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ROTATIONAL SPECTROSCOPY OF WEAKLY-BOUND COMPLEXES UTILIZING A HIGH-TEMPERATURE MOLECULAR SOURCE (MICROWAVE)

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University
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Shea, James Arthur
ROTATIONAL SPECTROSCOPY OF WEAKLY-BOUND COMPLEXES UTILIZING
A HIGH-TEMPERATURE MOLECULAR SOURCE
University of Illinois at Urbana-Champaign
University
Microfilms
I n t O m a t l O n 8.I 300 N.Zeeb Road, Ann Arbor, M! 48106
PH.D. 1984
ROTATIONAL SPECTROSCOPY OF WEAKLY-BOUND COMPLEXES
UTILIZING A HIGH-TEMPERATURE MOLECULAR SOURCE
BY
JAMES ARTHUR SHEA
B.S., Tufts University, 1979
THESIS
Submitted in partial fulfillment of the requirements
for the degree of Doctor of Philosophy in Chemistry
in the Graduate College of the
University of Illinois at Urbana-Champaign, 1984
Urbana, Illinois
UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN
THE GRADUATE COLLEGE
MAY 1 9 8 4
WE HEREBY RECOMMEND THAT THE THESIS BY
JAMES ARTHUR SHEA
ENTTTT.F.n
ROTATIONAL SPECTROSCOPY OF WEAKLY-BOUND COMPLEXES
UTILIZING A HIGH-TEMPERATURE MOLECULAR SOURCE
BE ACCEPTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR
DOCTOR OF PHILOSOPHY
THE DEGREE OF_
^cr^
AI^^OHJ
Head of Department
C o m m i t t e e o n Final Examinationf
Chairman
m
tUx) frl;
\c*iw.i&
/y*"
-7
*c±
t Reiy^fed for doctor's degree but not for master's
o 517
Ill
ROTATIONAL SPECTROSCOPY OF WEAKLY-BOUND COMPLEXES
UTILIZING A HIGH-TEMPERATURE MOLECULAR SOURCE
James Arthur Shea
Department of Chemistry
University of Illinois at Urbana-Champaign, 1984
Rotational spectroscopic studies of several weakly-bound molecular
complexes are presented here.
These studies were performed using a pulsed
Fourier-transform microwave spectrometer, employing a Fabry-Perot cavity
and a pulsed, supersonic nozzle.
A high-temperature molecular source that
permits the study of complexes involving low-vapor-pressure species
is
presented.
Chapter I presents studies of four weakly-bound species using the
original spectrometer developed by Balle and Flygare.
The spectroscopic
constants and molecular structures of ethylene-HF, furan-HCl, argoncarbonyl fluoride, and propyne-HF are determined.
A detailed force-field
analysis is given for argon-carbonyl fluoride, a complex which exhibits
unusually high "accidental" symmetry.
Propyne-HF is the first hydrogen-
bound complex to exhibit splittings due to hindered internal rotation
caused by the presence of the binding partner.
In Chapter II, the rotational Zeeman effect upon several weakly-bound
complexes is described.
SCO-HF are studied.
The linear complexes OCO-HF, OCO-DF, OCO-HCl, and
The asymmetric-top complex ArOCS is then discussed,
including an analysis of centrifugal distortion and the molecular force
field.
Molecular g-values, magnetic susceptibility anisotropics, and
quadrupole moments
are determined for all of the above species.
iv
In Chapter I I I , the heated-nozzle system is described in d e t a i l .
It
i s then used i n the study of complexes involving the m e t a l l i c element mercury.
The s t r u c t u r e and p r o p e r t i e s of HgHCl are presented and compared
with those of r a r e gas-hydrogen halide complexes.
Force constants and
normal frequencies of v i b r a t i o n are a l s o calculated.
i s also studied.
The HCNHg complex
I t i s found t h a t mercury behaves as a Lewis base—as
r a r e gases do—in HgHCl, but as a Lewis acid in HCNHg.
The
Hg quadru-
pole coupling constants in both complexes are then analyzed, r e s u l t i n g in
t h e f i r s t experimental estimate of the Sternheimer shielding constant for
the mercury atom.
F i n a l l y , other p r o j e c t s of i n t e r e s t for the heated
nozzle system are proposed.
V
ACKNOWLEDGEMENTS
My f i r s t thanks must go to Professor W. H. Flygare.
His ideas,
enthusiasm, and courage were a r e g u l a r source of i n s p i r a t i o n .
Although
most of the work in t h i s thesis took place a f t e r his untimely death, his
influence i s f e l t on every page.
I would l i k e t o thank Professor Don S e c r e s t for a c t i n g as my research
a d v i s o r after Professor Flygare's death.
I have greatly enjoyed our
i n t e r a c t i o n s , and am grateful for h i s advice and encouragement.
I have
a l s o enjoyed my i n t e r a c t i o n with Professors J . M. Lisy and H. S. Gutowsky.
Special mention must be made of Dr. Edward J . Campbell, for helping
i n the design and construction of t h e heated nozzle, his development of
t h e large-throughput spectrometer, and his experimental and t h e o r e t i c a l
e x p e r t i s e in general.
I t is no exaggeration t o say that much of t h e work
h e r e i n would have been impossible without h i s h e l p .
Various people whom I ' ve worked with have contributed in many ways.
Terry Balle, who designed and b u i l t the o r i g i n a l Fabry-Perot spectrometer;
B i l l Buxton, who, along with Ed Campbell, maintained t h a t instrument, and
who gave me a r e l a t i v e l y painless introduction t o the joys and frustrations
of graduate research; Bryant Fujimoto, whose conversations were as wideranging as they were enjoyable; B i l l Read, who b u i l t the zeeman s p e c t r o m e t e r , and whose i n s i s t e n c e on l e a r n i n g everything the hard way has proven
i n s t r u c t i v e in many r e s p e c t s ; Giles Henderson (visiting professor from
Eastern I l l i n o i s University) who provided fresh ideas, enthusiasm, hard
work, and an overriding belief t h a t research can be (and should be) both
productive and fun; and Steve Kukolich ( v i s i t i n g professor from the
vi
University of Arizona), who showed me the other side of that coin.
I'd
also like to mention Sean O'Brien, who worked tirelessly on the HgHF
search (but, then, a Cubs fan has to be patient), and who is currently
working on new uses for the hot nozzle (under Professor Lisy).
The service facilities at Illinois are second to none, and provided
invaluable support.
especially,
The machine shops of the chemistry department, and,
the Coordinated Science Laboratory constructed the heated
nozzle with great precision.
The electronics shop is largely responsible
for the data-taking system without which the spectrometer would merely
be several hundred pounds of scrap metal.
(In particular, I'd like to
single out C. J. Hawley for patiently essaying the role of detective in
The Case of the Burning Pulse Box and its too-numerous sequels.)
Last,
but not least, I'd like to thank the physical chemistry secretaries,
Evelyn earlier and Kim Mattmgly, for putting up with my alleged handwriting.
Financial support from the National Science Foundation and the
Petroleum Research Fund, administered by the American Chemical Society is
gratefully acknowledged.
I would especially like to thank the University
of Illinois School of Chemical Sciences for their show of faith in supporting the Flygare group after the expiration of the original NSF grant.
Support of an entirely different kind has been provided by those who
have helped me feed my various addictions: the people at the Pop shop
(R.I.P.), especially Paul Rock; Brian Morris at the Book Nook; and Betty
Elliott at the Walnut St. Tea Co. The Krannert center for the Performing
Arts and the various local movie theaters deserve mention, as well.
On a more personal level, thanks are owed to the people who have
helped make life more bearable here:
the "19A Gang", for getting me
vii
through the infamous " f i r s t year", and for showing me what friendship
is
(and, in some cases, what i t i s not); joe S t . Croix, f o r the o c c a s i o n a l ,
refreshing reminders t h a t not everyone i s a s c i e n t i s t ; and Jeanne Siemion
and Mary Alice Hegemann, on general p r i n c i p l e s .
two special people:
Special mention
goes to
t o Claire Schosser, for putting up with me when t h a t
c o u l d n ' t have been e a s y , for concern and support, and because she deserves
t o see her name in a t l e a s t one of these t h i n g s ; and t o Becky Smith, f o r
showing me t h a t what i s lost need not be gone for good, and simply because.
Finally, I thank my b r o t h e r s , Paul and P h i l , and my s i s t e r , J a n e t ,
for being t h e r e , and my p a r e n t s , Lawrence and Eleanor Shea, f o r a l l t h e i r
varied kinds of support, and for allowing me t o conduct my research u n f e t t e r e d by t h e bonds of nonexistence.
(Apologies t o Geo. Alec Effmger,
from whom I appropriated that phrase.)
(If anyone has been omitted from the above, I beg your indulgence.
Chalk i t up t o exhaustion and the rapid approach of s e n i l i t y . )
viii
PREFACE
WALT:
Dad, w h a t ' s g r a d u a l s c h o o l ?
GARP:
What?
WALT:
Gradual s c h o o l .
GARP:
W e l l , you s e e , W a l t :
Mom s a i d t h a t she t e a c h e s a t g r a d u a l s c h o o l .
G r a d u a l s c h o o l i s where you g o , and g r a d u a l l y
l e a r n t h a t you d o n ' t want t o go t o s c h o o l anymore.
Steve Tesich
The World According t o Garp
(screenplay)
"When you s a i l on t h e T i t a n i c , t h e r e ' s no p o i n t m t r a v e l i n g s t e e r a g e . "
Gregory Benford
Timescape
"Redundancy is our main avenue of survival."
Joe Haldeman
The Forever War
IX
TABLE OF CONTENTS
CHAPTER
I.
II.
PAGE
Rotational Spectra and Molecular Structures of WeaklyBound Complexes
A.
Introduction
1
B.
Ethylene-HF
5
C.
Furan-HCl
35
D.
Argon-Carbonyl Fluoride
59
E.
Propyne-HF
Hindered Internal Rotation in a
Hydrogen-Bound Complex
82
The Rotational Zeeman Effect in Weakly-Bound Complexes
A.
Introduction
B.
Linear Hydrogen-Bound Complexes:
OCO-HCl, and SCO-DF
C.
III.
104
OCO-HF, OCO-DF,
ArOCS
106
143
Rotational Spectra and Molecular Structures of MercuryContaining van der Waals Complexes Using a HighTemperature Molecular Source
A.
Introduction
174
B.
HgHCl
178
C.
HCNHg
207
D.
201
Hg Quadrupolar Coupling in HgHCl and HCNHg
226
E.
Other Possible Uses for the Heated Nozzle System
235
X
LIST OF TABLES
TABLE
PAGE
1-1.
Observed and C a l c u l a t e d T r a n s i t i o n F r e q u e n c i e s for C„H -HF. .
11
1-2.
Observed and C a l c u l a t e d T r a n s i t i o n F r e q u e n c i e s for C H.-DF. .
12
1-3.
Unperturbed C e n t e r F r e q u e n c i e s f o r C^H.-HF and C„H -DF. . . .
