanol is a asymmetric
rotator, we can split the rotational Hamiltonian into the sum of a symmetric and an
asymmetric part, Hmt° = HR.sym0 + HR.asyml. Thus the symmetric top eigenstates
JJ,
K> can be used as the basis set to treat the rotational component because the
asymmetric term is small enough to be considered as a perturbation. For the torsional
part, free internal rotor eigenstates 1 K, m> can be used as zeroth order eigenstates, and
rewritten in term of a new set of quantum numbers j i)t,
K>. Then the states
Iot, (7 , K,J>~ 1J, K> | ot, ct, K> can be used as the basis set for
in which the sum
HR.sym° + Hj will be diagonalized. Other components, f/R-asym1 and the coupling between
132
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
rotation and torsion, can be treated as perturbations to calculate their contribution to the
energy.
The presence of HR.asyml can remove the degeneracy o f A (or = 0) levels, and this
phenomenon is called asymmetry splitting. In practice, the asymmetry splitting AE(i)t, K,
J) between the energies of a | ut, A, K±, J> doublet is usually represented by the semiempirical formula [6 6 ]:
A£(u„«-,y) = ] ^ S ; [s(u„A :) + y ( j’+ i)r (u,.A:)]
[4.3]
(J - A ) !
where ^(ot, K) and F(ot, K) are the asymmetry splitting constants depending on the
quantum numbers ot and K. The values of S(ot, K) and F(ot, K) can be determined by a
least-squares
f it
of the observed asymmetxy splittings to the above equation. A detailed
description can be found in Ref. [6 6 ].
4.3.8 Observed Asymmetry Doublet Lines o f Methanol
In Table 4.2, we listed frequencies for twelve doublet asymmetry lines for K - 2 with ot =
1
and K = 2, 3 with ot = 0. We determined all their asymmetiy splittings A£(ut, K, J) in
the v - co state by the method below. Three of them correctly confirmed the observations
given in Ref. [26]. Three of them are new observations, namely Afs(0, 2, 5) = 85.39 MHz,
AE(0, 2, 8 ) = 511.25 MHz, and A£(0, 3, 9) = 18.03 MHz. These values agree very well
with the splittings calculated by using the approximate equation [4.3], with the
asymmetry splitting constants S(vt, K) and F(ot, K) given in Ref. [26]. The calculated
133
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
splittings are AE (0, 2, 5)cai = 85.54 MHz, A£(Q, 2, 8 ) cal -511.62 MHz, and AE(0,3, 9)
cal = 18.07 MHz, respectively.
f AE (0, 3,9)
V = €0
v = gr
0
Figure 4.15. CH3 OH energy level and transition diagram for K - 3A ut - 0 asymmetry
doublet system illustrating closed transition combination loops for calculation of the
asymmetry doublet splitting AE. Line frequencies (in MHz) are: c = 9P50 + 16695.28, d
= 9P50 + 16708.87, f3 = 31.615. The CO2 laser frequency cancels out in the calculation.
Frequencies c and d are from Table 4.2; ground-state millimeter-wave calculated
frequency f3 is from Ref. [6 8 ],
One example is given here for the splitting calculation. Figure 4.15 shows the
measured asymmetry doublet infrared transitions and energy levels, and gives the
frequencies in the caption. Using those frequencies, we calculate the asymmetry splitting
AE(0, 3, 9) between the 10, A, 3±, 9> doublet levels to be (c - d + f3 ) = (16695.28 -
134
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
16708.87 + 31.615) — 18.03 MHz. This value can be compared with the splitting
calculated from Equation [4.3] as follows. For ot = 0 and K=3, the fitted values of the
asymmetry splitting constants from Ref. [26] are 5(0, 3) = 2.7367xl0‘5 and T(0, 3) = 2.23x10"9. The calculated splitting is then AE(0, 3, 9)cal = 18.07 MHz, which agrees well
with our experimentally derived value.
