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Microwave spectroscopy and computational studies of multi-top internal rotation molecules, highly unsaturated transient molecules, and free radicals

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Wesleyan University
Microwave Spectroscopy and Computational Studies
of Multi-Top Internal Rotation Molecules, Highly
Unsaturated Transient Molecules, and Free Radicals
By
Lu Kang
A dissertation submitted to the faculty of Wesleyan University in partial fulfillment of
the requirements for the degree o f Doctor of Philosophy in Chemical Physics
^
Middletown, Connecticut, USA. April 2003 M
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UMI Number: 3127557
IN F O R M A T IO N T O U S E R S
T h e q u a lity o f th is re p ro d u c tio n is d e p e n d e n t u po n th e q u a lity o f th e co py
s u b m itte d . B ro k e n o r in d istin ct print, c o lo re d o r p o o r q u a lity illu stratio n s an d
p h o to g ra p h s , print b le e d -th ro u g h , s u b s ta n d a rd m a rg in s , a n d im p ro p e r
a lig n m e n t c a n a d v e rs e ly a ffe c t re p ro d u c tio n .
In th e u n lik e ly e v e n t th a t th e a u th o r did not s e n d a c o m p le te m a n u s c rip t
a n d th e re a re m issin g p a g e s , th e s e will b e n o te d . A ls o , if u n a u th o riz e d
c o p y rig h t m a te ria l h a d to b e re m o v e d , a n o te will in d ic a te th e d e le tio n .
UMI
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All rights re s e rv e d . T h is m ic ro fo rm ed itio n is p ro te c te d a g a in s t
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P ro Q u e s t In fo rm a tio n a n d L e a rn in g C o m p a n y
3 0 0 N orth Z e e b R o a d
P .O . B o x 1 3 4 6
A n n A rb o r, M l 4 8 1 0 6 - 1 3 4 6
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ACKNOWLEDGEMENTS
I would like to thank those people who help me generously throughout my career
at Wesleyan. I deeply appreciate their support, cooperation, and companionship in the
past six years. It is unlikely that I could have succeeded without their many efforts on
my behalf. I wish to thank them all at this moment.
ADVISOR
Professor Stewart E. Novick
COMMITTEE MEMBERS
Professor Joseph L. Knee
Professor Lutz Hiiwel
WESLEYAN FAULTY
Professor Wallace C. Pringle
Professor George A. Petersson
Professor Brian Stewart
Professor Kara Beauchamp
Professor Ralph Baierlein
Professor Robert J. Rollefson
Professor Fred M. Ellis
Professor Thomas J. Morgan
VISITORS AND COLLABORATORS
Professor Robert K. Bohn
Karissa G. Utzat
Geoffrey B. Churchill
Dr. Jens-Uwe Grabow
Professor James M. LoBue
Professor Patrick Thaddeus
Professor Stephen G. Kukolich
Dr. Michael C. McCarthy
Dr. James R. Cheeseman
Dr. John Dudek
Dr. John A. Montgomery, Jr.
Dr. Mark R. Nimlos
Dr. Michael Frisch
Dr. Yongxing Liu
Dr. James S. Hess
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CHEM ISTRY AND PHYSICS STAFF AND GRADUATE OFFICE
Lucile H. Blanchard
Anna Marie Milardo
Karen N. Karpa
Holly P. Castelli
Donald F. Albert
William S. Nelligan
Douglas Allen
Marina Melendez
Barbara Schukoske
WESLEYAN ELECTRONIC SHOP, MACHINE SHOP, AND ITS
Miroslaw J. Koziol
David H. Boule
Richard A. Widlansky
Tomas A. Castelli
Bruce Strickland
Shawn Hill
LABMATES
Dr. Wei Chen
Dr. Michaeleen R. Munrow
Dr. Ranganathan Subramanian
Wei Lin
D. Scott McCracken
Jodi Szarko
Edwin Saul Contreras
Eunice Li\
Jessica Schlier
I want to give special thanks to my advisor, Professor Stewart E. Novick, for his
guidance, understanding, and concern about my research work over the years. I am
deeply impressed by his wisdom, open mind, and dedication to science. His profound
knowledge and easygoing personality help me to cross the gap smoothly between
being a student and a scientist. It is my expectation that some day in the future I can
follow his example.
I am indebted to Professor Pringle and Professor Bohn for their support, advice,
and consultations. Their encouragement and friendship help me pass the harsh time in
ray research. Pete’s style of humor makes me realize that there is more to life than
just tedious experimental work.
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I am very grateful to Professor Knee and Professor Hiiwel for what they have
done on my proposal and my thesis. Their constructive comments, patient guidance,
and enthusiasm strengths my desire to be a scientist.
I would like to thank Dr. Grabow, Professor Thaddeus, Dr. McCarthy, Professor
Kukolich, Professor Petersson, Dr. Cheeseman, Dr. Montgomery, Jr., Dr. Hess, and
Dr. Frisch for their great help, consultations, and collaborations.
For their effort on my behalf I would like to thank Don, Bill, Doug, Lucile, Anna,
Holly, Karen; the electronic shop, Miroslaw; the machine shop, David, Dick, Bruce,
Tom; ITS, Shawn; and the graduate office, Marina and Barbara.
I thank my labmates and friends Wei Chen, Missy, Ranga, Wei Lin, Karissa,
Edwin, Scott, Jodi, Jessica, Eunice, Xiangyang, Naixin, Yongxing, Hari Babu, Jerom,
Jake, Jason, Rajesh, Ingrid, Xin, Yunting, Shijun, Congju, Wei Ou, Kevin, Eric,
Yong, Hong, Sergei, David, Thomas, Tom, and Paula for their steering guidance,
collaboration, and friendship. Especially, Yongxing, w ith his great patience, taught
me hand by hand to become a computer DIYer.
Finally, I would like to thank my wife, Xinmeng for her great understanding and
support in hard time. Thanks to my family for their love and caring.
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Dedicated to my family
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PREFACE
This thesis is a summary of my achievements in the study o f three different types
of molecular systems using Fourier Transform Microwave (FTMW) spectroscopy and
ab initio computational methods in Novick’s laboratory of the Southern New England
Microwave Consortium. The three different types of molecular systems include:
molecules with multiple tops undergoing hindered internal rotation, highly
unsaturated carbon chain molecules, and unstable free radicals. For ease of
understanding, this thesis is divided into four sections.
Section I is a brief introduction to rotational spectroscopy, including chapters 1
and 2. Chapter 1 explores the electronic and nuclear motions in a molecule,
particularly, the internal nuclear motions including rotation and vibration, which can
be studied by high resolution spectroscopy. Chapter 2 introduces fine and hyperfine
structures o f the rotational spectrum which are due to electronic spin - molecular
overall rotation interaction, (S*N), nuclear quadrupole coupling interaction, (IT),
nuclear magnetic dipole - molecular overall rotation interaction, (I-N), and electronic
spin - nuclear spin interaction, (I*S). This section briefly but not rigorously illustrates
those concepts that we will frequently encounter in the following chapters. The theory
about multi-top internal rotation is not included since detailed descriptions are given
in chapters 3 and 4. Readers with a fairly good background knowledge of rotational
spectroscopy can skip section I.
Section II, which includes chapters 3 and 4, involves the microwave spectroscopy
of molecules with multiple tops undergoing hindered internal rotation. Chapter 3,
with the title “Rotational Spectra o f Argon Acetone: A Two-Top internally Rotating
Complex ”, is a d raft form o f a p aper which appeared in the Journal o f Molecular
Spectroscopy 213, 122-129, (2002). The rotational constants, centrifugal distortion
constants, and torsional constants, as well as molecular structure were reported.
Chapter 4 is a manuscript in preparation for rotational spectroscopy o f molecules with
three-tops
undergoing
hindered
internal
rotation.
These
molecules
-I-
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are:
Trimethylsilane,
(CH3) 3SiH,
Trimethylsilylethyne,
(CH3)3SiCCH,
and
TrimethylsilyIbutadiyne, (CH 3)3SiCCCCH, as well as some of their silicon isotopic
species. A clearly distinguished, fully resolved spectrum with three-top torsional
hyperfine splittings is presented in chapter 4.
Section III, which includes chapters 5 and
6,
is about the spectroscopic and
quantum computational studies of highly unsaturated transient molecules. All the
molecules presented in this section are generated with a pulsed discharge nozzle
(PDN). Chapter 5, with the title of "Microwave Spectra o f Four New Perfluoromethyl
Polyyne
Chains:
Trifluoropentadiyne,
CF3 CCCCH,
Trifluoroheptatriyne,
CF3 CCCCCCH, Tetrafluoropentadiyne, CF3 CCCCF, and Trifluoromethylcyanoacetylene, CF3 CCCN”, is a draft form of a paper which appeared in the Journal o f
Physical Chemistry A, 106,3749-3753, (2002). The measured molecular constants are
in excellent agreement with our ab initio predictions. The molecular structure of
CF3CCCCH was determined based on the spectra of its isotopic species observed in
natural abundance. Chapter
6,
with the title of "Microwave Spectrum o f
Cyanophosphine, H 3PC N ”, is a manuscript in preparation for Chemical Physics
Letters. The molecular constants, the quadrupole coupling constants of
{%aa, 'hb,
Xcc), and the nuclear spin - molecular overall rotation (I-J) coupling constants of
(Caa, Cm, Ccc), were determined. The spectra of its ' ^C and
isotopomers were
observed. The measured molecular structure and spectroscopic constants are in
excellent agreement with ab initio predictions.
Section IV is about the microwave spectroscopy and computational studies of
unstable free radicals (open shell systems) and includes chapters 7 and
8.
We
fortunately had the opportunity to collaborate with Gaussian Inc. to develop a new
program package to handle the fine and hyperfine constants, which has recently been
released on Gaussian03. The performance of this new program package is shown
here. Chapter 7, with the title of "Microwave Spectroscopy o f 1,1 -Difluoropropargyl
Radical, HCCCF 2, in the
Ground Electronic State ”, is a manuscript in
preparation for the Journal o f Chemical Physics. The measured rotational constants
-II-
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and centrifugal distortion constants are in excellent agreement with ab initio
predictions. The measured fine and hyperfine constants are in good agreement with
our ab initio predictions. The small, but negative inertia defect,
-0.085147(44)
amuA^ implies that HCCCFi possesses a planar or quasiplanar structure. The
consistency o f the measured and the predicted molecular constants, as well as the
structural and physical similarities with 1,1-Difluoroallene, [H2C==C=CF2], imply
that the allenyl form, 3,3-Difluoropropadienyl, [HC= 0 =CF2], makes a significant
contribution to the resonance structure [HC=C—CF2 ^
HC==0 =CF2]. Chapter
introduces our most recent progress on the studies of the deuterated
8
1,1-
Difluoropropargyl radical, DCCCF 2, the Cyanodifluoromethyl radical, CF2 CN, and
the Cyanomethyl radical, H 2CCN. About 20 and 50 paramagnetic transitions for
DCCCF 2 and CF2CN have been detected and identified, respectively. A list of
measured frequencies of H2CCN in the 20 GHz frequency regions is provided for
ease o f reference. All work presented in chapter
8
is preliminary and is included to
facilitate further study.
In summary, 1complex, 20 molecules (including isotopic species) and 1 radical
have been studied and fully resolved; 3 radicals have been detected and identified.
They are:
Molecule with two-tops undergoing hindered intemal rotation.
Argon Acetone complex: A r— (CH3)2O
=0
Molecules with three-tops undergoing hindered intemal rotation,
Trimethylsilane: (CH3)3^*SiH, (CH 3)3^^SiH, (CH 3)3^°SiH
Trimethylsilylethyne: (CH 3)3^®SiCCH, (CH3)3^^SiCCH, (CH 3)3^®SiCCH
Trimethylsilylbutadiyne: (CH 3)3SiCCCCH
Perfluoromethyl polyyne chains,
Trifluoropentadiyne: CF3CCCCH, CF3CCCCD, CFaCCC’^CH, CFsCC’^CCH,
CFsC'^CCCH, CFj’^CCCCH, ‘^CFsCCCCH
-Ill-
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Trifluoroheptatriyne: CF3CCCCCCH
Tetrafluoropentadiyne: CF3CCCCF
Trifluoromethylcyanoacetylene: CF3CCCN
Astronomically interesting molecules,
Cyanophosphine: HjPCN, HjP'^CN, HaPC'^N
Unstable free radical,
1,1 -Difluoropropargyl Radical: HCCCF2
Detected and identified unstable free radicals,
Deuterated 1,1-Difluoropropargyl Radical: DCCCF2
Cyanodifluoromethyl radical: CF2CN
Cyanomethyl radical: H 2CCN
Beyond the spectroscopic studies, our collaboration with Gaussian Inc. resulted in
a new functional package that can handle fine and hyperfine constants. It has been
released on Gaussian03. A new dimension, ab initio calculation, has been introduced
to our lab. The Gaussian program package was installed on my specially designed and
self assembled (DIY) workstation, which was particularly optimized for scientific
computation.
Finally, these achievements owed much to my advisor, Professor Stewart E.
Novick, without his down to earth support, it would have been impossible for me to
reach this stage in my scientific career.
-IV-
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Table of Contents
Section I:
A Brief Introduction to High Resolution Rotational Spectroscopy
Chapter 1: Quantum and Classical Descriptions of Molecular M otions.......................1
§1.0
Introduction..................................................................................................... 2
§ 1.1
The Separation of Electronic and Nuclear M otions..................................... 3
§ 1.2
The Separation of Nuclear M otions.............................................................. 6
§1.3
Non-rigid Rotors (Harmonic Oscillator)..................................................... 12
§ 1.4
Selection R ules
§ 1.5
Rotational Spectroscopy of Polyatomic molecules.................................... 18
..................................................................................... 16
Chapter 2: Fine and Hyperfine Structures o f Rotational Spectrum.............................28
§ 2.0
Introduction...................................................................................................29
§ 2.1
Nuclear Quadruple Coupling Interaction................................................... 30
§ 2.2
Magnetic Hyperfme Structure..................................................................... 36
§ 2.3
Fine and Hyperfine Structures of Open-Shell System .............................. 38
Section II: Microwave Spectroscopy of Molecules with Multiple Tops
Undergoing Hindered Internal Rotation
Chapter 3: Rotational Spectra of Argon Acetone: A Two-Top Internally Rotating
Complex
....................................................................................................................
43
Abstract......................................................................................................... 44
Introduction...................................................................................................45
Experimental.................................................................................................47
Two top intemal rotation.............................................................................48
Results and analysis..................................................................................... 50
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References (tables and figures).................................................................... 54
Reference.......................................................................................................65
Chapter 4: Rotational Spectroscopy ofMolcules with Three Tops Undergoing
Intemal Rotation: The Microwave Spectra of Trimethylsilane, (CH 3)3 SiH,
Trimethylsilylethyne, (CH3)3SiCCH, and Trimethylsilylbutadiyne,
(CH 3)3SiCCCCH
.........................................................................................
69
A bstract..........................................................................................................70
Introduction................................................................................................... 71
Experimental................................................................................................. 73
Three top intemal rotation........................................................................... 75
Spectra and analysis......................................................................................77
Conclusion.................................................................................................... 79
Reference (tablesand figures)...................................................................... 80
Reference.......................................................................................................89
Section III: Spectroscopic and Quantum Computational Studies of Highly
Unsaturated Transient Molecules (Closed Shell Systems)
Chapter 5: Microwave Spectra o f Four New Perfluoromethyl Polyyne Chains:
Trifluoropentadiyne, CF3CCCCH, Trifluoroheptatriyne, CF3CCCCCCH,
Tetrafluoropentadiyne, CF3CCCCF, and Trifluoromethylcyanoacetylene,
CF3CCCN
......................................................................................................................... 91
A bstract......................................................................................................... 92
Introduction................................................................................................... 93
Experimental................................................................................................. 95
R esults............................................................................................................98
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Disscussion.......................................
100
Summary...................................................................................................... 103
Acknowledgement...................................................................................... 103
References (tables and figures)...............................................................—104
References and notes................................................................................... 117
Appendix.......................................
120
Chapter 6 : Microwave Spectrum of Cyanophosphine, HaPCN..................................126
Abstract........................................................................................................ 127
Introduction..................................................................................................128
Experimental
—..........
129
ab initio prediction...................................................................................... 131
Assignment and analysis.............................................................................132
Discussion....................................................................................................134
Acknowledgement...................................................................................... 136
References (tables and figures)..................................................................137
Reference.....................................................................................................148
Section IV: Microwave Spectroscopy and Quantum Computational Studies of
Free Radicals (Open Shell Systems)
Chapter 7: Microwave Spectroscopy o f 1,1 -Difluoropropargyl Radical, HCCCF 2, in
the ^Bi Ground Electronic State
........................................................................................................................150
Abstract........................................................................................................151
Introduction..................................................................................................152
Computational m ethods............................................................................. 155
Experiment...................................................................................................157
Analysis..............................................................................................
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159
Discussion.................................................................................................... 161
Acknowledgements..................................................................................... 164
References (tables and figures).................................................................. 165
Reference..................................................................................................... 174
Chapter 8 : Computational and Rotational Spectroscopic Studies o f Free Radicals;
Deuterated 1,1 -Difluoropropargyl, DCCCFa, Cyanodifluoromethyl,
CFjCN, and Cyanomethyl, HaCCN
.............................................................
177
§ 8.0 Introduction.................................................................................................. 178
§ 8. 1
Deuterated
1, 1 -Difluoropropargyl
radical, DCCCFa................................ 179
§ 8.2 Cyanodifluoromethyl, CF2C N ....................................................................182
§8.3 Cyanomethyl, H 2C C N ................................................................................ 186
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Section I
A Brief Introduction to High Resolution Rotational Spectroscopy
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CH A PTER ONE
Quantum and Classical Descriptions of Molecular Motions
-
1
-
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§1.0
INTRODUCTION
This chapter explores the electronic and nuclear motions in a molecule. Special
attention is given to the quantum and classical descriptions of intemal nuclei motions
including rotation and vibration, with which high resolution spectroscopy associate.
My purpose is to help the reader become familiar with frequently used expressions,
concepts, and labels that will appear in the following chapters without losing too
much theoretical completeness and consistency. Diatomic molecules, being the
simplest case, are explored in detail from § 1.2 to § 1.4 in order to introduce some
important concepts o f molecular spectroscopy. Analytical solutions for diatomic
molecular rotational and vibrational wave functions are available. § 1.1 introduces the
separation of electronic and nuclear motions under the framework of the BomOppenheimer approximation. § 1.2 investigates the separation o f nuclei translational,
rotational, and vibrational motions. The analytic solutions for nuclear rotational and
vibrational wave functions are also included in this section. § 1.3 explores the
definitions and relationship of many molecular spectroscopic expressions, concepts,
and labels. § 1.4 investigates the selection mles for rotational and vibrational
transitions. § 1.5 focuses on the descriptions of multi-atom molecular rotation in
varied c ases i ncluding 1inear, s ymmetric t op, and a symmetric top m olecules. M ore
detailed discussions about molecular spectroscopy can be obtained from those
references listed at the end of this chapter.
-
2-
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§ 1.1
THE SEPARATION OF ELECTRONIC AND NUCLEAR MOTIONS
A molecule is composed of nuclei and electrons. To a good approximation, those
nuclei and electrons can be treated as mass points in molecular spectroscopy. If we
neglect hyperfine and relativistic interactions, then the molecular Hamiltonian can be
written as:
I
or
i
^ ia
<
J>i ^ij
^
a
a
p> a
where a and P refer to nuclei, and i and j refer to electrons. m« and me refer to the
mass o f nucleus a and electrons. Z« and Zp refer to the atomic numbers for nuclei a
and p. q„,q^, -■ and q,.,q^, ••• symbolize the nuclear and electronic coordinates,
respectively[l]. Equation [1.2] is the abbreviation of [1.1]. The first term in equation
[ 1 . 1 ] and [ 1 .2 ], ^ ( q , ) , is the kinetic-energy operator for electronic motions; the
second term, iF^(q,.;q„), represents potential-energy due to the attractions between
electrons and nuclei,
=| q, - q „ | being the distance between electron i and nucleus
a; the third term, F^^(q,.,q^), represents the potential-energy due to the repulsions
between electrons,
=| q,. -q y | being the distance between electrons i and j\ the
fourth term, f^ (q ^ ), is the kinetic-energy operator for nuclear motions; the last term,
F^^(q^,q^), represents the potential-energy due to the repulsions between nuclei.
Tap =1 fia
I being the distance between nuclei a m d p .
The wave function and energy of a molecule are given by Schrddinger equation:
=
[1-3]
Theoretically speaking, the wave function T'(q,,q^.,---;q«,q^.*--) contains all the
information about molecular motions. Unfortunately, solving Schrddinger equation
[1.3] analytically with a complicated Hamiltonian like [1.1] without approximation is
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not possible. Technically speaking, a practical way to proceed is to obtain a well
behaved approximate wave function by making a reasonable approximation for the
solution o f the Schrodinger equation[l]. Fortunately, the Bom-Oppenheimer
approximation is the answer for the purpose! The idea lies in the fact that the nuclei
are much more massive than electrons, i.e.
» me- Electrons move so fast that the
nuclei displacements from the equilibrium configuration are negligible compared to
the electronic motion. Hence, to a good approximation, the electronic motion and
nuclear motion can be treated separately. The nuclei configuration is considered fixed
as far as the electron motion is concerned. Therefore, the nuclei energy (the last two
terms in equation [1.1]) is a constant under the fixed nuclei skeleton. Since the
omission o f a constant term
eigenvalue by
from the Hamiltonian only decrease each energy
and does not affect the wave fimctions, we can define an electronic
Hamiltonian:
ti.4]
H e,= t (q ,)+ K n (q,-;
) + Ke (q,-» )
[i-5]
Equation [1.5] is the abbreviation of [1.4]. The pure electronic kinetic-energy Eei is
obtained by electronic Schrddinger equation:
=
[i- 6 ]
where q„, ••• are introduced to the electron wave function as parametric dependent
variables, and are generally treated as constants[2]. The “true” variables in the
electronic Schrddinger equation [1.6] are the electronic coordinates q,,qy,---.
Explorations o f Egi and qP^(q,,q,.,---;qa>‘” ) are the favorite topics for electronic
spectroscopists and quantum computational theoreticians. The Eei can be derived from
electronic spectroscopy experiments. A good approximation of 'F^,(q,.,q^-,---;qa,-")
might be obtained from quantum theoretical computations (ab initio calculations).
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In the r esearch o f m olecular r otational s pectroscopy, w e are more i nterested i n
nuclear motions. Assuming that a molecule is in certain electronic state, whenever the
nuclei slightly change their configuration, according to the Bom-Oppenheimer
approximation, the electrons immediately adjust to this change and reach an
equilibrium state in that the electrons move much faster than nuclei. Thus, as the
nuclei move, the electronic kinetic-energy varies smoothly as a function of nuclear
coordinates,
. For convenience, we can define a new fimction (7(q„) as the
potential energy for nuclear motion, which consists of the electronic kinetic-energy
and the nuclei’s repulsion energy[2 ]:
We define the nuclear Hamiltonian as:
[ 1 -8 ]
^ ^ = 4 ( q J + f/(q J
[1.9]
Equation [1.9] is the abbreviation o f [1.8]. The first term of [1.8] is the nuclear
kinetic-energy operator; the second and third terms together are the potential energy
U(q„) for nuclear motion[3]. Finally, the nuclear Schrddinger equation is given by:
[ 1-10]
=
Inspecting [1.4] and [1.8], it is obvious that H = H^,+ H ^f. Furthermore, Bom and
Oppenheimer proved the molecular wave function to be adequately approximated as:
m v - ; q „ , - ) * q ^ . / ( q , v ; q . , - - ) 'F ^ ( q „ , - )
[l-H ]
Hence, the electronic and nuclear motions can be treated separately under the frame
of Bom-Oppenheimer approximation[3].
-5-
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§ 1.2
THE SEPARATION OF NUCLEAR MOTIONS
We have worked out the separation of electronic and nuclear motions for a
molecule based on Bom-Oppenheimer approximation ([1.6] & [1.10]). It is basic to
quantum mechanics and is appropriate for the electronic ground state, in which
rotational spectroscopists usually study. From now on, we are going to focus on the
nuclear motions. As we know, a molecule moving in a three-dimensional space
undergoes entangled motions that can be specified as translation, rotation, and
vibration. Assuming there are no couplings among them, we can further simplify
Schrddinger equation [1.11] so as to be able to investigate those nuclear motions
individually. The purpose is to work out the separation of nuclear motions. A
diatomic molecule is used as an example for its simplicity.
According to [1.7], [1.9], and [1.10], the nuclear Schrddinger equation[4] for
diatomic molecule is:
r
a'
2 m,
5q[
a"
[1-12]
Im^ dq^
For convenience, taking a new coordinate system:
[1.13a]
r = q ,-q ^
[1.13b]
m , H- m ^
Then we have the following relationship:
a _ a 8OK
or :
m,
Q
d
:<I +, do dr
aq, dQ aq, ar aq, m, +ni2 dQ
a _ a
dq 2
aQ
a
aQ d(\2
ar _
ar aq 2
\
aq,
aq, i^aq, J
aq,
A
aqj aq^/
m2
d
dr
[1.14a]
- j. -
a
a
m, + m^ aQ
dr
m;
(mi+m^) aQ
.
-jL -
[1.14b]
a'
2 m,
m, + m2 dQdr
dr
q2
2 M2
q2
-+ -
(m,-fm,)" aQ
m, + mj aQar
-
6
[1.14c]
dr
-
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[1.14d]
Inspecting [1.14c] and [1.14d], we find that:
a' ^ 1
^
1
w, aqf ni2 aq? w, +
^ m ,+w 3
dQ^
Wjm, ar^
1
[1.15]
F ore onvenience, d efme t he t otal m assM and the r educed m ass /<. N otice t hat t he
potential energy o f a diatomic molecule is only affected by the bond length, therefore:
M
[I.16a]
[1.16b]
n\ + Wj
U (r)^ U (q „ q 2 )
[1.16c]
Plug [1.15] and [1.16] into [1.12], the nuclear Schrodinger equation in the new
coordinate system is given by:
'P J Q ,r ) = £ ^ T ^(Q ,r)
[1.17]
The new coordinate system is called the center of mass coordinate system with the
center of mass as the origin. The first term on the left hand side of [1.17] represents a
translational motion of a virtual particle with a mass of M = m^+
at the center of
mass between two nuclei; the second and third terms together represent the internal
motions (in a more descriptive word, the relative motions) of nuclei in the molecule.
Since in free space, the translational motion o f a molecule will not affect its intemal
motions, the separation of them will be a good choice. Define the wave function as:
T ^ (Q ,r) = ^,(Q)<^,„,(r)
[1.18]
Substitution of [1.18] into [1.17], the nuclear Schrodinger equation is separated into
two parts: one describes the molecular translation, [1.19]; the other describes the
nuclear intemal motions, [ 1 .2 0 ].
[1.19]
2M
f
™ V ;+ f/(r)
2/<
)
[ 1.20]
=
-7-
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Translation is an “ external m otion” o f a m olecule. B ased o n the k nowledge o f
thermodynamics, the averaged translational kinetic-energy, {E^.), can be easily
determined from environmental parameters like temperature, pressure, etc., and
doesn’t depend upon the molecular intemal motions, i.e. rotation and vibration.
Therefore, [1.19] is out of our consideration.
Inspecting [1.20], we find that the original nuclear motions for a diatomic
molecule has been reduced to the problem of one particle with a reduced mass n
circling aroimd the center of mass (c. o. m.) with a radius r. This is a centrifugal force
field problem in that the potential energy only depends upon the nuclei’s distance and
not angles, thus, U(r) = U {r). To a good approximation, assuming that there is no
coupling between vibration and rotation, the nuclei’s intemal motion wave function
(in spherical coordinate system) can be adequately approximated as[3]:
^int (r) = ^int ('"> <P) «
(r)y^r
[1-21]
9)
The Laplacian operator in spherical coordinate takes the form of [1.22].
„ 2 a- 2 a
dr^
r dr
1 a"
i
a
80^
r'
80
1
r sin
0
a"
8 <p
[1.22]
Substitution of [1.21] and [1.22] into [1.20], and remember that U {x )^U {r), the
Schrodinger equation that describes the nuclear intemal motion can be expressed as;
—
—+■
dr
2a
+ U{r) +
r dr
Wvir)9r
9) = {Efj~Er )y/. {r)9r i^^9)
where,
is the square o f the angular momentum operator:
P ' =-n^
a' ■+ C O t0^ a + ' 1
ar
80 sin 0
[1-23 ]
[1.24]
dq>
Its eigenfunctions are the spherical harmonics, Yf{0,cp) ; the eigenvalues are
J { J +l ) h \
2 xrM i
/ = 0 ,i, 2 ,-
P '7 " {0, <p) = J { J + 1 ) ^ 7 / {0, (p)
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[1.25]
From a mathematical point o f view, all the variables are entangled in the third term of
[1.23], the separation o f variables is not applicable. Fortunately, from physical point
o f view, the period o f molecular rotation (on the scale of fractions of nano seconds) is
much longer than that o f molecular vibration (on the scale of pico seconds), therefore,
the bond length that appears in the period of molecular rotation is actually the
averaged bond length (r) for thousands o f vibration cycles, (r) can be treated as a
constant if only the molecular rotation is concerned. Hence [1.23] can be separated
into two parts; [1.26] describes the rotation, and [1.27] the vibration.
p2
[1.26]
I fi dr^
■■
+ t/(r)
r dr
[1.27]
[1.28]
Ef^ —Ej, = E^ + E^
The rotational energy E^ and rotational wave function ij/^{0,g)) = Y f {6 ,^ ) can be
easily obtained with the help of [1.25].
2 //<r
)
Y n e ,(p ) =
1
1
2 fx{r")
j{ j+ \)n ^
Y f ( 0 ,g>)
[1.29]
J = 0,1,2,•••
[1.30]
2 J + 1 { J - \M \) \ (1 - cos'
,
An
{J+\M\)\
-(cos
6 >-l)
J eJMtp
[1.31]
c f(c o s^ )'" " " '
l-'Jl
Molecular rotation has been completely solved, as shown by [1.29], [1.30], and
[1.31]. Before explicitly showing the solution of vibration, we need to play a
mathematical trick[3]. Define (j>{r) = ryf^{r) and substitute y/„(r) with ^{r)jr into
[1.27];
ft'
a'
2 fi
dr‘
[1.32]
■+ U (r) H r) = E J (r )
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We have to first determine the expression of the potential energy U(r) before we can
solve [1.32]. People generally study the rotational spectroscopy o f a molecule in its
lowest vibrational states, where nuclei only move slightly off their equilibrium
configuration. Thus, to a good approximation, the vibration can be treated as
“harmonic oscillator”[5]. Expand U(r) with its Taylor expansion:
U{r) = U (r,) + U 'irX r ~ r ,) ^
where
+ — — ( r - r j +•
3!
2!
[1.33]
symbolizes the equilibrium bond length and is a constant. For convenience,
set U (r j = 0; moreover, in the minimum of any potential curve, U ’(re)=0. Hence, if
we define x = r -
, and rewrite ^(r) to be S(x) [2]:
1
[1.34]
2
[1.35]
Then [1.32] takes the new form of:
2 /j
dx
1 ,x2^
- + -k
S ix) = E,S(x)
[1.36]
2
Equation [1.36] is the famous differential equation for “Harmonic Oscillation”. The
solution is given by[5]:
(-l)V
X = /? ^
S{x)
S (r-0
r
r
[1.37a]
[1.37b]
For spectroscopists, knowing the recursion relations and various matrix elements of
the wave fimction is more important than knowing their mathematical form[5]. The
following properties will be used in the future:
[1.38a]
[1.38b]
v+-
-
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[1.38c]
{ v |^ i v > = { v |C ’ |v ) = ( v |( r ’ |v ) :
[1.38d]
:V+ -
/
( v |r |v > :
J
v + -<V
[1.38e]
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§ 1.3
NON-RIGID ROTOR (HARMONIC OSCILLATOR)
Although the rigid rotor model gracefully describes the physical picture of
molecular rotation, such a simplified model is not enough for high resolution
spectroscopic studies. A more accurate model taking into account centrifugal
distortion and harmonic oscillation is going to be explored.
Again, the diatomic
molecule is chosen as an example to express the basic ideas.
For a rigid rotor diatomic molecule with an equilibrium bond length r«,, the
moment of inertia is/^ = pirl. Hence the rotational energy can be expressed as
= P ^ / 2 4 . Considering a non-rigid rotor, the bond length increases as the molecule
rotates because o f the centrifugal distortion[5]. Assuming the bond length is
in case
the molecule is rotating, the centrifugal distortion force is given by[5]:
Mr,
hr,
Fc has to be balanced to reach a steady state. According to Hook’s law[5]:
F c= K {r,-r,) = ^
hr.