13
1-4.
S p e c t r o s c o p i c C o n s t a n t s f o r Ethylene-HF and -DF
14
1-5.
A l t e r n a t e L e a s t - S q u a r e s F i t s of Ethylene-HF and DF, J = 0-+-1
Transition
15
1-6.
Molecular C o n s t a n t s of E t h y l e n e and Hydrogen F l u o r i d e
. . . .
17
1-7.
Moments of I n e r t i a and P l a n a r Moments of E t h y l e n e , E t h y l e n e HF and Ethylene-DF
22
1-8.
Geometric P a r a m e t e r s for Ethylene-HF and -DF
27
1-9.
Comparison of R cm and y f o r C2H4~HF and Some Other WeaklyBound Complexes
31
Observed and C a l c u l a t e d T r a n s i t i o n F r e q u e n c i e s for F u r a n H 35 C1
40
Observed and Calculated Transition Frequencies for FuranH 37 cl
44
Observed and Calculated Transition Frequencies for FuranD35Cl
45
Spectroscopic Constants for Furan-HCl, in MHz
47
1-10.
1-11.
1-12.
1-13.
35
1-14.
Derived Molecular Constants of Furan-H
1-15.
Molecular Constants of Furan and HCl
52
1-16.
Structural Parameters of Furan-HCl
54
1-17.
Bond Lengths and Potential Well Depths for Various HCl
Complexes
Observed and Calculated Rotational Transitions for Ar-F.C
1-18.
Cl
48
58
O. 66
xi
TABLE
1-19.
PAGE
Observed and Calculated Rotational Transitions for
Ar-F 2 C 18 0
68
1-20.
Spectroscopic Constants for Ar-F„CO, in MHz
69
1-21.
Molecular constants of Carbonyl Fluoride
70
1-22.
Structural and Vibrational Parameters of Ar-F CO
77
1-23.
Bond Lengths and Potential Well Depths for Various Argon
Complexes
78
1-24.
Frequency-Averaged Line Centers for Propyne-HF and -DF(MHz) . 84
1-25.
Molecular Structure and Constants of Propyne
94
1-26.
Spectroscopic and Structural Parameters of Propyne-HF . . . .
96
1-27.
Determination of HF Vector Directionality
97
1-28.
Nuclear Hyperfine Structure of the 0 „ ->• 1 ,
.
00
01
Transitions
Comparison of Bond Lengths of Propyne-HF and Some Other
Weakly-Bound Complexes
Spectroscopic Constants and Molecular Properties of OCO-HF,
OCO-DF, OCO-HCl, and SCO-HF
110
Observed and Calculated Rotational Zeeman Transitions for
OCO-HF, J=2+3
Ill
Observed and Calculated Rotational Zeeman Transitions for
OCO-DF, J=2-K3
112
Observed and Calculated Rotational Zeeman Transitions for
OCO-HCl, J=3->-4
113
Observed and Calculated Rotational Zeeman Transitions for
SCO-HF, J=3->-4
115
1-29.
II-l.
II-2.
II-3.
II-4.
II-5.
II-6.
II-7.
II-8.
n
„_
98
103
is is
Spectroscopic Constants of SCO-DF, 0 CO-HF,
OC 0-HF,
0 13 C0-HC1, 18 0C 18 0-HCl, and 34SCO-HF, all in MHz
117
Observed and Calculated Zero-field Rotational Transitions
for SCO-DF and 34SCO-HF
118
Observed and Calculated Zero-field Rotational Transitions
for 013C0-HF and 18 OC 18 0-HF
119
xii
TABLE
II-9.
11-10.
PAGE
Observed and Calculated Zero-field Rotational Transitions
for 013C0-HC1
120
Observed and Calculated Zero-field Rotational Transitions
for 18ocl8o-HCl
121
11-11.
Molecular Properties of Isotopic Species of CO
11-12.
Electric and Magnetic Properties of HF, DF, and HCl
128
11-13.
Structural Parameters of the Complexes in This Study
129
11-14.
Comparison Between Measured and Calculated g
132
11-15.
Comparison Between Measured and Calculated Magnetic
Susceptibility Anisotropics for Several Weakly-bound
Complexes in Units of 10" 9 MHz/G2
136
Comparison Between Measured and Calculated Qi1 Values,
All in D.A
1'
138
11-16.
and OCS . . . 127
Values
11-17.
Spectroscopic Constants and Molecular Properties of ArOCS . . 146
11-18.
Observed and Calculated Rotational Zeeman Transitions for
ArOCS
11-19.
148
Observed and Calculated Zero-field Rotational Transitions
for ArOCS
149
11-20.
Derived Molecular Constants of ArOCS
152
11-21.
Structure and Force Constants of OCS
157
11-22.
Vibrational Force Constants, Normal Frequencies, Mean-Square
Amplitudes, and Average Structure of ArOCS
Comparison of Force Constants and Normal Frequencies m
ArOCS, ArCO , and ArClCN
11-23.
11-24.
III-l.
Comparison Between Measured and Calculated Magnetic
Properties of ArOCS
159
161
166
III-2.
Observed and Calculated Transition Frequencies, for HgHCl. . . 180
201
Observed and Calculated Transition Frequencies for
HgHCl . ]84
III-3.
Spectroscopic Constants for HgHCl
186
III-4.
Structural Constants for HgHCl
189
III-5.
Stretching Force Constants and Frequencies, and LennardJones Parameters for HgHCl
194
xiii
TABLE
III-6.
PAGE
Bond Lengths and Potential Well Depths for Various Weaklybound Complexes . . . . .
196
III-7.
Bending Force Constants and Frequencies for HgHCl
198
III-8.
Atomic Polarizabilities and Atom-diatom Bending Angles and
Harmonic Bending Force Constants for Several Weakly Bound
Complexes
199
35
CI
III-9.
Properties Used in the Multipole Expansion of H
201
111-10.
Expectation Values Generated from the Potential of
Eq. (111-13), Compared with Experimental Values, When
Available
204
III-ll.
2
1/2
Angles 9 = arccos ((cos 6))
for Several Complexes Calculated Using the Potential of Eq. (111-12), after Table III-4
of Ref. 144
206
111-12.
Observed and Calculated Transition Frequencies for HCNHg. . . 209
111-13.
Observed and Calculated Transition Frequencies for HCN
111-14.
spectroscopic Constants for HCNHg
213
111-15.
Molecular Properties of HCN
216
111-16.
Structural Constants for HCNHg
219
111-17.
Comparison of Measured vs. Predicted B 0 Values for Various
isotopic Species of HCNHg, Assuming Both Obtuse and Acute
Values for y
221
stretching Force Constants and Frequencies, and Lennardjones Parameters for HCNHg
222
111-18.
201
Hg . 212
xiv
LIST OF FIGURES
FIGURE
1-1.
1-2.
PAGE
Observed time-domain spectrum of j=0-KL transition in
ethylene-HF. The signal was digitized at 0.5 ys per
point averaged over 10 pulses
4
Power spectrum of J=0-KL transition in ethylene-HF. The
spectrum has a 3.9 kHz per point resolution and +/-labelled
Doppler pairs
7
1-3.
Coordinate system used to characterize ethylene-HF
1-4.
Orientation of principal axes in ethylene and ethylene-HF . . 25
1-5.
Measured digital spectrum of the 2\i •+ 3]_2, 5/2 •> 7/2
and 3/2 -»- 5/2 transitions of furan-H35Cl at 5870.42 and
5870.38 MHz. Frequencies on the plot are relative to
5870.0 MH7.
37
Coordinate system used in the analysis of furan-HCl.
furan molecule lies in the yz-plane
50
1-6.
1-7.
1-8.
21
The
b-dipole Q-branch series (J=2 to 7, inclusive) for Ar-F„C
calculated from fitted rotational constants
1p
0,
62
Spectral pattern analogous to Figure 1-7, this time obeying
c-dipole selection rules, for Ar-F2C^60. The Lorentzians
are an artifact of the plotting program, and are not indicative of the observed linewidths, which are on the order
of 5-7 kHz
64
1-9.
The structure of argon-carbonyl fluoride
72
1-10.
Top view of Ar-F2C0, with van der Waals radii (see text)
drawn in. The dashed line indicates the van der Waals
radius of argon
81
Comparison of methanol (a), propyne-DF (b), and propyne-HF
(c) spectra. Frequencies are m GHz
86
1-12.
Definition of a and plot of barrier potential
89
1-13.
The principal inertial axes and structural parameters of
propyne-HF. Orthogonal zero-point bending modes result m
a precessional motion and a vibrationally-averaged quadrupole projection operator corresponding to the operationally-defined angle y (see Eq. 1-24)
93
I-ll.
XV
FIGURE
1-14.
II-l.
II-2.
Van der Waals contours of the propyne-HF subunits
101
Coordinate system used to characterize the structures in
this Section. Y = 0 or S
124
Coordinate system used to characterize ArOCS
154
III-l.
High-temperature pulsed molecular source used in this study.
(1) General Valve model number 8-14-900 solenoid valve
body; (2) Copper tubing to carry cooling water; (3) Extended plunger; (4) Varian flange, sealed by a copper
O-ring; (5) Liquid mercury within the heated reservoir;
(6) Nozzle opening. The Viton plug at the end of the
plunger forms a vacuum seal with a raised lip around this
opening. The reservoir is wrapped with heating tape. . . . 176
III-2.
Observed spectrum of the J = 3 •> 4 transition of
HgD CI,
along with two AF = 0 lines arising from other mercury
isotopic species. The envelope shown is calculated . . . . 188
III-3.
Coordinates used to describe the structure of HgHCl
191
III-4.
Angular potential for HgHCl, calculated using Eq. (111-13).
After Figure III-2 of Ref. 144
203
III-5.
Coordinates used to describe the structure of HCNHg
218
III-6.
Structure of HCNHg, with van der Waals radii of the atoms
drawn in. (R(Hg) is taken to be 2.0A, the value ascertained in Section III-B.)
228
III-7.
H
Plot of (-eqQ/h) vs. X ^ f o r
9 complexes. The slope of
this line is related to the quadrupolar shielding constant,
y , of mercury
233
1
CHAPTER I
Rotational Spectra and Molecular Structures
of Weakly-Bound Complexes
A.
Introduction
Over the past five years, the Flygare research group has studied the
structures and properties of weakly-bound complexes, otherwise known as
van der Waals molecules.
Complexes of this type have attracted a great
deal of interest over the last several years, and many review articles
have been written about them.
1-5
The study of van der Waals molecules
provides insight into the nature of weak binding, and, thus, of intermolecular forces which have long been of interest.
(Witness the van der Waals
equation, which describes deviations from ideal gas behavior.)
One type
of weak binding, hydrogen bonding, is extremely important in nature. For
example, the peculiar properties of liquid water, which is the ultimate
source of life on earth, are largely attributable to hydrogen bonding.
In general, the structures of condensed-phase substances are strongly
dependent upon their intermolecular potential surfaces.
Studies of
weakly-bound complexes can provide information valuable to the modeling
of these potential surfaces.