135
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Chapter 5
Conclusions
In the first part of this thesis (Chapter 2), detailed ab initio conformational studies of a
series of large biological molecules using the Gaussian 98 quantum chemistry package
were described. The FTMW experimental work, including the spectral assignment, was
carried out in NIST by our colleagues there. Five low energy conformers for 2(ethylthio)ethanol (HOEES) were found by limited-dimension potential energy (PE)
mapping, and three of them match well with the experimental findings both in rotational
constants and dipole moment components, leaving the other two with no experimental
partners. Although higher theory level, a bigger basis set and addition of zero point
energy corrections alter the conformer energy ordering slightly, these two no-match
conformers always stay in the lower energy group. Preliminary conformational studies
were also carried out for thiodiglycol, which is in the same family as HOEES, and two
other nitrogen-containing molecules (ethyldiethanolamine and methyldiethanolamine)
with subunits that resemble biomimetic species. Instead of mapping full or limited PE
surfaces, the conformer optimizations for these three molecules were started from direct
constructions of possible low energy structures by borrowing geometrical information
either from HOEES (for thiodiglycol) or other molecules having structural similarities.
All of the experimentally observed isomers were found among the ab initio predicted low
energy groups, and the matching is supported by both rotational constant and dipole
moment information. Like the HOEES case, calculated low energy conformers without
corresponding experimental partners also exist for the methyldiethanolamine molecule. A
136
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
possible explanation for this puzzle might be that these experimentally unobserved
conformers in fact lie at higher energy than the existing ones and are separated by
relatively low energy barriers. As previous studies suggest, the higher-lying conformers
will be efficiently cooled out in the molecular beams when the barrier between the higher
and lower energy conformers is less than 400 cm'1. It is of interest to note that all of the
no-matched conformers from the ab initio searches possess somewhat “complicated”
structures in which more than one type of intramolecular hydrogen bonding interaction is
involved. This phenomenon might indicate that the current ab initio approach is not as
reliable for treating the electronic energies when more hydrogen bonding interactions get
involved.
Following the ab initio conformational studies, a “diatomic” -twist anharmonic
correction approach was initially tested on the methyl top (-CH3) torsional motions for
the molecules methanol, ethane and 2-(ethylthio)ethanol (HOEES). Such a correction
approach proved to be able to give satisfactory results for all three molecules when
compared with their corresponding experimental fitted values. However, this approach
has not yet been tested on the backbone torsions for large molecules, whose torsional
motions are normally distributed among several dihedral angles. The first foreseeable
challenge in this attempt would be in defining a torsional angle that can be related to the
coordinate along the reaction path for which the torsional potential curve is calculated. If
this correction approach proves to be also valid for the backbone torsions, it would have
great potential for understanding the molecular mechanics of large bio-molecules.
137
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Virtually all molecules that display biological activity have large-amplitude motions,
such as these torsions.
Transferring to the experimental work described in Chapter 4, we have
demonstrated both of the dual operational modes of a newly built CO2 sideband
spectrometer. In the Doppler-limited wide-scan mode, frequency tunability has been
greatly improved via generation of microwave sidebands by hot and sequence band CO2
laser lines as well as high-/ lines of the 9.6 pm P branch. The almost continuous spectral
coverage will be valuable for spectral searching and providing overall spectral patterns to
facilitate assignment. In the second mode of operation of this spectrometer, the sidebands
have been successfully applied in observations of sub-Doppler saturation-dip spectra for
methanol (CH3 OH). This demonstrates the potential of the instrument for spectroscopic
measurements at sub-MHz resolution for molecules with vibrational transition moments
comparable to methanol. The frequencies for 20 CH3 OH absorption lines in the C-0
stretching band were measured with a precision of order ±200 kHz, adding to the
reference data set of accurately known CH3 OH infrared frequencies. The new lines
include a number of ^-doublets in the ground and first excited torsional states with very
small asymmetry splittings completely inaccessible to Doppler-limited observations. It
can be seen that, with the inter-compensate function between its two operational modes,
this spectrometer has great potential for spectroscopic studies, the study of CCVpumped
far-infrared lasers, and application in pollutant remote sensing. If operation of the laser
could also be extended to isotopic CO2 species such as 12C 180 2 , l3 C 18 C>2 and 13C1602 to
generate microwave sidebands, this would represent dramatic progress towards the
138
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
ultimate goal of fully tunable spectral coverage over the whole 9-12 pm mid-infrared
region.