[1.41]
The potential energy due to the centrifugal distortion can be expressed as[5]:
[1.42]
Obviously, the refined rotational energy for a non-rigid rotor is[5]:
p2
2J,
p4
+
[1.43]
iK llr^
In the lower vibrational excited states[5],
- ^
={ r c -r j« r ,
[1.44]
So that we can expand I, in terms of the power series of/e[5]
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1
1
h
Mr,
1
1
2 ( r,,- rJ
1
Substitution of (r^ - r j with
J _ _ ± ,1 2 P '
h~ h
,
1
3
1
3(r,,~rJ"
-----
[ 1 .4 5 ]
into [1.45], we obtain the expressions[5]:
P"
[1.46]
+-
3P'
6P'
[1.47]
+ -
Klcr/e
I /c
6p2
2„2
r2„2
Kr,
c c
[1.48]
K l//e
Therefore, the energy expressions for a non-rigid rotor is given by[5]:
p2
p4
£=£_+
^ 2L ' 2k I X
f p2
P"
^ 2 /,
2 /,
+ -
K l / J ,r X I K ^ I X I X
p4
3P^ ^ 3 P
K lX
j
p4
3P*"
4
24
3
24
2
p4
3
2
A
P®
+
-2 r3„4
/^^V ;
p4
6P
+
K l/Z e J
* * ■
p2
6P
2 k 1X
V
3P®
-
2<
r/
k^ I X
I/c
p6
-+ ---- ^-r-T + 2kI X
2 kH X
[1.49]
Substitute P^ with J(J+l)h^, we obtain the non-rigid rotor rotational energy[5]:
^
j { j + \ ) r■2
r I ii\y2 iir4
rr2i /j +
3 /r3/
^ ( rj +. i-\3*6
irr
[1.50]
Defining the molecular constants[5]:
«
^
h
8 ;r^ 4
^
h
8 ;rV r;
[1.51a]
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[1.51b]
IhKllr!
e e
6
fr
____
[1.51c]
IhK^llr*
'
We can easily expand the energy levels with power series of J(J+1):
F (J ) = B J { J +1) - D,J^ (J + I f +
( / + !)'+•••
[1.52]
where Be is the molecular rotational constant for equilibrium configuration, Dg and He
are centrifugal distortion constants, which represent the affect of centrifugal distortion
on the rotational motion o f a non-rigid rotor.
In addition to the affect from centrifugal distortion, the oscillation of nuclei
around the equilibrium configuration will also affect the molecular rotational energy.
As aforementioned, the bond length we used is actually the averaged one over many
vibrational cycles. If the nuclei only oscillate near their equilibrium positions, we can
expand the bond length in the v vibrational excited state as[5]:
1
=
V
1
v \- ' i
{r^+xf t
A
1
1
v V ’ /v
{\ + x/r,f 7
4
[1.53]
x2
_4
+5
\H
'e J
'e J
The integration over all odd ^terms vanishes (see [1.38c]). Inspecting the relationship
of [1.38a] to [1.38e], the expansion takes the format o f [1.55].
1
1
'=
1
3
V
I]
5
v + -- +.
2)
3f
0 ^ H—3‘ +
v+ —
2(
2j
8
—
•
[1.54]
Substitution of [1.54] into the expression of Be, [1.51a], we obtain the rotational
constants for vibrational excited state[5]:
B ,= B ,- a e \ v + - j + r,
^
V 4"
iV
v+ —
V
2y
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[1.55]
pr~
[1.55a]
Prl
Similar to Bv, Dy is also affected by the molecular vibration because there is a
factor o f 1/ r / that should be replaced by (v |l/r^ |v ). Because[5],
s-6
1+
p
2!
H
kP
H^
6-7-8
3!
b\
[1.56]
Dv can be expanded in the format of [1.57].
V +
P.=
i
[1.57]
+ ■
6-7
2 hK^P 2 \prl
[1.57a]
Finally, the energy level of non-rigid rotor under vibrational excited state is[5]:
( / ) = B J { J +1) - D„J - ( / -f 1)' + 7 7 / ' ( / +1)' + •••
[1.58]
The pure rotational transition frequency is given by[5]:
v{J) = F ,( J + 1 ) - F ^ J ) = I B X J +1) - 2(2Z), - H p i J -f 1)^ + 6/7, ( / +1)^ + -
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[1.59]
§ 1 .4
SELECTION RULES
Many stable diatomic molecules are closed shell systems with a 'S electronic
ground state. Except for cases like O 2 and NO, investigating the selection rules for
rotational and vibrational transitions under ‘Z electronic state wouldn’t lose
generality.
The molecular electronic dipole operator is defined as[2]:
I
a
For transitions between 'F' and 'F in the same electronic state, the electronic dipole
transition moment is given by[2]:
' PI
= Wn'lwltdWeiWNdT^J'^N = I w l [
[1.61]
where the integration in the square bracket is the permanent electronic dipole moment
in y/^ electronic state, being labeled as d =
ad"^a
electronic dipole transitions,
p
^ d e r to observe the
niust not vanish, so that possessing a
permanent electronic dipole moment d for a diatomic molecule at ‘Z electronic state
is the minimum requirement. Since y/^ is parametrically dependent on the nuclei
configuration, d is also a function of r . In spherical coordinate system:
d = idx + ]dy + ijd^ = id (r) sin 6 cos(p + j d (r) sin ^ sin ^ + kd (r) cos 0
[1.62]
Substituting [1.62] into [1.61] and remembering that y^^ « y/^yr^, the transition
moment turns out to be[2]:
¥
^ f
f
¥ ^ ld y /^ r ^ d r d 0 d < p
[1.63]
=
(y/]. |r V (r)|
\r^d(r)|y/^ ^
i sin 0 cos <p+ J sin 0 sin <p+ k cos0 Vr
) = f S', (r - r, )d (r)S^ (r - )dr
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[1.64]
y/\.Y sin^cos^i? + j s i n 6 dn(p + k c o s 0 y/r) =
[1.65]
{i sin 9 cos <p+ j sin 9sixi(p-¥k cos 9 ) \ j f (9, ^ )] sin 9d9d(p
where the wave function Sv is defined by [1.35].
Let’s first investigate [1.65]. According to the properties of Y f(9 ,(p ), the
quantumnumbers J \ M ’ and J , M have to satisfy therelationship [ 1.66] so a s to
make [1.65] not vanish.
A / = / - / = ±l; A M = M '- M = 0,±1
[1.66]
Hence [1.66] is the selection rule for valid rotational transitions.
Equation [1.64] represents the radial part of the transition moment, which given
the selection rules for vibrational transitions. Expand d(r) with its Taylor expansion;
d(r) = d ( r j + d' (r, ) { r + ^ d" (r, )(r
2!
3!
d"'(r, ) { r - r ^ f + ■■■
[ 1.67]
Substution of [1.67] into [1.65]:
(it/', y-d(r)\if/,^ =
+
S^,{x)S,{x)dx +«/’(/;)
£
* S v ' {x)dx + —
S,,{x)xSXx)dx
S , . { x ) d x + •••
In order the make the first term not vanish, v’ = v; in order to make the second term
not vanish, v’ = v ± 1 ; in order to make the third term not vanish, v’ = v ±2 ; in order to
make the fourth term not vanish,
= v ±3, etc. In summary, the selection rule for
vibrational transitions is give by:
Av = 0, ± 1 ,± 2 , ±3,---
[1.69]
Pure rotational transitions can only be observed in case of Av = 0.
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§ 1.5
ROTATIONAL SPECTROSOPY OF POLYATOMIC MOLECULE
We have briefly introduced the differences among electronic, vibrational, and
rotational spectroscopy in previous sections. Diatomic molecules were used to
illustrate the basic concepts for its simplicity. The theoretical models and
mathematical treatments of diatomic molecule are beautiful. It helps us to understand
the physical meaning o f various molecular constants that will be encountered in the
later chapters. Unfortunately, not all molecules are as simple as diatomic molecule, a
more thorough description for polyatomic molecule is needed. The topic of this
section is to learn about a more complicate case: the rotational spectroscopy of
polyatomic molecules.
Considering a collection of nuclei of mass nia located at position
relative to the
origin in a Cartesian coordinate system and all rotating with angular velocity co, the
angular momentum is given by[6]:
=
=
a
a
+yl +4
=
[ o ) { x , ( X ^ ■(D)]
a
)
[1.70]
( W +ya<^y+
)]
Writing out the vector components.
-ya^a^xJ - y l^ y J +
[1.71]
) j ~ ya^a^zJ
(4 +
-z^x^cojc - z^y^oy^k -zl(o,k + a), (xl +
Expressed in matrix format:
a
a
a
( O .,
a
a
Y ^ m a iy l+ y l)
a
>
Those matrix elements are constants, thus we define the moments o f inertia:
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[1.72]
a
^yy = J l ^ a ( 4 + 4 )
a
a
= ~ Y .V .,y a =
4
= ^wc
a
a
or
or
=
I^ =
a
= -T ,^ a ^ a y a =
a
[1.73]
In matrix form, P = /m[6]. Since / is a real symmetricmatrix,
it canalways
be
diagonalized with an appropriatetransformation matrix, i.e., theoff diagonalterms
will be annihilated. We can always find a special coordinate system, called principal
axis system, in which only the diagonal terms in / exist. We label the three axes of the
principle axis coordinate system as (a, b, c).
=
UJ
f 4 0 0" (co:
0 4 0 COb
0 4.
[1.74]
According to [1.74], th e rotational energy J?r= 14ry'/iy can b e expressed in a very
simple form[6]:
f 4 0 0" (co:
0 4 0 0),
.0 0 4 .
2
2/„
21,
24
[1.75]
The axis a, b, and c are labeled with I „ < h < hMolecules can be classified based on the values of the three moments of inertia.
The five cases are as follows[6]:
1.
Linear molecules, /« - 0,lb = /<..
2.
Spherical tops, la ~ h ~ 4 #= 0.
3.
Prolate symmetric tops, I a < h ~ 4-
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4.
Oblate symmetric tops, la = h < h-
5.
Asymmetric tops, Ia< h < Ic-
Each o f them will be investigated in this section.
LINEAR MOLECULES
Because Ia ~ 0 and Ib ~ Ic = I, the rotational energy is given by[6]:
p2
£
2/j
p2
27,
p2
=
[1.76]
27
Similar to the analysis for diatomic molecule, the rotational energy level expression is
T; (J ) = B J { J + 1) -
( / +1)' + •■•
[1.77]
Where the vibrational dependence is customarily parameterized by the equations[6]:
^ v = 5 , - a , ( v + i ) + r,(v + i ) ^ + -
[1.78]
D ,= i7 „ + ^ ,( v + i) + -
[1.79]
SPHERICAL TOPS
For a spherical top, 7„ = 7* = 7c = 7, thus the rotational energy expressed as[6]:
p2
p2
£
p2
p2
=
27,
21,
[1.80]
27, 27
Although the rotational energy expression looks like those of diatomic and linear
molecules, the spectroscopic properties are quite different in that spherical top
molecules have no dipole moments, thus we couldn’t observe the pure rotational
spectrum for spherical top molecules. I am not going to talk about spherical top
molecules in my thesis because it is beyond the topics of pure rotational spectroscopy.
SYMMETRIC TOPS (PROLATE AND OBLATE)
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For simplicity the prolate top is chosen as an example to be studied. The
treatments for prolate and o b late tops are the same, o n e c a n o b ta in the answer for
oblate top simply by switching the labels a and c.
The classical energy level expression for a rigid prolate top is[6];
p2
p2
p2
p2
1
1
^
£ = i k + i L + i L . = i k - + _i_(p2+ p2) = _ L p 2 +
24
24 24
21, 2 / / ^
21,
21,
where
21, J
+ P^^.
The symmetric top molecule is described in both space-fixed laboratory system,
X, Y, Z and the molecular coordinate system, x, y, z (or a, b, c). Since they both origin
at the center o f mass, the orientation of the molecular coordinate system relative to
the space-fixed laboratory system can be described by three Euler angles: 6 , (p, and;^.
Figure 2.1 illustrates the relation of these two coordinate systems.
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X
Figure 2.1: The Euler angles 6 , (p, x that relate molecular coordinate system (x, y, z) to
the space-fixed coordinate system (X, Y, ZJ16].
The transformation matrix T between these two coordinates can be obtained in the
following way:
1.
Rotate X and Y by an angle <p about Z into X ’ and Y
2.
Rotate X ’ and Y ’ by an angle d about Y ’ into X ” and z,
3.
Rotate X ’’ and Y' by an angle x about z into x and y .
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Thus the transformation matrix T is given by[6]:
^ cosx
&mx
0
T = -sinx
0
V
oosx
0
0
0
1✓ S. sin 0
0
1
0
-sin ^ Y cos^
0
-sm ^
cos 9y' \ 0
' COS^ COS^ COS2" - sin q>sin x
sin^
cos^
0
0^
0
1y
cos 6 sin ^ cos 2' + cos (psin x
- s in ^ c o s ^
- cos 9 sin (psinx + cos <pcos s x
sin 0 sin
sin ^ sin ^
cos0
-cos6>cos^sin;jf-sm^9COS J
sin 0 cos ^
[1.82]
Since the angular momentum operator in the space-fixed coordinate system is given
by[6]:
:------------- Sm^ZJ —
h =
V
sin0
d(p
sin 6' d x
sin 9
d<p sin 9 d x
d9
r —- c
Py = -in
*+
V
Py£, = ~ih
-
+ COS0 —
99
[1.83]
9
9(p
We can easily derive the expression of angular momentum operator in the molecular
coordinate system with the help of transformation matrix [1.82].
P ,= - m
=
- in
^ -cos ±.---y 9 ^------±-------------c o s rc o s ^ 9 sin
. y ---9 ^
sin ^ 9g>
sin^
9x
99
-sin y 9 sin y cos 0 9
± .—
+ — i ----------------- +
sin^ 9(p
sin^
9x
9
99
COS y —
[1.84]
p = -m Sx
The commutation relationship in the molecular frame is different from that of spacefixed laboratory frame.
[P ,,P ] = -/^P,
[Py,Pf.] = mP2
[1.85]
This anomalous commutation relationship in the molecular frame also results in
anomalous raising and lowering operator[6]:
Lowering Operator: P^ = P^ + i f y , and Raising Operator: P~ = P^ - iPy
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[ 1.86]
In contrast, in the space-fixed laboratory frame, these two operators are defined as;
Lowering Operator: P_ = P,, - iPj., and Raising Operator: P^ = P^ + rPy
[1.87]
Fortunately, both P, and P^ commute with P^, and P^and P^commute too. Thus a
set o f simultaneous eigenfunctions \JKM) can be found to satisfy these operators[6].
P IJKM ) = J { J + \)h^ IJKM)
P^ IJK M) = Mjh IJKM)
[1.88]
?^\JKM) = K%\JKM)
The effects of raising and lowering operators in different frames on the symmetric top
eigenfunctions are given by the equations[6]:
P^ IJKM ) = [J{J +1) - M {M +1)]^ h IJKM +1}
P IJKM ) = [J{J +1) - M {M - l ) f n IJKM -1)
[1.89]
P" IJKM ) = [J{J +1) - K {K - l ) f h \ J K - \M )
P“ IJKM ) = [J{J +1) - K {K +1)]^ h \JK + IM)
The Schrddinger equation for prolate top molecule is given by[6]:
1
2L
1
■+
21
\JKM) =
21h
J ( J + 1)^
2L
•+
v2/„
21,
J
\JKM)
[1.90]
As aforementioned, switching labels a and c, we obtain the expression for oblate top:
1
1
2L
21h
\J K M )^
-+
2L
\JKM)
+
2L
v2/.
21,
[1.91]
J
Defining molecular rotational constants:
A=
B=
2L
2L
C=
[1.92]
2L
The energy expressions for prolate and oblate tops can be written as [6]:
E P ro la te ^
+
J) +
= B J{J + 1) + (C ~ B)K^
OK
[1.93]
Considering the effect o f centrifugal distortion as the molecule rotates, the expression
o f the prolate top energy level is given by:
F { J ,K ) = BJ{J + l) + ( A - B ) K ^ - D j [ J { J + l) f - Dj,,J(J + l)K^ - D^K^
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[1.94]
The transition frequencies we can measured are[6]:
= F ( J + l , K ) ~ F(J, K ) = 2B (J + 1) - 4Dj ( J + 1)' - 2Dj^ ( J + l)K^
[ 1.95]
ASYMMETRIC TOPS
The Hamiltonian for an asymmetric rotor is given by[6j:
H =
*
21.
' -f"-
-
21,
[1.96]
21,
The Schrddinger equation for asymmetric top has no analytic solutions in that
does not commute with all three of P f , P^ and P j . For smaller values of J,
numerical solutions for the asymmetric top rotational energy are available. The idea
lies in the fact that we can use the wave functions of prolate and oblate tops as the
basis sets to generate the asymmetric top wave functions. We can generate the
\.
Hamiltonian matrix
rotational energy levels are obtained by
solving the secular determinant of it. If we write the Hamiltonian in the format as[6]:
h^H = A?l+E?l+C?^,
(P’ +P,= )+CP=+
[1.97]
f
2 j
(p ^ -p ’)
c-
A + B^
2
\
)
p2
-y
+
(A-B\
I 4 j
With the help of following symmetric top matrix elements[6];
JK
JKj =r J iJ + i )
JK
JK^ = h^K^
JK + 2 (P -) ' I/A J) =
[ 1.98]
[ ( / - K )(J + K + V ) ( J - K - 1)(J + K + 2 ) f
J K - 2 ( r f \ j K '^ = e [(J + K ) ( J - K + \){J + K - 1)(J - K + 2 ) f
The elements in the secular determinant can be easily derived. For example, the
secular determinant o f an asymmetric top for / = 1 basis sets is expressed as:
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/
(H ):
»
(l,l H l,o) '
( l,lH l,- l)
'( l , l H l , l )
\
V
(1,-1 i f 1,-1)
/
( ^ A +B
C + ------2
A~B
A
—
2
(l,0 H 1,0)
( l,0 ^ 1 ,- l)
0
\
A -B
0
2
^ A +B
C + ------2
0
0
A +B
J
[1.99]
The secular equation is given by [1.100].
C +i± ^ - A
2
A -B
2
0
A~B
2
0
0
[1.100]
0
A~B
Solving [1.100] we obtain three energy levels: A+B,A+C, and B+C.
The degree of asymmetry is quantified by asymmetry parameter fc (Ray’s
asymmetry parameter), w h ich runs from - 1 for a prolate top to +1 for an oblate top. at
is defined as[6];
2 B -A -C
A -C
[1.101]
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REFERENCE
[1]
IraN . Levine, Quantum Cemistry. 2nd ed. 1974; ALLYN AND BACON Inc.
[2]
Yunwii Zhang, Qingzheng Lu, and Yushen Liu, Molecular Spectroscopy.
1988; University of Sciences and Technologies o f China.
[3]
Ira N. Levine, Molecular Spectroscopy. 2nd ed. 1975; John Wiley & Sons,
Inc.
[4]
Jinyan Zeng, Quantum Mechanics. Modem Physics, ed. Guangzhao Zhou.
Vol. 1.1990; Science Publication Press.
[5]
Guowen Wang, Introduction to Atomic and Molecular Spectroscopy. 1985;
Pekin University Press.
[6]
Peter F. Bemath, Spectra o f Atoms and Molecules. 1995; Oxford University
Press.
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CH A PTER TW O
Fine and Hyperfine Structures of Rotational Spectrum
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§ 2.0
INTRODUCTION
The incredibly high resolution of Fourier Transform Microwave Spectroscopy
enables us to observe the fine and hyperfine structures of the spectrum which are due
to the effects o f nuclear quadrupole coupling interaction and nuclear magnetic dipole
- molecular overall rotation interactions. For an open shell system, the electronic spin
of the unpaired electron must be taken into account, and the fine structure due to the
electronic spin - molecular overall rotation interaction and the hyperfine structure due
to the electronic spin - nuclear spin interaction could be observed. § 2.1 introduces
the nuclear quadrupole coupling interaction, (IT), which arises from the interaction
between nuclear quadrupole moment and nonspherical distribution o f electronic
charge about the nucleus. § 2.2 describes the magnetic hyperfine stracture arising
from the coupling between nuclear magnetic moments and overall molecular rotation,
(I-N). § 2.3 focuses on open shell systems. The descriptions of fine stmcture arising
firom the electronic spin - molecular overall rotation interaction, (S‘N), and the
hyperfine structure arise from the electronic spin - nuclear spin interaction, (I*S), are
presented in this section.
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§ 2.1
NUCLEAR QUADRUPOLE COUPLING INTERACTION
The nuclear quadrupole coupling interaction arises from the interaction between
the nuclear quadrupole moment and the electronic field gradient at that nucleus[l]. A
non-spherical distribution of nuclear charge gives rise to a nuclear quadrupole
moment. A non-spherical distribution of electronic charge about the nucleus gives
rise to an electronic field gradient at the nucleus. If either the nuclear charge or the
electronic charge distribution about the nucleus is spherically symmetric, such an
interaction is quenched.
Known from electrodynamics, the electrostatic interaction between nucleus and
electron can be expressed as[2];
E=
jj
[2.1]
re - r n
where p ^ ( r j and
(r„) are the electronic and nuclear charge densities at
and r„
respectively. The origin of the coordinate system is taken to be the center of the
nucleus. Since
1
rre —r n
» r„, the expansion o f l/|r^ - r„ | is given by[2]:
1
yjre
[2.2a]
-2 r,r„ c o s (r„ rJ
The right hand side o f [2.2a] is the generator of Legendre polynomial, therefore[2],
1
1
r
Po(cos(r,, r„)) + -^ /] (cos(r,., r„)) +
P2 (co s(r„rJ) +
[2.2b]
where i] is Legendre polynomial, which is given by:
1
I
R(cos 0 ) = —,--------- —[ c o s ^ P - ll
^ 2'/! J c o s 'p L
J
Po(cos^) = l,
/ = 0,1,2,•••
/](cos6’) = cos(9,
[2.3]
Pj (cos &) = — [ 3 cos^ P - l ] ,
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Substitution o f l/|r^ -r„ | from [2.2b] into [2.1] shows the electrostatic interaction
energy in terms of Legendre polynomial expansion[l]:
E —E q+ + E
q +"-
[2.4]
The first or monopole term given by [2.5] represents the interaction which is
independent o f nuclear orientation[l].
P (rjp (r„ ) ,
Eo = II—
.
_
fP (r.)
= \p{r„)dt„
[2.5]
= ZeV^
The second or dipole term given in [2.6] vanishes in that no nuclear electronic dipole
moment has ever been observed[l,2].
Eo = \\p a ( n) P( r n)
\p„{Y„)r„dx„ • j ~ p , (
=
r , = - P ■E [2.6]
The third or quadrupole term given in [2.8] represents the quadrupole coupling
interaction, which does not vanish and which depends upon nuclear orientation. For
the ease o f understanding, let’s first familiarize ourselves with some necessary
dydadic operations[2].
Given r = ( x ,y ,z ) as a vector, rr is a dydadic tensor and can be written as[2]:
'x^
rr = y {x
y
z ) = yx
^zx
xy
xz
\
[2.7a]
yz
z^ /
The inner product of dydadics is defined as[2]:
ac:bd = ( a d ) ( c b )
[2.7b]
1:1 = (it + jj + k k ): (ii + jj + kk) = 3 [2.7c]
The irmer product o f unit dydadic is[2]:
The iimer product of r r and 1 is a scalar[2]:
r r : l = r r : ( i i + jj + kk) = r^
Hence the quadrupole coupling interaction term is expressed as[2]:
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[2.7d]
E q
=
J|p ,(r,)/?„(r„)~ i[3 (r„ -rj" -r^r^'\dT„dt,
= i J | A k 2 ^ ( 9 r , r . : r.r. - 3 r .r .: IrJ - 3 r,r,:b-.= + r>.=l:\)d r,d r,
[2.8]
= i fJ - - - # -*-^(3r.r. - c l ) : (3r,r, - / - / l ) * , * .
For convenience, define nuclear quadrupole moment Q, which is a dydadic tensor[l]:
Q = |p „ (*•„)(3r„r„ - r^l)dt„
[2.9]
On the other hand, inspecting the electronic field gradient at the center of the
nucleus in question[2]:
r —r
d t.
= - J p . ( r J V " I g.. |3
r
—
r
V I
«l yr,=o
[V „(r, - r„) ] |r ,- r „ f - ( r ,- r „ ) V „ ( |r ,- r „ f )
dr.
=- j p M
W e -rj
/ r =0
= - \ pM )
= “ |A ( r J
r - r«
re
V Ir c - r «l
-1
3 rr
KI -r„ "
/ r „=0
\dT .,
■|Pe(*V)^(3r,r, - r ^ \) d r .
[2.10]
Notice that V„r„ = 1, and the matrix format of unit dydadic I is:
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fl
fO
j
1 = j {i
k) = 0
.0
0 O'
1 0
0
1.
Substitution o f [2.10] into [2.8], the quadrupole coupling interaction energy Eg
can be concisely written as[l]:
I“
2
o
u
i„x,Y,z j=x,y,z
0
,»',
[2.11]
Notice that E = -V F , thus F^,- = -V£^.,.. The potential V is related to the inverse of r^,
as shown by [2.12], hence F^.,. is given by [2.13].
[2 . 12]
\
d-v
^dXjdX,^
^ 5 'F
= F ,-
A
[2.13]
[dXMjj
where (1/?;)^ represents the inverse distance from the Ath electron to the nucleus and
the summation is taken over all electrons contributing to V. If we associate r, with
rotational angular momentum J, Xi with Jj, and Xj with Jj, the conjugate operator is[l]
F
3 - ^ -----
[2.14]
=K
It is customary to evaluate the constant C by defining coupling constant
as that
observed for the maximum projection of J along Z-axis, that is, for the state M j = J :
C
J ( J + 1)L
2J-1
[2.15]
The generalized expression for the elements of the field gradient operator is given by;
r/ _
‘l.f
J ; J I "f*J,-J 1
3_i_i—
[2.16]
Similarly we can evaluate elements of nuclear quadrupole tensor Qij in the same
way. Accordingly, the nuclear quadrupole operator can be expressed as[l]:
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a =
1,1, + I X
eQ ^ 3_1J
7 (2 /-1 ) V
2
[2.17]
—
" y
Substitution o f [2.16] and [2.17] into [2.11] yields the Hamiltonian for the
quadrupole coupling interaction.
77,
1
<iQcij
X-
1,1, + 1,X
^
2
[2.18]
Since the components o f I and J are not commute, that is, 1,1^ 5*1^1, and J,J^ 5* J ^ J ,,
the evaluation o f [2.18] is tricky. A good description can be found in Ramsey’s
book[10]. The final form of the Hamiltonian of quadrupole coupling interaction is[l]:
&Qq.,
3 ( X J ) '+ ^ I - J - X X
2 /(2 /- 1 ) 7 (2 7 - 1 )
[2.19]
Because I and J are coupled to form a resultant F, that is, I + J = F, which is a good
quantum number, therefore, X J = 14(F^ _
- 1^). Plug it into [2.19], we obtained the
general energy expression for nuclear quadrupole coupling interaction[l]:
E
^
2 /(2 /- 1 ) 7 (2 7 - 1 )
3
-C(C + l ) - / ( / + l ) - 7 ( 7 + l)
where, C = F ( F +1) - / ( / +1) - 7(7 +1)
[2 .20]
[2.21]
The only thing left is the field gradient, as we known, for a symmetric top[l]:
[2.22]
dZ^
where qj is aligned to the direction of J. In practice, we generally specify the field
gradient along the principle axes, a, b, and c. With the help of direction cosine, the
expectation values for each o f field gradient along a, b, and c axes can be obtained.
The resulting formular for the quadrupole energy o f the symmetric top is given by[l]:
eQq
[2.23]
_ /(/ + !)
where Y { J ,I,F ) is Casimer function, which defined as[l]:
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F ( J ,/,F )
I C(C + 1) ~ / ( / + ! ) / ( J + 1)
[2.24]
2 ( 2 / -1 )(2 J + 3 )7(2/-1)
[2.25]
eQq = e Q l ^ Y x
where z is the highest order of symmetry axis (for prolate top, a; for oblate top, c).
egr/ or x is constant and generally obtained from experiment.
For an asymmetric top, things are complicate, according to [2.20] and [2.24],
2 /+ 3
E ^ = e Q q ,-^ Y (J ,I,F )
[2.26]
I! il^{j,K,K,M,,=j\cos\Z,gp,K„K,.Mj=j)
[2.27]
g - a ,b ,c
(j,K ^,K ^.,M j = J cos^(Z,g)|/ , K ^,K ^,M j = j'j can be obtained from numerical
computation, and Xgg (Zgg = ^Q^gg >S ~ a,b,c) is determined from experiment[l].
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§ 2.2 MAGNETIC HYPERFINE STRUCTURE
The classical Hamiltonian for the interaction of a magnetic dipole with magnetic
field is Hf^ = - p •H , where the magnetic dipole moment fi = g j f i , ! . P, is the
nuclear magneton and g, is the gyromagnetic ratio and unique to particular nucleus
[3]. The direction o f H is the same as that of J, thus we set:
H = (//,;)■
J
[2.28]
J|
[2.29]
HM
Since the magnetic field is generated by the molecular rotation, the field components
are proportional to the components of angular momentum. Also, the direction cosines
associate with J g /|j|, where g = a, b, c. Hence[l],
H j = H , cos(«, J) + H, cos(h, J) +
cos(c,
=
[2.30]
and.
=Ka^a +KJb'^KJc
[2.31]
~ ^bJh + Kb^b KJc
~
a ^cb^b ^cPc
The expectation value o f Hj is given by:
The cross terms vanish when they are average over the rotational state. Substitution of
[2.32] into [2.29], and notice that UJ = %(F^ ~
- 1^), the Hamiltonian and energy
expressions are given by[l,3]:
H y-
■■-M l -
y
y
h jp
SiPj
./(j+ i)
I J = C^I J
g ^ a ,b ,c
[2.33]
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Em = - ^ [ F ( F + 1 ) - / ( / + 1 ) - J ( J + 1)]
where C ^ ,
, and
[2.34]
are the diagonal elements of the nuclear magnetic coupling
tensor[lj. They are measured from the experiment. The evaluation of
and
^ over different top cases (linear, symmetric, and asymmetry) can be found in
chapter one.
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§ 2.3
FINE AND HYPERFINE STRUCTURES OF OPEN SHELL SYSTEM
When a molecule has unpaired electron(s), such as unstable species like the
propargyl radical, HCCCHj, cyanomethyl radical, HaCCN, etc., or a few stable free
radicals like O2 , NO, NO 2, CIO2 , etc., the unique pattern of the rotational spectrum
arises from the fine and hyperfine interactions. The total electron spin angular
momentum S and molecular rotational angular momentum N couple with each other,
which results in “fine structures” of the spectrum. If the radical contains at least one
nucleus with none zero nuclear spin, the nuclear spin angular momentum I couples
with S to produce additional structures in the spectrum, called the magnetic hyperfine
splitting. As we have introduced in § 2.1 and § 2.2, the nuclear spin angular
momentum (if I > 14) also generates hyperfine structures through either the nuclear
electronic quadrupole interaction (I > 1) or the nuclear spin - molecular overall
rotation interaction (I > Vz). This section deals with those interactions involving with
electron spin S interacting with N or I.
Before going deeply into the details of these fine and hyperfine interactions, we
have to first specify the notation of various angular momenta for open shell systems
and the basic principle o f the coupling schemes. These are slightly different from that
of closed shell systems. For an open shell system, R indicates the molecular “end-toend” rotational angular momentum; S, the total electron spin angular momentum for
unpaired electron(s); L, the total electron orbital angular momentum; and I, the total
nuclear spin angular momentum. N represents the coupling o f R and L, N = R + L; J,
the couphng o f N and S, J = N + S, which is called the total angular momentum. F is
the coupling of J and I, F = J + 1.
Van Vleck developed the Hamiltonians that describe the interaction between the
electronic spin and nuclear spin, and the interaction between the electronic spin and
the molecular rotation[4-8]. The effective Hamiltonian can be written as[6j:
i/ = 4 +
+ H , +H q
[2.36]
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Where the terms on the right hand side represent, respectively, the effect of rigid rotor
rotation o f the molecule, the interaction between electronic spin and molecular
rotation (spin-rotation interaction), the interaction between electronic and nuclear spin
(spin-spin interaction), the Fermi coupling interaction, and nuclear quadrupole
coupling interaction. The first and the last terms will not be discussed here because
they have been introduced in previous sections. Unlike atomic spectroscopy, where
the spin-orbit interaction, L*S, plays a significant role in the spectrum, the spin-orbit
interaction term is absent since the orbital angular momentum of the unpaired
electron in nonlinear molecules usually quenched.