The complexes studied by the Flygare group up to now have fallen into
two general classes.
The first involves the van der Waals attraction be-
tween a rare gas atom and a polar molecule.
6
7 8
KrHCl, KrHF, ' and ArclCN.
Examples of this type include
9
The second type of complex involves forma-
tion of a hydrogen bond, usually between a small organic molecule
2
and a hydrogen halide (or hydrogen cyanide).
typified by ethylene-HCl,
acetylene-HF,
This sort of complex is
and benzene-HCl.
In Chapter I,
rotational spectroscopic studies of four weakly-bound complexes will be discussed,
the rare-gas-containing complex argon-carbonyl fluoride (Section D ) ,
and the hydrogen bound complexes ethylene-HF, furan-HCl, and propyne-HF
(Sections B, C, and E, respectively).
The experimental technique used to study these complexes is that of
Fourier-transform microwave spectroscopy, utilizing a Fabry-Perot cavity
and a pulsed, supersonic nozzle, originally developed by Balle and
Flygare. '
'
An appropriate gas mixture, usually consisting of low
percentages of the complexmg molecules in 20 psi of argon carrier gas,
is prepared in a stainless steel holding tank above the Fabry-Perot cavity
at room temperature.
This mixture is pulsed into the cavity with a General
Valve model number 8-14-900 pulsed solenoid valve. The cavity is evacuated
-5
down to roughly 10
Torr, and the gas pulse undergoes rapid adiabatic
expansion, forming large numbers of complexes at low rotational temperatures, generally between 1-10 K.
After a delay of 0.5 ms, during which
time the gas molecules can reach the microwave interaction region, a 7T/2
microwave pulse of roughly 7 us duration is released into the cavity.
shape and duration of this pulse are determined by a pin diode.
radiation polarizes the gas molecules.
The
This
After the microwave pulse has
died away, a second p m diode opens, allowing the coherent emission of the
rotationally excited molecules to be detected by a superheterodyne receiver and digitized.
This process is repeated ten to twenty times, and
the results are averaged to produce a time-domain signal with a characteristic free induction decay.
A typical time-domain signal, that of
the J = 0 •*• 1 transition of the ethylene-HF complex, is presented in
Fig. 1-1.
The time-domain signal then undergoes a fast Fourier transform
l*J
Figure I-l.
Observed time-domain spectrum of J=0-*\L transition in ethylene-HF.
The signal was digitized at 0.5 us per point averaged over 10 pulses.
5
to give the frequency-domain power spectrum, as shown in Fig. 1-2.
The
molecular t r a n s i t i o n frequencies correspond to the midpoints of the
c h a r a c t e r i s t i c Doppler doublets, which a r e an a r t i f a c t of the gas dynamics
in the c a v i t y .
As a r e s u l t of t h e cooling during t h e gas expansion, the observed
spectra are of molecules in t h e ground v i b r a t i o n a l s t a t e alone.
Thus,
t h e spectra are g r e a t l y simplified over those of room-temperature waveguide experiments.
The high Boltzmann populations of the r o t a t i o n a l l e v e l s
of the ground v i b r a t i o n a l s t a t e favor determination of ground-vibrationals t a t e molecular p r o p e r t i e s , and the Fourier-transform technique has an
inherent advantage i n both r e s o l u t i o n and s i g n a l - t o - n o i s e r a t i o over i t s
16
frequency-domain counterpart.
Perhaps the primary disadvantage of t h i s
technique i s t h a t , s i n c e higher v i b r a t i o n a l s t a t e s cannot be assigned, t h e
equilibrium s t r u c t u r e s of t h e s e weakly-bound complexes cannot be probed
directly.
Rather, they must be inferred from other c l u e s , such as changes
in v i b r a t i o n a l behavior of t h e individual subunits of a complex upon
isotopic substitution.
The weakly-bound complexes to be discussed in t h e remainder of t h i s
chapter involve a v a r i e t y of types of bonding:
hydrogen bonding t o ir-
clouds in unsaturated hydrocarbons; hydrogen bonding t o an aromatic h e t e r o c y c l i c r i n g ; van der Waals bonding of argon to a p l a n a r molecule; and
hydrogen bonding to a TT-system in t h e presence of hindered i n t e r n a l r o t a t i o n .
B.
Ethylene-HF
The assignment of the r o t a t i o n a l spectrum of the ethylene-HF complex
i s p a r t of a systematic s e r i e s of studies of hydrogen-bound complexes
6
Figure 1-2.
Power spectrum of J=0->1 t r a n s i t i o n i n ethylene-HF.
The spectrum has a 3.9 kHz p e r point r e s o l u t i o n and
+ / - l a b e l l e d Doppler p a i r s .
7
8266.8025
8266.7026 8266.6836 8266.
MHz
involving ethylene.
The r o t a t i o n a l spectrum of ethylene-HCl
]0
was assigned
p r i o r t o t h i s study, and that of ethylene-HCN 17 has since been published.
The r o t a t i o n a l Zeeman effect has also been studied in ethylene-HCl.
18
Ethylene-HF i s nonplanar and T-shaped, with the HF axis perpendicular to
the plane of the ethylene molecule and b i s e c t i n g the carbon-carbon double
bond.
A hydrogen bond i s formed between the a c i d proton and the TT-electron
density of the ethylene molecule.
Ethylene-HF was generated by preparing mixtures of -0.05% HF (Linde,
99.9%) o r DF (KOR Isotopes, 98%) with ~4% ethylene (Linde, 99.5%) in 20 p s i
of argon (Linde, 99.99%), a l l of which a r e used without further
tion.
purifica-
Four R-branch, a-dipole t r a n s i t i o n s were measured for each of the
two i s o t o p i c species, ethylene-HF and ethylene-DF, in t h e frequency range
between 8 and 18 GHz.
The Hamiltonian used to f i t the observed d a t a is t h e sum of four
terms:
where JC_ i s the r i g i d - r o t o r Hamiltonian, Ji i s the spin-spin Hamiltonian/
R
SS
j
I
9
expressed as,
,
K
ss - -T
3(y -R)(y
^HP-HH/D -
R
-R)
7
]
2
(I
"2)
R
R is the vector joining the fluorine and hydrogen (or deuterium) nuclei,
and y the nuclear magnetic moment of the l'th nucleus.
~i
Hi - * W i •
Here, y
i s the nuclear magneton, g i s the nuclear g-value, and I , is
N
i
~i
the spin of the l ' t h nucleus. Using Eq. (1-2) and (1-3), we have
(I 3)
"
9
=
^ss
hTZu/v >
<*-*>
where D i s the spin-spin coupling t e n s o r with elements given by
9V,g„/rA,(R2($. .-3R R.)
a
F^H/D^N
ii
1 i
D. . =
-*
g
'
*— ,
J
R
SC i s the quadrupole Hamiltonian:
. ,
i , j = x,y,z.
. _.
(1-5)
KQ = Q(D):V(D) ,
(1-6)
where Q(D) is the nuclear quadrupole moment tensor, and V(D) is the electrie field gradient tensor for the deuterium nucleus in DF. The spinrotation Hamiltonian for the i' th nucleus is
3C
= - I -M -J ,
(1-7)
~1 ~ 1 ~
OI\
where M i s the s p i n - r o t a t i o n coupling tensor.
system, t h e tensor element M
In the molecular axis
(where g = a, b , or c) i s composed of
p o s i t i v e nuclear and negative e l e c t r o n i c c o n t r i b u t i o n s :
(M
) = (M nUC ). + (M eleC )
gg i
gg
i
gg
,
nuc
for the i ' t h nucleus.
(1-8)
i
E x p l i c i t forms for M
else
and M
have been given
elsewhere.
Matrix elements of the Hamiltonian in Eq. ( I - l ) were calculated in
t h e coupled basis
*F
+
VD
=
i
(1-9)
I + J =F
using expressions previously derived. 9 ' 11 The c a l c u l a t e d t r a n s i t i o n f r e quencies were obtained by diagonalizing the Hamiltonian matrix i n blocks
10
of F.
The observed transitions were fit using this procedure coupled
with a least-squaies fitting program.
Approximate values of A, B, and C
were used as first guesses in this program, along with rough estimates of
the appropriate hyperfine constants.
The 0 -1
and 1„ -2
transitions
00 M 0 1 + M
01 02
were fit simultaneously to two line centers, (
)_ (in ethylene-DF) ,
2
X (in ethylene-DF), and D .
aa
M..-M
, X hb ~X
r
D
hb~
D
cc'
and a
-t
The 0 n n - l n 1 t r a n s i t i o n i s independent of M ,
ou
O-L
aa
H off-diagonal elements of the coupling
tensors, while the l nl _ 2 n „ transition is only weakly dependent upon these
parameters, as is true in the case of acetylene-HF.
The K = 1 lines are
much more dependent upon the quantities which could be ignored in the
K = 0 case, and thus, because of the small number of observed transitions,
M, +M
were f i t holding (—•*-
) , x r
an<
^
D
constant as obtained from the
2
F
aa
K - 0 fit and fitting only line centers to the 1
xl
- 2
1*-
and
1-2
JLU
11
transitions.
The observed and calculated frequencies for ethylene-HF and -DF are
listed in Tables I-l and 1-2.
The calculated line center frequencies in
the absence of hyperfine effects are listed in Table 1-3 for both species.
The spectroscopic constants A, B, and C, and the appropriate hyperfine
interaction constants are listed in Table 1-4.
The measured line positions were originally fit using only spin-spin
and quadrupole parameters.
Comparison of the fit of the J = 0 -* 1 transi-
tion of ethylene-DF with that of acetylene-DF
virtually identical.
showed residues which were
As a result, an additional parameter - spin-rotation
on the fluorine atom - was fit in both molecules, causing these residues
to drop dramatically, as can be seen by comparing Tables 1-2 and 1-5.
A
similar refitting was then performed on the ethylene-HF data, the results
11
Table I - l .
Observed and Calculated Transition Frequencies for C_H.-HF
Transition
I F •*• I 1 F'
-V
°00
x
oi
- > •
-»\ l
x
io
->
2
2
2
02
12
11
Calculated (MHz)
Difference
1 1 -v 1
1
8266.6240
8266.6260
-2.0
0 0 -> 0
1
8266.6836
8266.6854
-1.8
1 1 -»• 1
2
8266.7026
8266.6972
5.4
1
0
8266.8025
8266.8041
-1.6
1 1 -*- 1
2
16525.1161
16525.1095
6.6a
1 1 ->- 1
1
16525.2282
16525.2282
0.0
1 1
1
2
16061.9192
16061.9218
-2.6
1 1 ->• 1
1
16061.9816
16061.9822
-0.6
1 1
^1
Observed (MHz)
•+
- > •
1 2
-V
1
3
16062.0050
16061.9969
8.1
1 0
-V
1
1
16062.0680
16062.0729
-4.9
1 1 ->• 1
2
17000.4232
17000.4253
-2.1
1 2
1
3
17000.5006
17000.5004
0.2
1
1
17000.5784
17000.5764
2.0
1 0
- * •
-V
T r a n s i t i o n not included i n
fit
(kHz)
12
Table 1 - 2 .