139
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
References
[1] M.C.L. Gerry, Some Things We Can Do with Cavity-Pulsed Microwave Fourier
Transform Spectrometers, SPIE Proceedings, 2089, 9th International Conference on
Fourier Transform Spectroscopy (1994).
[2] W. Gordy, Rev. Mod. Phys. 20, 668-717 (1948).
[3] C. E. Cleeton and N. H. Williams, Phys. Rev. 45,234-237 (1934)
[4] W. Gordy, W.V. Smith and R.F. Trambarulo, Microwave Spectroscopy, Wiley, New
York, 1953. Republication by Dover, New York (1966).
[5] C.C. Lin and J.D. Swalen, Rev. Mod. Phys. 31, 841-892 (1959).
[6 ] W. Gordy and R.L. Cook, Microwave Molecular Spectra, Wiley, New York (1968).
[7] A.C. Legon, Ann. Rev. Phys. Chem. 34, 275-300 (1983).
[8 ] E. Hirota and Y. Endo, Chapter 1 of Vibration-Rotational Spectroscopy and
Molecular Dynamics, World Scientific (1997).
[9] P. Thaddeus and M.C. McCarthy, Spectrochim Acta A. 57, 757-774 (2001).
[10] Y. Kawashima, T. Usami, K. Ohba, R.D. Suenram, G.Yu. Golubiatnikov, and E.
Hirota, 58th International Symposium on Molecular Spectroscopy, Columbus, Ohio
(2003).
[11] Y. Kawashima, R.D. Suenram, and E. Hirota, J. Mol. Spectrosc. 219,105-118
(2003).
[12] FJ. Lovas and R.D. Suenram, J. Chem. Phys. 87, 2010-2020 (1987).
[13]G.T. Fraser, A.S. Pine, and R.D. Suenram, J. Chem. Phys.
88
, 6157-6167 (1988).
[14] T. Ogata and F J. Lovas, J. Mol. Spectrosc. 162, 505-512 (1993).
140
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
[15JD.F. Plusquellic, R.D. Suenram, B. Mate, J.O. Jensen, and A.C. Samuels, J. Chem.
Phys. 115, 3057-3067 (2001).
[16] R.D. Suenram, Fourier Transform Microwave Spectroscopy: Historical Perspective
and the Evolution Toward an Analytical Technique, Newsletter of BaltimoreWashington Section of the Society for Applied Spectroscopy (1999).
(www.spectrometer.org/bwsas/ nov99sas.html)
[17] R.D. Suenram, F.J. Lovas, D.F. Plusquellic, A. Lesarri, Y. Kawashima, J.O. Jensen,
and A.C. Samuels, J. Mol. Spectrosc. 211, 110-118 (2002).
[18] M.A. Temsamani, Ph.D. Thesis, Universite Libre de Bruxelles, Bruxelles, Belgium
(1996).
[19] H. Burger and W. Thiel, Chapter 2 of Vibration-Rotational Spectroscopy and
Molecular Dynamics, World Scientific (1997).
[20] I.M. Mills and A.G. Robiette, Mol. Phys. 56, 743-765 (1985) and references therein.
[21] L. Hermans-Killam, Infrared Astronomy, Educational website of the Infrared
Processing and Analysis Center (IPAC) operated by the California Institute of
Technology, Jet Propulsion Laboratory (JPL) under contract to the National
Aeronautics and Space Administration (NASA). (2003).
(http://www.ipac.caltech.edu/Outreach/Edu/outreach.html)
[22] D.M. Sonnenfroh, E.J. Wetjen, M.F. Miller, M.G. Allen, C. Gmachl, F. Capasso,
A.L. Hutchinson, D.L. Sivco, J.N. Baillargeon, and A.Y. Cho, Mid-IR Gas Sensors
Based on Quasi-CW, Room-Temperature Quantum Cascade Lasers, AIAA 20000641, presented at 38th AIAA Aerospace Sciences Meeting and Exhibit, Reno,
Nevada (2000).
141
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
[23] P.K. Cheo, Z. Chu, L. Chen and Y. Zhou, Appl. Opt. 32, 836-841 (1993).