SPIN-ROTATION INTERACTION
The electron spin - molecular rotation interaction may arise from two causes. The
first is the interaction o f the electron spin with the magnetic field produced by
molecular rotation. The second is an indirect coupling via orbital motion and through
the intermediary interaction of excited orbital states, which has been treated by Van
Vleck and Henderson. Fortunately, both of these two interactions share the same form
of dependence upon N and S, thus, similar to the analyses in § 2.2, the Hamiltonian
can be written as[5j:
Hs-u =
i= a,b,c j= a ,b ,c ____________
N ( N + 1)
®
A (iv+1)'
^
®
P.37]
The off diagonal terms usually have little effect and can be neglected. The only thing
different from § 2.2 is that the electronic spin - magnetic dipole moment is given by
j^e ~ Ssfis^ » where fig is the electronic magneton and gg is the gyromagnetic ratio
of electron. Notice that J represents molecular “end-over-end” rotational angular
momentum in § 2.2. Here N is “end-over-end” rotational angular momentum. Since J
= N + S, represents the total angular momentum in this section, N-S == 54(J^ S^). The energy expression for spin-rotation interaction is finally given by[5-8]:
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-
Uaa^l + ShbNl +
^
Where
, % , and
).
i / [ j ( j +1) - N {N +1) - S{S + D]
.
[2.38]
are measurable constants from the experiment.
SPIN-SPIN INTERACTION
The nuclear spin - electronic spin interaction arises from the interaction between
the magnetic field produced by nuclear spin magnetic dipole and electron’s magnetic
dipole. For simplification, w e use an atomic model as an example to illustrate the
basic idea[9]. The magnetic field produced by the nuclear spin dipole expressed as[9]:
r
r
+
[2.39]
Where the first term is the usual field associated with a magnetic dipole; the second
term needs further explanation. Normally, when one considers a dipole field, it is
implicit that one is interested in the field far from the dipole. However, every field
line outside the loop must return inside the loop. If the size o f the current loop goes to
zero, then the field will be infinite at the origin, and this contribution is what is
reflected by the second term in [2.39].
The Hamiltonian of spin-spin interaction can be written as[l,2]:
[2.40]
Substitution of [2.37] and fi^ = gsPs^ into [2.40], we obtain the general format of
spin-spin interaction Hamiltonian:
'■s-s ~
SsSiPsfi!
3
r
Where the first term is called dipole-dipole coupling term, which represents the
A
nuclear spin and electronic spin interaction, denote by
^
, and the second term is
called the Fermi contact term, denote by H p . The expressions o f them are given in
[2.42] and [2.43].
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u
-M A A
«S-/ ^3
I-S-3
[ 2 .4 2 ]
[2.43]
The calculation o f matrix elements are complicate and tedious, readers who
interested in these can reference to C. C. Lin’s and R. F. Curl, Jr.’s papers[5,6,8].
-41-
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REFERENCE
[ 1]
'^Microwave MolecularS p e c t r a Walter Gordy and Robert L. Cook, John
Wiley & Sons, Inc. 1984.
[2]
“Introduction to Atomic and Molecular Spectroscopy*’; Guowen Wang,
Pekin University, 1985.
[3]
“High-Resolution Spectroscopy o f Transient Molecules”; Eizi Hirota,
Springer-Verlag Berlin Heidelberg 1985.
[4]
J. H. Van Vleck; Rev. ofMod. Phys.. Vol. 23(3). 213-227, 1951.
[5]
C. C. Lin; Phys. Rev., Vol. 116(4), 903-910, 1959.
[6]
G. R. Bird, J. C. Baird, A. W. Jache, J. A. Hodgeson, R. F. Curl, Jr., A. C.
Kunkle, J. W. Bransford, J. Rastmp-Andersen, J. Rosenthal; J Chem. Phys.
Vol. 40(11), 3378-3390, 1964.
[7]
W. T. Raynes; J. Chem. Phys. Vol. 41(10), 3020-3032,1964.
[8]
R. F. Curl, Jr., J. L. Kinsey; J. Chem. Phys. Vol. 35(5), 1961.
[9]
Randal C. Telfer; http://www.pha.ihu.edii/~rtl9/hYdro/node9.html
[10]
“Molecular Beams”; Norman F. Ramsey, Oxford at the Clarendon Press,
First published 1956, reprinted 1963.
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Section II
Microwave Spectroscopy of Molecules with Multiple Tops
Undergoing Hindered Internal Rotation
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CH A PTER TH REE
Rotational Spectra of Argon Acetone: A Two-Top Internally
Rotating Complex
Published in Journal o f Molecular Spectroscopy 213(2), 122-129 (2002)
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Rotational Spectra of Argon Acetone: A Two-Top Internally
Rotating Complex
Lu Kang, Alison R. Keimowitz, Michaeleen R. Munrow, and Stewart E. Novick
Department o f Chemistry, Middletown. Connecticut 06459
ABSTRACT
The rotational spectra of the argon acetone weakly bound complex was studied by
pulsed jet Fabry Perot Fourier transform microwave spectroscopy. Over 500
transitions of the complex were measured between 5.5 and 26 GHz from J = 2 - I to J
= 1 2 -1 1 . The two methyl groups undergo hindered internal rotation resulting in four
or five internal rotation states. The microwave transitions are within these states,
resulting in a splitting o f each rotational transition into four and sometimes five
distinct transitions. The three-fold barrier to internal rotation is determined to be 260
cm'*, 2 % less than the 266 cm'* barrier in acetone itself. The structure of the complex
has the argon atom above the heavy atom plane of the acetone, 3.52 A from the C= 0
bond and approximately in the Cs plane which is perpendicular to C -C -C plane of
acetone.
Keywords: van der Waals, complexes, microwave, spectra, internal rotation, twotop, Fourier transform microwave spectroscopy, argon acetone.
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INTRODUCTION
Weakly bound complexes in which one of the molecules which make up the
complex has one or more internal tops which undergo hindered internal rotation can
serve as sensitive probes o f the "van der Waals" bond. Specifically, the 3-fold barrier
to internal rotation o f the methyl group in many common small organic molecules
have been measured by microwave spectroscopy, yielding barriers to internal rotation
that typically vary between approximately
200
and 1600 cm*' [ 1 , 2 ], energies which
are comparable to the dissociation energies of weakly bound complexes [3]. We can
investigate the effect o f intemal rotation upon complexation or, more easily, examine
the effect o f complexation on the intemal rotation barrier. Weakly bound complexes
in which one of the complexing molecules has a methyl group and thus may exhibit
intemal rotation include the complexes of methanol [4], acetaldehyde, methyl
cyanide, methyl acetylene, dimethyl amine, trimethyl amine, trimethyl phosphene,
trimethyl cyano methane, methyl cyclopropane, dimethyl ether, methyl nitrate, and pfluorotoluene [5]. The intemal rotation of complexes involving methanol have been
studied extensively and include Ar CH3 OH, in which a dramatic lowering of the
torsional barrier height was presumably observed, from 373 cm'* in uncomplexed
methanol to 68.5 cm"’ in the argon complex [4]. The authors conclude that this
apparent lowering is an artifact o f the analysis and is due, in fact, to large amplitude
"librational motion" o f methanol, essentially the strongly hindered O-H wagging
motion in the complex. This apparent barrier decrease in methanol c omplexes was
first understood and described by Fraser et al. [6 ]. Most of the cases where methyl
intemal rotation has been observed in complexes (unfortunately) involves methanol
as one of the binding partners [7, 8 ], but there are some other cases where libration
should not be as much o f an issue. In the argon acetaldehyde complex, the analysis of
the methyl intemal rotation is complicated by a second internal motion, the inversion
through a planar configuration [9], In the argon p-fluorotoluene complex the methyl
1
I
barrier appears to increase significantly upon complexation (from 4.8 cm* to 23 c m ')
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[ 1 0 ], but the interpretation is not straightforward, as the symmetry upon complexation
requires a V 3 potential term in addition to the Vf, term required by the fluorotoluene's
plane o f symmetry. Likewise, in the SO2 toluene complex, the V3 potential is fit to an
astonishing 83 cm'* compared to toluene's Vg of 4.9 cm'* [11]. In Ara N~
methylpyrrole the Vg symmetry o f the methyl barrier is maintained upon
complexation, making for a more straightforward comparison; the Vg barrier
decreases from 67.8 cm'* to 55.7 cm'* when the two argon atoms bond to the opposite
sides o f the ring plane [ 1 2 ].
In order to investigate the effect o f complexation upon internal rotation, we have
collaborated in a series of microwave investigations on the structure and spectra of
complexes with similar symmetry for the methyl tops both in and out of
complexation. These complexes include argon dimethyl ether [ 13], argon dimethyl
sulfide [14], and argon acetone, the subject o f this study.
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EX PEM M ENTAL
The microwave spectrum of the Ar (CH 3)2CO complex was recorded using a
pulsed-jet Fabry-Perot Fourier transform microwave spectrometer which has been
described elsewhere [15]. Many upgrades to the spectrometer have occurred since
that initial publication including coaxial expansion of the gas with the cavity axis for
increased sensitivity and resolution, changes in the microwave circuitry for decrease
in the microwave noise, and automatic scanning for ease of use.
Briefly, a 1 % mixture of acetone in argon with a total backing pressure of
approximately 1 atm is expanded through a 0.5 mm diameter pulsed supersonic
nozzle into the high Q Fabry-Perot microwave cavity tunable between 5 and 26.5
GHz. A microwave pulse is timed to coincide with the arrival of the gas pulse
containing the weakly bound complexes "synthesized" by the low temperature (~3 K)
expansion. If a molecular absorption line lies within the ~500 kHz bandwidth of the
microwave pulse/cavity combination, a macroscopic polarization is induced in the
molecules. The free induction decay o f this polarization is collected and averaged
over multiple pulses and is Fourier transformed to yield the spectrum of the transition.
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TWO TOP INTERNAL ROTATION
Acetone has two equivalent methyl tops which undergo hindered intemal rotation.
For molecules with a single top with a three-fold barrier, rotational energy levels split
into two torsional sublevels labeled A (torsional symmetry of 0) and the doublydegenerate £ (torsional symmetry of ±1). For a molecule with two equivalent methyl
tops, Myers and Wilson showed that the rotational levels are split into four torsional
states labeled AA, AE, EA, and EE under the direct product group C3; ® c ; [16],
which can also be labeled as (0 ,0 ), (± 1 ,± 1 ), (± 1 ,+ 1 ), and [(0 ,± I) and (± 1 ,0 )], states
of 1-, 2-, 2-, and 4-fold degeneracy, with the numbers labeling the torsional symmetry
of each top [17]. In the event of the inequivalancies of the two tops, the final fourfold
degenerate state can split into two twofold states labeled EfE (0,±1) and EE) (±1,0).
The selection mles are such that rotational transitions occur within the torsional
substates causing a frequency splitting of a transition into 3 (AE and EA not
resolved), 4, or 5 (EE split) transitions. An altemative labeling scheme used by some
authors is AA = A, AE = E+, EA = E_, and EE = G [17,18].
To analyze the spectrum we used the program XIAM written by Holger Hartwig
and first presented by Hartwig and Dreizler [17]. XIAM analyzes the internal rotation
splitting of one, two, or three symmetric tops within the molecule using a version of
the intemal axis method (lAM) of Woods [19], which the authors call a "combined
axis method" or CAM, since it utilizes a combination of several different coordinate
systems. An important axis system is based on the vector(s) p which are fixed in the
molecular frame but oriented with respect to the intemal top axes so as to allow only
coupling between the z component of the overall angular momentum in the principal
axis system and the top angular momentum [20]. In XIAM separate p axis systems
are defined for each top. For two tops, the Hamiltonian is given as [2 1 ]
ff = H,., + ff,, +
where
Hy, + H ,, + Hy, +
+ H,,
(I)
is the standard rigid rotor Hamiltonian plus the Watson A reduction
centrifugal distortion Hamiltonian, 77, and
are the intemal rotation Hamiltonians
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for tops
1
top,
and 2 ,
and
and
are the intemal rotation centrifugal distortions for each
are the intemal-rotation overall-rotation distortion operator, and
Hy2 involves top-top coupling. In order to understand the meaning of the
spectroscopic constants we will present, we repeat here relevant parts of the
definitions o f the Hamiltonian terms.
The intemal rotation term,
, is given by
w, “
(2)
where F is the effective rotational constant of topi, or, is the torsional angle of the
top, p^y is the angular momentum of the top, py is the magnitude of the rho-vector
(p^ = A l^lF ^, p^ =BAjFyy, py -=CA^fFyy, where the X are the direction cosines
between the top axis and the principal axes and F q is the rotational constant of the
top), Ppy is the angular momentum along the p, axis, and V 3J is the height of the 3fold barrier to intemal rotation for topi.
The intemal-rotation overall-rotation distortion term,
, is given by
=2A,„.(P„, ~PyP,yfP^^^^^{p.y ~ P^P.d" P^ + P" iP
O)
There are similar terms for H2 and Hard- The top-top coupling term, H 12, is given by
~ P'n [ ( / ’a l
~
P\Pp\ ) iP a 2 ~ P l^ p l )
"t* iPaZ
~ Pl^pZ )(P a l ~ Pl^pX ) ]
(^ )
Finally, there are geometric angles P and y, Euler angles between the p-axis system
for each top and the principal axes, fi = cos'*{p^ / p) and y = cos~‘[p^ I{pi + p^)^],
which can be adjusted as part of the spectroscopic fit.
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RESULTS AND ANALYSIS
Over 500 microwave transitions were measured for the argon acetone complex.
The transitions came in groups of 4 lines with all the lines in a group generally within
10 MHz o f each other. In some o f these groups a small additional splitting could be
resolved, giving 5, rather than 4 states. Our first task was to assign each of the four
transitions to one o f the torsional substates. We were greatly aided in this task by an
approximate sum rule given by Nelson and Pierce [22],
4'^ee- 2 v'aa- '" ea“ ^ ae= 0
(5)
based on a second order perturbation calculation of the intemal rotation splittings. We
found that this mle worked well on some groups of transitions (generally transitions
involving only K„ = 0 and 1 states) giving deviations from zero to on the order of 10
kHz. However, on transitions involving higher K„ states the deviations from zero
could be on the order of 10 MHz. Never the less, with the aid of Eq. (1), it was
possible to begin to assign the complete spectrum.
Table 1 gives the microwave transitions of the five intemal rotor states of argon
acetone. The frequencies of the EjE, EEj, AE, and EA states are given as offsets from
the AA transition firequencies. In most cases the degeneracy o f the EE state is not split
beyond our resolution o f a few kHz and the same frequency is given twice. Two
global spectroscopic fits of the 500 transitions are given in Table 2. In Fit I, both tops
are forced to be equivalent, while in Fit II, all parameters of each top are
independently fit. In both Fit I and Fit II the few EE state transitions which are not
identical are included in the fit with their separate values. The two fits yield
essentially identical spectroscopic constants and have root mean squared deviation of
the fit of 20 kHz.
Structure
In the combined axis method and Hamiltonian, in contrast to the principal axis
method (PAM) o f analysis of internal rotation, the rotational constants A, B, and C, of
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Hrr are the actual rigid rotor constants {A = tij2 I^, etc.) and can be used directly to
extract structural information. We use the standard assumption that the structures of
the individual moieties are unchanged upon complexation. We use the structure of
acetone as given by Nelson and Pierce [22]. Since three coordinates are required to
orient the argon atom with respect to the acetone, and since A, B, C, of the complex
have been determined, the structure can be fit with just the one isotopomer we have
studied. Kraitchman's equations [23] can be used, as we have done before, to
determine the
position of the argon atom [24]. One considers the unsubstituted
molecule to be the complex with an argon atom of mass zero (that is, acetone itself),
and the substituted structure to be the actual argon-acetone complex. In acetone, the
a"’ and b"' principal axes are in the plane of the heavy atoms, with the
axis being
the quasi-C 2 axis, the c™axis is perpendicular to the heavy atom plane, and the centerof-mass is along the C2 axis, 0.09 A behind the C =0 bond. In this coordinate system
(the principal axis system (FAS) of acetone), the rs coordinates o f the argon atom are
(a"’, b™, c™) = (0.337, 0.538, 3.504) A; the m-superscript is a reminder that this is in
the PAS o f the uncomplexed acetone "monomer". Were the argon to be in the
bisecting symmetry plane of acetone, then
would be zero. The ro position of the
argon atom can be calculated using a version of Schwendeman's STRFTQ program
updated by Hillig [25] giving (a™, b'^, c’^) = (0.306, 0.454, 3.521) A. The argon atom
is above the plane o f the acetone, 3.52 A from the C= 0 bond, but slightly off to one
side. This asymmetry o f the argon position amounts to a tilt of only 5° of the C -C -C
plane tilting about the C =0 axis under a stationary argon. Most likely, this asymmetry
is mostly a consequence of "wide amplitude" rocking in this weakly bound complex
and is not a reflection o f an appreciable asymmetry in the (unmeasured) Vg structure.
Figure 1 shows three views of the structure of the complex. In Fig. la, the orientation
is with respect to the principal axes of the complex (not the PAS o f acetone), with the
b axis oriented directly out of the page. Fig. lb is oriented with respect to PAS of
acetone, with b^ axis out of the page. In this figure, the 5° tilt of argon out o f the
b'^c^ plane is apparent. Fig. Ic, is an orientation required, below, for the discussion of
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the V 3 barrier.
There are two independent measurements of the structure. The first (fit I) is the
Kraitchman, r^, (or the slightly different ro), determination of the position of the argon
atom in the complex, as determined from the rotational constants o f the complex as
given in the above paragraph and shown if Figs la, lb, and Ic. The second (fit II) is
the direct fit o f the direction cosines between the two intemal top axes,
1
and
2
and
the a, b, c, principal axes system of the complex that is part of the CAM p-axis fit of
the intemal rotation. As given in Table 2, these angles are (fit II, intemal rotation)
Z {l,a ) = 93°, Z (l,b ) = 30°, (l,c) = 60°, Z(2,a) = 93°, Z(2,b) = 150°, and Z(2,c) =
60°. These are a completely symmetric set of angles (a's and c's are the same and b's
are supplements), showing a fit in which the two tops are geometrically equivalent. In
contrast, the rotational constant stmcture determination, if interpreted as due to a rigid
complex has the argon atom 5° off center (see above), giving these angles as (fit I,
stmcture) Z {l,a) = 80°, Z (l,b ) = 36°, Z (l,c ) = 56°, Z(2,a) = 91°, Z(2,b) = 152°, and
Z(2,c) = 62°. Fit I is similar, but not identical to, the direct fit (fit II) of the direction
cosines as part o f the CAM p-axis intemal rotation analysis. This implies that the
asymmetry of the stmctural fit (I), which is shown in Figs. l a - lc and denoted in
Table 3, is an artifact o f treating a weakly bound wide amplitude bender (the relative
motion between the argon and the acetone, not the intemal rotation), in terms o f a
best or averaged rigid stmcture, which can be far from the equilibrium stmcture.
Barrier to Internal Rotation
As presented in Table 2, the spectra can be fit by assuming that for the two methyl
tops the three-fold barrier to intemal rotation is same and equal to 260 cm '. This is
2% less than the 266 cm"' barrier in acetone itself, measured by Vacherand, et al. in
1986 by a global fit o f the rotational transitions of acetone up to 300 GHz, using the
Intemal Axis Method [26]. We presume that this slight decrease, from acetone to
argon acetone, is an actual V3 barrier lowering since the methyl tops are each attached
to relatively massive "frames"and thus libration should not be a significant effect. The
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simple qualitative explanation of this barrier change is that the major 3-fold potential
of the O -H 3C interaction, V 3, is augmented by a much smaller Ar-HsC 3-fold
potential, V 3'. Figure Ic shows the complex in a V 3 minimum configuration, with one
o f the protons in each methyl group pointing towards the carbonyl oxygen [27]. It can
be seen in this figure that this is a geometry with the protons pointing away from the
argon atom and at a distance o f about three and one-half Angstroms from argon. At
these large distances, van der Waals forces, even between argon and non-acidic
protons, are slightly attractive, thus V 3 and V3’ are out of phase. The net result of the
out-of-phase sum is a decrease in the total 3-fold barrier in the complex compared to
acetone itself, as observed.
A related system is the argon methane complex which has been studied both
theoretically [28] and experimentally [29]. The very fact that this is a bound complex
shows that the non-acidic hydrogen atoms of methane do indeed form a bond with the
argon atom. However, the favorable orientation of argon is not towards the comer of
methane's tetrahedron, but rather towards the face. The Ar to methyl-carbon distance
is about 0.2 A greater in argon acetone than the minimum energy distance in argon
methane; at this greater distance, the potential in Ar CH4 varies between -130 to -50
to -110 cm'^ (for argon opposite the face, edge, and apex of the CH4 tetrahedron)
[28]. Were argon’s interaction potential, V 3', with CHs-group of acetone the same as
its interaction with CHs-group of methane, then the orientation of Fig. Ic would be at
the minimum in V 3 (methyl rotation in acetone) and near the minimum of V 3', giving
a net increase in the barrier to intemal rotation upon complexation. In fact, there is a
net decrease in the barrier upon complexation. Therefore, we conclude, that the two
V 3 potentials, the major one between H and O, and the minor one between H and Ar
are essentially out-of-phase.
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REFERENCES
Figure and Table Captions
Table 1.
The microwave transitions of the five intemal rotor states of argon
acetone. The frequencies of the transitions of the AA state is given in
MHz. The frequencies of the E{E, EEp AE, and EA states are given as
offsets from the AA transition frequencies, in MHz. The observed calculated frequencies are given in kHz for a fit in which the two tops
are set to be equivalent.
Table 2.
Spectroscopic constants of argon acetone. Two fits are given. In Fit I,
both tops are forced to be equivalent. In Fit II, all parameters of each
top are independently fit. The two fits are essentially identical.
Table 3.
Stmctural constants of argon acetone from a Kraitchman analysis.
Figure 1.
The stmcture o f Ar acetone complex, shown in three views.
a.
Here the orientation is with respect to the principal axes of the
complex with the b axis oriented directly out o f the page.
b.
Here t he figure i s o riented w ith r espect to PAS of a cetone, with b
axis out of the page. The 5° tilt of argon out of the b^c^ plane is
apparent.
c.
This orientation shows that when the intemal rotation angle, a, of the
methyl group is such that one o f the hydrogens is closest to the oxygen
and Y'iia) is a minimum, the hydrogens point away from the argon
atom.
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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TABLE 1. Microwave Transitions of Argon Acetone
CD
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A type transitions
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k,k.
AA
0-C
EiE-AA
0-C
EEj-AA
O-C
AE-AA
0-C
EA-AA
0-C
lu
5645.767
-3
-0.136
1
-0.136
0
0.354
9
-0.925
-5
2o2
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loi
5687.262
-6
-0.795
1
-0.795
0
-1.375
-5
-1.816
-5
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—
1,0
5728.837
-2
-0.880
-6
-0.880
-6
-2.532
-24
-0.969
-7
6i6
__
524
5913.422
-5
3.849
-8
3.849
-17
12.685
25
-1.692
-9
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—
2 ,2
8468.052
-6
-0.512
2
-0.512
-3
-0.660
0
-1.378
-5
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—
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8529.607
-7
-1.180
-1
-1.180
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-2.061
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8530.551
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-1.540
-11
-1.540
-12
-2.454
-21
-1.687
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8592.630
-7
-1.013
-2
-1.015
-4
-2.572
-10
-1.492
-6
4 i4
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3,3
11289.624
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-0.726
-1
-0.726
-2
-1.080
-2
-1.825
-6
4 o4
—
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11370.407
-7
-1.546
0
-1.546
-2
-2.745
-7
-3.445
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11371.146
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0.290
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0.290
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-56
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11374.751
-7
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2.564
-10
-3.960
-29
-2.260
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11455.679
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The microwave transitions o f the five internal rotor states o f argon acetone. The ifrequencies of the transitions of the AA state
is given in MHz. The frequencies of the EjE, EEj, AE, and EA states are given as offsets from the AA transition frequencies, in
-
MHz. The observed - calculated frequencies are given in kHz. The rms o f the fit is 20 kHz.
CD
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-61-
TABLE 2. Spectroscopic Constants of Argon Acetone
Asymmetic Rotor Constants
Internal Rotation Constants
Fit I --both tops treated as equivalent
Top2
Topl
A
4991.810(3) MHz
P
0.009422(3)
0.009422(3)
B
1442.445(1) MHz
P
1.76627(5)
1.76627(5)
C
1401.028(1) MHz
T
0.5095(3)
0.5095(3)
Aj
6.436(3) kHz
Vj
259.63(9) cm'^
259.63(9) cm'’
A jk
81.29(9) kHz
Fo*
154.722 GHz
154.719 GHz
Ak
-78.6(1) kHz
F*
156.183 GHz
156.180 GHz
§j
0.187(1) kHz
Aj/ji
198.8(7) kHz
198.8(7) kHz
5k
28.1(7) kHz
A/Cm
-566.(2) kHz
-566.(2) kHz
5.(1) Hz
F,2*
^JK
1.11(9) kHz
-729.7 MHz
cos'X*
93.2515(8)°
93.2515(8)°
cos’%*
30.07(2)°
149.88(2)°
COS'^Xc*
60.1507(2)°
60.10(2)°
Fit II - tops are treated as non-equivalent
A
4991.810(3) MHz
p
0.00941(5)
0.00942(5)
B
1442.445(1) MHz
p
1.7663(2)
1.7661(2)
C
1401.028(1) MHz
Y
0.509(2)
2.631(2)
Aj
6.436(3) kHz
Vj
260.(1) cm'’
259.(1) cm'’
A jk
81.29(9) kHz
Fo*
154.990 GHz
154.618 GHz
Ak
-78.6(1) kHz
F*
156.451 GHz
156.079 GHz
5j
0.187(1) kHz
Ajm
197.(6) kHz
200.(6) kHz
28.1(7) kHz
A km
-569.(8) kHz
-562.(9) kHz
5.(1) Hz
F,2*
6k
«>JK
®k
1.10(9) kHz
-U
-730.3 MHz
•
93.253(3)°
93.250(4)°
cos*'Xb*
30.0(1)°
149.9(1)°
COS"'Xc*
60.2(1)°
60.1(1)°
COS Aa
-62-
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Note: Two fits are given. In Fit - 1, both tops are forced to be equivalent. In Fit - II, all
parameters of each top are independently fit. The two fits are essentially identical.
* Constants denoted by the asterisk are not directly fit fi*om the spectroscopic data but
are calculated from other fitted constants.
-63-
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE 3. Structural Constants of Argon Acetone from a Kraitchman Analysis
Coordinates o f the argon atom in the principal axis coordinate system
of acetone^
of the complex
cT
0.337A
cT
2.109A
6”'
0.538A
b'^
-0.022A
c"'
3.504A
c™
0.006A
Angles between the rotors and the PAS of the complex
Topi
Topa
COS‘’A.a
80.48°
90.66°
cos'’Lb
35.60°
151.94°
co s'X
56.07°
61.95°
Distance
Ar—O
3.604A
Ar —
3. 549A
Ar—€=0"^
3.520A
1. In acetone, the a™ and 6"’ principal axes are in the plane of the heavy atoms, with
the
axis being the quasi-Ca axis, the
axis is perpendicular to the heavy atom
plane, and the center-of-mass is along the Ca axis, 0.09 A behind the C=0 bond.
2. In the complex, the a axis approximately connects the center-of-mass of acetone
and the argon atom, while the c axis is approximately parallel to the quasi-Ca axis of
acetone.
3. The carbonyl carbon atom.
4. The perpendicular distance from the argon atom to the C =0 bond.
-64-
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 1.
■>
X.
#)
m
\c)
H G . 1, The structure of Ar acetone complex, shown in t t e e views, (a) Here the orientation Is with respect to the principal axes of the complex with the b axis
oriented directly out of the page, (b) Here the figure is oriented with respect to PAS of acetone, with &''‘ axis out of the page. The 5° tilt of argon out o f the
plane is apparent. <c) This orientation .shows that when the internal rotation angle, a , of tl>e methyl group is such that one of the hydrogens is clo.sest to the oxygen
and Vjfa) is a minimum, the hydrogens point away from the argon atom.
-65-
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
REFERENCE
[1]
C. C. Lin and J. D. Swalen, Rev. Mod. Phys. 31, 841-892 (1959).
[2]
D. G, Lister, J. N. Macdonald, and Noel L. Owen, Internal Rotation and
Inversion, Academic Press, NY (1978).
[3]
K. R. Leopold, G. T. Fraser, S. E. Novick, and W. Klemperer, Chem. Rev. 94,
1807-1827(1994).
[4]
X.-Q. Tan, L. Sun, and R. L. Kuczkowski, J. Mol. Spectrosc. 171,248-264
(1995), and references therein.
[5]
S. E. Novick, Bibliography o f Rotational Spectra o f Weakly Bound Complexes
(2002), available on the Web at
http://www.wesleyan.edu/chem/faculty/novick/vdw.html
[6]
G. T. Fraser, F. J. Lovas, R. D. Suenram, J. Mol. Spectrosc. 167,231-235
(1994).
[7]
X.-Q. Tan, 1.1. loannou, K. B. Foltz, and R. L. Kuczkowski, J. Mol.
Spectrosc. I l l , 181-193 (1996).
[8]
M. Haeckel and W. Stahl, J. Mol. Spectrosc. 198,263-277 (1999).
[9]
LI. loannou, and R. L. Kuczkowski, J Mol. Spectrosc. 166, 354-364 (1994);
and 1.1. loannou, R. L. Kuczkowski, and J. T. Hougen, J. Mol. Spectrosc. 171,
265-286 (1995).
[10] J, Rottstegge, H. Hartwig, and H. Dreizler, J. Mol. Spectrosc. 195,1-10
(1999).
[11]
A. Taleb-Bendiab, K. W. Hillig II, and R. L. Kuczkowski, J. Chem. Phys. 98,
3627-3636(1993).
-
66
-
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
[12]
S. Huber, J. Makarewicz, and A. Bauder, M ol Phys. 95,1021-1043 (1998).
[13]
Xiu Jun Li and Stewart E. Novick, work in progress.
[14]
James M. LoBue, Wei Chen, Michealeen R. Munrow, and Stewart E. Novick,
to be published.
[15]
A. R. Eight Walker, W. Chen, S. E. Novick, B.D. Bean, and M. D. Marshall,
J Chem. Phys. 102, 7298-7305 (1995).
[16]
R. J. Myers and E. B. Wilson, Jr., J. Chem. Phys. 33,186-191 (1960).
[17]
H. Hartwig and H. Dreizler, Z. Naturforsch. 51a, 923-932 (1996).
[18]
F. J. Lovas and H. Hartwig, J Mol Spectrosc. 185, (1997).
[19]
R. C. Woods, J. Mol. Spectrosc. 2 1 ,4-24 (1966); ibid, 2 2 ,49-59 (1967).
[20]
J. T. Hougen, I. Kleiner, and M. Godefroid, J. M ol Spectrosc. 163, 559-586
(1994).
[21]
Holger Hartwig, private communication. The explicit terms in the
Hamiltonian are given in the text file that accompanies the XIAM program.
This information is also available in the relevant referenced literature.
[22]
R. Nelson and L. Pierce, J. M ol Spectrosc. 1 8 ,344-352 (1965).
[23]
J. Kraitchman, Am. J. Phys. 4 8 ,17-24 (1953).
[24]
M. R. Munrow, W. C. Pringle, and S. E. Novick, J. Phys. Chem. 103,22562261 (1999).
[25]
K. Hillig; R. Schwendeman, private communications.
-67-
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
[26]
J. M. Vacherand, B. P. Van Eijck, J. Burie, and J. Deraaison, J Mol.
Spectrosc. 118, 355-362 (1986).
[27]
J. S. Crighton and S. Bell, J. Mol. Spectrosc. 118, 383-396 (1986).
[28]
T. G. A. Heijmen, T. Korona, R. Moszynski, P. E. S. Wormer, and A. van der
Avoird, J. Chem. Phys. 107, 902-913 (1997); T. G. A. Heijmen, P. E. S.
Wormer, A. van der Avoird, R. E. Miller, and R. Moszynski, J. Chem. Phys.
110, 5639-5650 (1999).
[29]
R. E. Miller, T. G. A. Heijmen, P. E. S. Wormer, A. van der Avoird, and R.
Moszynski, J. Chem. Phys. 110, 5631-5657 (1999).