Observed and c a l c u l a t e d T r a n s i t i o n F r e q u e n c i e s f o r C H .-DF
Transition
I F -> I ' F '
33
°00
+
-0.7
1 3
2 2
8226.6249
8226.6250
-0.1
33^,35
2 2
2 2
8226.6455
8226.6455
0.0
11 + 11
8226.7157
8226.7160
-0.3
8226.7376
8226.7378
-0.2
16445.2115
16445.2115
0.0
1 5
2 2
15986.9172
15986.9204
-3.2
11 + 11
15986.9398
15986.9324
7.4
15
2 2
16915.5626
16915.5692
1 1 -> 1 7
2 2
2 2
16915.5842
16915.5812
3.0
11 + 11
16915.6524
16915.6562
-3.8
16915.6862
16915.6784
7.8
1 1
2 2
+
2 2
+
->
2
12
1 3
2 2
+
2 2
x
io
1 1
2 2
-> 2
02
\ l
->•
2
11
(MHz) D i f f e r e n c e (kHz)
8226.5117
^ 1
2 2
01
(MHz) C a l c u l a t e d
8226.5110
->•
1 1
2 2
X
3 1
Observed
13
2 2
2 2
+
2 2
11
2 2
2 2
+
13
2 2
-6.6
1
13
T a b l e 1-3.
Unperturbed Center F r e q u e n c i e s for C H -HF and C„H.-DF
Transition
°oo-
V
V"
2
02
hi*
2
12
ho*
°oo"
2
11
V
^ l *
2
02
^ l -
2
12
2
11
w
V (MHz)
o
8266.6853
16525.1094
16061.9823
17000.4858
8226.6517
16445.2115
15986.9468
16915.5936
14
Table 1-4. Spectroscopic Constants for Ethylene-HF and -DFC
C2H4-HF
C2H4-DF
A(MHz)
24122(13)
24093(12)
B(MHz)
4367.968(3)
4345.488(2)
C(MHz)
3898.717(2)
3881.164(2)
<DaaVkHz)
-237.4(82)
X (D) (kHz)
M, , +M
(- b \^) p (kHz)
-38.3(87)
280(7)
-7.3(38)
M +M
Errors listed in parentheses for D, X' anc^ ( ~
) a r e one standard
deviation in the fit. Errors in A, B, and C are described in the text.
15
Table 1-5.
Alternate Least-Squares Fits of Ethylene-HF and DF, J = 0+1
Transition.
a)
Ethylene-DF, without spin-rotation:
I F + I'F'
Observed (MHz)
Calculated (MHz)
Difference (kHz)
8226.5110
8226.5105
0.5
kl
8226.6249
8226.6310
-6.1
3 3 + 35
22+22
8226.6455
8226.6407
4.8
33 +
2 2
33
22
8226.7157
8226.7129
2.8
k k +k k
8226.7376
8226.7396
-2.0
3
1+ Ik
2 2
kk+
2 2
22
22
V = 8226.6510 MHz; D = = -0.0357 MHz; X° = 279.78 kHz
o
aa
b)
Ethylene-HF, with spin-rotation on fluorine:
1 1 ->- 1 1
8266.6240
8266.6232
0.8
0 0 + 0 1
8266.6836
8266.6864
-2.8
1 1 + 1 2
8266.7026
8266.7008
1.8
1 1 + 1 0
8266.8025
8266.8023
0.2
V
M^ +M
= 8266.6863 MHz; D = -0.24179 MHz; ( "•
o
aa
2
) = -4.872 kHz
16
of which can be found in Table 1-5.
These f i t s were performed using
the Hamiltonian of Eq. (1-7) , with I = —, in the exact diagonalization method described above.
To show that t h i s fit was significant, a
third f i t including spin-rotation was run, with I = 1, to account for
deuterium effects.
The quality of t h i s fit was not significantly greater
than that which did not lcnlude spin-rotation, and the magnitude of
M..+M
(
J ~ ^ ) n w a s q u i t e s m a l l : 0 . 4 8 ± 1 . 8 1 kHz. Thus, t h e e f f e c t s of
any d e u t e r i u m s p i n - r o t a t i o n i n t e r a c t i o n s a r e t o o s m a l l t o b e r e s o l v e d
w i t h our c u r r e n t i n s t r u m e n t .
Similar fluorine spin-rotation
have a l s o been o b s e r v e d i n cyclopropane-DF,
21
effects
whose J = 0 + 1 t r a n s i -
was r e f i t u s i n g t h e same t e c h n i q u e a p p l i e d t o t h e e t h y l e n e a n d a c e t y l e n e
complexes.
This a l s o gave a d r a m a t i c a l l y improved f i t , with a value o f
M, ,_+M
Du
-8.90 ± 3.70 kHz for
the other complexes.
(
CC
), this comparable to values obtained for
In none of these molecules was the deuterium spin-
rotation constant found to be significant.
exhibit a change (2-3 kHz) in (D )
All three complexes also
when spin-rotation is taken into
aa uh
account.
S p i n - r o t a t i o n c o n s t a n t s f o r ethylene-HF a r e n o t t a b u l a t e d .
due t o an ambiguity i n assignment o f t h e s p i n - r o t a t i o n e f f e c t .
This i s
Both n u -
c l e i i n t h e HF s u b u n i t have s p i n s o f 1 / 2 , and thus c a n n o t be d i s t i n g u i s h e d
by t h e f i t t i n g program.
S i n c e t h e n u c l e a r g - v a l u e s o f hydrogen and f l u o r i n e
a r e comparable, t h e y p r o v i d e no d i s t i n g u i s h i n g c h a r a c t e r i s t i c , and t h e
MM
r a t i o F / H f o r f r e e HF, a b o u t 4 . 3 (See Table 1 - 6 ) , i s not s u f f i c i e n t l y
l a r g e t o r u l e out hydrogen c o n t r i b u t i o n t o s p i n - r o t a t i o n
effects.
The v a l u e s f o r A, B, a n d C r e p o r t e d h e r e were o b t a i n e d w i t h o u t e x p l i c i t l y i n c l u d i n g c e n t r i f u g a l d i s t o r t i o n terms i n t h e a n a l y s i s .
The r e a s o n
17
Table 1-6.
Molecular C o n s t a n t s of E t h y l e n e and Hydrogen F l u o r i d e
C
2H4a
HF
DF
A (MHz)
145987(120)
__
__
B(MHz)
30022.0(39)
616365.5b
325584.98 d
C(MHz)
23837.2(48)
< D aa>HF ( k H z )
XD(kHz)
M, , +-M
J £)
—
-286.75°
-44.34°
~
354.238e
< V F(kH2>
-307.637e
M,, +M
(-^rSS)H(kH8)
71.1286
5.755e
0.925595b
0.92326d
R (H-F)(A)
o
a
Ref. 22.
Ref. 23.
°Ref. 24.
d
—
—
Ref. 25.
S
Ref. 26.
-158.3566
18
for this is that there are only four R-branch line centers available for
each of the two isotopic
species; no others fall within the frequency
range of our spectrometer.
Q-branch transitions are available, but not
enough of them fall within the necessary range to allow a full asymmetric
top distortion analysis (using T's).
Moreover, the use of Q-branch transi-
tions is not valid in a near-symmetric top treatment (using D_, D_.
J
JK
and D ). Thus, the information regarding internal dynamics and bonding
K
that can be determined from centrifugal distortion is unavailable here.
To minimize the error that centrifugal distortion is likely to introduce, the following method of calculating rotational constants was used.
Closed-form expressions in the symmetric-top limit for the measured
R-branch transitions are:
V(0
oo" 1 oi ) =
B + c
-
4D
(1
J'
"10)
V(l 01 -2 02 ) = 2A + B + C - 2[(B-C) 2 + (A-C)(A-B)]1/2 - 32Djr
(I-ll)
V(lu-2ll) = B
(1-12)
V(1
+
10 _ 2 1 l } = 3 B
Thus, v(l
+ C
-2
XU
3C - 32 D j - 4D J K ,
'
32D
J "4 V
)-V(l
XX
-2
XX
(1 13
•
- >
) = 2 (B-C), with all distortion terms sub-
X £*
tracted out.
If we take 4D, to be negligible compared to (B+C) - a reaJ
sonable assumption, since D values for previously studied hydrogen-bonded
J
and van der Waals complexes are usually only a few kilohertz - we then see
that:
B
- i tv(0 oo- 1 oi )
+
i< v < 1 i 0 - a ii ) -
v(1
ir2i2))]-
(I 14)
-
19
and
c
" i [ v ( 0 o o - V - i ( v ( 1 io- 2 ii > "
v{1
ir2i2))]-
(I 15)
-
A i s determined by i n s e r t i n g t h e calculated values for B and C i n t o
Eq. ( I - l l ) and solving, again n e g l e c t i n g D .
J
The e r r o r s in A, B, and C
listed in Table 1-4 are estimated by adding a presumed error of 5 kHz to
each line center and recalculating the rotational constants. The magnitude of the difference between these values gives the reported errors.
The constants determined by this method are used to derive the molecular
structure.
The coordinate system used to define the geometry of ethylene-HF is
shown in Fig. 1-3. The quantities to be determined are R , the distance
cm
between the centers-of-mass of the two components, and the angles 9 and cp,
which locate the center of mass of the HF subunit in the xyz coordinate
system.
The angles £ and a describe the orientation of the HF axis in
the xyz coordinate system. We will assume here that the structural
and electronic properties of ethylene and HF, as listed in Table 1-6, are
unchanged upon complex formation.
We begin our structural analysis of the complex by considering the
planar moments P , P, , and P , where
*
a b
c
P
c
= -(I
2 aa
+I,,-I
with cyclic permutations for P
bb
cc
, li
,
(1-16)
and P. . We note that P is equal to the
a t >
c
inertial defect within a factor of -2.
In the case of acetylene-HCl,
) = LJ m c
For a rigid planar molecule, P = 0.
acetylene-HF,
and ethylene (See Table 1-7) ,
the values of P range from -0.02 to -0.6 amu A . These small nonzero values
are consistent with planar equilibrium structures for these molecules, with
to
O
Figure 1-3.
Coordinate system used to characterize ethylene-HF.
21
<x
1
22
Table 1-7.
Moments of Inertia and Planar Moments of Ethylene, Ethylene-HF
and Ethylene-DF
C2H4-HF
C2H4-DF
33.464
.464
20.950
20.976
16
833
16.833
115.701
116.300
348
20
20.348
129.627
130.213
«
111.962
111.547
16.856
112.189
112.769
3.490
17.438
17.445
C
I (amu-A )
aa
I,. (amu-A2)
bb
I (amu'A2)
cc
IpD(amu-A2)
2
P (amu-& )
a
P. (amu-A2)
b
P (amu'A )
c
2H4
- 0.028
3.512
3.531
23
small contributions from zero-point vibration. In ethylene-HF and -DF,
2
however, the value of P of 3.512 amu A for each species is too large
to be explained in this manner, indicating that the complex is non-planar.