[24] D. Richter, A. Fried, B.P. Wert, J.G. Walega, F.K. Tittel, Appl. Phys. B 75, 281-288
(2002).
[25] P.K. Cheo, IEEE J. Quantum Electron. QE-2G, 700-709 (1984).
[26]Z.D. Sun, F. Matsushima, S. Tsunekawa, and K. Takagi, J. Opt. Soc. Am. B 17,
2068-2080 (2 0 0 0 ).
[27] G. Magerl, J.M. Frye, W.A. Kreiner, and T. Oka, Appl. Phys. Lett. 42, 656-658
(1983).
[28] O. Pfister, F. Guemet, G. Charton, Ch. Chardonnet, F. Herlemont, and J. Legrand, J.
Opt. Soc. Am. B 10, 1521-1525 (1993).
[29] P. Pracna, K. Sarka, J. Demaison, J. Cosleou, F. Herlemont, M. Khelkhal, H.
Fichoux, D. Papousek, M. Paplewski, and H. Burger, J. Mol. Spectrosc. 184, 93-105
(1997).
[30] M. Miirtz, B. Freeh, P. Palm, T. Lotze, and W. Urban, Opt. Lett. 23, 58-60 (1998).
[31]K.M. Evenson, C.-C. Chou, B.W. Bach, and K.G. Bach, IEEE J. Quantum Electron.
30, 1187-1188(1994).
[32] Z.D. Sun, R.M. Lees, L.-H. Xu, M.Yu. Tretyakov, and I. Yakovlev, Int. J. Infrared
Millimeter Waves 23, 1557-1574 (2002).
[33] Gaussian 98, Revision A. 6, M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria,
M.A. Robb, J.R. Cheeseman, V.G. Zakrzewski, J.A. Montgomery, Jr., R.E.
Stratmann, J.C. Burant, S. Dapprich, J.M. Millam, A.D. Daniels, K.N. Kudin, M.C.
Strain, O. Farkas, J. Tomasi, V. Barone, M. Cossi, R. Cammi, B. Mennucci, C.
Pomelli, C. Adamo, S. Clifford, J. Ochterski, G.A. Petersson, P.Y. Ayala, Q. Cui, K.
142
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Morokuma, D.K. Malick, A.D. Rabuck, K. Raghavachari, J.B. Foresman, J.
Cioslowski, J.V. Ortiz, B.B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I.
Komaromi, R. Gomperts, R.L. Martin, D J. Fox, T. Keith, M.A. Al-Laham, C.Y.
Peng, A. Nanayakkara, C. Gonzalez, M. Challacombe, P.M.W. Gill, B. Johnson, W.
Chen, M.W. Wong, J.L. Andres, C. Gonzalez, M. Head-Gordon, E.S. Replogle, and
J.A. Pople, Gaussian, Inc., Pittsburgh PA (1998).
[34] W.J. Hehre, L. Radom, and P.v.R. Schleyer, J.A. Pople, ab initio Molecular Orbital
Theory. John Wiley & Sons, Inc. (1986).
[35] J.B. Foresman, and JE. Frisch, Exploring Chemistry with Electronic Structure
Methods, Second Edition, Gaussian, Inc., (1993,1995-96).
[36] F. Brouwer, Quantum chemistry in molecular modeling, University of Amsterdam
(1995). (http://www.caos.kun.nl/~borkent/compcourse/ffed/ch510.html)
[37] R.D. Suenram, J.U. Grabow, A. Zuban, and I. Leonov, Rev. Sci. Instrum. 70,21272135 (1999), and references therein.
[38] U. Andresen, H. Dreizler, J.U. Grabow, and W. Stahl, Rev. Sci. Instrum. 61, 36943699 (1990).
[39] A.E. Derome, Modem NMR Techniques fo r Chemistry Research, Pergamon (1987).
[40]R.S. Ruoff, T.D. Klots, T. Emilsson, and H.S. Gutowsky, J. Chem. Phys. 93, 31423150(1990).
[41] H. Yoshida, T. Harada and H. Matsuura, J. Mol. Struct. 413-414, 217-226 (1997).