-
68
-
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CHAPTER FOUR
Rotational Spectroscopy of Molecules with Three Tops
Undergoing Internal Rotation:
The Microwave Spectra of Trimethylsilane, (CH3)3SiH,
T rimethylsilylethyne, (CH3)3SiCCH, and
Trimethylsilylbutadiyne, (CH3)3SiCCCCH
Manuscript in preparation
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Rotational Spectroscopy of Molecules with Three Tops Undergoing Hindered
Internal Rotation:
The Microwave Spectra of Trimethylsilane, (CH3 )3 SiH, Trimethylsilylethyne,
(CH 3 )3 SiCCH, and Trimethylsilylbutadiyne, (CH3 )3 SiCCCCH
Lu Kang and Stewart E. Novick
Department o f Chemistry, Wesleyan University, Middletown, CT 06459
ABSTRACT
The microwave spectra of Trimethylsilane, (CH 3)3SiH, Trimethylsilylethyne,
(CH3) 3SiCCH, and Trimethylsilylbutadiyne, (CH3) 3SiCCCCH, as well as some of
their silicon isotopic species were studied by Fourier transform microwave (FTMW)
spectroscopy. The torsional splittings arise from the internal rotation o f (CH 3)3$iH
and (CH3) 3SiCCH were distinguishable. The accurate torsional barriers due to the
hindered torsions o f methyl groups for (CH3)3SiH and (CH 3)3SiCCH were determined
to be 573.4 cm’’ and 581.4 cm'^ respectively. (CH 3)3 SiCCCCH was made from the
pulse discharge nozzle with precursors, and the spectra were observed.
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INTRODUCTION
Many spectroscopists have been interested in the molecules with three-top
internal rotation for quite a long time due to the complexities of their spectroscopy [ 1 6 ].
The spectra can be congested and unresolved due to the torsional hyperfine
splittings which arise from the internal rotations. The so-called internal rotation is
actually the hindered torsions of the tops with respect to their own local symmetry
axes. Before our present work, few o f clearly resolved rotational spectrum for a
molecule with three-top internal rotation had been recorded [7]. The main purpose of
this paper is to introduce our most resent progress on the study of symmetric top (Csv)
molecules with a trimethylsilyl group, (CH 3)3Si~, for instance, Trimethylsilane,
(CH 3) 3SiH,
Trimethylsilylethyne,
(CH 3)3SiCCH,
and
Trimethylsilylbutadiyne,
(CH 3)3SiCCCCH using the high resolution Fourier transform microwave (FTMW)
spectroscopy. Our purpose is mainly concerned with the investigation of the torsional
hyperfine splittings of several three-top molecules and the determination of their
accurate molecular constants, and more importantly, the associated torsional barrier,
V3 . Although microwave spectroscopy is not the only way to determine the torsional
barrier of the molecules that undergo the internal rotation, among all of the applicable
techniques, it usually provides us with the high quality measurements on the torsional
barriers for gas phase molecules.
Trimethylsilane, (CH3)3SiH, as well as its isotopic species have been studied by
Fierce et al. with the traditional Stark cell modulation microwave spectroscopy [2].
A set of fairly good rotational constants and the molecular structures were
determined. Unfortunately, the torsional hyperfme splittings were not well resolved
due to the low resolution of the spectrometer, thus the torsional barrier couldn’t be
determined from the rotational analysis. The authors had to analyze vibrational
satellites (v^ == 1, V3 = 1) and the isotropic species (CD3 ) to derive the torsional barrier
V3 = 1.83 kcal/mol. This is inconsistent with the torsional barrier of V 3 = 2.49
kcal/mol determined from the Raman spectroscopy [1]. Trimethylsilyethyne,
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(CH 3)3SiCCH, has been studied by Alexander et a l with microwave spectroscopy but
the torsional splittings were not resolved [8 ]. These authors also synthesized
Trimethylsilylbutadiyne, (CH3)3SiCCCCH, and searched for it very carefully, but
unsuccessfully. The negative result was attributed this to be the small dipole moment
of(C H 3)3 SiCCCCH.
Since most o f the problems that arise in the accurate and detailed analysis of the
spectra o f three-top molecules with the traditional techniques come from the
indistinguishable torsional splittings, we attempted to make use of the high resolution
(a few kHz) o f modem Fourier transform microwave spectroscopy to investigate the
spectroscopy of these three-top molecules. We realized, similar to what Merke et a l
have mentioned [7], that molecules with three intemal tops seem to be closed to the
resolution limit even for FTMW spectrometers. Careful selection o f the molecular
system is necessary so as to be able to resolve the torsional hyperfine splittings. Since
the higher the torsional barrier, the narrower the splittings [9], those three-top
molecules with fairly low torsional barrier are good candidates for fully resolved
spectra. Also, in order to observe the pure rotational spectrum, the molecule must
possess a permanent dipole moment. For all of the normal three-top molecules,
Trimethylsilane and Trimethylsilyethyne satisfy both of these prerequisites quite well,
thus they become our choice for the present study. According to our density
functional level of ab initio calculation, B3LYP/6-311++g(d,p), (CH3)3 SiCCCCH
possesses a dipole moment of 0.78 Debye, which is comparable to that of OCS, 0.716
Debye. Since the latter is a well known benchmark test molecule for the FTMW
spectroscopy, there is no reason for (CH 3)3SiCCCCH to be undetectable simply
because o f the “ small” dipole moment. We did observe it in the present work and
found a very interesting thing, which will be introduced in the following section.
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EXPERIM ENTAL
Trimethylsilane, (CH3)3SiH (City Chemicals LLC.), and Trimethylsilyethyne,
(CH 3)3 SiCCH (GFS Inc.), were commercially available and used without further
purification. Trimethylsilylbutadiyne, (CH3)3SiCCCCH, was “synthesized” by
discharging a gas mixture o f (CH 3)3SiCCH and HCCH with the pulse discharged
nozzle. Spectra were recorded with the supersonic pulse-jet Fourier transform
microwave spectrometer at Wesleyan University. The supersonic beam expansion
dramatically lowers the rotational temperature of the molecules to ~5 Kelvin or less,
dramatically increases the sensitivity of the detectability of low J transitions.
Descriptions o f FTMW can be found everywhere including publication from this
laboratory [10]. Many modifications have been made since the initial publication,
including coaxial expansion of the gas with the cavity axis for increased sensitivity
and resolution, changes in the microwave circuitry for decreasing the noise level and
automation scanning for ease of use.
In the experiments, a ~1% precursor gas seeded in the argon carrier gas with a
stagnation pressure o f 1 atm is expanded into the high Q Fabry-Perot cavity through a
0.5mm General Valve nozzle. A microwave pulse is synchronized to the arrival of the
gas pulse at the center o f the cavity, where a macroscopic polarization is induced in
the molecules. We then measure the free induction decay (FID) of this polarization
and Fourier transform the signal to yield the spectrum. The experiment for Trimethyl­
silylbutadiyne, (CH 3)3SiCCCCH, is a little bit different. A ~1% [(CH3)3SiCCH +
HCCH, 1:1] in Argon with a background pressure of 1 atm is expanded th ro u ^ a
0.8mm diameter General Valve nozzle. The expanding pulse then passes through a 1
cm discharge region with a pulsed 1,000 volts potential difference. The resulting
plasma discharge with a current of typically 20mA serves to dissociate the acetylenic
C—H bond on both of HCCH and (CH3) 3SiCCH. The subsequent collision of those
fragments in the discharge region produces the (CH3)3SiCCCCH.
-73-
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To take the advantages of the high resolution of FTMW, we took 8192 data points
at 200 ns per point. This total collection time of ~ L 6 ms corresponds to a frequency
resolution o f 0.6 kHz per point. With such a high resolution, the center of the peak
can be determined within 1 kHz. The signals o f (CH3)3SiCCCCH were too weak to be
detected with so high a resolution, thus we took 2048 data points for each
measurement. The resolution limit for (CH 3)3SiCCCCH spectra is ~3 kHz.
-74-
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THREE TOP INTERNAL ROTATION
The detailed treatments o f three-top internal rotation have been given by Dreizler
and his co-workers [5,11]. Merke et al. presented the theory in a comprehensive from
[7]. For ease o f understanding, we simply list the Hamiltonian that we used in the
analysis for three-top intemal rotation system. Details can be found in the references
above.
The Hamiltionian can be written as a sum of partial Hamiltionians describing the
various kinds of interactions:
H = Hrot + H a + Htors + Hrr + H„ + Hrt
The first term, Hnt represents the molecular overall rotation of the target molecule
as a rigid rotor in the free space. The second term, H a represents the centrifugal
distortion o f a symmetric top for the whole molecule. The third term, Htors represents
the internal rotation o f the top as a Mathieu oscillator, and it describes the hindered
torsion of the three intemal rotors. The magnitude of this interaction is determined by
F and V3 . F can be considered as the effective rotational constant of the three rotors,
and V 3 is the torsional barrier. The fourth term, Hrr arise from the deviation o f the
new principal axis from its rigid rotor principal axis due to the torsion of the intemal
rotation. It can be thought of as the “Coriolis terms”. The fifth term, Hu represents
the kinetic interaction between the intemal rotors. The magnitude is measured by Fy (i
j and i, j = 1, 2, 3). The last term, Hn represents the interaction between the intemal
rotation and the overall rotation of the whole molecule. The torsional constants were
determined by the least-square fitting of the XIAM program package [12], which is
based on the Hamiltonian previously mentioned.
If the torsion o f three methyl groups is a feasible motion, the molecular symmetry
group o f o u r targetmolecules is G i 6i- Lehmann and Pate w orkedout itscharacter
table [13]. In the high barrier limit, the 27 torsional states are degenerate, whereas in
the low or intermediate barrier height,
6
out of the 27 torsional states are
distinguishable for a symmetric top molecule, as listed in the Table III of Ref. [13].
-75-
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We label the torsional states by their m quantum numbers of each top
\nt],
m2, m3) in
the lower barrier limit, which introduces 27-fold quasidegeneracy of the ground
vibrational state. Briefly speaking, \0. 0, 0) is labeled as At with 1-fold degeneracy;
\±1 , 0 , 0 ) is labeled as h with 6 -fold degeneracy; \±1 , ± 1 , 0 ) is labeled as h with 6 fold degeneracy; |±i, +1, 0) is labeled as I4 with 6 -fold degeneracy; \±1, ±1, +1) is
labeled as I3 with 6 -fold degeneracy; and \±1, ±1, ±1) is labeled as E2 with 2-fold
degeneracy. Note that the three tops are equivalent os the six fold degeneracy of I2
follow from the equivalence of \+l, 0 , 0 ), \-l, 0 , 0 ), \0 , +1 , 0 ), \0 , - I ,
0 ), \0 , 0 ,
+ /),
\0, 0, -1 ) states. Our purpose is to observe the torsional hyperfme splittings arise from
these
6
distinguishable torsional states, and derive useful information based on our
analyses o f them.
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SPECTRA AND ANALYSIS
Trimethylsilane, (CH 3)3SiH
The s pectrum o f th e 1 - 0 t ransition o f ( CH3)3SiH i s g iven i n F igure-1, w hich
clearly displays the
6
distinguishable torsional hyperfine splittings. F igure-2 shows
the spectrum of the 2 - 1 transition. It possesses a similar pattern to that of Figure-1,
but is contaminated with a few unassigned lines which probably come from the K
0
branches. The measured frequencies of the main isotopomer, (CH 3)3^®SiH, as well as
it’s silicon isotopic species, (CH 3)3^^SiH and (CH3)3^®SiH are listed in Table-1. The
fitted molecular and torsional constants are listed in Table-2. The rotational constants
are very close to the values determined by Pierce and Petersen [2], but the torsional
barrier, V3 , is dramatically smaller than their reported value.
Trimethylsilyethyne, (CH 3)3SiCCH
The spectra o f (CH 3) 3SiCCH are very congest and only the K = 0 branch can be
barely distinguished. Theproblem come from the 0 verlap o f different K branches,
which results in an intermingled, messy spectrum. Furthermore, the 1 - 0 transition of
(CH3)3SiCCH predicted at 3.9 GHz is out of the spectrum range (5.5 - 26.5 GHz) of
our spectrometer, thus a clean spectrum with torsional hyperfine splitting pattern like
that o f Figure-1 for Trimethylsilane which avoids the contamination from K 7^ 0
branches, is unobtainable. Fortunately, the similarity between (CH 3) 3SiCCH and
(CH3)3SiH is a great help in making the assignments for Trimethylsilyethyne. Table-3
lists the measured frequencies for all three of the silicon isotropic species and Table-4
lists the determined molecular and torsional constants. The torsional barrier for
(CH3)3SiCCH is comparable to those of (CH 3)3SiH and (CH3)3 SiCl [7].
Trimethylsilylbutadiyne, (CH 3) 3SiCCCCH
The searching for (CH 3)3SiCCCCH transitions was a test of the detection limit of
our spectrometer. With the help of the discharge nozzle and the careful optimization
-77-
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o f the machine conditions, several transitions were finally observed. The spectra were
very congest and messy, even worse than those of (CH 3)3SiCCH, thus the torsional
hyperfine splittings are not resolvable. The assignment was based on the contour of
those transitions. The measured frequencies are listed in Table-5. Before the
experiment, we carefully studied the rotational constants of (CHsfsSiCCH [8],
(CH 3) 3SiCN [14, 15], and (CH3)3SiCCCN [8]. Since the Bo of (CH3)3SiCN is larger
than that of (CH 3)3SiCCH, we estimated that the B q of (CH 3) 3SiCCCCH would be
slightly smaller than that of (CH 3)3SiCCCN, which is reported to be ~712 MHz by
Alexander et a/. [8]. Thus we performed a condensed scan over the frequency regions
predicted based on the assumption o f Bo ~ 700 - 712 MHz, and found nothing for two
weeks. Finally, we found what the truth is: the Bo of (CH 3)3SiCCCCH is slightly
larger than that o f (CH3)3 SiCCCN by about 2 MHz. The molecular constants of
(CH 3) 3SiCCCCH and its isoelectronic analogue, (CH3) 3SiCCCN, are listed in Table-6
for comparison.
-78-
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CONCLUSION
The rotational spectra of Trimethylsilane, (CH3) 3SiH, Trimethylsilylethyne,
(CH 3)3 SiCCH, and Trimethylsilylbutadiyne, (CH 3)3SiCCCCH and some of their
silicon isotropic species have been recorded with a Fourier transform microwave
spectrometer. The torsional hyperfine splittings due to the intemal rotation of three
identical methyl groups can be distinguished. From the analyses of the torsional
hyperfine stmctures of the spectrum, more accurate molecular and torsional constants
were derived. Those molecular constants are very close to the previously determined
values which were derived without taking into account of the affects of the internal
rotations of the methyl groups. The torsional barriers for our target molecular species
were derived based on the rotational analysis including intemal rotations. Although
our values are in some disagreement with those values determined by other
techniques, they are very close and self-consistent (the torsional barriers for the
silicon isotopic species are the same in the error limit), and also very similar to that of
(CH 3)3SiCl (577cm'’), which was also determined by FTMW spectroscopy.
Interestingly, the number o f the methyl groups on the center silicon atom does not
dramatically increases the torsional harrier height, which, in fact drops slightly upon
increasing the number o f tops, which is quite different from what happened for its
carbon atom analogues. The comparison between these systems is given in Table-7.
Perhaps this can be explained by the lowering of steric effects due to the larger
covalent radius o f silicon compound to that o f carbon.
-79-
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r4
os
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
o
00
■CD—
Di
O
o.
c
o
CD
Q.
■CD
D
C/)
(/)
Figure-2: The 2 - 1 transition o f Trimethylsilane, (CH 3)3SiH
0300
O
O
■D
cq '
0.250 r
O
’
CD
0.200 i-
—
i
CD
■—
Di
O
o.
c
a
o
■—
D
Oi
CD
Q.
g
0.150 h
B
S'
i
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O.lOO
Al
■CD
D
0.050
\ /
\/
f V
(/)
(/)
W \
Kl>>’, ,
0.000
21380.75
21381.00
21381.25
21381.50
21381.75
21382.00
Frequency (MHz)
-81-
21382.25
21382.50
21382.75
21383.00
Table-1: The measured torsional splitting frequencies of (CH3 ) 3 SiH
(CHa)3^*^SiH
O-C
(CH3)3'"SiH
O-C
/MHz
/kHz
/MHz
/kHz
lc 5 )3 S iH
/MHz
cm :
/kHz
lo — Oq: A]
10690.5213
0.4
10676.0098
0.0
10661.9463
1.1
I2 - A l
-0.1214
1.0
-0.1215
-0.1
-0.1213
0.3
Ii-A,
-0.2363
4.8
-0.2383
1.3
-0.2371
2.5
I4 - A ,
-0.2446
3.8
-0.2451
1.8
-0.2440
2.9
E 2 - Al
-0.3620
-5.8
-0.3623
-8.3
-0.3601
-6.2
I3 - A ,
-0.3693
1.5
-0.3623
6.2
-0.3715
-3.0
Al
21380.9206
-0.2
21351.8988
0.0
21323.7690
-0.5
I2 - A ,
-0.2424
1.9
-0.2422
0.7
-0.2390
3.8
Ii-A,
-0.4800
1.4
-0.4776
0.9
-0.4750
3.4
I4 - A ,
-0.4871
8.8
-0.4908
2.1
-0.4850
7.9
E2 - A 1
-0.7217
10.5
-0.7232
-16.3
-0.7175
- 10.8
I3 - A l
-0.7390
1.2
-0.7232
12.5
-0.7320
3.7
/ kHz
5.5
o /k H z
7.8
/kH z
5.6
2 o — lo:
0
0
-82-
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table-2: The molecular constants and torsional constants of (CH3)3 SiH
(CH^^^SiH
(C H ^ aS iH
(CHaV^SiH ..
B /M H z
5345.1462(13)
5337.8915(19)
5330.8592(14)
C /M H z
3096.8"
3096.8"
3096.8"
A j/kH z
4.83"
4.83"
4.83"
Ajk / kHz
-7.76"
-7.76"
-7.76"
A k / I cH z
3.57"
3.57"
3.57"
164.3472"
164.3382"
164.3295"
Fo/G H z
158.4*
158.4*
158.4*
Fij / GHz
5.9472"
5.9382"
5.9295"
V 3 / cm'^
573.37(38)
573.66(54)
573.37(39)
F /G H z
“ Fixed values from ab initio preditions, see Ref. [16].
* Fixed value according to
= 3.19 amuA^, see Ref. [ 1 , 2 ].
Derived values from XIAM.
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Table-3: The measured torsional splitting frequencies of (CH3 )3 SiCCH
(C H sV ^iC C H
/MHz
O-C 7 o 5 )?S iC C H
O-C
(o E ^ ^ C C H
O-C
/kHz
/kHz
/MHz
/kHz
/MHz
2 o-— I q: A]
7848.6201
-0.1
I2 - A]
-0.0264
0.1
I4 - A]
-0.0528
-0.9
li-As
-0.0574
-3.2
I3 - A 1
-0.0810
-2.6
E2 - A ,
-0.0875
-4.4
3o-- 2 o : A,
11772.9171
0.2
11767.1541
- 0.2
I2 ~A ,
-0.0408
- 1.0
-0.0400
-0.5
I4 - A l
-0.0812
-3.4
-0.0809
-0.1
I] --Al
-0.0879
-6.6
I3 - A ,
-0.1236
0.9
15697.1975
-0.1
15689.5152
0.8
15682.0009
0.4
I2 - A 1
-0.0535
-0.5
-0.0541
-1.4
-0.0542
-1.7
I4 - A l
-0.1072
-3.6
-0.1051
-2.1
Ii - Al
-0.1072
1.1
-0.1075
0.1
-0.1071
0.2
I3 - Al
-0.1532
3.4
-0.1538
1.9
-0.1535
1.8
19621.4570
0.0
1961.8526
-0.8
19602.4606
-0.5
I2 - A 1
-0.0670
-0.8
-0.0659
-0.1
-0.0667
- 1.1
I4 --Al
-0.1318
-2.4
-0.1321
-3.4
-0.1307
-2.4
Ii - Al
-0.1358
-0.6
l3~Ai
-0.1906
5.0
-0.1906
3.8
-0.1911
2.8
E2 - A l
-0.2048
2.4
60 — 5o: Al
23545.6897
0.0
23.534.1662
0.3
23522.8956
0.2
E2 - A ,
4o — 3o: Al
E2 - A 1
5o — 4q: Al
-8 4 -
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
I2 ~ A ,
-0.0806
-1.3
-0.0805
-1.7
-0.0811
-2.5
I4 —Ai
-0.1583
-3.2
-0.1592
-5.0
-0.1523
1.5
Ii - Ai
-0.1632
- 1.1
-0.1638
-3.1
Is-A i
-0.2301
4.4
-0.2305
2 .6
-0.2321
0.4
o /k H z
2.9
a / kHz
2.5
a /k H z
2 .1
E2 - A
1
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Table-4: The molecular constants and torsional constants of (CH3 )3 SiCCH*
(O W ^ C H
(CH3)?S iC C H
(CH3)3^“SiCCH
A /M H z
3101"
3101"
3101"
B /M H z
1962.1439(4)
1961.1835(4)
1960.2442(4)
A j/k H z
0.2219(73)
0.2197(70)
0.2190(75)
F /G H z
160.4379"
160.4368"
160.4358"
Fo / GHz
158.4^
158.4*
158.4*
Fij / GHz
2.0379"
2.0368"
2.0358"
V3 / cm'^
581.40(46)
581.85(51)
582.00(43)
" A rotational constant was fixed to be the predicted value by B3LYP/6-31 l++g(d,p)
method.
* Fixed value according to la = 3.19 amuA^ for (CH 3)3SiH, see Ref. [1,2].
^ Derived values by XIAM.
*The molecular constants determined by Alexander et al. are Bo=l 962.163(26) MHz,
Aj=0.25(15) kHz, without information of torsional constants [8 ].
-
86 -
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Table-5: The measured frequencies o f (CH3 )3 SiCCCCH
J V - -J k
Vobs/MHz
5v / kHz
5o — 4o
7139.5231
1.1
6o — 5o
8567.4228
-0.4
7o — 6o
9995.3213
-1.2
8 o - - 7o
11423.2220
2.1
%~— 8o
12851.1144
-0.5
Table-6: The comparison of the molecular constants of (CH3)3SiCCCCH and
(CH3)3SiCCCN
(CH3)3SiCCCCH
(CH3)3SiCCCN
A /M H z
B /M H z
A j/kH z
o /k H z
Ref.
3101“'^
713.95284(20)
0.0124(16)
06
^
711.86457(91)
0.01797(79)
[C
“ A rotational constant was fixed to be the predicted value by B3LYP/6-31 l++g(d,p)
method.
^ Present work.
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Table-7: The torsional barriers of molecules with single/multi-top internal rotation
Molecules
Method
Tosional barrier,
CHj-SiHs
MW
590.5 [17]
1047.7 [18]
Raman
C H 3 -C H 3
(CH3)2SiH2
MW
576.5 [4]
1353.0 [19]
Raman
( C H 3) 2 C H 2
(CH3)3SiH
FTMW
573.4 *
1186.5 [1]
Raman
( C H 3 ) 3C H
( C H 3) 2 S i = C H 2
FTMW
351.4 [20]
759.5 [3,21]
MW
( C H 3) 2 C = C H 2
(CH3)3SiC=CH
FTMW
581.4*
1183.0 [1]
Raman
(C H 3 )3 C C = C H
(CH3)3Si-Cl
FTMW
576.5 [7]
1578.5 [6]
Far-IR
( C H 3) 3 C - C 1
(CH3)3Si-F
Raman
871.5 [1]
1505[22]
MW
( C H 3 ) 3C - F
V3
/ cm"’
Method
Molecules
* Present work
-
88 -
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REFERENCE
[1]
J. R. Dung, S. M. Carven, and J. Bragin, J. Chem. Phys., 53(1), 38-50,1970.
[2]
L. Pierce and D. H. Petersen, J. Chem. Phys., 33(3), 907-913, 1960.
[3]
V. W. Laurie, J. Chem. Phys., 34(5), 1516-1519,1961.
[4]
L. Pierce, J Chem. Phys., 34(2), 498-506,1961.
[5]
H. Dreizler, Chem. Forsch, 10, 59-155,1968.
[6]
J. R. Durig, S. M. Carven, and J. Bragin, J. Chem. Phys., 51(12), 5663-5673,
1969.
[7]
I. Merke, W. Stahl, S. Kassi, D. Petitprez, and G. Wlodarczak, J. Mol.
Spectrosc., 216,437-446,2002.
[8]
A. J. Alexander, S. Firth, H. W. Kroto, and David R. M. Walton, J. Chem.
Sac. Faraday Trans., 88(4), 531-533, 1992.
[9]
David G. Lister, John N. Macdonald, and Noel L. Owen, Internal Rotation
and Inversion. 1978: Academic Press Inc. (London) LTD.
[10]
A. R. Hight Walker, W. Chen, S. E. Novick, B. D. Bean, and M. D. Marshall,
J. Chem. Phys., 102, 7298-7305,1995.
[11]
K. Voges, J. Gripp, H. Hartwig, and H. Dreizler, Z. Naturforsch A., 5 1 ,299305,1996.
[12]
H. Hartwig and H. Dreizler, Z. Naturforsch A., 5 1 ,923-932,1996.
[13]
K. K. Lehmann and B. H. Pate, J. Mol. Spectrosc., 144, 443-445,1990.
[14]
J. R. Durig, W. O. George, Y. S. Li, and R. O. Carter, J. Mol. Spectrosc., 16,
47-51,1973.
[15]
K. Georgiou and A. C. Legon, J. Mol. Spectrosc., 78, 257-263,1982.
[16]
D. C. McKean, Spectrochimica Acta A, 5 5 ,1485-1504, 1999.
[17]
G. Pelz, P. Mittler, K. M. T. Yamada, and G. Winnewisser, J. Mol. Spectrosc.,
156, 390-402,1992.
[18]
N. M. Ahmadi, J. Mol. Spectrosc., 2 1 4 ,144-151,2002.
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[19]
R. Engeln, J. Reuss, D. Consalvo, J. W. I Van Bladel, A. Van der Avoird, and
V. Pavlov-Verevkin, Chem. Phys., 144, 81-92,1990.
[20]
H. S. Gutowsky, Jane Chen, P. J. Hajduk, J. D. Keen, C. Chuang, and T.
Emilsson, J. Am. Chem. Soc., 113,4747-4751,1991.
[21]
J. Demaison and H. D. Rudolph, J. Mol. Struct., 24, 325-335,1975.
[22]
D. R. Lide, Jr. and D. E. Mann, J. Chem. Phys., 29, 914,1958.
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Section III
Spectroscopic and Quantum Computational Studies of Highly
Unsaturated Transient Molecules (Closed Shell System)
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CH A PTER FIVE
Microwave Spectra of Four New Ferfluoromethyl Folyyne
Chains; Trifluoropentadiyee, CF3—C=C—C = C -H ,
Trifluoroheptatriyne, CF3—C =C—C =C —C=C” H,
Tetrafluoropentadiyne, CF3—C =C— C =C—F, and
Trifluoromethylcyanoacetylene, CF3— C =C—C =N
Published in Journal o f Physical Chemistry A, 106, 3749-3753 (2002)
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Microwave Spectra of Four New Perfluoromethyi Poiyyne
Chains; Trifluoropentadiyne, CF3-"C=C—C=C“ H,
T rifluoroheptatriyne, CF3“ C =C —C = C ” -C=C~H ,
Tetrafluoropentadiyne, CF3—C^C—C=C—F, and
T rifluorom ethylcyanoacetylene, CF3—C =C—C =N
Lu Kang and Stewart E. Novick
Department o f Chemistry, Wesleyan University, Connecticut 06459
Abstract
Four fluoromethyl polyynes, 5,5,5-trifluoro-1,3-pentadiyne, CF 3—C =C —C=C-H,
7,7,7-trifluoro-1,3,5-heptatriyne, CF3—C^C—C s C - C s C - H ,
1,3-pentadiyne,
CF3—C=C—C=C—F,
and
1,5,5,5-tetrafluoro-
4,4,4-trifluoro-1-nitrile-2-butyne,
CF3—C=C—C=N, were studied by pulsed-jet Fabry Perot Fourier transform
microwave spectroscopy. The molecules were produced by pulsed high voltage
discharges o f dilute mixtures of precursor gases such as trifluoropropyne in an argon
carrier pulsed jet. The carbon-13 and deuterium substituted isotopomers of
trifluoropentadiyne were studied and the molecular structure was determined.
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Introduction
Highly unsaturated long chain hydrocarbons, both closed-shell species and
radicals, make up the majority o f the molecules detected in the interstellar medium [ 1 ,
2]. These molecules have been identified, in the most part, by radio telescopes which
operate in the microwave and millimeter regions o f the spectrum. Such work is made
possible by previous laboratory microwave spectroscopic studies of the likely
interstellar molecules [3]. A recent example is the laboratory study of the rotational
spectra o f a series methylpolyynes, methylcyanopolyynes, cyanopolyynes, and
isocyanopolyynes [4], which was performed, at least in part, to provide the radio
astronomers with a list o f frequencies (or equivalently, spectroscopic constants), for
future astronomical searches. Thus, for example, the microwave spectroscopy of
methylpolyacetylenes
such
isoelectronic
analog,
nitrile
as
1,3,5-heptatriyne,
CH 3—(C=C)2—C=N
CH3—(C=C)3-H ,
are
well
and
studied
its
both
spectroscopically [5-7] and through ab initio calculations [8 ].
A related series o f molecules, for which only the shortest members o f the series
have been studied, are the fluorinated polyynes and cyanopolyynes. Trifluoropropyne
[9-14], CF3CSCH, trifluoroacetonitrile [15-19], CFsC^N, and tetrafluoropropyne
[2 0 ], CF3C=CF, have been investigated by microwave spectroscopy in the ground
vibrational state and their structures have been determined. In these studies it was
found that, in contrast to expectations, the bond lengths, particularly that of the
carbon-carbon triple bond, were not affected by the proximity of the electronegative
fluorines to the extent predicted by theory.
In preparation for our microwave spectroscopic study of the hyperfine structure of
conjugated fluorinated radicals such as HC=C—CF2, we prepared gas samples
containing trifluoromethylacetylene which were excited with a pulsed high voltage
discharge. In addition to the expected radical, longer perfluoromethyi poiyyne chain
molecules were produced that have not been studied in the ground state with high
resolution spectroscopy. They are:
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( 1 ) CFb—C=C—C=CH, 5,5,5-trifluoro-1,3-pentadiyne;
(2) CFs” C =C ~C =C —C=CH, 7,7,7-trifluoro-l,3,5-heptatriyne;
(3) CF 3—C=C—C=CF, l,5,5,5-tetrafluoro-l,3-pentadiyne; and
(4) CF 3—C=C—C sN , 4,4,4-trifluoro-l-nitrile-2-butyne, also referred to as trifluoro­
methylcyanoacetylene.
Photoelectron spectra o f the tetrafluoropentadiyne, (3) [21], and of the
trifluorobutynenitrile, (4) [22], produced in a discharge, have been described, but no
spectroscopic studies o f (1) or (2) have been reported. We report here the microwave
spectroscopic study o f molecules (1) through (4). The
structure of (1),
trifluoropentadiyne, is determined from the moments of inertia o f the parent, the
deuterated, and each o f the single-substituted carbon-13 isotopomers in natural
abundance.
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Experimental
The microwave spectra o f the four fluorinated methyl acetylenes, (1) — (4), were
recorded u sing a Fabry-Perot pulsed-jet Fourier transform microwave spectrometer
which has been described eIsewhere [23]. M any medifications ofthespectrom eter
have been made since that initial publication including coaxial expansion of the gas
with the cavity axis for increased sensitivity and resolution, changes in the microwave
circuitry for decrease in the microwave noise, and automatic scanning for ease of use.
In these experiments, a pulsed high voltage o f typically 1000 V is applied
between electrodes separated b y
1
cm immediately following the pulsed gas valve
whose nozzle diameter is typically 0.8 mm. The resulting plasma discharge with a
current o f typically 20 mA serves to “synthesize” the extended chains from smaller
pieces. The precursor gas is a 1% mixture of two or three gasses in a carrier gas of
argon or neon with a total pressure of approximately 1 atm. The resultant mixture of
precursors and products are expanded into the high Q Fabry-Perot microwave cavity
which is tunable between 5 and 26.5 GHz. A microwave pulse is timed to coincide
with the arrival o f the gas pulse in the center of the microwave cavity. If a molecular
transition lies within the ~500 kHz bandwidth of the microwave pulse/cavity
combination, a macroscopic polarization is induced in the molecules. The free
induction d ecay o f this polarization i s c ollected and a veraged o v erm ultiple pulses
and is Fourier transformed to yield the spectrum of the transition. The free induction
decay was digitized at 100 ns per point for 4096 points, giving a discrete Fourier
transform with a point every 2.44 kHz. With this, we can estimate peak centers, on
most transitions, to within 1 kHz.