Comparing P and P for the complexes (See Table 1-7 and Fig. 1-4) with
the planar moments of free ethylene, one finds a strong correlation between
Po and Pc of the complexes with, respectively, Pa and P.
J3 of ethylene.
equivalence of P
The
(complex) and P, (ethylene) indicates that cp = 0, that
is, the inertial defect in ethylene-HF (DF) is accounted for if the plane of
the ethylene molecule is perpendicular to the plane containing the three
heavy nuclei. Given the additional equivalence of p, (complex) and
Pa (ethylene), it is clear that all of the mass located off the z-axis
can be accounted for by the atoms of the ethylene molecule, and that the
HF subunit must lie along the a-inertial axis.
That the A rotational
constant in ethylene-HF is changed by less than 0.2% upon deuteration of
the HF is consistent with this last conclusion.
Direct comparison of the
A rotational constant of ethylene-HF or -DF with the C rotational constant
of ethylene indicates that the a-mertial axis of the complex must nearly
coincide wth the z-axis.
Next, we determine whether the HF proton lies toward or away from
the ethylene subunit.
This is done by examining the shift in R
as
cm
defined previously, upon deuteration.
Using the coordinate system of
Fig. 1-3 we obtain for the elements of the moment-of-mertia tensor
J
xx
I
yy
I
=
^(ethyl61^
= I
yy
= I
+
V
cos2
(ethylene + I
+ I
He
(ethylene) + I
£
+
Jpc00320'
,
(J-17>
(1-18)
fD
sin2? + I
sin 2 ?,
(1-19)
to
Figure 1-4.
Orientation of principal axes in ethylene and ethylene-HF.
b
Q
i
1
>~b
Free Ethylene
Ethylene-HF
to
26
Z
xa
I
X
zx
=1
yz
where I
+
=
1
HF S l n ?
= 1
=1
zy
xy
COS?
+
r
PD
sinG
COS0
(I
'
= 0 ,
"20)
(1-21)
yx
is the "pseudo-diatomic" moment of inertia, defined as
M
M
thylene F
I pn - *
*
R2 •
PD
M . . , +M „ cm
ethylene HF
Because of the errors in the rotational constants resulting from our
d-22)
inability to obtain centrifugal distortion information, and because of the
very small mass of the HF proton in comparison to the fluorine mass, it is
not possible to accurately determine the value of the angle a using moment
of inertia arguments. Accordingly, we have set a = 0 in Eqs. (1-17)-(1-21).
We have also set cp = 0.
R
is found by using Eqs. (1-18) and (1-22),
which are affected neither by the off-diagonal elements of the tensor, nor
by the values of 9 and £> We also note that the defined y-axis corresponds
to the c principal axis of ethylene-HF, and to the b-axis of free ethylene,
so that Eq. (1-18) can be written:
I
= I. , (ethylene) + I + I
.
J
cc
bb
HF
PD
(1-23)
Icc ' I.,
are all known, leaving
T ' . and thus cRm ' ,
bb (ethylene),
*
'' and I„_
^ only PD
HF
to be determined using Eq. (1-22).
This procedure was followed for both
isotopic species, resulting in the values shown in Table 1-8.
Comparison
of the two R values shows a difference of 0.0452A1 between the DF and HF
cm
species.
Nearly all of this discrepancy can be accounted for by the shift
in position of the center of mass of HF upon deuteration, which is 0.0419A.
Since substitution of the heavier deuterium nucleus for hydrogen would move
the center of mass of the complex toward the deuterium site, the fact that
27
Table 1-8.
Geometric P a r a m e t e r s f o r Ethylene-HF and -DF
C
C2H4-HF
R (&)
cm
2
V
D F
3.0966
3.0514
ya(degrees)
19.8(17)
17.5 ( + 1 0 . 5 , - 1 7 . 5 )
Y (degrees)
~
22.0(11)
3.1407
3.1348
r°(A)
C a l c u l a t e d from s p i n - s p i n c o u p l i n g
C a l c u l a t e d from X •
Edge-to-fluorine
distance.
constant.
28
R
of ethylene-DF is shorter than that of ethylene-HF clearly indicates
that the acid proton is located between the fluorine atom and the ethylene
subunit.
The parameters which remain to be determined are the angles E, and 0.
We determine 9 by diagonalizing the tensor whose elements are calculated
with Eqs. (1-19)-(1-23), varying 8 until the best fit to the measured rotational constants B and C is achieved.
For the purposes of this calculation,
? was taken to be equal to 20°, the operationally-defined angle obtained
from analysis of the hyperfine constants. The best fit to the experimental
data corresponds to 9 = 0.
This procedure was followed for all values of
£ ranging from zero to 45°. In all cases, 6 was found to be zero.
Hyperfine structure in these complexes arises from HF spin-spin
coupling in ethylene-HF, and DF spin-spin coupling, deuterium nuclear
quadrupole coupling, and the fluorine spin-rotation interaction in ethylene-DF. To interpret the measured spin-spin constants and the deuterium
quadrupole coupling constant, we consider the expression
C = \ C <3 cos Y'-l>
2 o
,
(1-24)
giving the projection of the free HF or DF spm-spin constant, or deuterium
quadrupole coupling constant, C , onto the a-axis of tne complex, averaged
o
over the zero-point bending motion, y'
is defined as the instantaneous
angle between the HF axis and the a-inertial axis of the complex. Contributions from zero-point motion in 9 and cp are considered negligible because of the large mass of the fluorine nucleus. Values of the operation2
1/2
ally-defined angle y = arc cos ((cos Y'))
t determined using the hyperfine constants listed above, are shown for ethylene-HF and -DF in Table 1-8.
29
Since it has already been established that the proton is pointed toward
ethylene, the choice of acute values for y,
equal to 180°-Y, is correct.
rather than obtuse values
One would expect that Y in ethylene-DF
would have a smaller value than that in ethylene-HF, due to the additional
mass of the deuterium nucleus. Because of the large uncertainty in (D ) „,
aa DF
Y as determined from this constant cannot yield a meaningful comparison.
However, the angle given by the deuterium quadrupole coupling constant,
22.0(11), appears to be equal to or slightly larger than that found from
(D ) t m ' 19.8(17). An apparent increase in y as determined from x l n
aa HF
comparison to y as determined from (D ) has occurred in both acetyaa HF
11
27
lene-HF
and OC-HF.
Possible deviations from Eq. (1-24) will be dis-
cussed later.
In the absence of contributions from ethylene - the relation between
the fluorine spin-rotation constant m
free DF and its value m
ethylene-DF
can be expressed as
DF
where M^_ and B^„ are the spin-rotation and rotational constants of free
DF
DF
—
B+C
DF, B = -—— for ethylene-DF, and Y 1 S the operationally-defined angle
O
2
derived from X • Using the appropriate values and Eq. (1-25), we calculate
M +M
(
) = -1.86 ± 0.01 kHz. Comparing this to the measured value of
-7.3(38) kHz leaves -5.4(38) kHz which can be attributed to complexation.
This is composed of nuclear and electronic parts, as shown in Eq. (1-8).
Using the explicit form for M
(Ref. 20) and the determined structure
of the complex, the ethylene nuclear contribution to spin-rotation can
be calculated, and has a value of 1.9 kHz.
This leaves an estimated
electronic contribution from ethylene of -7.3(38) kHz. Thus it seems
30
t h a t t h e s i m p l e p r o j e c t i o n d e s c r i b e d by Eq.
(1-25) i s not s u f f i c i e n t
to
p r e d i c t s p i n - r o t a t i o n e f f e c t s upon c o m p l e x a t i o n , a s t h e e t h y l e n e s u b u n i t
makes ma^or c o n t r i b u t i o n s t o both t h e n u c l e a r and e l e c t r o n i c p a r t s of
t h e s p i n - r o t a t i o n coupling c o n s t a n t of e t h y l e n e - D F .
The s t r u c t u r e of ethylene-HF h a s been shown t o b e as f o l l o w s :
ethy-
lene-HF i s n o n - p l a n a r and T - s h a p e d , w i t h t h e HF a x i s p e r p e n d i c u l a r t o t h e
p l a n e of t h e e t h y l e n e s u b u n i t and b i s e c t i n g t h e c a r b o n - c a r b o n d o u b l e bond.
A hydrogen bond i s formed b e t w e e n t h e a c i d p r o t o n a n d the TT-electron
d e n s i t y of e t h y l e n e .
This s t r u c t u r e i s i n agreement with t h a t deduced
from a r e c e n t i n f r a r e d s t u d y of e t h y l e n e - H F ,
28
in which e t h y l e n e
exhibited
a p e r t u r b e d o u t - o f - p l a n e b e n d i n g mode i n t h e complex, and no p e r t u r b e d
i n - p l a n e b e n d i n g mode.
The s t r u c t u r e i s a l s o c o n s i s t e n t w i t h observed
10
s t r u c t u r e s of e t h y l e n e - H C l ,
30
21
pane-HCl
and -HF.
29
acetylene-HCl
11
and - H F ,
and c y c l o p r o -
The DF s p e c i e s of t h e s e complexes a r e now found t o
s h a r e the f e a t u r e of s p i n - r o t a t i o n h y p e r f i n e e f f e c t s .
follow the trends in R
e s t a b l i s h e d by t h e s e r i e s o f
These complexes
hydrogen-bonded
complexes cyclopropane-HCl, a c e t y l e n e - H C l , and e t h y l e n e - H C l (see Table 1-9)
T h a t i s , t h e R ' s a l l f a l l w i t h i n a r a n g e of 0.15 &, the c y c l o p r o p a n e
cm
bond b e i n g t h e s h o r t e s t , f o l l o w e d by a c e t y l e n e , t h e n e t h y l e n e .
A l l of
t h e complexes in t h e hydrocarbon-HF s e r i e s have s h o r t e r bond l e n g t h s than
t h e i r c o u n t e r p a r t s i n t h e hydrocarbon-HCl s e r i e s .
It
should a l s o be
n o t e d t h a t t h e b e n d i n g a n g l e s in t h e hydrocarbon-HF s e r i e s a r e a l l
equal.
R
I t can a l s o be seen t h a t t h e r e i s a c o n s i d e r a b l e d i f f e r e n c e
nearly
in
between t h e hydrogen-bonded complexes above and t h e more weakly bound
van d e r Waals complexes w i t h r a r e g a s e s
(see Table 1 - 9 ) .
The bending
a n g l e s of t h e l a t t e r complexes are a l s o c o n s i d e r a b l y l a r g e r t h a n t h o s e
of t h e hydrogen-bonded s p e c i e s .
31
T a b l e 1-9.
Comparison of R
and Y f o r
cm
C.H.-HF
9 &
2 4
and Some O t h e r W e a k l y -
Bound Complexes
Y (degrees)
cm
C2H4-HF
3.097
20
C2H2-HF£
3.075
20
2.977
19
C 2 H -HCl
3.67
21
C2H2-HC1€
3.64
21
3.52
21
Ar-HF-
3.510
42
Kr-HF
3.610
39
C.H,-HF'
3 6
b,c
C-H.-HC1
•i
c,f
6
Ref.