[42] E.-M. Sung and M.D. Harmony, J. Am. Chem. Soc. 99, 5603-5608 (1977).
[43] K.-M. Marstockk, H. Mollendal, and E. Uggerud, Acta Chem. Scand. 43, 26-31
(1989).
143
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
[44] H. Yoshida, T. Harada, T. Murase, K. Ohno and H. Matsuura, J. Phys. Chem. A,
101, 1731-1737 (1997).
[45] G.A. Jeffrey and W. Saenger, Hydrogen Bonding in Biological Structures, SpringerVerlag, Berlin (1991).
[46] Private communication with R.D. Suenram, National Institute of Standards and
Technology.
[47] XII. Geometry data, Computational Chemistry Comparison and Benchmark
DataBase (CCCBD), official website of National Institute of Standards and
Technology, (2003). (http://srdata.nist.gov/cccbdb/)
[48] P.Y. Ayala andH.B. Schlegel, J. Chem. Phys. 108, 2314-2325 (1998).
[49]E.B. Wilson, J.C. Decius, and P.C. Cross, Molecular Vibrations, Dover, New York,
McGraw-Hill (1955).
[50] Program GMATPC is Schachtschneider’s GMAT modified to work on a PC, as
provided by Professor J. Bertie, University of Alberta.
[51 ] Private communication with J. Bertie, University of Alberta.
[52] Moment program to calculate the principal axes, as provided by F.J. Lovas, National
Institute of Standards and Technology.
[53] Integrated Spectral Data Base System for Organic Compounds (SDBS), National
Institute of Advanced Industrial Science and Technology of Japan, (2001).
(http://www.aist.go.jp/RIODB/SDBS/)
[54] J.B. Lambert, H.F. Shurvell, D.A. Lightner, and R.G. Cooks, Introduction to
Organic Spectroscopy, Macmillan Publishing Company (1987).
[55] W.H. Shaffer and B.J. Krohn, J. Mol. Spectrosc. 63,323 (1976).
144
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
[56] M.A. Temsamani, L.-H. Xu and D.S. Perry, Can. J. Phys. 79, 467-477 (2001).
[57] L-H, Xu and J.T. Hougen, J. Mol. Spectrosc. 173, 540-551 (1995).
[58] N. Moazzen-Ahmadi, E. Kelly, J. Schroderus, and V.-M. Homeman, J. Mol.
Spectrosc. 209, 228-232 (2001).
[59] Xm. Vibration data. Computational Chemistry Comparison and Benchmark
DataBase (CCCBD), official website of National Institute of Standards and
Technology, (2003). (http://srdata.nist.gov/cccbdb/)
[60] Lemelson-MIT Program, Inventor o f the Week Archive, School of Engineering,
Massachusetts Institute of Technology, (2000).
(http://web.mit.edu/invent/iow/patel.html)
[61] S. Carpenter, AU About Lasers, Department of Physics, Davison College.
(http://www.phy.davidson.edu/StuHome/sethvc/Laser-Final/co2.htm)
[62] L.-H. Xu, R.M. Lees, K.M. Evenson, C.-C. Chou, J.-T. Shy, and E.C.C.
Vasconcellos, Canad. J. Phys. 72, 1155-1164 (1994).
[63] A. G. Maki, C.-C. Chou, K. M. Evenson, L. Zink, and J.-T. Shy, J. Mol. Spectrosc.
167,211-224(1994).
[64] P.K. Cheo, Generation and Applications o f 16 GHz Tunable Sidebands from a COj
Laser, J.L. Hall and J.L. Carlsten, Laser Spectroscopy III., Proceedings of the Third
International Conference, Jackson Lake Lodge, Wyoming, USA, Springer-Verlag
(1997).
[65] S, Zhao, Ph. D. Thesis, U. of New Brunswick, Canada (1993).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
[6 6 ] G. Moruzzi, B.P. Winnewisser, M. Winnewisser, I. Mukhopadhyay, and F. Strumia,
Microwave, Infrared and Laser Transitions o f Methanol, CRC Press: Boca Raton,
Fla. (1995).
[67] Z.D. Sun, S. Ishikuro, Y. Moriwaki, F. Matsushima, S. Tsunekawa and K. Takagi, J.