The precursor gas mixtures used for production of the four species varied slightly.
For the production of (1) CFs—CsC—C^CH, a mixture of 0.5% CFjCsCH + 0.5%
HC=CH in argon or neon was used. F or the deuterated isotopomer, 0.2% DC=CD
was
substituted
for
the
normal
acetylene.
For
the
production
of
(2)
CF3—C=C—C=C—C=CH, a mixture of 0.5% CFaC^CH + 0.5% HC=CH in argon
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or neon was used. For the production o f (3) CF3—C=C—C=CF, a mixture of 0.5%
CFsC^CH + 0.5% HC=CH + 0.5% CF 3H in argon or neon was used. For the
production o f (4)
CF3—
C=C—C^N, a mixture of 0.5% CFsC^CH + 0.5% HC=CH
+ 0.5% CHsC^N in argon or neon was used.
The discharge which “synthesizes” these molecules is created using high voltage
electrodes placed immediately after the pulsed nozzle. These electrodes and the
insulated cup which holds them in place fits inside a hole bored in one o f the mirrors
that constitute the tuned microwave cavity. The upstream electrode is held at -1000
V; 1 cm downstream is the ground electrode. We always make the downstream
electrode the ground to help minimize sparking to the grounded mirror. The discharge
voltage pulse is timed to coincide with the gas mixture exiting the pulsed nozzle. We
have found t hat th e sign o f the v oltage o f t h e n pstream e lectrode i s c ritical in the
formation o f the discharge related species. At least part of the energy of the plasma is
transferred to the inert gas (the color of the discharge is blue for argon and orange for
neon). It is likely that the collisions of the rare gas ions with the molecules result in
the molecular fragmentation that precedes molecular buildup. In the case of the
upstream electrode being negative, the Ar"^ ions experience an electrical force pulling
them upstream against the direction of the downstream jet flow. This results in an
increased number of energetic collisions between the Ar^ ions and organic precursors
of the radicals. It has been reported that having a positive upstream voltage is
efficacious in the production of radicals and ions [24]. We have found that the sign of
the voltage o f the upstream electrode is critical and dependant upon the species we
are attempting to produce. For example, the production of the HCCCO radical from
an acrolein (CHaCHCHOj/Ar discharge is optimized with +600 V on the electrode;
production o f HCCCN from CHzCHCN/Ar was about the same with both signs; the
perfluoro compounds o f the present experiment (and their all-hydrogen analogs) all
optimize with the negative voltage upstream. In fact, we could not detect any signal in
the present experiment when the voltage sign was switched. We note that the
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discharge with the positive upstream voltage (ion flow with the jet flow) is more
intense and easier to strike as the electrodes get sooty.
For a carbon-13 isotopomer of CF3—C=C—C=C~H, detected in natural
abundance, a typical molecular transition reached a signal-to-noise-ratio of 5/1 in
about 1000 gas pulses, which at 3 pulses per second amounts to an averaging time of
about five minutes per transition. Such a transition is shown in Figure 1.
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Results
Microwave Spectra
Frequencies and assignments of the various isotopomers of CF3—C=C—C=CH,
trifluoropentadiyne, a re presented i n T able 1S, t hose o f t h e n ormal i sotopomers o f
CF 3—C=C—C=C—C=CH, trifluoroheptatriyne, in Table 2S, of CF3—C=C—C—CF,
tetrafluoropentadiyne, in Table 3S, and of CF3—C=C—C=N, trifluorobutynenitrile
in Table 4S. These four tables are supporting information published in the Web
edition o f this journal. The transitions of the first three molecules were fit with a
simple rigid rotor plus centrifugal distortion energy expression for a symmetric top,
E = B J{J +1) - D j [ J { J +1)]' - D j^J{J + l)K"
For the nitrile, a hyperfine term involving the nuclear quadrupole coupling constant
for the spin -1 nitrogen nucleus, Xaa must be added,
3K^
J ( J + l)
-1
where fil.J.F) is the Casimir function [25], and F is the total angular momentum
quantum number. The total angular momentum is the sum o f the rotational angular
momentum and the spin angular momentum of the nitrogen nucleus, F = J + I. Only
K = 0 transitions were detected for the trifluorobutynenitrile, thus the Dm constant
was not measured for this molecule, and the formula for E q is simplified. The
spectroscopic constants of the four molecules studied are presented in Table 1.
Molecular Structure
O f the four molecules studied, CF3—C=C—C=C-H, trifluoropentadiyne, gave
transition signals intense enough to allow observation of the transitions of the carbon13 substituted isotopomers in natural abundance. (See Figure 1).
We present a complete experimental determination of the structure of 5,5,5trifluoro- 1,3 -pentadiyne. We have measured the rotational constants (essentially the
inverses o f the moments of inertia) of seven isotopomers o f trifluoropentadiyne: the
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normal isotopomer, five singly-substituted carbon-13 isotopomers, and the deuterated
isotopomer. These rotational constants are presented in Table 1. Kraitchman’s
equations [26, 27] were solved to give the substitution, or r,, structure of the molecule
which is, in general, closer to the equilibrium structure than is the average, or tq,
structure in which all the isotopomer’s moments of inertia would be simultaneously
fit to a single best structure. In the
structure calculation, once the normal
isotopomer’s moment o f inertia is measured, each measured isotopically substituted
moment o f inertia gives a coordinate for that substituted atom. Since the molecule is a
symmetric top, we set the b and c coordinates of the carbon atoms and the hydrogen
atom to be zero; the a inertial axis is the symmetry axis. Thus in F3 C5 —C4 SC3
—C2=Ci~H, we can determine the a-coordinate of the five carbon atoms and the
hydrogen atom and thus all the CC bond lengths and the CH bond length. The
fluorine atom positions were determined by fitting their coordinates to the first and
second moment equations for the normal isotopomer, Em,a, = 0, and /* = Em,fa/ +
c,/). Thus we have fit seven structural parameters, six bond lengths and one angle,
from seven moments o f inertia. With the number of unknowns equal to the number of
equations, there is no independent check on the fitting procedure. Indeed, when we
use the ro calculational procedure for these seven structural parameters, we obtain
identical results for the bond lengths and the CFC angle. The errors from the carbon
atom and deuterium atom rs coordinates are used to calculate the errors for the CF
bond length and the CFC angle with the use of standard error propagation. Errors in
the substitution structure arise when the substituted atom is near the center of mass of
the molecule. Costain has empirically estimated this contribution to the error to be
Sr « (0.0012A^)/|rj [28]. In our calculations we use 0 . 0 0 1 5 for heavy atoms, and
0.003 A^ for the hydrogen atom as the conversion factor for this error [29]. The
resulting
structure o f trifluoropentadiyne is presented in Table 2 and shown in
Figure 2.
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Discussion
For CF 3—C=C-H, ab initio calculations at the SCF level with a double-^ basis set
augmented by polarization functions on carbon [30] predicted a very short C=C bond
length o f 1.185A, which was not found experimentally. The experimental distance
was found to be shortened, but by 0.007A to
1 .2 0 1 A,
from the 1.208A CC triple bond
length ofC H 3 -C = C -H .
In the present case of CF3—C=C— C=C-H, the situation is reversed, in that the
CC triple bond closest to the trifluoromethyl group is lengthened by 0.007A to
1.215 A from the corresponding bond length of 1.208A in CH3—C=C —C=C~H [31,
32] The various distances and angles for CF3C4H, CF3C2H, and CH3C4H are
presented in Table 2. The magnitude of differences in the distances between
corresponding bond lengths in CF3C4H verses those of CH3C4H is greatest near the
CF3— end of the molecule. The differences of the bond lengths of CF3C4H minus
those o f CH3C4H are -0.010, +0.007, -0.006, -0.001, and +O.OOIA as we march from
CFs—CCCCH,
through
CFjC^CCCH,
CF3CC—CCH,
CFsCCC^CH,
to
CF3CCCC-H.
This shortening of the CC single bond and the lengthening of the CC triple bond
nearest the CF3 group can be understood qualitatively in terms of the electron
withdrawing ability of the fluorines. Figure 3 shows four resonance structures for
trifluoromethylpentadiyne.
Resonance structure #1
is, of course, the main
contribution to the e lectronic s tructure o f the m olecule. H owever, s ince fluorine i s
highly electronegative and thus capable o f electron withdrawing, resonance structures
#2 — #4, in which one of the fluorine atoms has a full negative charge make some
contribution to the total electronic structure. (The relative importance of the
resonance structures is #1 > #2 > #3 > #4). Resonances #2 through #4, involving
interactions between a and
tc bonds
are referred to as involving “hyperconjugation”.
Resonance structures #3 and #4 both replace the F3C—C=C end of the molecule with
F” F2C==C==C. Thus if we include these two resonance structures in the description of
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100
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the bonding of the molecule, the single bond has some double bond character, thus
shortening it, and the triple bond has some double bond character, thus lengthening it,
as observed experimentally. Resonance structure #3 is more important than #4
because opposite charges are closer together in #3 (it takes energy to separate
opposite charges), thus the shortening/lengthening occurs in the two bonds near the
CF3 end o f the molecule.
The subtle effect upon the electronic structure of the methylacetylenes upon
fluorination of the methyl group can also be observed in CF3—C=C —C=N,
trifluoromethylcyanoacetylene. Here we have measured the nuclear quadrupole
coupling constant for the spin-1 nitrogen nucleus, Xaa, to be -4.40(4) MHz. This is
larger in magnitude than values of this constant for methylcyanide [33], CH 3CN
(-4.214(14) MHz); for methylcyanoacetylene [34], CHaCsCCN, (-4.0(2) MHz); and
for
methylcyanodiacetylene
CHbC^C— C=CCN,
[7],
(-4.25(3)
MHz).
(Methylcyanoacetylene is the closest analog of CF3CCCN, but its value of Xaa is the
least well measured; the correct value is most probably -4.2 MHz as in the shorter
and the longer chain version). The nuclear quadrupole coupling constant is
proportional to the product o f quadrupole moment of the nucleus in question and the
electric field gradient at that nucleus caused by all the positive and negative charges
of the molecule, but most especially by the electrons nearest the nucleus. Thus, a
qualitative understanding o f the increase in the magnitude of/afl(’‘*N), from 4.2 to 4.4
MHz upon fluorination o f CH3CCCN to CF3CCCN, can be obtained from the
electron distribution surrounding the nitrogen nucleus. The relevant resonance
structures are those analogous to #1 and #4 of Figure 3: F3C—C=C —C=N
F~
F2C==C=C=C=N®. While resonance structure #4 is the least important, subtle
electronic variations which seem not to affect bond lengths can have a major effect
upon electric field gradients and thus upon nuclear quadrupole coupling constants
[13].
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101
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Townes and Schawlow [25]
give a simple correlationbetween electric
field
gradients, q, and electron bonding. Assume that the pa bonding orbital isfractionally
5 -hybridized
by an amount^, in both resonance structures # 1
=N:
(#1)
= N :
(#4)
and in resonance #4
then the non-bonding lone-pair electrons must be
(1
- fs) s-character and f^pa
character. Since s electrons are spherically symmetric, only p electrons contribute to a
field gradient along the molecular axis. Due to their different orientations, electrons in
the pTi orbitals have field gradients, qi, along the a axis that are -Vz of the field
gradients due to the electrons in the p„ orbitals, qo; that is, qj = -Vzqo [25, 35],
Resonance structure #1 has a field gradient at the nitrogen nucleus of
q{# 1) = (1 - X )^o + 2 q, + 2 X ^0 = f,q^
where t he first t erm is due to th e b onding p „ e lectron, the s econd t erm to the two
bonding pn electrons, and the third term is due to the two non-bonding lone pair
electrons. A reasonable value for fs is 0.45 [25]. Resonance structure #4 has a field
gradient at the nitrogen nucleus of
q{#4) = ( \ - f )q^ + g, + 2 f q ^ = ( f + X)?o
where the terms are in the same order as above; there is only one bonding p^ electron
for resonance structure #4. The difference, q(#4) - q(#l), is equal to ‘/iqo [36]. Thus
the slight contribution o f resonance #4 to the electronic structure of CF3CCCN
rationalizes the increase o f the magnitude of /oa(''^N) in CF3CCCN over that in
CH3CCCN.
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Summary
We have studied, by microwave spectroscopy, four related fluoromethyl
acetylenes; CF3C4H, CFsCgH, CF3C4F, and CF3C2CN. The molecular structure of the
first o f these, CF3—C=C—C=C~H, was determined and the bond lengths discussed
in terms o f the electron withdrawing capability o f the electronegative fluorines. The
same analysis was used to understand the nuclear quadrupole coupling constant of the
nitrogen in the nitrile, CF3—C=C—C=N.
Acknowledgment
We wish to thank Jens-Uwe Grabow for supplying us with the new version of his
Windows-based software ftmw++ which now operates the spectrometer, and for all
his help in installing and debugging this program. This work was supported by the
National Science Foundation.
Supporting Information Available:
The complete set o f the observed transitions, assignments, and the deviations
from the predicted frequencies (obs. - calc.) for the four molecules discussed in this
paper are presented in Tables IS, 2S, 3S, and 4S. This material is available free of
charge via the Internet at http ://pubs .acs.org.
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Table 1. Spectroscopic constants of CF 3—C=C—C=C-H,
CF3~ C = C —C=C—C s c -H , CF3~C=C-™C=C—F, and CFs—C^C—CsN"
B/M Hz
Dj/kHz
CFsCCCCH
887.57431(4)
0.0175(2)
2.499(2)
CF3CCC ‘^CH
862.69511(4)
0.0164(3)
2.39(3)
CF 3CC '^CCH
875.11021(4)
0.0163(2)
2.44(1)
CF3C'^CCCH
884.16204(5)
0.0161(3)
2.55(3)
CF3 '^CCCCH
887.46051(9)
0.0163(5)
2.49(6)
’^CFsCCCCH
885.43963(6)
0.0158(3)
2.59(4)
CF3CCCCD
848.60969(3)
0.0145(2)
2.375(7)
CF3CCCCCCH
379.57154(4)
0.00215(8)
0.79(2)
CF3CCCCF
499.09390(3)
0.0044(1)
1.145(4)
CF3CCCN"
885.94615(6)
0.0188(5)
a. The number in parenthesis is the one standard deviation error o f the constant from
the least-squares fit.
b. D jk was not measured for the nitrile, as only K = 0 transitions were recorded.
c. For this molecule, an additional spectroscopic constant was measured, the nuclear
quadrupole coupling constant of the nitrogen nucleus projected along the a axis. It is
= -4.40(4) MHz.
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Table 2. The r* structure o f F3 C5 —C4 SC3 —C2 =Ci~H and related molecules®
C F 3— C S C — C s C - H ^
C F 3— C s C - H ®
C H 3 — C S C — C s C - H '*
r(C i-H )
1.0563(8)
1.0510(17)
1.055(1)
r ( C 2= C ,)
1.2075(6)
1.2012(8)
1.209(1)
r(C 3 -C 2 >
1.3689(11)
1.375(4)
r(C 4 = C 3 )
1.2153(56)
1.208(4)
r(C 5 -C 4 )
1.4455(57)
1.4742(45)
1.456(3)
rCF—Cs)
1.3413(21)
1.3372(22)
1.105(1)
Z (F— C 5 —F)
107.20(8)°
108.27(20)°
108.58(5)°
a. Distances in Angstroms, angles in degrees. The numbers in parentheses are the
estimated errors of the substitutional method (see text).
b. This work.
c. Reference [13]. Since there are two fewer carbon atoms in trifluoromethylacetylene
than in the other two molecules in the table, the numbering scheme is not a perfect
match. F3CsC(4 or2)=CiH is used.
d. Reference [31]. r(F— C 5 ) is to be read as r(H— C 5 ) and Z (F — C 5 —F) is to be read
as Z (H—Cs—H) for methyldiacetylene.
-105-
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 1S
Transition frequencies of CF3 CCCCH isotopomers
Isotopomers
CF3CCCCH
4
5
6
J”
K
3
4
5
0
0
0
1
2
3
4
0
1
2
3
4
0
1
2
3
4
5
0
1
2
3
4
5
0
1
2
3
4
5
0
1
2
10
CFsCCC'^CH
11
10
4
3
4
0
0
1
0
1
Observed
(MHz)
7100.5895
8875.7325
10650.8751
10650.8469
10650.7588
10650.6048
10650.3996
12426.0150
12425.9839
12425.8751
12425.7016
12425.4586
14201.1530
14201.1148
14200.9916
14200.7934
14200.5123
14200.1532
15976.2866
15976.2414
15976.1055
15975.8811
15975.5683
15975.1614
17751.4159
17751.3660
17751.2163
17750.9653
17750.6154
17750.1666
19526.5419
19526.4872
19526.3220
RMS (kHz)
Obs, - Calc.
(kHz)
-0.5
6901.5564
8626.9423
8626.9193
10352.3266
10352.2978
-0.3
- 0.6
0.3
- 0.6
-0.7
-106-
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-
1.8
-1.5
0.3
2.2
-1.9
2.8
-1.3
2.6
- 1.2
0.2
2.1
0.0
1.7
-1.5
0.2
1.0
-0.3
0.2
- 0.1
- 1.0
-0.5
1.5
-0.6
-0.2
-0.1
0.1
- 1.0
- 1.0
0.0
0.4
0.7
0.4
1.2
-
CFsCC’^CCH
CFsC'^CCCH
CFa^CCCCH
7
6
8
7
9
8
10
9
4
5
3
4
6
5
7
6
8
7
9
8
10
9
11
10
4
5
6
7
3
4
5
6
8
7
9
8
10
9
11
10
4
5
3
4
0
1
0
1
0
1
0
1
12077.7085
12077.6766
13803.0888
13803.0515
15528.4651
15528.4204
17253.8366
17253.7881
RMS (kHz)
-0.6
1.0
0.6
1.5
0.9
-0.8
-0.1
-0.8
0.75
0
0
1
0
1
0
1
0
1
0
1
2
0
1
0
7000.8780
8751.0940
8751.0711
10501.3088
10501.2772
12251.5192
12251.4871
14001.7310
14001.6909
15751.9367
15751.8923
15751.7609
17502.1384
17502.0901
19252.3384
RMS (kHz)
0.5
0.0
1.5
0.3
-2.0
-1.4
0.6
1.0
-0.1
0.4
-0.1
0.1
-0.7
-0.2
0.5
0.85
0
0
0
0
1
0
1
0
1
0
1
0
1
7073.2921
8841.6127
10609.9312
12378.2469
12378.2102
14146.5606
14146.5164
15914.8707
15914.8249
17683.1746
17683.1258
19451.4784
19451.4239
RMS (kHz)
-0.2
0.3
0.6
0.4
-0.6
0.9
-0.2
1.0
1.0
-1.7
0.5
-0.6
1.0
1.1
0
0
7099.6786
8874.5966
-1.3
-0.3
-107-
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
13
CFsCCCCH
CF3CCCCD
6
5
7
6
8
7
9
8
10
9
11
10
4
5
6
7
3
4
5
6
8
7
9
8
10
9
11
10
4
5
3
4
6
5
7
6
8
7
9
8
1
0
1
0
1
0
1
0
1
0
1
0
8874.5749
10649.5111
10649.4825
12424.4242
12424.3901
14199.3352
14199.2981
15974.2400
15974.1943
17749.1444
17749.0927
19524.0471
RMS (kHz)
2.9
-0.9
0.4
-0.5
0.3
0.5
3.3
-1.6
-2.4
-0.5
-2.3
2.8
1.8
0
0
0
0
1
0
1
0
1
0
1
0
1
7083.5140
8854.3898
10625.2612
12396.1335
12396.0966
14167.0010
14166.9611
15937.8668
15937.8180
17708.7287
17708.6797
19479.5887
19479.5306
RMS (kHz)
1.0
1.4
-0.7
0.4
-0.2
-0.8
0.8
-0.5
-2.6
-0.8
2.1
0.8
-0.2
1.2
0
0
1
2
0
1
2
0
1
2
0
12
0
1
6788.8736
8486.0899
8486.0653
8485.9945
10183.3050
10183.2763
10183.1885
11880.5169
11880.4807
11880.3820
13577.7264
13577.6865
13577.5728
15274.9318
15274.8890
-0.2
0.3
-0.6
-0.1
1.3
1.1
-1.2
1.2
-1.8
-0.7
1.1
-0.8
-0.5
-0.3
-0.3
-108-
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
10
9
11
10
2
0
1
2
0
1
2
15274.7626
16972.1350
16972.0883
16971.9463
18669.3357
18669.2835
18669.1269
RMS (kHz)
-109-
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1.6
-0.7
0.1
0.6
-0.2
-0.1
0.0
0.8
Table 2S
J”
K
8
9
7
8
10
9
11
10
0
0
1
0
1
0
1
12
11
J’
^
Transition frequencies of CF3 CCCCCCH
1
13
12
1
14
13
1
15
14
1
16
15
17
16
18
17
1
1
1
Observed
(MHz)
6073.1418
6832.2810
6832.2633
7591.4227
7591.4077
8350.5626
8350.5472
9109.7008
9109.6836
9868.8405
9868.8231
10627.9786
10627.9600
11387.1173
11387.0915
12146.2530
12146.2276
12905.3901
12905.3631
13664.5277
13664.4966
RMS (kHz)
-
Obs. - Calc.
(kHz)
1.6
-0.5
-4.0
0.5
1.2
0.1
2.0
-1.3
0.3
-0.7
2.4
-1.0
2.4
0.1
-2.1
-1.1
-1.4
-0.1
-0.3
2.3
-0.5
1.6
110-
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Table 3S
Transition frequencies o f CF3 CCCCF
.
K
7
8
6
7
9
8
10
9
11
10
12
11
13
12
14
13
15
14
16
15
17
16
19
18
0
0
1
0
1
0
1
2
3
0
1
2
0
1
2
0
1
2
0
1
2
0
1
2
3
0
1
0
1
0
1
2
3
Observed
(MHz)
6987.306
7985.492
7985.478
8983.674
8983.659
9981.860
9981.837
9981.771
9981.658
10980.041
10980.017
10979.942
10979.813
11978.222
11978.196
11978.113
12976.401
12976.371
12976.282
13974.580
13974.546
13974.450
14972.757
14972.723
14972.621
14972.449
15970.936
15970.896
16969.107
16969.071
18965.445
18965.402
18965.271
18965.054
RMS (kHz)
Obs. - Calc.
(kHz)
-2
-1
3
-3
2
-1
0
3
4
-2
0
0
-2
-1
1
0
-2
-1
-1
-1
-2
-2
-1
0
1
1
4
1
1
5
-1
-1
-1
-1
2
-Ill-
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 4S
Transition frequencies of CF3 CCCN
J’
F’
4
4
4
5
5
5
6
6
6
7
7
7
8
8
8
9
9
9
3
4
5
4
5
6
5
6
7
6
7
8
7
8
9
8
9
10
3
3
3
4
4
4
5
5
5
6
6
6
7
7
7
8
8
8
F”
K
2
3
4
3
4
5
4
5
6
5
6
7
6
7
8
7
8
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-
Observed
(MHz)
7087.470
7087.564
7087.599
8859.400
8859.453
8859.475
10631.304
10631.337
10631.352
12403.197
12403.221
12403.234
14175.084
14175.099
14175.112
15946.961
15946.975
15946.987
RMS (kHz)
Obs. - Calc.
(kHz)
0
0
1
1
1
0
0
-1
0
0
0
0
1
-1
1
-2
-1
2
1
112-
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure Captions
Figure 1.
The J = 5 — 4, K = 0 and K = 1 microwave transition of CF3—
—C=C- H in
natural abundance. The spectrum required 1000 microwave/gas pulses and took 5.5
minutes to accumulate.
Figure 2.
The rs structure o f 5,5,5-trifluoro-1,3 -pentadiyne.
Figure 3.
Resonance structures of 5,5,5-trifluoro-l,3-pentadiyne. The relative importance of
these resonance structures to the bonding o f the molecule is #1 > #2 > #3 > #4.
-113-
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
r4
s00
fs
s
00
q
c4
s00
00
00
o
a
0
s
m
a
os
u
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N
X
q
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1
in
00
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z00
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t
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a.
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
c
CD
3
cr
P
in
o
o
<<1
CX)
o
CM
o
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'O
CO
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pL,
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 3
R
.C
C =C — C =C
H
F 'V
©
C
C = C
C== C
H
C =C
H
F #
F
©
.C = C = = C
F 'V
F
^
^
..........
-
•i-i
r1
116
-
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
References and Notes
[1]
A list of the molecules detected in the dense interstellar clouds and other
astronomical sources can be found at
http://www.cv.nrao.edu/~awootten/allmols.html
[2]
Allamandola, L. J.; Hudgins, D. M.; Bauschlicher Jr., C. W.; Langhoff, S. R.
Astron. Astrophys. 1999,352, 659.
[3]
Winnewisser, G.; Herbst, E.; Ungerechts, H. In Spectroscopy o f the Earth's
Atmosphere and Interstellar Medium, Rao, K. N.; Weber, A., Eds.; Academic
Press, NY, 1992,423.
[4]
McCarthy, M. C.; Chen, W.; Travers, M. J.; Thaddeus, P. Astrophy. J. Supp.
Ser. 2000,729,611.
[5]
Alexander, A. J.; Kroto, H. W.; Maier, M.; Walton, D. R. M. J. Mol.
Spectrosc. 1978, 70, 84.
[6]
Bester, M.; Yamada, K.; Winnewisser, G.; Joentgen, W.; Altenbach, H. J.;
Vogel, E. Astron. Astrophys. 1984,137, L20.
[7]
Chen, W.; Grabow, J.-U.; Travers, M. J.; Munrow, M. R.; Novick, S. E.;
McCarthy, M. C.; Thaddeus, P. J. Mol. Spectrosc., 1998,1 9 2 ,1.
[8]
Amau, A.; Tunon, I.; Andres, J.; Silla, E. Chem. Phys. Lett. 1990,166, 54.
[9]
Anderson, W. E.; Trambarulo, R,; Sheridan, J.; Gordy, W. Phys. Rev. 1951,
82, 58.
[10] Shoolery, J. N.; Shulman, R. G.; Sheehan, W. F.; Schomaker, V.; Yost, D. J.
Chem Phys. 1951,19, 1364.
[11]
Mills, I. M. Mol. Phys. 1969,1 6 ,345.
[12]
Kasten, W.; Dreizler, H. Z. Naturforsch. A. 1984,3 9 ,1003.
[13]
Cox, A. P.; Ellis, M. C.; Legon, A. C.; Wallwork, A. J Chem. Soc. Faraday
Trans. 1993,8 9 ,2937.
[14] Harder, H.; Gerke, C.; Maeder, H.; Cosleou, J.; Bocquet, R.; Demaison, J.;
Papousek, D; Sarka, K. J. Mol. Spectrosc. 1994,167,24.
-117-
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
[15]
Sheridan, J.; Gordy, W. J. Chem. Phys. 1952,20, 591.
[16]
Thomas, L. F.; Heeks, J. S.; Sheridan, J.; Z. Electrochim. 1957, 61, 935.
[17]
Foreman, P. B.; Chien, K. R.; Williams, J. R.; Kukolich, S. G. J. Mol.
Spectrosc. 1974,52,251.
[18]
Kasten, W.; Dreizler, H.; Job, B. E.; Sheridan, J. Z. Naturforsch, A. 1983,38,
1015.
[19]
Friedrich, A.; Gerke, C.; Harder, H.; Maeder, H.; Cosleou, J.; Wlodarczak, G.;
Demaison, J. Mol. Phys. 1997,91, 697.
[20]
Cox, A. P.; Ellis, M. C.; Summers, T. D.; Sheridan, J. J. Chem Soc. Faraday.
Trans. 1992,88, 1079.
[21]
Bieri, G,; Heilbronner, E.; Stadelraann, J.-P.; Vogt, J.; von Niessen, W. J. Am.
Chem. Soc. 1977, 99, 6832.
[22]
Bieri, G.; Heilbronner, E.; Homung, V.; Kloster-Jensen, E, Maier, J. P.;
Thommen, F.; von Niessen, W. Chem. Phys. 1979,3 6 ,1.
[23]
Hight Walker, A. R.; Chen, W.; Novick, S. E.; Bean, B. D.; Marshall, M. D. J.
Chem. Phys. 1995,102, 7298.
[24]
Anderson, D. T.; Davis, S.; Zwier, T. S.; Nesbitt, D. J. Chem. Phys. Lett.
1996, 258,207. And David Nesbitt, private communication.
[25]
Townes, C. H.; Schawlow, A, L. Microwave Spectroscopy, McGraw-Hill:
New York, 1955.
[26]
Kraitchman, J. Am. J. Phys. 1953,2 1 ,17.
[27]
Gordy, W.; Cook, R. L. Microwave Molecular Spectra, 3"* ed.; Wiley: New
York, 1984; Chapter 13.
[28]
Costain, C.C. Trans. Am. Crystallographic Assoc. 1966, 2,157.
[29]
Van Eijck, B. P. J. Mol. Spectrosc. 1982,91, 348.
[30]
Dixon, D. A.; Smart, B. S. J. Phys. Chem. 1989, 93,1112.
[31]
Nielsen, C. J.; Saebo, S. Acta Chemica Scaninavica A, 1983,3 7 ,267.
[32]
The error estimates in the positions of the atoms in the
structure calculation
is an order o f magnitude greater than the errors in the rotational constants
-
118-
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
would imply. This larger error is partially an attempt to estimate how the
structure differs from the hypothetical re structure (see, for example Ref. 29).
Our quoted bond length difference of 0.007A, being a direct comparison of r®
derived bond lengths, is meaningfiil.
[33]
Kemp, M. K.; Pochan, J. M.; Flygare, W. H. J. Chem. Phys. 1967, 71, 765.
[34]
Bester, M.; Tanimoto, M.; Vowinkel, B.; Winnewisser, G.; Yamada, K. Z.
Naturforsch. A, 1983, 38, 64.
[35]
Gordy, W.; Cook, R. L. Microwave Molecular Spectra, 3'^‘’ ed.; Wiley: New
York, 1984; Chapter 14.
[36]
Since resonance structure #4 nominally involves a positive ion, there is
compression o f all the orbitals, and thus an additional increase in the field
gradient, which involves an integral of 1/r^. This increase is estimated to be a
factor o f 1.25(Reference 25, pg 239).
-119-
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Appendix
Included are some o f our pre-experimental works that help us figure out the
molecular structures and the rotational constants.
-
120-
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CD
■—
Di
O
o.
c
o
CD
Q.
■CD
D
C/)
W
o'
o
Table A1
Experimental and calculated structures o f CF3CCCCH.
o—
ty
CD
h-c
O
O
■D
,/A
C,=C2/A
C2 — Cj/A
C3 SC 4 /A
C4 — C 5 /A
Cs^Cfi/A
ZFCsF/°
B/MHz
Dipole
1.05622
1.20756
1.3689
1.2153
1.4455
1.3412
107.2°
1.0563(5)
1.2077(6)
1.3693(11)
1.2215(37)
1.4384(51)
1.3466(35)
107.3684°
1.0562(3)
1.2075(4)
1.3685(7)
1.2112(23)
1.4510(17)
1.337
107.106°
r™
1.05622(4)
1.20756(6)
1.3689(1)
1.2153(4)
1.4455(4)
R H F /6-3llg
1.0514
1.1877
1.3765
1.1836
1.4423
1.3622
106.80°
894.0
4.28
RHF/6-311g**
1.0519
1.1882
1.3766
1.1838
1.4437
1.3618
106.87°
893.7
4.21
RHF/6-31g
1.0671
1.1751
1.4074
1.1766
1.5163
1.3746
107.94°
862.7
1.70
RHF/6-31g*^
1.0553
1.1959
1.3778
1.1915
1.4490
1.3658
106.84°
886.7
4.36
B3LYP/6-311g
1.0619
1.2097
1.3622
1.2089
1.4352
1.4004
106.53°
878.5
4.29
B3LYP/6-311g'*‘*
1.0624
1 .2 1 0 2
1.3620
1.2092
1.4335
1.4039
106.41°
877.6
4.47
B3LYP/6-31g
1.0654
1.2172
1.3634
1.2165
1.4414
1.3936
106.83°
875.3
4.07
B3LYP/6-31g**
1.0667
1.2184
1.3638
1.2174
1.4382
1.4043
106.31°
MP2/6-31g
1.0709
1.2265
1.3850
1.2358
1.4571
1.4063
106.83°
852.5
4.80
■CD
D
M P2/6-311g
1.0678
1.2293
1.3825
1.2274
1.4469
1.4083
106.58°
860.4
4.78
(/)
(/)
[a]; We use 7 Bo’s o f isotopomers to fit 7 structure parameters.
cq'
o
r’o*'”
o
CD
"n
c
CD
—
i
CD
■—
Di
O
o.
c
a
o
o
■—
Di
o
CD
Q.