11.
Ref.
21.
'Distance i s
Ref. 10
e
Ref. 29
f
Ref. 30
g
Ref. 31
h
Ref. 8.
from c e n t e r of C - C bond t o
center-of-mass of
HX.
32
Another common feature of t h e hydrocarbon-HF complexes i s t h a t the
value of Y determined from the deuterium quadrupole coupling constant i s
equal t o or s l i g h t l y l a r g e r than t h a t determined from the spin-spin coupling constant in the HF species.
One would expect the heavier deuterium
nucleus t o hinder the s i d e - t o - s i d e swing of the DF subunit, causing a
smaller value for y.
anomaly.
There are a t l e a s t two p o s s i b l e sources of t h i s
F i r s t , i t i s l i k e l y t h a t the e l e c t r i c f i e l d gradient a t the
deuterium s i t e i s perturbed by t h e presence of t h e ethylene molecule.
This
perturbation can be evaluated using a multipole expansion of the m t e r 2
molecular potential, V(R) , with q
= (—-).
9r 2
aa
V(R)
= y
y
.JZL. q
m
i=0 m=~l
*
We have
,
(i-26)
r
where
m
q
a
r» ,3 , ,„ m * ,„,
= |dV(Y,)
J - - **a
., , . 1
(0',cp') (r') P(r').
Y ? m ,is the appropriate spherical harmonic.
(1-27)
The potential series must
converge rapidly in order to make this approximation.
An expansion of
this kind was used to show that the long-range effect of the acetylene
binding partner was consistent with the measured value of x
lene-HF.
in acety-
For ethylene, nonzero molecular moments are the quadrupole
and hexadecapole, with tensor elements as shown in Stogryn and Stogryn's
paper.
33
As ethylene belongs to the D
point group, nonzero elements
34
can be determined from symmetry considerations,
leaving the expressions;
33
0
q
2
1 , 5 , l/2„
Q
" 2 W
zz
(I
"28)
*2 2 -£# V2 ««V
(I 29)
&1/2*
d-30)
q°-f
4
q
2
TT
'
zzzz
2
= 3 <T^r)1/2
4
loir
<?/ = T ( ^ r > 1 / 2
4
2 70i
(*
-*
)
yyyy xxxx
(1-31)
(4*
+4$
-3$
) ,
xxxx
yyyy
zzzz
(1-32)
w h e r e Q d e n o t e s quadrupole e l e m e n t s and $ , h e x a d e c a p o l e e l e m e n t s .
w i t h odd m a r e z e r o .
m u l t i p o l e moments,
A l l q.
The c a l c u l a t i o n of V was c a r r i e d o u t u s i n g a v a i l a b l e
'
r e s u l t i n g m a quadrupole c o n t r i b u t i o n to t h e
13
-3
e l e c t r i c f i e l d g r a d i e n t a t t h e d e t e r i u m s i t e e q u a l t o 2.345 x 10 e s u cm
13
-3
a n d a hexadecapole c o n t r i b u t i o n equal t o - 7 . 9 9 3 x 10
e s u cm .
This
s e r i e s has c l e a r l y n o t converged by t h e second nonzero t e r m , and t h e
p h y s i c a l s e n s e of a d d i n g i n h i g h e r - o r d e r t e r m s , which depend
increasingly
o n j u s t t h o s e o u t e r p o r t i o n s o f t h e e t h y l e n e wavefunction t h a t can b e
e x p e c t e d t o b e a f f e c t e d most b y t h e p r e s e n c e o f t h e HF m o l e c u l e , i s d o u b t ful.
Although i t i s c l e a r from t h e f i r s t two terms t h a t t h e magnitude of
t h e e f f e c t c o u l d be l a r g e enough t o produce m e a s u r a b l e changes in t h e o b s e r v e d v a l u e of x i t h e s e r i e s a t t h i s p o i n t h a s t h e wrong o v e r a l l s i g n
f o r e x p l a i n i n g t h e measured e f f e c t .
This s i m p l y u n d e r s c o r e s t h e problems
i n h e r e n t i n t h e use o f an e x p a n s i o n a t t h e s e v e r y s h o r t d i s t a n c e s .
A second p o s s i b l e e x p l a n a t i o n stems from a n a p p r o x i m a t i o n used i n o u r
d e t e r m i n a t i o n of s t r u c t u r e :
t h a t m o l e c u l a r p r o p e r t i e s of e t h y l e n e a n d H/DF
a r e unchanged upon c o m p l e x a t i o n . Ref. 28 shows a measurable change i n t h e
37
H-F s t r e t c h i n g frequency, w h i l e an e a r l i e r CNDO/2 c a l c u l a t i o n
predicts
an e l o n g a t i o n of t h e H-F bond b y t h o u s a n d t h s o f Angstroms.
Moreover,
34
38
Pimentel
asserts that,
i n any A-H---B hydrogen-bonded s p e c i e s , a s h o r t e n -
ing of t h e A-B d i s t a n c e below t h e sum of t h e van d e r Waals r a d i i of A
and B should be accompanied by a l e n g t h e n i n g of t h e A-H bond.
Since the
angles b e i n g compared a r e derived from t h e HF s p m - s p i n c o u p l i n g c o n s t a n t
and t h e DF d e u t e r i u m quadrupole c o u p l i n g c o n s t a n t , i t i s u s e f u l t o compare
t h e e f f e c t s of b o n d l e n g t h e n i n g u p o n these c o n s t a n t s .
Previous s t u d i e s
have mentioned t h e e f f e c t of such a change upon (D ) , due t o i t s
aa HF
dependence.
The magnitude of t h i s e f f e c t c a n be e s t i m a t e d by
27
(—)
3
r
differentiating
Eq. (1-5) with r e s p e c t t o r and i n s e r t i n g p a r a m e t e r s a p p r o p r i a t e t o HF,
y i e l d i n g dD/dr =* + 9.2 kHz/.OlJL
E f f e c t s of a change i n t h e DF bond length
27
D
were n o t c o n s i d e r e d
when d e a l i n g with X • However, r e c e n t s t u d i e s have
D
39
shown a marked dependence of x u p o n the m t e r n u c l e a r d i s t a n c e ,
which has
D
°
been c a l c u l a t e d a s dx / d r =* -33 kHz/.OlA.
C l e a r l y , t h e e f f e c t of a change
i n H/DF bond l e n g t h not o n l y a f f e c t s x > b u t does so t o a s i g n i f i c a n t l y
g r e a t e r extend t h a n i t d o e s (D ) „ _ • Thus, t h e n e t e f f e c t of l e n g t h e n i n g
aa H F
o
t h e bonds in HF a n d DF i s t o change the " e f f e c t i v e f r e e v a l u e s , " D
and
aa
o
X , i n s u c h a way t h a t b o t h v a l u e s appear t o o l a r g e , e s p e c i a l l y in t h e
case of e t h y l e n e - D F . TO i l l u s t r a t e t h i s e f f e c t , y v a l u e s were c a l c u l a t e d
o
by a d d i n g i n c r e m e n t s to b o t h HP a n d DF bond l e n g t h s , d e t e r m i n i n g D
and
aa
X , a n d , from t h e s e and t h e e x p e r i m e n t a l r e s u l t s for
ing f o r t h e t r u e v i b r a t i o n a l l y a v e r a g e d a n g l e s , Y H P
(D ) TI _ and x » s o l v aa He
and Y n F - Adding 0.010A
t o each H/D-F bond gave y values w h i c h were n e a r l y e q u a l ; adding 0.015& to
each c a u s e d y
DF
t o become about t h r e e degrees s m a l l e r t h a n y
40
c o n s i s t e n t with t h e phenomenon o b s e r v e d in OC-HCl,
and o t h e r s y s t e m s .
OC-HBr,
HF
41
, which i s
30
C,H g -HCl,
Since t h i s s t u d y was c o n d u c t e d , t h e phenomenon was a l s o
observed i n the phosphine-HF complex.
42
35
The r e s u l t s of t h i s study have p r e v i o u s l y appeared a s an a r t i c l e
t h e J o u r n a l of Chemical P h y s i c s .
C.
in
43
Furan-HCl
Furan-HCl a p p e a r s t o be t h e f i r s t complex c o n t a i n i n g an a r o m a t i c
h e t e r o c y c l e t o be o b s e r v e d and c h a r a c t e r i z e d i n t h e g a s p h a s e .
and i t s d e r i v a t i v e s a r e widely used i n o r g a n i c s y n t h e s e s .
Furan
Furan may
a c t l i k e a b a s e and i s r e a d i l y p r o t o n a t e d i n a c i d i c s o l u t i o n s .
The o b -
s e r v a t i o n of t h e microwave r o t a t i o n a l s p e c t r u m allows t h e d e t e r m i n a t i o n o f
a p r e c i s e s t r u c t u r e f o r t h i s 1 : 1 complex.
The C
p l a n a r s t r u c t u r e was
d e t e r m i n e d from t h e r o t a t i o n a l c o n s t a n t s and s u p p o r t e d by a d d i t i o n a l d a t a
35
37
from i s o t o p i c s p e c i e s i n v o l v i n g D CI, H c l , and 2-D f u r a n .
44
45
orbital calculations
f o r t h i s complex.
and a c a l o n m e t r i c s t u d y
Molecular
have been c a r r i e d out
S i n c e furan p o s s e s s e s b o t h an oxygen lone p a i r and a n
a r o m a t i c TT-electron s y s t e m , s t u d i e s of complexes of t h i s type may aid i n
d i s c e r n i n g t h e r e l a t i v e i m p o r t a n c e of t h e s e p r o p e r t i e s i n hydrogen bond
formation.
Furan-HCl was g e n e r a t e d b y p r e p a r i n g m i x t u r e s of ~3% furan (MCB
R e a g e n t s , 98%) w i t h ~3% HCl ( L i n d e , 99%) o r DC1 (Merck, 98%) i n 20 p s i
of a r g o n . Four i s o t o p i c s p e c i e s of furan-HCl were a s s i g n e d - twenty R35
b r n a c h , a - d i p o l e t r a n s i t i o n s w e r e measured f o r furan-H C l , f i v e for
37
3S
3^
furan-H
C l , e i g h t f o r furan-D
C l , and two f o r 2-D furan-H
Cl.
f u r a n was made by d e c a r b o x y l a t m g D-furoic a c i d by r e f l u x m g i n
The 2-D
quinolme
w i t h a copper c a t a l y s t .
The D - f u r o i c a c i d was o b t a i n e d by exchanging
35
f u r o i c a c i d w i t h D„0. A t y p i c a l furan-H Cl s p e c t r a l measurement i s shown
i n F i g . 1-5.
Note t h a t t h e u s u a l Doppler d o u b l i n g
these transitions.
was not observed on
to
Figure 1-5. Measured digital spectrum of the 2
-*• 3
, 5/2 -> 7/2 and
3/2 -*• 5/2 transitions of furan-H35Cl at 5870.42 and 5870.38
MHz.