Mol. Spectrosc. 211 162-166 (2002).
[6 8 ] Z.D. Sun, Ph. D. Thesis and references therein, U. of Toyama, Japan (2000).
[69] K. Shimoda, High-Resolution Laser Spectroscopy, Topics in Applied Physics,
Volume 13, Springer-Verlag (1976).
[70] A.G. Maki and J.S. Wells, Wavenumber Calibration Tables From Heterodyne
Frequency Measurements, NIST Special Publication 821, US Government Printing
Office, Washington (1991).
[l\]Microcal Origin, Version 6.0, Microcal Software, Inc.
[72] V.S. Letokhov and V.P. Chebotayev, Nonlinear Laser Spectroscopy, Springer Series
in Optical Sciences, Springer-Verlag (1977).
[73] W.S. Struve, Fundamentals o f Molecular Spectroscopy, John Wiley & Sons, Inc.
(1989).
[74] L.-H Xu and F.J. Lovas, J. Phys. Chem. Ref. Data 26 17-156 (1997), and references
therein.
146
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CURRICULUM VITAE
Candidate's foil name:
Qiang Liu
Place and date of birth:
Baoding, Hebei, P.R.China
May 14, 1974
Universities attended:
Beijing Normal University, Beijing, P.R. China,
1993-1997
Refereed Journal Publications:
1. R.D. Suenram, D.F. Plusquellic, A.R. Hight Walker, Qiang Liu, Li-Hong Xu, J.O.
Jensen and A.C. Samuels, “Rotational Spectra, Conformational Structure and
Dipole Moment of 2-(Ethylthio)ethanol by Jet-Cooled FTMW and Ab initio
Calculation,” J. Mol. Spectrosc. (Accepted, July, 2003).
Conference Abstracts (presented by underline author):
1. Zhen-Dong Sun, Qiang Liu, V. Dorovskikh, M.Yu. Tretyakov, R.M. Lees, and LiHong Xu, “CO2/MWSB Generation with High-J, Sequence, and Hot Band CO2
Laser Lines and Broad-Band Scan Capability,” Annual Congress, Canadian
Association of Physicists, Charlottetown, June 8-11 (2003). [Abstract in Phys. In
Canada 59, 58 (2003)].
2. Zhen-Dong Sun, Qiang Liu, V. Dorovskikh, M.Yu. Tretyakov, R.M. Lees, and LiHong Xu, “CO2/MWSB Generation with High-J, Sequence, and Hot Band CO2
Laser Lines and Broad-Band Scan Capability,”, 58th Int. Symp. on Molecular
Spectroscopy, Columbus, Ohio, June 16-20 (2003). [Paper RD10].
3. Zhen-Dong Sun, V. Dorovskikh, Qiang Liu, M.Yu. Tretyakov, R.M. Lees, and LiHong Xu, “Dual-Mode CO2 -Laser/Microwave-Sideband Spectrometer with
Broadband and saturation Dip Detection,” CIPI/NCE 4th Annual Scientific
Meeting, Edmonton, June 19-21 (2003). [Paper ENV-6 ].
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
4. Qiang Liu, Li-Hong Xu, R.D. Suenram, D.F. Plusquellic, F.J. Lovas, A.R. Hight
Walker, J.O. Jensen and A.C. Samuels, “Rotational Spectra, Conformational
Structures and Dipole Moments of Hydroxyethyl Ethyl Sulfide by Jet-Cooled
FTMW and Ab Initio Calculation,” Symposium on Chemical Physics, University
of Waterloo, Oct. 25-27( 2002).
5. Qiang Liu. Li-Hong Xu, R.D. Suenram, D.F. Plusquellic, A.R. Hight Walker, J.O.
Jensen and A.C. Samuels, “FTMW and Ab initio Studies of Conformations and
Structures for HOEES - A Mustard Gas Hydrolysis Product,” Annual Congress,
Canadian Association of Physicists, Quebec City, Quebec, June 2-5 (2002).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Документ
Категория
Без категории
Просмотров
0
Размер файла
11 652 Кб
Теги
sdewsdweddes
1/--страниц
Пожаловаться на содержимое документа