[b]: We set the ZCCF=111.5° and fit the other 6 bond lengthes.
[c]: We set the C -F bond length to be 1.337A and then fit the other 6 structure parameters.
[d]: The bond length was calculated by KRA program.
-121-
4.55
CD
■—
Di
O
o.
c
o
CD
Q.
■CD
D
C/)
W
o'
o
Table A2
Experimental stractures of comparison molecules: X = H / F
o
zxcx
o
o
■D
F3C-Cs C-C=C-H
cq '
ZCCX
107.2°
ro
X —C/A
1.3412
>'s
XaC—C/A
o = c /A
C— C/A
CD
1.3689
1.2076
1.0562
a
1.44554(46)
1.21529(45)
1.36888(10)
1.20756(6)
1.056222(5)
3
HjC-C^C-C^C-H ro
110.32(3)°
1.107(1)
1.454(1)
1.209(2)
1.376(2)
1.208(1)
1.056(1)
b
I's
110.35(5)°
1.105(1)
1.456(3)
1.208(4)
1.375(4)
1.209(1)
1.055(1)
b
110.46(1)°
1.1070(2)
1.4543(1)
1.2082(2)
1.3722(1)
1.2086(1)
1.0571(1)
b
0 = N /A
H jC -O C -C =N
HaC-OC-N^C
108.30°
r/
ro
•>
r:
1.10
1.458
1.203
•>
r:
■CD
D
c — n /A
N ssC /A
c
1.4541(16)
1.2081(24)
1.3158(17)
1.1756(6)
d ,e
110.6°
1.0918(11)
1.4540(16)
1.2080(25)
1.3159(17)
1.1756(6)
d ,f
1.2159(109)
1.3057(106)
110.71(7)°
1.0903(14)
1.4557(16)
1.2059(19)*
1.3157(16)*
1.2104(61)
1.3109(56)
1.2056(17)*
1.3157(12)*
1.206(2)
1.316(2)
110.70(7)°
1.0902(14)
1.090(1)
1.1754(13)
1.4561(18)
1.456(2)
[a] Present work.
[b] The paper provided ZCCH, we calculated ZHCH base on that. Ref. [12]
[c] Most probable structure. Ref. [16}
[d] Ref. [17]
[e] Bond length
1.157
1.0940
110.7(4)°
Ts
1.379
110.53(4)°
CD
Q.
(/)
(/)
Note
1.2153
CD
■—
Di
O
co.
a
o
Q
■—
D
Oi
c —H/A
1.4455
3O’
—
i
C==C/A
fixed to be 1.0940 A.
-122-
1.1756(6)
d ,b
1.175(2)
d, i
CD
■—
Di
O
o.
c
o
CD
Q.
■CD
D
C/)
(/)
[f] ZCCH fixed to be 110.6°.
Calculated &om double substitution method,
g: Calculated by taking assunptions for propyne
■§D
h: All the H substituted by D.
CQ
i: Structure listed in the abstract.
(y// == L0198(12) A). See Ref.
O’
CD
—
i
CD
■—
Di
O
co.
a
o
■D
O
CD
Q.
■CD
D
(/)
(/)
-123-
[18];
CD
■—
Di
O
o.
c
o
CD
Q.
■CD
D
(/)
W
o'
o
Table A3
Experimental structures of comparison molecules: Y = H / F / C 1 / CH3
o
h - c /A
o
o
■D
cq '
F— C/A
ZFCF
C— CA
1.337(2)
108.3(2)°
1.474(5)
1 2 0 1
FjC-C^C-F
r.
1.339(2)
108.02(20)°
1.457(3)
1 2 0 2
FjC-C^C-Cl
ro
1.336(6)
107.0±1.0°
F3 C -O C -C H 3 *
Best fit
1.340
106°08’
H3 C -O C -H
i'o
1.0940(4)
108.3(1)°
1 1 0
^S
1.0895
108.3°
1 1 0
Refence
.
(1 )
1.051(2)
[5]
.
(2 )
1.274(4)
[19]
1.453(2)
1.199(5)
1.627(9)
[23]
1.455
1.189
1.455*
[2 2 ]
.6 ( 2 )°
1.4595(5)
1.2088(6)
1.0548(3)
[2 1 ]
.6 °
1.4586
1.2066
1.0561
1 2 1
]
o = N /A
FjC -C sN
CD
Q.
r~
1.328(2)
109.2(2)°
1.492(5)
1.154(1)
[5]
ro
1.335
107.5°
1.461
1.153
[5],[20]
ro
1 .1 1 2
109.27°
109°40’
1.4582
1.1572
[24], [25]
rs
1.1036
109.49°
109°27’
1.45836
1.15710
[27], [25]
c — n /A
(/)
(/)
c — y /A
H3 C - O C - F
H 3 C-CSN
■CD
D
O s c /A
fz
—
i
■—
Di
O
o.
c
a
o
Q
■D
O
ZCCH
F3 C -O C -H
O’
CD
CD
ZHCH
F jC -N ^
HjC-N^C
N s =C/A
r^a
1.325(3)
108.7(3)°
1.404(6)
1.172(4)
[5]
^av
1.324(1)
108.8(1)°
1.407(3)
1.171(3)
[5]
1.42393
1.16616
[25], [26]
1.10146
109.82°
109°?’
1.10146
The imderlined values are assumed value.
Those angles denoted by Italic font are calculated from ZCCH.
*; B y assumption that both C—C bond lengths are 1.455 A, C—H = 1.097 A, ZHCH = 108°30’
It refers to the C—C bond length o f ^ — CH3 part
-124-
■CD—
Di
O
o.
c
o
CD
Q.
■CD
D
C/)
W
o
o'
Table A4
ab initio calculated stractures of CF3CCCCCCH (bond length in A)
o
o
o
■D
H -Ci
C,=C 2
RHF/6-31g
1.0541
1.1961
1.3757
1.1977
1.3738
1.1922
RHF/6-311g
1.0513
1.1891
1.3740
1.1912
1.3727
B3LYP/6-31g
1.0653
1.2199
1.3582
1.2275
B3LYP/6-311g
1.0616
1.2123
1.3564
B3LYP/6-311g(d,p)
1.0622
1.2129
1.3563
C2 - C
3
B/MHz
Dip(
C7 - F
ZFCF
1.4492
1.3626
107.0(f
380.4
4.86
1.1845
1.4425
1.3621
106.85°
382.8
4.77
1.3548
1.2196
1.4417
1.3936
106.78°
375.7
4.82
1.2199
1.3534
1.2117
1.4351
1.4002
106.53°
377.8
5.04
1 .2 2 0 2
1.3532
1 .2 1 2 2
1.4322
1.4045
106.37°
377.5
5.27
C3=C4
C4 - C
C6 - C
5
7
cq '
O
’
CD
B3LYP/6~311++g(d,p)
CD
■D
O
Q.
C
a
o
Q
■D
O
CD
Q.
■CD
D
C/)
C/)
-125-
CH A PTER SIX
The Microwave Spectrum of Cyanophosphine, H2FCN
Manuscript in preparation
-
126 -
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The Microwave Spectrum of Cyanophosphine, H2PCN
Lu Kang, Stewart E. Novick, Michael C. McCarthy"’*, and Patrick Thaddeus"'*
Department o f Chemistry, Wesleyan University, Middletown, CT 06459, USA
" Harvard-Smithsonian Center fo r Astrophysics, 60 Garden Street, Cambridge, MA
02138, USA
* Division o f Engineering and Applied Sciences, 29 Oxford Street, Cambridge, MA
02138, USA
Abstract
The fl-type transitions o f the microwave rotational spectra of cyanophosphine,
H 2PCN, have been investigated in selected regions between 10 and 42.5 GHz by
Fourier transformation microwave (FTMW) spectroscopy. Rotational, centrifugal
distortion and
quadrupole coupling constants as well as the spin-rotation coupling
constants of ^'P have been determined. Density functional theory ab initio
calculations were performed, and the calculated values o f the molecular constants are
in excellent agreement with our experimentally determined results. The
and '*N
isotopomer transitions were also observed very closed to the predicted frequencies.
The derived ro structure is quite comparable to the ab initio predicted H 2PCN
equilibrium geometry.
-127-
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Introduction
Over the past several decades, cyanoamide, NH2CN, has been the subject of
extensive spectroscopic studies motivated by both its theoretical and astronomical
importance [ 1 ,2]. The observedinversion transitions ofN H aC N indicated th a tth e
molecule possesses a pyramidal equilibrium structure and undergoes a largearaplitude inversion motion. This system can be treated by the semirigidbender
models developed by Bunker and Szalay [3-6]. Moreover, cyanoamide is among the
list of the “Known Interstellar and Circumstellar Molecules” [2]. Many third row
atom containing andcyano group containing molecules as well as radicals such as
MgCN, SiCN, NH 2 CN, CH2CN, HCCN, PN and CP, have been detected in space in
the past few decades [2]. Spectroscopic studies indicated that phosphine, PH 3, plays
an important role in the microwave emission spectrum o f planetary atmospheres [79]. Since both phosphorus and cyano containing species are favorable topics for
astronomical studies, our present ab initio and rotational spectroscopic study was
undertaken on cyanophosphine, H2PCN, because it is a reasonable candidate for
astronomical detection in the interstellar medium and in planetary atmospheres. Our
laboratory observed frequencies and experimental determined molecular constants
provide the basic reference information for those radio telescopes in the search for
and analysis o f this species in the space.
Although H2PCN is a heavy-atom analog of NH 2CN, it does not show a
spectroscopically resolvable inversion doubling seen in NH 2CN. This strongly
suggests that the inversion barrier o f the PH 2 group is much higher than its light-atom
counterpart, NH 2 . Note that the microwave spectra of PH3 also show no evidence of
inversion doubling [ 1 0 ].
-128-
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Experimental
The spectrum o f H2PCN was recorded with the pulse-discharged pulse-jet Fourier
Transform Microwave (FTMW) spectrometers both at Wesleyan and Harvard, which
have been described elsewhere [11-13], Many modifications have been made since
the initial publication including coaxial expansion of the gas with the cavity axis for
increased sensitivity and resolution, changes in the microwave circuitry for
decreasing the noise level, and automatic scanning for ease o f use. Most o f the spectra
under 22 GHz were taken with the Wesleyan spectrometer, while the high frequency
transitions at ~31 GHz and ~42 GHz were taken with the Harvard spectrometer which
incorporated frequency doubling which has extended its range to 43 GHz.
In the experiments, a 0.3% gas mixture of PH3 and CH3CN (1:1) in argon with a
background pressure o f
1
atm is expanded through a
0 .8
mm diameter general valve
nozzle. The expanding gas then pass through a 1 cm discharge region with a pulsed
900 volts potential difference. The resulting plasma discharge with a current of
typically 20 mA serves to dissociate the PH 3 and CH3CN into various fragments. The
collision o f t hose fragments in th e d ischarge r egion p reduces t he H 2PCN. The gas
mixture is expanded into the high Q Fabry-Perot cavity. A microwave pulse is timed
to coincide with the arrival of the gas pulse at the center of the cavity, where a
macroscopic polarization is induced in the molecules. We then measure the free
induction decay o f this polarization and Fourier transform the signal to yield the
spectrum o f the transition. The gas flow is traveling coaxially with the cavity axis and
thus the molecular interaction with the counter-propagating microwave radiation
results in a Doppler-doubled spectral transition. Figure 1 shows the recorded
Doppler-doubled split transitions. Generally, the peak center can be determined
within ~1 kHz.
Although the spectra of ’^C and
abundance for the
=
0
isotopomers can be detected at natural
branches, averaging of thousands o f gas/microwave pulses
are required to build up the signal strength (e.g. to obtain large enough signal to noise
ratio to distinguish the transition 1ines). In practice, w e further diluted the original
-129-
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sample [0.3% PH 3+CH 3CN (l;l)/A r] with enriched CHs'^CN or CHjC’^N samples to
increase the rare isotopomer ratio to about 30%. With enriched samples, the
isotopomers’ transitions can be observed within a couple hundred shots, about one
tenth the amount o f experimental work to observe them in natural abundance.
-130-
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ab initio predicition
The e xperimental w ork and d ata a nalysis for an a symmetric r otor s ystem w ere
greatly facilitated by an accurately predicted molecular geometry. Cohen et al.
studied the
microwave
spectroscopy of Ethynylphosphine, HaPC^CH, and
determined its molecular structure [14]. Thus H 2PC=CH, isoelectronic to HaPCN,
acted as a test o f the accuracy of various ab initio methods and basis sets for the
geometry optimization o f HjPCN. We found that the density functional theory
method, B3LYP, in conjunction with the basis sets, cc-pVQZ for P, and
6-
311++g(d,p) for H, and C, best reproduced the experimental geometry o f HaPC^CH.
Table 1 lists our calculated and Cohen’s experimentally determined structure, and
Table 2 lists the calculated and experimentally determined molecular constants and
the dipole moments. Both of the predicted geometry and molecular constants are
quite c omparable t o t hose v alues o btained from e xperiment. H ence w e applied t he
same method and basis sets to HjPCN. Notice that the ab initio calculated molecular
constants are the equilibrium state molecular constants, which are slightly different
from vibrational ground state molecular constants. To obtain the best predictions, we
scaled the calculated equilibrium state molecular constants to obtain a better
estimation for vibrational ground state. This is based on the assumption that the
deviation between the ground state and equilibrium state molecular constants of
HaPCN is about the same as those of H 2PCCH. This is reasonable because of their
similarity. Hence, for example.
H^PCN
H jPC C H
where
was calculated from B3LYP method with a “gen” basis sets {P/cc-
pVQZ & H,C,N/6-31 l++g(d,p)}. Other vibrational groimd state molecular constants
can be derived by the same way. Table 3 lists the calculated, scaled and
experimentally determined molecular constants.
-131-
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Assignment and analysis
Lines o f the main isotopomer and isotopically enriched samples containing '^C
and'^N were measured and assigned to the sequence from J = l - 0 t o / = 4 ~ 3 , and
A'a = 0, 1 states. Although HjPCN has both a and c dipole moments, the c-type
transitions are outside our spectral range, therefore only a-type transitions were
measured. The hyperfine structures due to the quadrupole coupling interaction of
and the spin-rotation interaction of^^P (Ip = 54) were observed. No hyperfine structure
due to
(I = 54) was observed. All the transitions for each isotopomer were fit
separately using Pickett’s program package, SPFIT [15]. The frequencies and
assignments o f 50 transitions of H2PCN and 35 transitions o f HaP'^CN as well as 12
transitions o f HjPC’^N are given in Table 4, Table 5 and Table 6 .
The angular momentum coupling scheme is given as follows: the molecular
rotational angular momentum J first couples with the nuclear spin of
to form
(In = 1), In,
and Fj couples with the nuclear spin of ^^P (Ip = 54) to form F, briefly
shown as: Fi = J + In and F = Ft + Ip.
The Hamiltonian we used to assign and analyze the spectra is given by:
H
—
+ H jj.
Hrot is the typical Hamiltonian for an asymmetric top rotor, including centrifugal
distortion terms:
H,„, = Ao
+ Co
Hguad represents the '^’n
- A,
(I n
- A^j :
=1) nuclear quadrupole coupling interaction, and can be
written as:
3/2Z
Hsr represents the spin-rotation interaction o f P (Ip = 54), and denoted as:
H,„=Ip-C.J
The resulting molecular constants, including rotational constants, centrifugal
distortion constants and quadruple coupling constants for ’"‘N as well as the spin-
-132-
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
rotation constants for
are listed in Table 3. Since only the a-type transitions are
within our spectral range, A© is immeasurable, thus we fixed it to be the scaled value.
1
Since the a -type t ransitions o f 3 i sotopomers, i ncluding H 2PCN, H 2P CN, and
H 2PC^^N were observed,
that only
6
6
independent Bo’s and Co’s were obtained. Considering
parameters are needed to describe the geometry o f H 2PCN, our
experimental data are barely enough to derive the ground state effective geometry, ro.
Thus we used STRFITQ program package to derive the ro structural parameters and
compared with the ab initio optimized equilibrium structure,
These two structures
are quite comparable. Figure 2 shows both the experimentally determined ro structure
and ab initio optimized re structure.
A new version o f Gaussian98 program package (gOl, internal version of
Gaussian98 under development when we used it, now just recently released on
GaussianOS) has the capability to calculate fine and hyperfine constants. It was used
to estimate the contributions o f the spin-rotation hyperfine structure to the spectrum
of H 2PCN due to th e e xistence o f n on-zero nuclear s pins. W e e alculated the s pinrotation coupling constants for ‘H,
and ^‘P, which, conceivably, could have some
contribution to the observed spectral splitting. Table 7 lists our calculated results,
which indicates that the spin-rotation coupling constants o f ^‘P are about an order of
magnitude larger than those of 'H and
and thereafter make the most significant
contribution to the spectrum of H 2PCN. This has been proven by our experiment that
no spin-rotation hyperfine splitting due to 'H and
were observed at our resolution.
-133-
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Discussion
The hyperfine splitting due to the spin-rotation coupling interaction arises from
the interaction between the nuclear magnetic dipole moment and the magnetic field
associated with the rotating molecule. Flygare pointed out that spin-rotation constants
are intimately relate to NMR magnetic shielding constants and developed the theory
that connected them [16-18]. The connection arises from the fact that the shielding
constants and the spin-rotation constants have identical dependences on the energy
summation over all the electronic states. Briefly, the spin-rotation coupling constants
contain information on the electronic environment o f the nucleus, and thus provide an
alternative w ay t o o btain the m agnetic s hielding constants especially for those gas
phase and transient molecules that are unfavorable for NMR experiments. NMR
determined magnetic shielding constants are relative values with respect to a standard
(H3PO3 for
compounds). We can derive the absolute values of magnetic shielding
constants from spin-rotation constants, avoid the side effects from environment (e.g.
solvent). Kukolich [19-21] and Gerry [22-25] as well as their co-workers have
successively applied Flygare’s theory to their experimental work.
Ramsey showed that the nuclear magnetic shielding tensor is contributed by
diamagnetic {</) and paramagnetic {(f) terms [26]. The averaged magnetic shielding
ofkth nucleus is given by:
=
+
(1)
Flygare pointed out, that a good approximation is:
d i (k )« (xi
(free atom k) +
^
(2)
—
Since crj,(/ree atom k) can be found in various tables [27, 28], crj„(^) can be easily
obtained if we know the molecular geometry. The paramagnetic shielding is given by:
«*> =
3m^c
^
-134-
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
<3)
where nte is electronic mass, c is the speed of the light,
and
is the g factor for kth nucleus.
, and
is the nuclear magneton,
are the moment of inertia of a,
b, and c axis respectively. Finally, the averaged magnetic shielding can be expressed
as:
< (‘ ) = < ( > « “tom k) - — -H ------ ( C J , + C J , * C J , )
Gm^hc^^gj,
(4)
The moment o f inertia o f each principal axis can be derived from measured rotational
constants A, B and C. The magnetic shielding for free atom
is +961 ppm [28].
Substitution o f t hose v alues ( for m ain i sotopomer) i nto e quation (4) w e obtain t he
absolute averaged
magnetic shielding to be +438 ppm. We also calculated the
absolute magnetic shielding for ^'P of H 2PCN with the same method and basis set that
used to optimize the molecular geometry. The calculated result is +538 ppm, which is
qualitatively comparable to our experimentally derived value.
-135-
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Acknowledgement
Financial support from National Science Foundation is gratefully acknowledged.
W et hank Dr. J. R . C heeseman, Dr. J. A . M ontgomery and D r. M . J. F risch from
Gaussian Inc. for the calculations of spin-rotation constants. We also thank Professor
S. G. Kukolich for his helpful comments.
-136-
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CD
■—
Di
O
o.
c
o
CD
Q.
■CD
D
C/)
W
o'
o
Figure 1: The hyperfme splittings caused by the nuclear spin o f
(Ip = Vz) of the loi — Ooo transition of H 2PCN
o
O
O
■D
cq'
o
10554.0848 MHz
Fi'F-Fi"F": 2
o
CD
0.300
"n
c
10554.0769 MHz
F , ’F ' - F i " F ” : 2
CD
—
i
CD
■—
Di
O
co.
a
o
o
■—
Di
^
0.250
CO
c
c
0.200
o
0.150
CD
Q.
0.100
■CD
D
(/)
(/)
0.050
0 000
■ 10553.70
,
10553.80
10554.00
10554.10
Frequency (MHz)
-137-
10554.30
10554.50
Figure 2: ab initio predicted /■« vs. experimental tq structures of H2 PCN
\\
a
.-P-
-.
\\
... ...................
\
\\
M
H
-----------------W
\
\
\\
\\
\\
\
\\
\s
b
ab initio
Experimental tq
r(C=N)/A
1.1561
1.1577(1)
r(C—P )/A
1.7878
1.7870(12)
A
1.4176
1.4244(26)
Z(NCP) / °
173.92
174.63(14)
Z(CPH )/°
95.16
95.69(79)
Z(H PH )/°
94.21
93.88(17)
±132.64
±132.75(1)
f (P— H) /
Z(NCPH) / “
ah initio prediction done by B3LYP/ {P/cc-pVQZ & H,C,N/6-311++g(d,p)}
Experimental structure derived by using STRFITQ program package.
-138-
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 1: Molecular structure o f HaPCCH
B3LYP/aug-cc-pVTZ
B3LYP/gen
Experiment
r(P-H) / '
1.4206
1.4194
1.414(5)
K P-C) / '
1.7760
1.7703
1.774(5)
r(C = C )/ '
1.2037
1.2071
1.208(assumed)
r(C-H ) / '
1.0620
1.0636
l,058(assumed)
Z (H -P -H ) / °
93.8253
93.9025
93.9(5)
Z (H -P -C ) / °
97.2540
97.3577
96.9(5)
Z (P -C = C ) / °
173.1959
173.0000
173(2)
Z (C sC -H ) / °
179.3423
179.1097
180.0(assumed)
Z(HPCC) / °
±132.5908
±132.5370
gen: generated basis set: P/cc-pVQZ & H,C/6-31 l++g(d,p).
b) Ref. [14].
-139-
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 2: Molecular Constants and dipole moments ofHaPCsCH®^
B3 LYP/aug-cc-pvtz
B3LYP/gen
Experiment
A
130266.98
130509.83
130345.248(16)
B
5110.5162
5121.8229
5113.92758(76)
C
5086.8654
5097.7959
5090.19602(72)
Aj X 10^
1.339
1.337
1.35131(80)
Ajk X 10^
60.115
60.111
64.943(34)
Ak
2.338
2.390
2.4525(27)
a Dipole moment
0.1500
0.1494
0.155(1)
c Dipole moment
0.5468
0.5500
0.555(1)
The Rotational and centrifugal distortion constants are in unit of MHz, and Dipole
moments are in the unit o f Debye.
gen; generated basis set, P/cc-pVQZ & H,C/6-311++g(d,p).
Ref. [14].
-140-
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CD
■—
Di
O
o.
c
o
CD
Q.
■CD
D
C/)
W
o'
o
Table 3: ab initio predicted and experimental determined molecular constants of H 2PCN
o
o
o
■D
Constants
B3LYP/gen
Scaled Calc.
HaPCNexp.
HaP^^CN exp.
HzPC^^Nex/j.
A (MHz)
129708.24
129544.7
129544.7(fixed)
129544.7(fixed)
129544.7(fixed)
B(M Hz)
5297.1021
5288.9366
5289.2745(3)
5260.2867(4)
5102.8908(48)
C(M Hz)
5272.1154
5264.2556
5264.5825(2)
5235.9235(4)
5079.9041(48)
Aj (kHz)
1.646
1.664
1.625(7)
1.637(16)
1.525(16)
Ajk (kHz)
65.237
70.481
69.26(12)
67.95(16)
64.88(24)
Ak (MHz)
1.978
2.030
2.030(fixed)
2.030(fixed)
2.030(fixed)
N: x«b (MH z)
-4.595
-4.5893(13)
-4.5883(21)
N :x»(M H z)
2.464
2.6774(18)
2.561(21)
N:X cc(MHz)
2.132
1.9120(18)
2.028(21)
P: C„a (kHz)
118.810*
79.1(47)
90.0(84)
153(17)
P:Ci,6(kHz)
6.036*
13.5(15)
17.1(35)
2.4(37)
P:Cec(kHz)
5.628*
3.7(16)
1.6(34)
13.8(37)
cq '
Q
CD
O
’
CD
—
i
CD
■—
Di
O
o.
c
a
o
Q
■—
D
Oi
CD
Q.
■CD
D
(/)
(/)
gen: generated basis set: P/cc-pVQZ and H, C/6-311++g(d,p).
Spin-rotation constants were calculated by Dr. James Cheeseman with the internal version o f Gaussian98,
Scaled Calc.: See text. Values in this column should be compared with H2PCN main isotopmer’s molecular constants.
-141-
Table 4: Observed frequencies of HaPCN
Frequency
(MHz)
10552.6954
0 -C
(kHz)
-3.6
1.5
10552.6954
-3.6
1
1.5
10552.7042
-1.2
0
1
0.5
10552.7042
-1.2
0
0
1
0.5
10554.0769
3.3
0
0
0
1
1.5
10554.0769
3.3
-
0
0
0
1
1.5
10554.0848
0.6
0.5
-
0
0
0
1
1.5
10556.1426
-2.6
0
0.5
-
0
0
0
1
0.5
10556.1426
-2.6
2
2
2.5
-
1
1
1
1
1.5
21081.5512
1.7
1
2
3
3.5
-
1
1
1
2
2.5
21082.9602
-0.3
2
1
2
3
2.5
-
1
1
1
2
1.5
21082.9705
-0.9
2
1
2
1
0.5
-
1
1
1
0
0.5
21084.4838
0.5
2
1
2
1
1.5
-
I
1
1
0
0.5
21084.5262
2.4
2
0
2
2
1.5
-
2
1.5
21106.2774
0.1
2
0
2
2
2.5
-
1
0
1
2
2.5
21106.2852
0.7
2
0
2
1
0.5
-
1
0
1
0
0.5
21106.5012
3.0
2
0
2
1
1.5
-
0
1
0
0.5
21106.5150
-2.6
2
0
2
2
2.5
-
1
0
1
1
1.5
21107.6672
3.8
2
0
2
3
2.5
-
1
0
1
2
1.5
21107.7540
2.4
2
0
2
3
3.5
-
1
0
1
2
2.5
21107.7618
0.8
2
0
2
1
0.5
-
1
0
1
1
0.5
21109.9417
-2.8
2
0
2
1
1.5
-
1
0
1
1
1.5
21109.9539
-3.4
2
1
1
2
1.5
-
1
1
0
1
0.5
21130.9185
-5.0
2
1
1
2
2.5
-
1
1
0
1
1.5
21130.9316
-4.3
/
1
iiTa’
0
k:
1
/
0
k:
k:
0
0
-
0
0
0
1
1.5
-
0
0
0
1
1.5
-
0
0
1
2
1.5
0
0
I
2
1.5
-
1
0
1
2
2.5
1
0
1
0
1
0
1
2
1
2
1
Fi
1
0.5
0
1
1
0.5
1
0
1
1
1
0
1
1
0
1
0
F j” F ”
1
0.5
-142-
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2
1
1
1
0.5
-
1
1
0
0
0.5
21133.6708
1.8
2
1
1
1
1.5
~
1
1
0
0
0.5
21133.7230
1.8
3
1
3
3
2.5
-
2
1
2
2
1.5
31623.6514
-1.9
3
1
3
3
4.5
-
2
1
2
2
2.5
31623.6514
-3.2
3
1
3
4
4.5
-
2
1
2
3
3.5
31624.0546
-3.5
3
1
3
4
3.5
-
2
1
2
3
2.5
31624.0546
-4.5
3
1
3
2
2.5
-
2
1
2
1
1.5
31624.0810
5.2
3
1
3
2
1.5
-
2
1
2
1
0.5
31624.0810
4.8
3
0
3
3
2.5
-
2
0
2
3
2.5
31659.9002
-1.2
3
0
3
4
3.5
-
2
0
2
3
3.5
31659.9062
-2.7
3
0
3
2
2.5
2
0
2
1
1.5
31661.1552
-1.0
3
0
3
3
2.5
-
2
0
2
2
1.5
31661.3887
3.2
3
0
3
4
3.5
-
2
0
2
3
2.5
31661.4336
2.8
3
0
3
4
4.5
-
2
0
2
3
3.5
31661.4444
4.6
3
0
3
2
1.5
~
2
0
2
2
1.5
31663.4375
-2.0
3
0
3
2
2.5
-
2
0
2
2
2.5
31663.4463
-4.0
3
1
2
3
3.5
-
2
1
1
2
2.5
31697.7354
2.1
3
1
2
2
2.5
-
2
1
1
1
1.5
31698.1164
-0.1
3
1
2
4
4.5
-
2
1
1
3
3.5
31698.1464
0.8
4
1
4
4
4.5
-
3
1
3
3
3.5
42164.9532
-0.5
4
0
4
3
3.5
-
3
0
3
2
2.5
42214.8808
-0.6
4
0
4
5
4.5
-
3
0
3
4
3.5
42215.0058
0.4
4
0
4
5
5.5
-
3
0
3.
4
4.5
42215.0137
-0.5
4
1
3
5
4.5
-
3
1
2
4
3.5
42263.9024
0.4
RMS error = 2.5 kHz
-143-
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 5: Observed frequencies of HaP'^CN
f
0
Ka"
0
Ki
0
F i'
1
f
"
0.5
Frequency
(MHz)
10495.0464
0-C .
(kHz)
-5.6
-
0
0
0
1
1.5
10495.0464
-5.6
1.5
-
0
0
0
1
1.5
10495.0581
-0.9
1
1.5
-
0
0
0
1
0.5
10495.0581
-0.9
1
2
1.5 ~
0
0
0
1
0.5
10496.4287
2.6
0
1
2
1.5
0
0
0
1
1.5
10495.4287
2.6
1
0
1
2
2.5
-
0
0
0
I
1.5
10496.4404
2.6
1
0
1
0
0.5
-
0
0
0
1.5
10498.4956
-2.3
1
0
1
0
0.5
-
0
0
0
1
0.5
10498.4956
-2.3
2
1
2
2
2.5
-
1
1
1
1
1.5
20966.5904
1.0
2
1
2
3
3.5
-
1
1
1
2
2.5
20968.0029
1.0
2
1
2
3
2.5
_
1
1
1
2
1.5
20968.0146
-1.4
2
0
2
2
1.5
-
1
0
2
1.5
20990.9826
-0.8
2
0
2
2
2.5
-
1
0
1
2
2.5
20990.9893
-1.9
2
0
2
1
1.5
-
1
0
1
0
0.5
20991.2246
0.1
2
0
2
2
2.5
-
1
0
1
1
1.5
20992.3740
4.1
2
0
2
3
3.5
-
1
0
1
2
2.5
20992.4629
5.5
2
0
2
1
0.5
-
1
0
1
1
0.5
20994.6484
-0.9
2
0
2
1
1.5
-
1
0
1
1
1.5
20994.6616
-1.9
2
1
1
2
2.5
-
1
1
0
1
1.5
21015.3174
-2.3
2
1
I
3
3.5
-
I
1
0
2
2.5
21016.7412
-2.5
2
1
1
3
2.5
-
1
1
0
2
1.5
21016.7500
-0.1
3
1
3
3
2.5
-
2
1
2
2
1.5
31451.2178
4.0
3
1
3
3
3.5
~
2
1
2
2
2.5
31451.2178
4.3
3
1
3
4
4.5
-
2
1
2
3
3.5
31451.6153
-3.0
J
1
Ka
0
K,
1
Fi
1
F'
0.5
1
0
1
1
0.5
1
0
1
I
1
0
1
1
0
1
-1 4 4 -
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
3
1
3
2
2.5
-
2
1
2
1
1.5
31451.6275
-1.5
3
0
3
3
3.5
-
2
0
2
3
3.5
31486.9648
-3.5
3
0
3
2
2.5
^
2
0
2
1
1.5
31488.4472
2.6
3
0
3
4
4.5
-
2
0
2
3
3.5
31488.4971
-1.8
3
0
3
2
2.5
-
2
0
2
2
2.5
31490.5068
-2.2
3
1
2
3
3.5
2
1
1
2
2.5
31524.3105
3.0
3
1
2
2
2.5
-
2
1
1
1
1.5
31524.6953
-1.3
3
1
2
4
4.5
-
2
1
1
3
3.5
31524.7198
1.6
RMS error = 2.6 kHz
■145-
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 6: Observed frequencies of HiPC'^N
f
0
"
0.5
Observed
(MHz)
10182.7793
0~C.