Frequencies on the plot are relative to 587Q.0 MHz.
37
N
CO
O
o
in
o
38
All of the r o t a t i o n a l t r a n s i t i o n s measured for each of the four
i s o t o p i c species of furan-HCl exhibited s p l i t t i n g s which were c l e a r l y
c h a r a c t e r i s t i c of the chlorine quadrupole coupling e f f e c t .
No o t h e r
hyperfine effects - including deuterium quadrupole coupling, in t h e case
of furan-DCl - were resolved.
These l i n e s were f i t to a Hamiltonian
which i s the sum of two terms:
K = KD + K_
R
2
where K i s the d i s t o r t e d - r o t o r Hamiltonian,
(1-33)
46
and K is t h e quadrupole
Hamiltonian of Eq. (1-6) , with the chlorine nucleus taking the p l a c e of
deuterium.
Calculated t r a n s i t i o n frequencies were obtained by d i a g o n a l i z i n g
the Hamiltonian matrix in blocks of F, where
F = I
a
+ J .
(1-34)
The observed t r a n s i t i o n s were f i t using t h i s procedure coupled w i t h a
l e a s t - s q u a r e s f i t t i n g program which f i t s to l i n e centers and elements of
the quadrupole coupling tensor x / where
X
A
gg
=
eq
Q,
gg
g = a,b,c.
(1-35)
Estimates of Y , y,
, , and the l i n e centers were used as f i r s t guesses in
aa ftbb
the f i t t i n g program. Off diagonal elements of x were neglected i n the f i t .
Once l i n e centers were obtained, they were f i t t o determinable d i s t o r t i o n
parameters e s t a b l i s h e d by Watson
47
- A", B", c " , T,, T . T" .. , and t"
1
i.
DDDO
CCCC
48
using a program w r i t t e n by Kirchhoff.
In the case of furan-HCl, a l l
t r a n s i t i o n s are of t h e type AK , = 0 , with the r e s u l t t h a t x"
is
—1
aaaa
indeterminate. Thus, i t was neglected i n the f i t . Since furan-HCl
39
is planar, T 3 could be determined from planarity conditions, and was also
held fixed in the fit.
The observed transitions of furan-H
Cl, furan-H
Cl, and furan-D
Cl
can be found in Table 1-10 - 1-12, along with their calculated values.
The spectroscopic constants for furan-H
above, are listed in Table 1-13.
35
Cl, determined by the fit described
These constants are used in turn to deter-
mine the distortion-free rotational constants, from which the molecular
structure is derived, as discussed in that next section.
tional constants for the H
Approximate rota-
37
35
Cl and D Cl isotopic species were obtained
by a simple fit to A, B, C, D , and D
J
JK
in the symmetric-top limit, and
are also available in Table 1-13.
The distortion-free rotational constants (A, B, and c) presented in
Table 1-14 were used to determine the structure of furan-HCl. The A",
B" and C" rotational constants and T"'s from the fit program are used to
determine the Kivelson-Wilsor parameters (A1, B 1 , C , T'
, X'
,
aaaa
cccc
T
' ,_. , T'
and T'
) . The distortion-free parameters (A, B, and C)
aabb
aacc
bbcc
are then obtained from the Kivelson-Wilson parameters by standard techniques.
T
46
x
and T, , , , are independent
parameters whereas T"
e
r
aaaa
bbbb
cccc
and T, are related due to planarity conditions.
,
As a result, the
final distortion-free values of A, B and C will vary depending on which two
of the (T"
, T,, T-) group are taken as independent parameters.
cccc
1
2
results of this analysis are given in Table 1-14.
The
The above analysis was
done using the coordinate system of Figure 1-6 and the following equations
for the elements of the moment of inertia tensor:
I
=1
2
2
2
(furan) + I_n(sin cpsm 9+cos 6) + I
2
2
2
(sin £sin a+cos a ) ,
(1-36)
40
. .
35
Observed and Calculated Transition Frequencies for Furan-H Cl
Observed(MHz)
F ->• F'
1 / 2 •*• 3 / 2
Calculated(MHz)
5718.6737
Difference (kHz)
-
7.1
5718.66663
3 / 2 ->• 5 / 2
14.7
5718.6519
5 / 2 •+ 7 / 2
5721.9335
-
1.5
5721.9381
-
6.1
-
5.0
5721.9320
7 / 2 -> 9 / 2
3 / 2 -* 5 / 2
5571.3748
5571.3798
5 / 2 -> 7 / 2
5571.5255
5571.5211
4.4
7 / 2 •> 9 / 2
5574.8344
5574.8338
0.6
3 / 2 -> 5 / 2
5870.3833
5870.3776
5.7
5 / 2 •+ 7 / 2
5870.4220
5870.4219
0.1
1 / 2 -*• 3 / 7
5873.6571
5873.6655
7 / 2 •+ 9 / 2
5873.7367
5873.7341
5 / 2 -v 7 / 2
5713.2615
5713.2627
7 / 2 ->• 9 / 2
5726.4462
5726.4450
5 / 2 -> 7 / 2
5709.7883
5709.7885
-
0.2
3 / 2 •+• 5 / 2
5719.2119
5719.2189
-
7.0
7 / 2 •> 9 / 2
5722.9805
5722.9732
3 / 2 -> 5 / 2
7623.1399
-
8.4
2.6
-
1.2
1.2
7.3
-
7.4
7623.1325
5 / 2 •+ 7 / 2
7/2 ^ 9/2
'
7623.1314
1.1
7624.6685
5.3
7624.6728
1.0
7624.6738
9 / 2 •> 1 1 / 2
41
Table 1-10.
Transition
3
13 -
3
12 ^
4
04
4
4
14
13
-> 5
05
Continued
p + pi
Observed(MHz)
Calculated(MHz)
5/2 -> 7/2
7428.9286
7428.9284
0.2
7 / 2 •+ 9/2
7429.6388
7429.6361
2.7
3/2 -v 5/2
7430.2462
7430.2450
1.2
9 / 2 -+ 11/2
7430.9580
7430.9622
5/2 -*• 7/2
7827.4710
7827.4698
7/2 -> 9/2
7828.1310
7828.1322
-
3/2 •+ 5/2
7828.7857
7827.7863
- 0.6
9/2 •*• 11/2
7829.4587
7829.4581
0.6
9523.0823
- 3.0
9523.0761
3.2
9523.9846
2.2
9523.9892
- 2.4
5/2 -*• 7/2
Difference(kHz)
- 4.2
1.2
1.2
9523.0793
7/2 -»• 9/2
9/2 •+ 11/2
9523.9868
11/2 -> 13/2
4
14
4
13
4
23
•+• 5
15
•> 5 .
3
14
-*- 5 .
24
7/2 -*• 9/2
9285.3008
9285.3019
-
9/2 -*• 11/2
9285.8957
9285.8991
- 3.4
11/2 -> 13/2
9286.5671
9286.5626
4.5
7/2 -»• 9/2
9783.3515
9783.3507
0.8
11/2 -> 13/2
9784.5838
9784.5846
- 0.8
9/2 -»- 11/2
9528.5211
9528.5203
0.8
7/2 -> 9/2
9528.9069
9528.9089
- 2.0
11/2 ->• 13/2
9531.1693
9531.1671
2.2
5/2 ->- 7/2
9531.5395
9531.5405
-
1.1
1.0
42
Table 1-10.
Transition
4
5
22
•+• 5
23
05 * 6 0 6
Continued
F ->• F'
Observed(MHz)
Calculated(MHz)
9/2 ->- 11/2
9545.8506
9545.8478
2.8
7/2 + 9/2
9546.2333
9546.2358
- 2.5
11/2 -*- 13/2
9548.4921
9548.4906
1.5
5/2 •+ 7/2
9548.8616
9548.8634
- 1.8
11418.3500
- 2.7
11418.3442
3.1
11418.9489
2.4
11418.9541
- 2.8
7/2 •+ 9/2
Difference(kHz)
11418.3473
9/2 •+ 11/2
11/2 -»• 13/2
11418.9513
13/2 -+• 15/2
5
5
5
5
15 * 6 1 6
14 * 6 1 5
24 - 6 2 5
23
+ 6
24
9/2 -*• 11/2
11140.3946
11140.3900
4.6
7/2 -> 9/2
11140.7662
11140.7678
- 1.6
11/2 •*• 13/2
11140.8525
11140.8532
- 0.7
13/2 -*• 15/2
11141.2306
11141.2329
- 2.3
9/2 •*• 11/2
11737.8277
11737.8260
1.7
7/2 -> 9/2
11738.2121
11738.2039
8.2
11/2 + 13/2
11738.2620
11738.2714
- 9.4
13/2 •*• 15/2
11738.6506
11738.6511
- 0.5
11/2 •> 13/2
11433.6419
11433.6425
- 0.6
13/2 -v 15/2
11435.1561
11435.1555
0.6
11/2 -»- 13/2
11463.9391
11463.9386
0.5
13/2 -• 15/2
11465.4463
11465.4468
- 0.5
43
Table 1-10.
Continued
Observed(MHz)
Transition
6
06
+ 7
07
9/2
- > •
11/2
Calculated(MHz)
Difference(kHz)
13308.2862
2.9
13308.2800
9.1
13308.7132
- 3.1
13308.7190
- 8.9
13308.2891
11/2 ->• 13/2
13/2
+
15/2
13308.7101
6
16 * 7 17
15/2
+
17/2
11/2
+
13/2
12994.1028
12994.1007
2.1
9/2
-V
11/2
12994.3382
12994.3376
0.6
13/2
- > •
15/2
12994.4566
12994.4611
- 4.5
15/2
+
17/2
12994.7008
12994.6990
1.8
The frequency reported for this transition is the midpoint of a 30 kHz
splitting which appeared on no other lines in the observed spectrum.
cause of this splitting is not understood.
The
44
Table I-ll.
Transition
3
J
03
•*• 4
04
Observed and Calculated Transition Frequencies for Furan-H
F •*• F1
Observed (MHz)
3/2 -»• 5/2
Calculated (MHz)
Difference (kHz)
7395.0577
-5.3
7395.0533
-0.9
7396.2637
1.6
7396.2653
0.0
9238.5757
-1.2
9238.5731
1.4
9239.2886
0.5
9239.2902
-1.1
7395.0524
5/2 •+ 7/2
7/2 -> 9/2
7396.2653
9/2 -> 11/2
4
•+• 5
*04
°05
5/2 •+ 7/2
9238.5745
7/2 •> 9/2
9/2 -+ 11/2
9239.2891
11/2 -> 13/2
4
14
•+• 5
15
4
-»• 5
13
14
5
3
05
-> 6
06
7/2 ->• 9/2
9013.9575
9013.9596
-2.1
9/2 •> 11/2
9014.4262
9014.4255
0.7
7/2 •> 9/2
9482.7626
9482.7561
6.5
9/2 •* 11/2
9483.2132
9483.2103
2.9
11/2 -»• 13/2
9483.7272
9483.7321
-4.9
11077.9895
-2.6
11077.9874
-0.5
11078.4638
1.4
11078.4654
-0.2
7/2 •* 9/2
11077.9869
9/2 ->• 11/2
11/2 -v 13/2
11078.4652
13/2 •+ 15/2
37
Cl
45
Table 1-12.