(kHz)
-1.4
0
0
0.5
10182.7910
-1.9
1
1
1
1.5
20342.2920
3.7
1.5 -
1
0
1
0.5
20365.5340
0.2
2
2.5
-
1
0
1
1.5
20365.5420
0.1
1
1
2.5
~
1
1
0
1.5
20388.2578
-0.9
3
1
3
3.5
-
2
1
2
2.5
30513.3448
-3.5
3
1
3
2.5
-
2
1
2
1.5
30513.3564
1.0
3
0
3
3.5
-
2
0
2
2.5
30548.2120
0.6
3
1
2
3.5 -
2
1
1
2.5
30582.3056
0.3
3
1
2
2.5
~
2
1
1
1.5
30582.3184
0.2
4
0
4
4.5
-
3
0
3
3.5
40730.7618
0.2
K ’ F
1 0.5
J
1
0
1
0
1
2
1
2
K„'
0
k;
-
J
0
1.5
-
0
2
2.5
~
0
2
2
0
2
-
RMS error = 1.7 kHz
-146-
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 7: The spin-rotation coupling constants calculated by B3LYP/gen*
Calc.
Calc.
Calc.
Obs.
Caa (kHz)
-14.347
3.0457
118.8095
83.2(49)
Cbb
(kHz)
-0.1212
1.3530
6.0357
11.0(16)
Ccc
(kHz)
-0.2251
0.1408
5.6282
4.2(16)
gen = P/cc-pVQZ, and H,C,N/6-31lg++(d,p)
-147-
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reference
[1]
R. D. Brown, P . D. Godfrey, and B. Kleibomer, Journal o f Molecular
Spectroscopy, 114, 257-273, 1985.
[2]
M. C. McCarthy and P. Thaddeus, Chem. Soc. Rev., 3 0 ,177-185,2001.
[3]
J. T. Hougen, P. R. Bunker, and J. W. C. Hohns, Journal o f Molecular
Spectroscopy, 3 4 ,136-172,1970.
[4]
P. R. Bunker and B. M. Landsberg, Journal o f Molecular Spectroscopy, 67,
374-385,1977.
[5]
P. Jensen and P. R. Bunker, Journal o f Molecular Spectroscopy, 9 4 ,114-125,
1982.
[6]
V. Szalay, Journal o f Molecular Spectroscopy, 102,13-32,1983.
[7]
D. R. Deboer and P. G. Steffes, Icarus, 123,324-335,1996.
[8]
J. P. Hoffinan, P. G. Steffes, and D. Deboer, Icarus, 140,235-238,1999.
[9]
A. T. Tokunaga, R. F. Knacke and S. T. Ridgway, Astrophys. J , 232, 603615,1979.
[10]
V. §pirko and D. PapouSek, Mol. Phys., 36(3), 791 -796,1978.
[11]
A. R. Might Walker, W. Chen, S. E. Novick, B. D. Bean, and M.D. Marshall,
J. Chem. Phys., 102, 7298,1995.
[12] T. J. Balle and W. H. Flygare, Rev. Sci. Instrum., 52(1), 33-45,1981.
[13] M. C. McCarthy, M. J. Travers, A. Kovacs, C. A. Gottlieb, and P.Thaddeus,
Astrophys. J. Suppl. Ser., 113, 105, 1997.
[14]
E. A. Cohen, G. A. McRae, H. Goldwhite, Sal Di Stefano, and R. A. Beaudet,
Inorg.Chem., 2 6 ,4000-4003, 1987.
[15]
H. M. Pickett, J. Mol. Spetrosc., 148,371,1991.
[16]
W. H. Flygare, J. Chem. Phys., 41(3), 793-800,1964.
[17]
W. H. Flygare and J. Goodisman, J. Chem. Phys., 49(7),3122-3125,1968.
[18] T. D. Gierke and W. H. Flygare, JACS, 94(21), 7277-7283,1972.
-148-
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
[19]
S. G. Kukolich, D. J. Ruben, J. H. S. Wang, and J. R. Williams, J. Chem.
Phys., 58(8), 3155-3159,1973.
[20]
S. G. Kukolich, J. H. S. Wang, and D. J. Ruben, J Chem. Phys., 58(12), 54745478,1973.
[21]
J. H. S. Wang and S. G. Kukolich, JACS, 95(13), 4138-4141,1973.
[22]
B. Gatehouse, H. S. P. Muller and M. C. Gerry, J. Mol. Spectroc., 190,157167,1998.
[23]
R. E. Wasylishen, D. L. Bryce, C. J. Evans, and M. C. L. Gerry, J. Mol.
Spectroc., 204, 184-194,2000.
[24]
M. C. L. Gerry and C. J. Evans, J. Phys. Chem. A, 105, 9659-9663, 2001.
[25]
N. R. Walker, J. K.-H. Hui, and M. C. L. Gerry, J Phys. Chem. A, 106, 58035808,2002.
[26]
N. F. Ramsey, Phys. Rev., 78,699, 1950.
[27]
R. A. Bonham and T. G. Strand, J. Chem. Phys., 40, 3447,1964.
[28]
W. H. Flygare, "Molecular Structure And Dynamics”. 1978: Prentice-Hall Inc.
399.
-149-
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Section IV
Microwave Spectroscopy and Quantum Computational Studies of
Free Radicals (Open Shell System)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
C H A PTER SEVEN
Microwave Spectroscopy of 1,1-Difluoropropargyl Radical,
HCCCF2, in the
Ground Electronic State
Manuscript in preparation
-150-
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Microwave Spectroscopy of 1,1-Difluoropropargyl Radical,
HCCCF2, in the
Ground Electronic State
Lu Kang and Stewart E. Novick
Department o f Chemistry, Wesleyan University, Middletown, CT 06459, USA
The electronic ground state (^Bi) rotational spectrum o f 1,1-Difluoropropargyl,
HCCCFa, has been recorded with the Fourier transform microwave (FTMW)
spectrometer equipped with a pulsed discharged nozzle (PDN). Five successive atype pure rotational transitions (from N = 1 - 0 to 5 - 4, and Ka = 0, 1, 2) were
measured between 6.5 and 32.5 GHz with an uncertainty of 5 kHz. The molecular
constants, including fine and hyperfine constants, were precisely determined. These
constants are compared to our predictions based on a Density-Fimctional-Theory
(DFT) level ab initio calculations. The rotational and centrifugal distortion constants
are: Ao = 11126.261(49) MHz, Bo = 3927.5218(13) MHz, Co = 2904.2454(12) MHz,
An = 0.566(14) kHz, Ank = 19.144(84) kHz, Ak = ~30(13) kHz, 5n = 0.190(12) kHz,
and 6k = 14.60(43) kHz. The spin-rotation coupling constants are: €„a = -43.6737(58)
MHz, €bb - -17.5891(31) MHz, and Ccc = 0.3595(19) MHz. The hyperfine coupling
constants are: o ^ = 145.734(14) MHz,
Taa ~ -230.2536(36) MHz, V^fTbb-Tcc) =
-121.7046(59) MHz, and Tab = 13.44(24) MHz for the methylenic fluorine atoms (F);
and ap = -32.5416(33) MHz, % Ta„ = 24.2369(76) MHz, and %(Tbb-Tce) = -4.1180
(37) MHz for the acetylenic hydrogen atom. The derived small inertial defect, A®=
-0.085147(44) a m u A \ indicates HCCCFa is a planar o r quasiplanar structure. The
consistency of the measured and the predicted molecular constants, as well as the
structural and physical similarities with 1,1-Difluoroallene, [H2C=C=CF 2], imply
that the allenyl form, 3,3-Difluoropropadienyl, [HO=C==CF2], make a significant
contribution to the resonance structure [HC=C—CF2'^ H C = C = C F 2].
-151-
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INTRODUCTION
Halogenated methyl radicals (HnCX3.„, n = 0, 1, 2 and X = F, Cl, Br, I) have been
studied for over half a century [1, 2]. One of the most interesting topics is the large
difference between the halomethyl radicals and their lighter analogue, methyl radical,
CH 3. Among all o f the halomethyl radicals, substantial interest was devoted to the
fluorinated species, in that, in contrast to other analogues, none of the fluoromethyl
radicals is planar [3-5] or electronically stabilized {Andrews, 1969 #22;Andrews,
1969 #23;Andrews, 1969 # 6 ;Smith, 1970 #25}. Both theoretical [10-14] and
spectroscopic {Schuler, 1965 #4;Pimentel, 1966 #10;Jacox, 1968 #ll;Andrews, 1969
# 6 ;Y. Endo, 1982 #3;C. Yamada, 1983 # 6 6 ;Hirota, 1983 #65} studies revealed that
CF3 and HCF2 are pyramidal. The best determined umbrella angle is 18.15° for CF3
[4, 17, 18], and 15.63° for HCF2 [19]. For example, the umbrella angle is defined for
HCF2 by the angle between the C -H bond and the H - F - F plane. Comparing with
the umbrella angle o f 19.5° for tetrahedral geometry, it is obviously that sp^ instead of
sp^ orbital hybridization dominates the valence shell bonding o f C. The geometry of
H 2CF had been heavily debated for almost four decades [3-5, 11, 13, 14, 20-26].
Experimentalists supported the planar structure based on their observations [3,21,23,
25] whereas theoreticians always provided a “possible alternative suggestion” [11,14,
20, 27]. It wasn’t until recently that the quasiplanar structure now agreed upon, i.e.,
the inversion barrier is lower than zero point energy (ZFE) [5, 13]. The nonplanarity
of fluoromethyl radicals couldn’t be interpreted with VSEPR theory although it works
perfectly for methyl radical. The heavier halogen atom(s) substituted methyl radicals
have been studied too. Monohalomethyl radicals, H 2CCI [9, 14, 28-30], H 2CBr [3135] and H 2CI [36] had been proved to be planar. Dihalomethyl radicals are planar or
quasiplanar. HCCI2 is planar [7, 37], and HCBr2 [6 ] might be quasiplanar because its
very s mall i nversion b anier s imilar t o that
0
f H 2CF [5]. The Matrix IR spectra of
HCI2 and CI3 have been assigned with the assumption of planar structures [38].
Trihalomethyl radicals other than CI3 are known to be flat pyramidal with an
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umbrella angle around I P [39], More interestingly, halogenated methyl radicals other
than fluorinated species are electronically stabilized {Andrews, 1969 # 6 }. For
example, Andrews and Smith found that electronic stabilization for chloromethyl
radicals o f approximately 4 ±1 kcal/mol per C—Cl bond [9], and even stronger for
bromomethyl radicals [40], Over the years o f intense study, it has been found that
both the electronic stabilization energy and the planarity o f heavy halogenated methyl
radicals can be interpreted by the (p-d)Tr bonding [6 , 7, 9, 28, 36, 38] and by the
covalent and charged ionic resonance structures [40, 41]. Figure-1 illustrates these
two effects. Unfortunately, none of explanations works for fluoromethyl radicals.
First, there is no d orbital on fluorine atom’s valence shell, thus (p-d)7t bonding is
impossible. Second, the ionic resonance structure is not acceptable due to the large
electronegativity o f the fluorine atom. Hence, it seems that fluoromethyl radicals
should be close to CH3 and possess the planar geometry. However, they are the most
nonplanar. Since the rigid planarity (Dsh) of methyl radical, CH 3 [42], can be
gracefully interpreted by orbital hybridization, it has been taken as a classical
example for the interpretation of sp^ orbital hybridization in various textbooks. The
stractural disagreement between methyl and fluoromethyl radicals is a serious
challenge to the orbital hybridization theory. Perhaps the electrostatic repulsion might
play a significant role in determining the geometry o f fluoromethyl radicals. The
deviation o f planarity being to the repulsion between the unpaired electron in the half­
filled 2 pz orbital o f C and the lone pair electrons in the p orbital of fluorine atom(s).
To test this, we studied the rotational spectroscopy of HCCCFa. The idea lies in the
possibility that the substitution of H in HCF2 with an acetylene group, CCH, will help
to delocalize the unpaired electron on the C, and reduce the strong repulsion between
the lone pair and unpaired electrons. The release of strain force on the —CF2 group
might result in a planar or quasiplanar geometry. Microwave spectroscopy can help
us investigate the planarity by evaluating the inertia defect. A® = 1° - 1° - 1°.
Beyond the structural aspects, further motivation arises from environmental
concern. Fluorinated alkyl radicals play an important role in ozone depletion. They
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are immediate products in the oxidation of fluorohydrocarbons (HFCs), which are
taking the place of chlorofluorocarbons (CFCs) as the working media of refrigeration
industry. With the increasing production and exhaustion of HFCs due to the industrial
demand, the affect of HFCs to the environmental change deserves more attention. The
merit o f HFCs over CFCs can be attributed to their dramatic short life span in the
atmosphere. It was believed that the hydrogen terminal of HFCs would be easily
degraded. However, the subsequent reaction mechanics involved with fluorinated
alkyl radicals hasn’t been well established, largely due to the scarcity of basic
information. We hope our present work could be helpful for further understanding the
degradation o f HFCs.
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COMPUTATIONAL METHODS
Electronic structure calculations of open-shell systems are difficult. The ground
state equilibrium geometries of closed-shell systems are usually well reproduced by
high-level ab initio methods coupled with large basis sets, e.g., couple-cluster method
with single and double substitutions [CCSD] or account of triple excitations
[CCSD(T)], and Denning’s correlation consistent polarized multiple zeta basis set, ccpVXZ (X = D, T, Q, 5, 6), or augmented with diffuse functions, aug-cc-pVXZ. Many
experimentalists suffer from the critical requirement of computer resources and
unendurably long computing time due to the low efficiency of couple-cluster
methods. However, if not combined with large basis sets, those expensive methods do
notnecessarilyoutperform thennrestrictedDensity-Functional-Theory (DFT) [43]
with Becke’s three-parameter hybrid exchange functional [44] combined with the
Lee-Yang-Parr non-local functional [45] method (denoted as DFT/UB3LYP [46]) for
the geometry optimization o f open-shell systems. Jacox drew this conclusion based
on the comparison o f her experimental observations in the past four decades and the
theoretical predictions on many open shell systems (Uconn-Wesleyan-Yale joint
chemical physics seminar, Fall, 2003). Levchenko et al. [5] also pointed out that the
good performance of DFT/UB3LYP is in agreement with recent benchmark studies of
the equilibrium properties o f doublet radicals [47-49]. Thus DFT/UB3LYP became
our choice for the geometry optimization.
All the calculations were performed with a test version o f the Gaussian98
program package called gOl, which has recently been released on Gaussian03. This
program includes a new functional package which can calculate the spectroscopic
fine and hyperfine constants for singlet states ( / and C, the nuclear quadruple
coupling, and nuclear spin-rotation interaction tensors) along with the more complete
set of fine and hyperfine constants for doublet radicals such as electron spin-rotation,
6,y, Fermi contact terms, ap, and nuclear spin-electron spin interactions, Tij. We first
optimized the geometry with UB3LYP/aug-cc-pVQZ level of calculation. The diffuse
function is crucial for the correct descriptions of the molecular properties such as
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centrifugal distortion constants, dipole moments, spin densities, etc. UCCSD(T)/ccpVTZ level o f calculation was also performed for the comparison. The smaller ccpVTZ basis set was used only because it is the largest basis set that our computer can
handle under the UCCSD(T) level calculation (Within the 16 GB virtual memory
limitation for 32 bit CPU system). Even though, it took more than a month to do the
job!
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E X P E R IM E N T
The rotational spectra o f
HCCCF2
were recorded by a supersonic jet expansion
Fourier transform microwave spectrometer equipped with a pulsed discharge nozzle
(PDN). The descriptions of the FTMW can be found elsewhere [50-52]. Many
modifications have been made since the initial settlement including the coaxial
expansion of the gas pulse with the cavity axis for increased sensitivity and
resolution, changes in microwave circuitry for decreasing the noise, and the software
updated for automatic scanning. A gas sample of ~0.3% HCCCF3 seeded in Argon
carrier gas at a stagnation pressure of ~ 1 atm is expanded through a
0.8
mm diameter
general valve nozzle. HCCCF3 was commercially available (~'97%, first from Matrix
Scientific Co., then firom Lancaster Inc.), and used without further purification. The
expanding gas pulse encounters a 900 volts discharge that serves to dissociate a C-F
bond from HCCCF3 to generate
H C C C F2.
The plasma continues the supersonic
expansion and the rotational temperature is cooled to ~5 Kelvin. W ith such a low
temperature, only the low rotational levels are populated. The gas pulse expands into
the high Q Fabry-Perot microwave cavity, a microwave pulse is synchronized to the
arrival of the molecular beam in the center of the cavity. If the transition lies within
the 300 kHz bandwidth of the microwave pulse and cavity mode combination, a
macroscopic polarization is induced in the molecules. The fi*ee induction decay of this
polarization is collected and averaged, usually for a few hundred gas pulses, and then
is Fourier-Transformed to yield the spectrum of
H C C C F2.
The Full-Width-Half-
Maximum (FWHM) of the peaks are ~5 kHz, which is comparable to the resolution
limit of the spectrum.
More than 120 frequencies of five successive a-type rotational transitions (from N
= 1 ~ 0 to 5 - 4, and Ka = 0, 1, 2) were measured between 6.5 and 32.5 GHz with an
uncertainty of 6 kHz, as listed in Table-1. Ka = 1,2 branches are fairly strong and can
be detected without d i f f i c u l t y . Due to the accurate predictions, the initial search for N
= 2 - 1 and Ka = 0 branch between 13500 MHz and 13600 MHz was straightforward.
Unfortunately, some
p a ra m a g n e tic
lines between 20109 MHz and 20140
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MHz
seriously impeded our work. They were not only close to the N = 3 - 2 and K* == 0
transitions o f HCCCF2 (mainly between 20076 MHz and 20105MHz), but were also
of comparable intensities. We fell into trouble with the assignment at first because
those transitions were taken for granted to be from HCCCF2 . The problem was finally
solved when we realized that those “unexpected” frequencies are the N = 1 ~ 0 and Ka
= 0 transitions o f H 2CCN [53]. They were astronomically observed by the 45m radio
telescope at 20 GHz frequency region [29] with fairly large inaccuracy (30-50 kHz)
[53]. It seems that some cyanide residues existed in the impurities cause the problem.
Things improved when we switched to the Lancaster sample, although a few strong
lines o f H 2CCN still there.
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ANALYSIS
In order to investigate the geometry of HCCCF 2, we employed two sets of
coupling schemes for the identifications of the assignment. If
planar Cav structure, the
fitte d
constants
based
H CCCFa
possesses a
on these two coupling schemes will be
identical, otherwise, they will be different. We first made no assumption about the
geometry and treated the nuclear spins of fluorine atoms independently. Hence, the
coupling scheme is given by:
(1)
J - N + S, F i = J + I fi, F 2 - F , + If2,F=F2 + Ih
where FI and F2 denote the fluorine
1 and 2; Ipi
a to m
and
If 2 are the nuclear spin for
each o f them. However, there is an a l t e r n a t i v e way to consider the coupling scheme if
and only if HCCCFj possesses the planar Cav geometry. In this case, FI and F2 can be
treated identically due to the symmetry. If we couple their nuclei’s spins together to
obtain a unique nuclei’s spin for
flu o rin e
atoms. Ip = Ipi + Ip2, then the second
coupling scheme is given by:
J = N + S, Fi = J + Ip, F = Fi + Ih
(2)
For ease o f expression, we called the
one as uncoupled scheme and the second
firs t
one as coupled scheme.
Since the nuclear spin of fluorine nucleus is 54, Ip can be 0 or 1. We refer to
HCCCFa with Ip = 0 as ortho-HCCCFa, and Ip = 1 as para-HCCCFa. As we known,
the total wave function can be expressed as:
(3)
^toi m ust b e o f n egative p arity with r e s p e c t to the i nterchange o f the two fluorine
'J
nuclei. Since Weiec has negative
scheme) and Wvibr has positive
(electronic ground state is Bi for planar
p a rity
p a rity
(vibrational ground state), it requires that
= ® . Only two choices are possible: both
or negative parity. Notice that, for
Ka = 1, 3, 5, -• ■,
'Prof
= ©• Hence, t o
a -ty p e
and
have positive,
transitions: Ka = 0, 2, 4,- - , 'Vmt = ®, and
en su re t h
a
t
is of negative parity:
'Pror = © and ^„uci = ®, where Ka = 0 , 2 ,4 , ■• , and Ip = 1
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Trot = © and Wnuci = 0 , where Ka= 1, 3, 5, ■, and If = 0
Thus, the even numbered Ka transitions are associated with the nuclear spin triplet
state ( I f = 1) and the odd numbered Ka transitions are associated with the nuclear spin
singlet state (Ip = 0). These states were treated separately in the fit.
The Hamiltonian used for the analysis consists of five terms that given as follows;
H = H„, +
+ H„ +
( ff ) + H,„ (F)
(4)
The first two terras represent the rotational and centrifugal distortion energies.
h
„ = 4 .n ; + s X +
c „n ,"
(5)
-A,,N: -{5»N*
-N ;)-(N 1 -N=)(^,N>
(6)
The third term represents the spin-rotation interaction energy.
H ,.= € ,,N .S ,+ e„ N .S ,+ £ „ N A
(7)
The last two terms represent the magnetic hyperfine interactions between the
unpaired electron and the proton, or the fluorine atoms, respectively.
H v ,m = K V s - i,+ ( r „ ) „ s .i„ ,+ ( r „ ) ,,s .i„ + ( r „ ) „ S A .
(8)
FI
c^FJc
H 4/.(i^) = (aF)FS-lF +(r„„),SJp„ + (r,,),S ,Ip ,
(1 0)
Where ap is the Fermi contact term; and T„„, Tbb, Tec, etc., denote the diagonal terms
of the second rank tensors of the magnetic dipolar interaction between I and S; S
denotes the electron spin, and Ij (z = FI, F2, or H) denote the nuclear spin correspond
to zth nucleus; S«, S*, Sc and Ii„, lib, he are the components of S and I| along the
principal axis a, b, and c, respectively. Expression (9) is applied for the uncoupled
scheme and (10) for the coupled scheme. All the predicted and fitted constants are
listed in Table-2.
-
160-
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DISCUSSION
Microwave spectroscopy can be used to investigate the planarity of the molecules.
First, according to the rotational constants (uncoupled scheme), the inertial defect is
A°= -0.085147(44) amuA^, which can be taken as an evidence for planarity or
quasiplanarity in that all the planar molecules bear a small inertia defect that is very
close to zero. Second, due to the high resolution of microwave spectroscopy, one
could easily observe the double splitting caused by the inversion motion if HCCCF2
is nonplanar, and can even figure out the umbrella angle, similar to what Endo and his
co-workers did for HCF 2 [19]. We haven’t observed the double splitting due to the
inversion motion in the spectrum. Third, those measured molecular constants,
including fine and hyperfine constants, based on different c oupling schemes, agree
with each other within error limit. One thing that deserves our attention is that the
inertial defect o f an ideal, i.e., rigid, planar molecule vanishes, whilst the “wellbehaved” planar molecule generally possess small positive inertia defects about
0.05—0.5 amuA^ due to the out-of-plane vibrational motion [54]. The typical inertia
defect o f a nonplanar molecule is a fairly large negative number. For example, A °= 3.200 amuA^ for H 2CCCF2. Interestingly, the inertia defect of HCCCFa is a small
negative number, A°= -0.085147(44) amuA^, which perhaps suggest a small
derivation from planarity. The inertia defect o f H2CF [23] is -0.009 am uA\ also a
small negative number. However, few of quasiplanar molecules have been identified,
the signs (+/-) and magnitudes of their inertia defects have not been extensively
studied. S imilar t o t he d escription o f H 2CF given by Endo e ta I. [23], HCCCF2 i s
essential planar but not excluding the possible of quasiplanarity.
The ab initio predictions are in excellent agreement with the experimental
measurements. It implies that the predicted geometry might be very close to the actual
geometry. To check if the agreement is accidental or meaningful, we applied the same
level of calculations to DCCCF2 and CF2 CN radicals, and searched dozens of
paramagnetic transitions in the predicted frequency regions. Furthermore, the
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structural similarities o f predicted CF2 part in HCCCF 2 with those of the experimental
determined HCF 2 {r(C—F) = 1.3245(26)A, ZFCF = 111.53(15)°} [19] and CF3
(r(C—F) = 1.318(2)A, ZFCF = 110.76(40)°} [4] strengthened our confidence on the
ab initio optimized structure of HCCCF2 . These facts convinced us that the predicted
structure o f HCCCF 2 deserves some further analysis. Figure-2 shows the molecular
structures o f HCCOFa, and its most closely related “closed shell” systems, HCCCF3
and H 2 CCCF2 . Comparing these molecular structures, we found that the C— C single
bond length o f HCCCF2 radical (1.3534A) is dramatically shorter than that of the
normal species (~1.54A), and almost comparable to the normal C==C double bond
length ('-1.33A); the C=C triple bond (1.2177A) is obviously longer than the normal
triple bond (-1.205A). Moreover, C—F bond length, ZFCF, and ZCCF of C—CF2
part are similar to those of H2CCCF2, and the bond lengths of HC=C group are closer
to those o f HCCCF 3 . Suchunique behavior o f HCCCF 2 might b e attributed to the
resonance structure [HC=C—CF2 <-*HC==C==CF2]. The C—C single bond and C=C
triple bond both bear C=C double bond character and tum out to be shorter and
longer respectively. Actually, the C—C bond has more double bond character than
single bond character. The planar C2v symmetry of HCCCF 2 also proves the
resonance structure argument. Had HCCCF2 strictly kept the propargyl form,
HC=C—CF2 , no delocalization of the unpaired electron in the 2pz orbital, the —CF2
part would resemble that of HCF2 and be nonplanar due to the electrostatic repulsion
effect. Had HCCCF 2 strictly kept the allenyl form, HC=C==CF2, the HC=C part
would be nonlinear due to the sp^ orbital hybridization. This breaks up the C2v
symmetry and is not consistent with our experimental observations. It seems that both
the propargyl form and the allenyl form play significant roles in the resonance
structure o f HCCCF 2 . Details are displayed in Figure-3. Some evidence comes from
the analysis of atomic spin density. According to the UB3LYP/aug-cc-pVQZ
calculation o f HCCCF2, the spin density is 0.548 for fluoromethylenic carbon and
0.500 for acetylenic carbon. Comparing with HCCCH2 (0.842 for methylenic carbon
and 0.546 for acetylenic carbon), they are quite close. This could be understood by
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the fact that th e unpaired electron o n the
2
o rbital a t fluoromethylenic carbon i s
squeezed to the hyper conjugated acetyl group, HC=C, due to the large charge density
o f fluorine atoms in the fluoromethylenic group, —CF2 . The delocalization of
unpaired electron from fluoromethylenic carbon to the acetyl group greatly releases
the strain force on the —CF2 and results in a flat geometry. This is a good explanation
o f why HCCCF 2 is planar or quasiplanar whereas its close analogue, HCF2 , is
pyramidal. Further proof come from the experiment. McConnell and Chesnut gave an
semi empirical formula, aF(H) = Qp^t, which relates the spin density at a carbon that
connected to the hydrogen atom with the Fermi contact constant,
in the a:-orbital at the adjacent carbon atom;
0
is the spin density
is an empirical parameter with the
value o f -64.4 MHz [55] for n electron type radicals. According to this formula, the
substitution o f ap(H) with measured value, -32.5478 MHz, gives the spin density to
be 0.505 for the acetylenic carbon. It is only off by 1% from the prediction! The
almost equally populated spin densities enables HCCCF2 to possess two active
centers, fluoromethylenic carbon and acetylenic carbon. Thus, any HFCs with
HCCCFa as the intermediate might be expected to be very reactive. The reaction
involved with the acetylenic carbon might help in the degradation of HFCs in the
atmosphere.
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ACKNOW LEDGMENTS
We thank Dr. James Cheeseman from Developing Center of Gaussian Inc. for
helping us calculate the fine and hyperfine constants. Dr. John Montegometry, Jr. and
Dr. Michael Frish from Gaussian Inc. helped us set up the internal version of
Gaussian program package. We appreciated the assistances of Dr. M. C. McCarthy
and Professor P. Thaddeus from allowing us to use the Harvard spectrometer to
capture some transitions between 26.5 and 32.5 GHz. We also thank Prof. Wallace
Pringle and Prof. Robert Bohn for the constructive comments. This project was
support by National Science Foundation.
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Figure-1: The (p-d)ji bonding and the covalent and charged ionic resonance structures
(p-d)TC bonding favors
planar structure
Covalent and charged ionic
resonance structure favors
pyramidal structure
©
••
••
••
: X««
••
C
•X:
••
D3 h
‘X
X = C!, Br, I
sx:
••
^3v
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Figure-2: The molecular structures of HCCCF3 , HCCCF2 , and H2 CCCF2
F
1.2 01(1 )
H
C
''1 .0 5 1 (1 )^
V
— C
” C J 108.3°(2)
1-4 74 (5)^ '^
^J
F
V.
1.2177
H 1.0611 C =
H /a
7> .
^
1.3534
I1-306(2)
N*.
1.302( 12)
-
166
-
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Figure-3: The resonance structures o f HCCCFa
1,1-Difluoropropargyl
H
H
^ C
j = = C
=
C-
H
3,3-Difluoropropadienyl
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Table-1: Measured HCCCF? transitions
Transitions (Nuclear Spin Singlet State Ip = 0)
I n ~ In
3/2 - 1/2
1 -0
12625.4280
- 1.6
2 i2 -
In
3/2 - 1 /2
3/2 - 1 /2
2 -1
12637.7372
0.6
2 i2
-
111
5/2 - 3/2
5/2 - 3/2
3 -2
12640.2900
5.2
2) 2
- In
5/2 - 3/2
5/2 - 3/2
2 -1
12640.9320
-0 . 1
2)1
- In
3/2 - 1/2
3/2 - 1 /2
1 -1
14663.7664
-2.4
111
3 /2 -1 /2
3/2 - 1 /2
1 -0
14680.4685
-1.7
2
ii - In
5/2 - 3/2
5/2 - 3/2
3 -2
14681.8551
-12.0
2
ii - In
5/2 - 3/2
5/2 - 3/2
2 -1
14683.9864
- 10.6
2
ii -
111
3/2 - 1 /2
3 /2 - 1/2
2 -1
14687.5377
-0.3
-
111
5/2 - 3/2
5/2 - 3/2
2 -2
14699.9409
-6.7
3i3 -
2 i2
5/2 - 3/2
5/2 - 3/2
2 -1
18897.8615
9.7
3 i3 ~ 2 i 2
7/2 - 5/2
7/2 - 5/2
4 -3
18899.0988
3.7
3 i 3 - 2 i2
7/2 - 5/2
7/2 - 5/2
3 -2
18899.4141
1.9
3 i3 - 2 i 2
5 /2 -3 /2
5/2 - 3/2
3 -2
18899.5303
8.5
3 i3 - 2 i2
5/2 - 5/2
5/2 - 5/2
2 - 2
18912.5618
2.2
3 i2 - 2 ii
7/2 - 5/2
7/2 - 5/2
4 -3
21957.7325
3.0
3 i2 - 2 ii
7/2 - 5/2
7/2 - 5/2
3 -2
21958.6890
25.8
4 i4 - 3 i 3
9 /2 -7 /2
9 /2 -7 /2
5 -4
25094.2784
-3.4
4 i4 - 3 i3
9/2 - 7/2
9/2 - 7/2
4 -3
25094.4815
-6.4
4 i4 - 3 i 3
7/2 - 5/2
7/2 - 5/2
3 -2
25094.9413
-18.2
4 i 4 ~ 3 i3
7/2 - 5/2
7/2 - 5/2
4 -3
25094.2988
1. 0
5 i 5 - 4 i4
1 1 /2 -9 /2
1 1/2-9/2
6 -5
31216.9434
-4.1
5 i 5 ~ 4 i4
1 1 /2 -9 /2
1 1/2-9/2
5 -4
31217.0537
8.8
2n
o=
0-C
(kHz)
J '- J
3/2 - 1/2
2\i~
8.6
F ’- F
Frequency
(MHz)
kHz for 23 transitions.
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Transitions (Nuclear Spin Singlet State Ip = 0 )
N „ x - N k.k.
f ;~ F i
F ’- F
Frequency
(MHz)
0-C
(kHz)
lot “ Ooo
3/2 - 1/2
3 /2 -3 /2
1 -1
6767.8442
1.1
lo t- Ooo
3/2 - 1 /2
1/2
-
1/2
1 -0
6821.2495
-8.4
lo i- Ooo
3/2 - 1 /2
1/2
-
1/2
0 -1
6826.3567
-0.7
lo t- Ooo
3/2 - 1/2
3/2 - 1/2
2 -1
6833.5876
0.3
loi“ Ooo
1/2
-
1 /2
3/2 -1 /2
1 -0
6834.6010
-2.3
lo i- Ooo
3/2 - 1/2
5/2 - 3/2
2 -1
6841.9412
1.0
loi~ Ooo
3 /2 -1 /2
5/2 - 3/2
3 -2
6842.1384
1.6
lot-Ooo
1/2
-
1/2
1/2 - 3/2
0 -1
6922.7636
-4.0
lo i- Ooo
1/2
-
1/2
1/2 - 3/2
1 -2
6933.0388
-4.7
2 o2 - 1 o i
3/2 - 1 /2
3/2 - 1/2
1 -0
13471.8587
4.4
2 o2 - 1 o i
5 /2 -3 /2
5/2 - 5/2
2 - 2
13480.8448
3.2
2 o2 ~ 1 o i
3/2 - 1 /2
3/2 -1 /2
1 -1
13484.2714
-6.5
2 o2 - 1 o i
5/2 - 3/2
5/2 - 5/2
3 -3
13491.3407
-3.5
2 o2 - 1 o i
3/2 - 1 /2
3/2 - 1/2
2 -1
13494.7001
5.8
2 o2 - 1 o i
5/2 - 3/2
5 /2 -3 /2
2 -1
13554.9334
-5.4
2 o2 - 1 o i
5/2 - 1 /2
5/2 - 3/2
3 -2
13556.1642
-7.5
2 o2 - 1 o i
5/2 - 3/2
3/2 - 1 /2
1 -0
13557.8143
-7.5
2 o2 - 1 o i
5/2 - 3/2
3/2 - 1/2
2 -1
13558.2816
-6 . 6
2 o2 - 1 o 1
3/2 - 1 /2
1/2
-
1/2
0 -1
13561.8762
5.6
2 o2 - 1 o !
3 /2 -1 /2
5 /2 -3 /2
2 -1
13562.4001
3.2
2 o2 - 1 o 1
3/2 - 3/2
5/2 - 3/2
3 -2
13563.2055
1.3
2 o2 - 1 o 1
3/2 - 1 /2
1/2
-
1/ 2
1 -0
13566.7602
7.9
2 o2 - 1 o 1
5 /2 -1 /2
5/2 - 3/2
2 -2
13568.1642
-7.8
2 o2 - 1 o 1
5/2 - 3/2
7/2 - 5/2
3 -2
13568.6343
0.7
2 o2 - 1 o 1
5/2 - 3/2
7/2 - 5/2
4 -3
13569.0502
0.4
2 o2 “ 1 oI
5/2 - 3/2
3/2 - 1/2
1-1
13572.7702
4.1
2 o2 - 1 oI
3/2 - 3/2
3 /2 -3 /2
1 -1
13626.7719
-7.0
-169-
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2 o2 - 1 o1
3/2 - 3/2
3 /2 -3 /2
2 -1
13637.1951
-0 . 2
2 o2 - 1o1
3/2 - 1 /2
3/2 - 3/2
1 -2
13640.0063
-5.8
2 o2 - 1 o1
3/2 - 3/2
1 /2 -3 /2
0 -1
13704.3734
1.7
2 o2 - 1 o1
3/2 - 1 /2
1/2 - 3/2
1 -2
13734.9194
9.4
3 o3 - 2 o2
5/2 - 3/2
5/2 - 3/2
2 -1
20076.6676
5.0
3 o3 - 2 o2
5 /2 -3 /2
5 /2 -3 /2
3 —2
20080.2260
5.4
3 o3 - 2 o2
7/2 - 5/2
7/2 - 5/2
4 -3
20084.7863
1.4
3 o3 ~ 2 o2
7 /2 -5 /2
7/2 - 5/2
3 -2
20085.1348
3.1
3 o3 - 2 o2
7/2 - 5/2
5/2 - 3/2
3 -2
20089.1698
-3.7
3 o3 - 2 o2
7/2 - 5/2
5/2 - 3/2
2 -1
20089.8462
-2 . 1
3 o3 “ 2 o2
5/2 - 3/2
7/2 - 5/2
3 -2
20094.5485
1.4
3 o3 “ 2 o2
5/2 - 3/2
7/2 - 5/2
4 -3
20095.8607
0.7
3 o3 - 2 o2
5/2 - 3/2
3 /2 -1 /2
1 -0
20098.5974
-12.3
3 o3 - 2 o2
5 /2 -3 /2
3/2 - 1 /2
2 -1
20099.5805
-12.7
3 o3 - 2 o2
7/2 - 5/2
9/2 - 7/2
4 -3
20104.0933
2.7
3 o3 - 2 o2
7 /2 -5 /2
5 /2 -3 /2
2 -2
20104.3294
3.2
3 o3 - 2 o2
7/2 - 5/2
9/2 - 7/2
5 -4
20104.6458
2 .0
3 o3 - 2 o2
5/2 - 3/2
3/2 - 3/2
1-1
20176.2072
4.7
322 “ 221
5 /2 -3 /2
7/2 - 5/2
3 -2
20419.4637
3.0
3 2 2 -2 2 1
5/2 - 3/2
7/2 - 5/2
4 -3
20432.4528
5.5
322 -2 2 1
7 /2 -5 /2
5/2 - 3/2
3 -2
20493.3126
-9.0
322 -221
7/2 - 5/2
5/2 - 3/2
2 -1
20498.1916
-3.1
3 2 2 -2 2 1
7/2 - 5/2
7/2 - 5/2
3 -2
20499.0391
4.3
322 -2 2 1
5/2 - 3/2
5/2 - 3/2
3 -2
20500.9439
-3.0
322 -2 2 1
7/2 - 5/2
7/2 - 5/2
4 -3
20501.9100
3.6
322 -2 2 1
7/2 - 5/2
9/2 - 7/2
4 -3
20516.8376
2.7
322 -2 2 1
7/2 - 5/2
9/2 - 7/2
5 -4
20517.5400
3.1
3 2 2 -2 2 !
5/2 - 3/2
3 /2 -1 /2
2 -1
20572.8934
-1.4
321 -2 2 0
5/2 - 3/2
5/2 - 3/2
3 -2
20891.7713
-9.8
-170-
R eproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
321 - 2 2 0
5/2 - 3/2
5/2 - 3/2
2 -1
20891.9736
2.8
321-220
7/2 - 5/2
5/2 - 3/2
3 -2
20895.4164
4.0
321 - 2 2 0
7 /2 -5 /2
7/2 - 5/2
3 -2
20897.3942
5.8
321 - 2 2 0
7 /2 -5 /2
7/2 - 5/2
4 -3
20899.0334
5.4
321-220
7/2 - 5/2
5/2 - 3/2
2 -1
20899.7234
-1.7
321 - 2 2 0
7/2 - 5/2
9/2 - 7/2
5 -4
20907.0418
0 .1
321 - 2 2 0
5/2 - 3/2
3/2 - 1/2
2 -1
20950.0444
4.3
4 o4 - 3 o3
9/2 - 7/2
9/2 - 7/2
5 -4
26354.6202
0 .2
4 o4 - 3 o3
9/2 - 7/2
9/2 - 7/2
4 -3
26355.7221
-1.8
4 o4 - 3 o3
7 /2 -5 /2
7/2 - 5/2
3 -2
26355.7423
1.5
4 o4 - 3 o3
7/2 - 5/2
7/2 - 5/2
4 -3
26357.6447
4.0
4 o4 - 3 o3
9 /2 -7 /2
7/2 - 5/2
4 -3
26358.6985
-4.1
4 o4 - 3 o3
9/2 - 7/2
7/2 - 5/2
3 -2
26359.4618
-5.0
4 o4 - 3 o3
7/2 - 5/2
9/2 - 7/2
4 -3
26363.4324
5.9
4 o4 - 3 o3
7/2 - 5/2
9/2 - 7/2
5 -4
26365.1055
7.6
4 q4 ~ 3 o3
9/2 - 7/2
1 1 /2 -9 /2
4 -3
26377.7207
2.6
4 o4 - 3 o3
7/2 - 5/2
5/2 - 3/2
2 -1
26377.7634
-3.5
4 o4 - 3 o3
9/2 - 7/2
11 /2 -9 /2
6 -5
26378.3478
2.3
423 -322
9/2 - 7/2
7/2 - 5/2
4 -3
27239.8047
-4.6
423 -322
9/2 - 7/2
7/2 - 5/2
3 -2
27241.9883
0.3
423 “ 322
7/2 - 7/2
9/2 - 9/2
5 -4
27242.9092
-1 2.8
423-322
7/2 - 7/2
9/2 - 9/2
4 -3
27244.9697
4.4
423 -322
9/2 - 7/2
9/2 - 7/2
5 -4
27245.5635
-0.5
422-321
7/2 - 5/2
9/2 - 7/2
5 -4
28199.3535
1 .0
422-321
7/2 - 5/2
9/2 - 5/2
4 -3
28202.2451
0 .1
422-321
7/2 - 5/2
7/2 - 7/2
4 -3
28203.8350
- 1. 8
422 -321
9/2 - 7/2
1 1/2-9/2
6 -5
28204.9180
3.4
422 -32!
9 /2 -7 /2
7/2 - 5/2
4 -3
28205.0176
-3.5
422-321
9/2 - 7/2
1 1 /2 -9 /2
5 -4
28206.1797
2.2
-171-
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
^ 21—^21
9 /2 - 7/2
7/2 - 5/2
3 -2
28206.6348
-0 . 2
422 -321
9 /2 - 7/2
9/2 - 7/2
5 -4
28207.2968
3.1
422 - 3 2 J
9 /2 - 7/2
9 /2 -7 /2
4 -3
28207.4814
2.3
422-321
7 /2 - 5/2
7/2 - 5/2
3 -2
28208.8487
-5.4
422 -321
7 /2 - 5/2
5/2 - 3/2
3 -2
28214.4629
-0 . 6
5o5“4 o4
9 /2 - 7/2
1 1/2-9/2
6 -5
32348.0361
-3.4
5o5—4o4
9 /2 - 7/2
1 1 /2 -9 /2
5 -4
32354.8535
-0 . 8
5o5-4 o4
1 1 /2
--9/2
9 /2 -7 /2
4 -3
32358.2764
1.1
5o5-^04
1 1 /2
--9/2
9/2 - 7/2
5 -4
32361.1357
2.5
5o5—4o4
9 /2 - 7/2
9/2 - 7/2
4 -3
32375.5860
-1.7
5o5~4o4
9 /2 - 7/2
9/2 - 7/2
5 -4
32376.1947
-0.9
5o5-4 o4
1 1 /2
--9/2
13/2-11/2
6 -5
32385.7509
6. 1
5o5-4 o4
1 1 /2
--9/2
13/2-11/2
7 -6
32386.3564
2.0
5o5~4o4
1 1 /2
--9/2
1 1/2-9/2
5 -4
32386.9073
-0. 1
5o5-4 o4
1 1 /2
--9/2
11/2 - 9/2
6 -5
32387.5586
-3.9
5o5-4 o4
9 /2 - 7/2
7/2 - 5/2
4 -3
32399.7930
-4.3
o = 4.6 kHz for 101 transitions.
-172-
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table-2: Molecular Constants of HCCCFa Radical
Golbal fit
11126.261(49)
Ortho-HCCCFs
(If = 1 )
11126.2623(52)
Para-HCCCF2
(If = 0 )
11126.41(16)
3926
3927.5218(13)
3927.5199(17)
3927.5215(90)
2901
2904.2454(12)
2904.2465(11)
2904.2459(63)
0.44
0.566(14)
0.565(12)
0.565*
17
19.144(84)
19.006(92)
19.006*
xlO^
-1.5
-30(13)
-30*
-30*
x
10^
0.13
0.190(12)
0.171(23)
0.171*
k x
10^
9.6
14.60(43)
14.6*
14.6*
^aa
-43.23574
-43.6737(58)
-43.6765(64)
-43.659(25)
6bb
-19.73976
-17.5891(31)
-17.5888(33)
-17.5882(123)
€cc
2.1575956
0.3595(19)
0.3544(22)
0.3704(40)
apCH)
-43.22553
-32.5416(33)
-32.5436(36)
-32.5370(152)
VlTaa
31.277356
24.2369(76)
24.2272(97)
24.2414(141)
% ( T ,,- T c c )
-4.818667
-4.1180(37)
-4.1407(95)
-4.1236(87)
ap(F)
97.522839
145.734(14)
145.727(14)
Not Valid
K T aa
-244.2898
-230.2536(36)
-230.2515(36)
Not Valid
V4^bb~^c^
-128.6172
-121.7046(59)
-121.7036(60)
Not Valid
T o6
16.088685
13.44(24)
13.40(24)
Not Valid
6.3 k H z / 124
4.6 k H z / 101
UB3LYP/
aug-cc-p VQZ“
11108
Bo
Co
Constants
(MHz)
Ao
A
xlO ^
n
A nk xlO^
A
k
6n
6
R M S /#
( I
f
= 0 ,1 )
8.6
k H z /23
": Present work; the geometry of HCCCF2 was optimized by UB3LYP/aug-cc-pVQZ.
*: Fixed value
#: Number o f measured transitions.
-173-
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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Chem. Phys., 107(8), 2728-2722, 1997.
-176-
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CH A PTER EIG H T
Computational and Rotational Spectroscopic Studies of Free
Radicals: Deuterated 1,1 -Difluoropropargyl, DCCCF2,
Cyanodifluorom ethyl, CF2CN, and Cyanomethyl, H2CCN
Work in progress
-1 7 7 -
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
§ 8.0
INTRODUCTION
This chapter introduces some of my incomplete, but ongoing projects about the
unstable free radicals (open
shell
system), including the deuterated
1,1-
Difluoropropargyl radical, DCCCF 2, the Cyanodifluoromethyl radical, CF2CN, and
the Cyanomethyl radical, H 2CCN. § 8.1 introduces our current progress on the study
of DCCCF2 . §
8.2
contains the information of our most resent achievement on both
the computational and experimental investigations of CF2CN. § 8.3 presents a table
that lists the astronomically detected and the laboratory observed
1
—» 0 transitions of
HaCCN in the 20 GHz frequency region. It can be used as a good reference to avoid
the possible wrong assignment of free radical transitions in this frequency region.
-178-
R eproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
§ 8.1
DEUTEMATED 1,1-BIFLUOROPROPARGYL RADICAL, DCCCF 2
F o l l o w i n g t h e w o r k o f 1 ,1 - D i f l u o r o p r o p a r g y l r a d i c a l , H C C C F 2 , w e c o n t i n u e d o u r
s tu d y o n its d e u te ra te d
s p e c i e s , D C C C F 2 . T h e c h e m i c a l p r o p e r t i e s o f t h e s e tw o
is o to p o m e r s s h o u ld b e v e r y c lo s e to e a c h o th e r, b u t th e y c o u ld b e q u ite d if fe r e n t
s p e c tro s c o p ic a lly . A s I h a v e m e n tio n e d in C h a p te r 7, H C C C F 2 is e s s e n tia lly p la n a r
a lth o u ^
th e
p o s s ib ility
C u rre n tly , th e re
a re n o
o f p o s s e s s in g
a
q u a s ip la n a r s tr u c tu re
is n o t e x c lu d e d .
a p p ro p ria te e x p e rim e n ta l te c h n iq u e s th a t c a n
d is tin g u is h
p l a n a r a n d q u a s i p l a n a r m o l e c u l e s e f f i c i e n t l y . T h e m o s t p o p u l a r a n d p r a c t i c a l w a y is
to p e r f o r m th e a b in itio g e o m e tr y o p tim iz a tio n , a lth o u g h c a r e m u s t b e ta k e n to u s in g
c o m p u t a t i o n a l m e t h o d a n d b a s i s s e t s a p p r o p r i a t e d to t h e m o l e c u l e b e i n g s tu d i e d . I n
v ie w o f th is , w e in v e s tig a te d th e s p e c tr o s c o p y o f D C C C F a in th e h o p e it c o u ld h e lp in
th e d e te r m in a tio n o f th e s tr u c tu re o f H C C C F 2 . T h e re a re tw o m a in p o in ts : F irs t, th e
d e u te r a tio n o f H C C C F 2 g r e a tly in c re a s e s th e b a r r ie r h e ig h t o f th e o u t-o f- p la n e
v i b r a t i o n a l m o t i o n (B jnv) i f i t i s q u a s i p l a n a r . I f , i t tu r n s o u t t h a t , t h e Bjnv o f H C C C F 2 is
o n l y s l i g h t l y l o w e r a n d t h e Binv o f D C C C F 2 is h i g h e r t h a n t h e z e r o p o i n t e n e r g y
(Z P E ), th e n , w h ile F IC C C F 2 c a n b e c h a r a c te r iz e d a s q u a s ip la n a r ; D C C C F 2 c a n b e
c o n s id e re d tr u ly p la n a r. In th is c a s e , w e s h o u ld b e a b le to
o b s e rv e th e d o u b le
s p l i t t i n g s a r i s e f r o m t h e o u t - o f - p l a n e v i b r a t i o n a l m o t i o n o f D C C C F 2 i n t h e s p e c tr u m ,
ju s t lik e w h a t E n d o
et al. h a v e o b s e r v e d f o r H C F 2 . S e c o n d , i f H C C C F 2 is f a ir ly
rig id ly p la n a r , o r o n ly s lig h tly n o n p la n a r ,
D C C C F 2 s p e c tru m
i.e., Bmv « Z P E , t h e n t h e p a t t e r n o f t h e
w i l l b e s i m i l a r t o t h a t o f H C C C F 2 , e x c e p t f o r th e h y p e r f i n e
s p littin g s c a u s e d b y th e n u c le a r s p in o f D .
T h e e x p e r i m e n t i s s i m i l a r t o t h a t o f H C C C F 2 . T h e o n l y d i f f e r e n c e is t h a t t h e g a s
s a m p le b u b b le s th r o u g h th e D 2O
(2 0
m l ) + N a 2C 0
3
( 0 . 6 g ) s o l u t i o n tw i c e b e f o r e i t
r e a c h e s t h e n o z z l e . T h e b u b b l i n g s y s t e m is c o o l e d d o w n w i t h i c e w a t e r i n o r d e r to
r e d u c e t h e p a r t i a l p r e s s u r e o f D 2 O v a p o r i n t h e s a m p l e g a s . T h e t r a n s f e r is n o t p e r f e c t,
a b o u t 9 0 % o f H C C C F 3 is d e u te r a te d a c c o r d in g to th e in te n s ity c o m p a r is o n o f th e
H C C C F 3 a n d D C C C F 3 s p e c tr a . T h e p r e d i c t e d s t r o n g t r a n s i t i o n s f o r e l e c t r o n i c s p in
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triplet state (Ka = 0, 2) are in the frequency ranges o f 6.3 GHz, 12.6 GHz, 18.7 GHz,
and 24.7 GHz. For the electronic spin singlet state (Ka = 1, 3), the strong lines are
predicted to be at -11.8 GHz, 13.6 GHz, 17.7 GHz, 20.3 GHz, 23.5 GHz, and 25.5
GHz. We didn’t scan the 6.3 GHz and 25.5 GHz frequency regions because the
machine condition is very poor at the edge of its spectrum span. The searching of
11.8 GHz and 13.6 GHz frequency regions failed due to the technical difficulty — a
sharp spike in the middle of the window caused by “leakage” of the pumping
frequency into the detection electronics swamped other potential molecular signals.
The paramagnetic transitions found in the experiment are listed in TABLE 1.
TABLE 1. Observed paramagnetic transitions of DCCCFa
Transitions
Frequency
J = 2 —♦ l,K a = 0, electronic spin triplet state
12625.2976 MHz
12625.3325 MHz
12629.9092 MHz
12629.9588 MHz
12629.9727 MHz
12635.6146 MHz
12635.9204 MHz
J = 3 —V2, Ka = 0, electronic spin triplet state
18761.6586 MHz
18761.7635 MHz
J = 3 —>2, Ka= 1, electronic spin singlet state
20340.8736 MHz
20340.8856 MHz
20340.9548 MHz
20340.21 MHz ?
20340.43 MHz ?
J = 4 —>3, K a = l , electronic spin singlet state
23494.3969 MHz
23494.4692 MHz
-ISO-
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J = 4 —> 3, Ka = 0, electronic spin triplet state
24693.0600 MHz
24704.6719 MHz
The information we obtained currently is insufficient to make an assignment, but
barely enough to convinced us that we found the DCCCF 2 transitions. Our future plan
is to search those frequency regions more carefully and investigate the pattem of the
spectrum in order to make the assignment.
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§ 8.2
CYANODIFLUOROMETHYL RADICAL, ^:F2CN
W e w e r e a s to n is h e d a t th e p e r f o n n a n c e o f th e a b in itio p r e d ic tio n o f H C C C F a .
T h e f a c t t h a t t h e a b i n i t i o p r e d i c t i o n s a n d t h e e x p e r i m e n t a l m e a s u r e m e n t s a r e in
e x c e lle n t a g re e m e n t w ith e a c h o th e r in s p ire d u s to try a n e w ra d ic a l w ith th e h e lp o f
th e s a m e le v e l o f a b in itio c a lc u la tio n . C y a n o d if lu o r o m e th y l r a d ic a l, C F 2 C N , b e c a m e
o u r t a r g e t i n t h a t i t is i s o e l e c t r o n i c t o H C C C F j a s i n t h e p r e v i o u s s t u d y , t h e g e o m e t r y
o p tim iz a tio n
of
C F 2C N
w as
p e rfo rm e d
by
U B 3 L Y P /a u g -c c -p V Q Z
le v e l
of
c a l c u l a t i o n . H o w e v e r , i n c o n t r a s t to t h e H C C C F 2 s tu d y , t h e m o l e c u l a r c o n s t a n t s u s e d
f o r th e f re q u e n c y p r e d ic tio n a re n o t th e c a lc u la te d o n e s , b u t th e s c a le d v a lu e s . T h e
s c a le
fa c to r
o f c e rta in
m o le c u la r
c o n s ta n t w a s
th e
ra tio
o f th e
c o rre s p o n d in g
e x p e rim e n ta l v a lu e d e r iv e d b y th e a b in itio p r e d ic te d v a lu e o f H C C C F 2 . T h is id e a h a s
b e e n a p p lie d to s tu d y H 2P C N a n d w a s in e x c e lle n t a g r e e m e n t w ith th e e x p e rim e n t, a s
in tr o d u c e d in c h a p te r 6.
W ith th e h e lp o f th e h ig h q u a lity p r e d ic tio n , th e s e a r c h in g o f C F 2 C N tra n s itio n s
w a s s tra ig h tfo rw a rd . M o r e th a n 5 0 p a r a m a g n e tic lin e s th a t b e lo n g to f o u r s u c c e s s iv e
tra n s itio n s (fro m J = l - > 0 t o J = 4 - ^ 3 ,
Ka =
0 , 1; o n e o f t h e m e a s u r e d f r e q u e n c i e s
m ig h t b e f ro m K a = 2 tr a n s itio n ) w e r e c a p tu r e d , a s lis te d in T A B L E 2.
T A B L E 2 . O b s e r v e d p a r a m a g n e tic tr a n s itio n s o f C F 2C N
T ra n s itio n s
J =
1 —» 0 , Ka =
F re q u e n c y
0 , e le c tro n ic s p in tr ip le t s ta te
7 0 0 1 .5 9 1 6 M H z
7 0 4 8 .7 5 9 6 M H z ?
7 0 5 2 .5 5 2 8 M H z
7 0 7 2 .3 8 5 2 M H z
7 0 8 5 .2 0 4 8 M H z
J = 2 —
I, Ka =
1, e l e c t r o n i c s p i n s i n g l e t s ta te
1 3 0 4 1 .0 8 4 0 M H z
1 3 0 5 1 .3 5 3 8 M H z
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13053.7976 MHz
J = 2 —♦ l , Ka = 0, electronic spin triplet state
13945.0089 MHz
13945.0604 MHz?
13948.8600 MHz
14009.6344 MHz
14013.1868 MHz
14014.6658 MHz
14014.6827 MHz
14014.9962 MHz
14017.4440 MHz
14022.7478 MHz
14024.6248 MHz
14024.7282 MHz
14024.8194 MHz
14032.8638 MHz
14033.3314 MHz
14039.9560 MHz
J = 2 —^ l , K a = l , electronic spin singlet state
15228.9570 MHz
15229.1659 MHz
15229.2666 MHz
15230.0381 MHz
J = 3 -+ 2, Ka = 1, electronic spin singlet state
19503.8317 MHz
19504.9347 MHz
19505.5188 MHz?
19506.4650 MHz
J = 3 —>2, Ka = 0, electronic spin triplet state
20728.8872 MHz
20732.7783 MHz
20740.8510 MHz
20741.8187 MHz
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20745.1298 MHz
20747.3304 MHz
20748.2198 MHz
20748.2345 MHz
20748.5451 MHz
20757.5906 MHz
20757.6154 MHz
20758.4783 MHz
20759.2534 MHz
J=3
2, Ka = 2, electronic spin triplet state?
21251.7174 MHz
J = 3 —> 2, Ka= 1, electronic spin singlet state
22766.4883 MHz
22766.6161 MHz
22766.9384 MHz
22777.1886 MHz
22779.3212 MHz
J = 4 —> 3, Ka = 1, electronic spin singlet state
25885.6832 MHz
25885.7496 MHz
25886.3020 MHz
25886.9040 MHz
To make the correct assignment, more information about the pattern of the
spectrum is needed. With the help of ab initio prediction (some molecular constants
were fixed to be the predicted ones), our tentative assignment for about a dozen lines
was in a good shape and can reproduce the most of the other transitions within the
frequency range of a couple hundred kilohertz. The fitted molecular constants based
on the tentative assignment are given in TABLE 3.
TABLE 3. Fitted molecular constants based on the tentative assignment and the ab
initio prediction.
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Molecular Constants
Fitted/Fixed/Adjusted values
A
11070.7(2) MHz
B
4081.2(2) MHz
C
2989.7(1) MHz
Aj
0.6 kHz, fixed (scaled from prediction)
A jk
20 kHz, fixed (scaled from prediction)
Ak
-32.4 kHz, fixed (scaled from prediction)
Can
-35.2(1) MHz
^bb
-18.5(1) MHz
6cc
0.8 MHz, adjusted value to minimize the error
aKF)
-170 MHz, fixed (scaled from prediction)
m y ia a
-248.5(2) MHz
(1 /4 )(T ,,-T ,,)
-109.2(1) MHz
(3/2K,„(N)
-6.2 MHz, fixed to be the predicted value
imiXbb-Xcc)
3.(1) MHz
5.3 MHz, fixed to be the predicted value
(3/2)T„,
-29.0 MHz, fixed to be the predicted value
(l/4)(T i,-T cc)
-12.9 MHz, fixed to be the predicted value
RMS error = 306 kHz
Unfortunately, this work was hindered by the limitation o f the machine time.
More progresses will be expectable in the near future whenever machine time is
available.
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§ 8.3 CYANOMETHYL RADICAL, H:2 6 CN
H 2C C N h a s b e e n a f a v o r ite s u b je c t f o r s p e c tr o s c o p y s tu d y s in c e
1960s. It w a s
a lso
f o u n d in in te r s te lla r s p a c e b y th e r a d io te le s c o p e s . T h e m illim e te r w a v e s p e c tr o s c o p y
o f H a C C N h a s b e e n r e c o rd e d in th e la b o ra to r y . A lth o u g h s o m e o f th e tr a n s itio n s in
th e m ic r o w a v e fre q u e n c y r a n g e h a d b e e n d e te c te d in th e sp a c e , th e y w e r e in c o m p le te
a n d in s u f f ic ie n t to b e ta k e n a s a g o o d r e f e r e n c e b e c a u s e th e p a r a m a g n e tic te s t
( m a g n e t i c f i e l d o n / o f f ) is o f c o u r s e u n a v a i l a b l e f o r t h e a s t r o n o m i c a l o b s e r v a t i o n s . T h e
m o t i v a t i o n o f m y p r e s e n t s t u d y o f H 2 C C N is t o p r o v i d e a s u f f i c i e n t a n d c o m p l e t e
re fe re n c e o f H 2C C N tra n s itio n s in th e
20
G H z f re q u e n c y re g io n s b e c a u s e b o th W e i
L in a n d m e s u f fe re d q u ite a lo t f ro m th o s e m y s te r io u s p a r a m a g n e tic tr a n s itio n s d u r in g
o u r s e a r c h in g fo r ra d ic a ls in th e 2 0
G H z re g io n s . A lth o u g h th o s e “ m y s te r io u s ”
p a ra m a g n e tic tra n s itio n s w e re la te r id e n tif ie d to b e fro m H 2C C N , th e u n e x p e c te d
a p p e a r a n c e o f th e m m is le d u s to th e w r o n g a s s ig n m e n t a n d s e rio u s ly i m p e d e d o u r
p ro g re s s o n t h e s e a rc h in g a n d a s s ig n m e n t o f t h e t a r g e t m o le c u le s .
My
f ir s t r a d ic a l
p r o je c t, H C C C F a , w a s g r e a tly d e la y e d b y th e u n e x p e c te d a p p e a r a n c e o f H 2 C C N in
th a t th e y a r e so c lo s e to th e
in c o rr e c t a s s ig n m e n ts .
I w as
2
—> 1 t r a n s i t i o n s o f H C C C F 2 . T h i s m i s l e d m e t o m a k e
e n t a n g l e d w i t h t h e m o v e r h a l f a y e a r u n t i l it w a s r e a l i z e d
t h a t t h e t r a n s i t i o n s w e r e n o t d u e to H C C C F 2 . E v e n w h e n
tr a n s itio n s a re f ro m H 2 C C N ,
I had
I
r e a liz e d th a t th o s e
to m a k e c o m p a r is o n te s ts to d is tin g u is h th e m , o n e
b y o n e , d u e to th e in c o m p le te n e s s o f th e r e f e r e n c e s . W e i L in s u f fe re d f ro m th e s a m e
th in g w h e n h e s e a rc h e d H 2 S iC N r a d ic a l in th e 2 0 G H z re g io n s . H is s e a r c h in g r e g io n s
w e re o v e rla p p e d w ith H 2 C C N tra n s itio n s . F o r a w h ile , W e i L in th o u g h t h e h a d f o u n d
H 2 S 1C N t r a n s i t i o n s . U n f o r t u n a t e l y , t h o s e l i n e s t u m e d o u t t o b e f o r m H 2 C C N . S in c e
m e th y lc y a n id e , C H 3C N , is s u c h a f r e q u e n tly u s e d c o m p o u n d f o r th e s tu d y o f c y a n o
g ro u p c o n ta in e d tr a n s ie n t m o le c u le s /r a d ic a ls , a n d th e in te n s itie s o f th o s e H 2C C N
tr a n s itio n s a r e s o im p r e s s iv e ly s tr o n g th a t is in e v ita b le th a t w e w ill e n c o u n te r th e m in
f u t u r e s tu d i e s . T h u s , a g o o d r e c o r d o f t h e s e s t r a n s i t i o n s is n e c e s s a r y . T A B L E 4 . l i s t s
a ll th e a s tro n o m ic a lly d e te c te d a n d o u r la b o r a to r y o b s e rv e d H 2C C N fre q u e n c ie s in th e
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20 GHz frequency region. I hope this list will be helpful in the identification of
radical species and the assignment of paramagnetic transitions in the future.
TABLE 4. Astronomically detected and laboratory observed H 2CCN transitions in the
20 GHz frequency region
Astronomically detected frequencies"
Laboratory observed frequencies
20109.559 MHz
20109.5519 MHz
20113.7623 MHz
20115.801 MHz
20118.021 MHz
20118.0269 MHz
20118.160 MHz
20118.1295 MHz
20119.602 MHz
20119.6069 MHz
20121.621 MHz
20123.961 MHz
20123.9727 MHz
20124.262 MHz
20124.4337 MHz
20124.461 MHz
20125.9809 MHz
20126.0412 MHz
20126.021 MHz
20128.7462 MHz
20128.7798 MHz
20128.820 MHz
20129.6061 MHz
20129.7365 MHz
20135.4768 MHz
20139.7522 MHz
20139.8004 MHz
20139.783 MHz
“ The FWHM is ~37 kHz for the radio telescope. See: S. Saito and S. Yamamoto,./. Chem. Phys.,
107( 6 ), 1732-1739(1997)
'' The FWHM o f our FTMW is ~5 kHz, The resolution limit is -1 kHz.
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