Transition
3
J
03
-*• 4
*04
35
Observed and Calculated Transition Frequencies for Furan-D Cl.
F ->• F'
Observed(MHz)
3/2 •> 5/2
Calculated(MHz)
Difference(kHz)
7596.4249
- 3.0
7596.4188
3.1
7598.0072
0.7
7598.0088
- 0.9
9489.8290
- 0.7
9489.8261
2.2
9490.7652
0.4
9490.7664
- 0.8
7596.4219
5/2 ->- 7/2
7/2 •*• 9/2
7598.0079
9/2 -> 11/2
4
04 *
5
05
5/2 •+ 7/2
9489.8283
7/2 -> 9/2
9/2 ->- 11/2
9490.7656
11/2 •*• 13/2
4
14 *
4
4
13
5
05
5
15
-> a5
l4
->• 6
06
7/2 -v 9/2
9254.3889
9254.3892
- 0.3
5/2 -*• 7/2
9255.0085
9254.9978
10.7
9/2 -+ 11/2
9255.0637
9255.0695
- 5.8
11/2 -v 13/2
9255.6879
9255.6825
5.4
7/2 •+ 9/2
9747.8393
9747.8359
3.4
5/2 ->• 7/2
9748.4366
9748.4338
2.8
9/2 -»• 11/2
9748.5081
9748.5162
- 8.1
11/2 •*• 13/2
9749.1169
9749.1183
- 1.4
11378.6354
- 0.6
11378.6336
1.2
11379.2589
- 1.4
11379.2599
- 2.4
7/2 •> 9/2
11378.6348
9/2 -*• 11/2
11/2 -*• 13/2
11379.2575
13/2 •> 15/2
46
Table IJ-12.
Transition
5 ,. •*• 6
15
16
5
14 * 6 15
6
06 - ? 07
Continued
F + F'
Observed(MHz)
9/2 -*• 11/2
11103.3438
11103.3486
- 4.8
7/2
11103.7408
11103.7377
3.1
11/2 ->• 13/2
11103.8175
11103.8215
- 4.0
13/2 •*• 1 5 / 2
11104.2139
11104.2127
1.2
9/2 -> 11/2
11695.2685
11695.2755
- 7.0
7/2 -»• 9/2
11695.6733
11695.6646
8.7
11/2 •+ 13/2
11695.7289
11695.7413
-12.4
13/2 -* 15/2
11696.1330
11696.1324
0.6
13262.1797
- 2.7
13262.1783
- 1.3
13262.6284
5.4
13262.6274
4.4
•*• 9/2
9/2 + 11/2
Calculated (MHz)
Difference(kHz)
13262.1770
11/2 -*• 13/2
13/2 •+ 15/2
13262.6318
15/2 •> 17/2
47
Table 1-13.
Spectroscopic Constants for Furan-HCl, in MHz.
Furan-H
35 .
Cl
Furan-H
37 c
Cl
Furan-D
Cl
9395(24)
A
9421.3(39)
B
1004.2001(27)
972.3608
1000.1395(27)
C
904.5526(26)
878.5864
901.4376(27)
T,
-0.9392(12)
9461.
-0.0751(2)
1.82(4)
0
aaaa
bbbb
-0.00401(19)
-0.00217(17)
cccc
JK
v
0.00046
0.00024(9)
0.217
0.208(5)
-52.803(17)
-41.600(82)
-54.539(70)
25.626(54)
20.46(18)
26.96(15)
27.177(54)
21.14(18)
27.58(15)
aa
^bb
v
cc
Errors in parentheses are one standard deviation in the fit.
Held fixed in the fit.
Standard deviations unavailable for rotational parameters of furan-H Cl.
48
Table 1-14.
Derived Molecular C o n s t a n t s of Furan-H
From T
and X
J.
£*
35
From x, and x
1
cccc
Cl
From x„ and X
2
cccc
A (MHz)
9420.988
9421.049
9421.055
B(MHz)
1003.958
1004.019
1004.025
C(MHz)
904.480
904.389
904.380
1.720
1.808
1.816
A(amu & )
49
Figure 1-6.
Coordinate system used in the analysis of furan-HCl.
The furan molecule lies in the yz-plane.
50
*-y
51
I
yy
I
= I
DO
= I
zz
(furan)
+ I
(furan)
+ I
aa
PD
2
2
2
(cos cpsin S+cos 6) + I
sin29 + I
HCJ.
2
2
2
(cos £sxn a+cos a ) ,
(1-37)
sin2a,
(1-38)
HCl
PD
2
2
I
= -I
sincpcoscpsin 0 - I
cosCjsin a s i n ? ,
(1-39)
I
= -I
coscpsm9cos0 + I
cos^sinacosa,
(1-40)
I
= -I
smcpsin9cos6 + I
..sin^sinacosa.
(1-41)
I
i s t h e " p s e u d o d i a t o m i c " moment of i n e r t i a ,
a n a l o g o u s t o Eq.
(1-22) .
The
d i a g o n a l i z a t i o n of t h i s t e n s o r y i e l d s c a l c u l a t e d v a l u e s f o r A, B, and C.
Molecular c o n s t a n t s needed for t h e s e e q u a t i o n s can be found in T a b l e 1-15.
F i r s t , t h e s i m i l a r i t y between A of furan-HCl and A of furan should b e
noted.
The two v a l u e s a r e c l o s e enough t o l e a d one t o t h i n k t h a t the i n e r -
t i a l axes of t h e monomer and t h e complex are i d e n t i c a l , o r very n e a r l y s o .
This i m p l i e s t h a t t h e c h l o r i n e atom, t h e source of n e a r l y a l l of
mass of HCl, l i e s v i r t u a l l y on t h e a - a x i s of f u r a n .
the
The small d i s c r e p a n c y
i n A v a l u e s becomes u n d e r s t a n d a b l e upon e x a m i n a t i o n of t h e i n e r t i a l
A = I
- I
cc
aa
defect,
- I. . .
oD
(1-42)
o2
The v a l u e of ~1.8 amu A
planar molecules
seems l a r g e when compared with t h o s e of t y p i c a l
o2 49
(for example, f u r a n , f o r which A = 0.049 amu A ) ,
but i t
i s n o t u n r e a s o n a b l e f o r a weakly-bound complex.
argon and t h e l i n e a r m o l e c u l e cyanogen c h l o r i d e ,
In the complex between
9
which must c l e a r l y be
p l a n a r , A =* 2.75 amu A .
These p o s i t i v e i n e r t i a l d e f e c t s a r e b e l i e v e d t o be caused by i n - p l a n e
v i b r a t i o n s between t h e s u b u n i t s o f t h e complex.
This s u p p o s i t i o n i s s u p -
p o r t e d by t h e f a c t t h a t t h e c a l c u l a t e d A can b e made t o a g r e e w i t h the
52
T a b l e 1-15.
M o l e c u l a r C o n s t a n t s of Furan and HCl.
Furan
H35C1
H37C1
D35C1
A(MHz)
9447.1210(10)
—_
__
— ..
B(MHZ)
9246.7449(10)
312989.297b
312519.121b
161656.238
C(MHz)
4670.8234(10)
—
—
~
X°(MHz)
—
-67.61893b
-53.294C
-67.39338°
Ref.
49.
Ref.
25.
°Ref. 50.
X°(37CD = X°(35CD/1.2688.
53
observed value if a for furan-HCl is set to 17.7°.
R „ of furan-HCl, the
CM
distance separating the centers-of-mass of the subunits, was fit successively to B and to C.
taneously.)
(No structure was consistent with B and C simul-
The resultant R
's, along with corresponding 0---C1 distances,
calculated assuming the above value for a and all other angles set to zero,
are listed in Table 1-16.
An important conclusion which can be drawn from Table 1-16 stems from
the fact that R
shifts among the three isotopic species are consistent
with a structure in which HCl lies along the a axis of furan, with the proton between the chlorine atom and the oxygen atom of furan.
R
In this case,
would only change between isotopic species as a result of shifts in the
center of mass of HCl.
This is reflected in the Table 1-16 values, with
small discrepancies arising from the fact that the fixed value of a from
35
H Cl) is probably slightly different from the corresponding DC1 value.
35
37
Also, the A, B and C values of furan-D Cl and furan-H Cl are the result
of approximate fits to symmetric-top distortion constants D T and D , with
J
JK
the probable result of discrepancies between these rotational constants and
the distortion-free values.
It is possible to fit the above rotational constants for furan-HCl
to a structure in which HCl makes a hydrogen bond to the oxygen of furan
as shown in Fig. 1-5, or one in which the furan subunit is rotated 180°
about its c-inertial axis, making the HCl hydrogen bond to the region
between the 3-carbon atoms. The hydrogen bonding to oxygen was verified
by measuring the 4n. - 5„_ transition, centered at 9477.060 MHz, and the
04
05
35
55 - 6
transition, centered at 11360.512 MHz, for the 2-D furan-H Cl
isotopic species.
The predicted frequencies for these transitions, assuming
54
Table 1-16.
Structural Parameters of Furan-HCl.
Furan-H
35
Cl
Furan-H
37
Cl
Furan-D
35
Cl
4.3588
4.3609
4.3216
4.3686
4.3700
4.3305
D(0'"C1) (A)a
3.2600
3.2603
3.2555
D(O---Cl)(A)b
3.2698
3.2694
3.2644
17.09(8)
16.75(22)
15.45(16)
15.47(11)
15.86(36)
14.75(26)
cm
cm
0. (deg)c
D
9 (deg)c
Determined from the B rotational constant.
Determined from the C rotational constant.
"Errors are estimated using the errors on the measured \
values.
55
hydrogen bonding t o the oxygen, a r e 9483.86 and 11368.40 MHz.
I f we assume
hydrogen bonding t o the B-carbon a t o m s , t h e p r e d i c t e d f r e q u e n c i e s
9393.43 and 11260.64 MHz.
are
The s t r u c t u r e w i t h hydrogen bonding t o the o x y -
gen g i v e s b e t t e r agreement w i t h t h e observed l i n e s by a f a c t o r of 10.
This
i s t a k e n t o be v e r y s t r o n g evidence t h a t t h e HCl hydrogen bond forms t o
t h e l o n e p a i r of oxygen.
Furan-HCl i s a s s e r t e d t o be a p l a n a r complex, w i t h t h e a t t r a c t i v e
force
e x i s t i n g between t h e acid p r o t o n of HCl and t h e lone p a i r e l e c t r o n p a i r on
t h e oxygen atom o f furan.
Thus, e x c u r s i o n s o f t h i s p r o t o n from t h e a - a x i s
should b e c o n s t r a i n e d by i t s involvement m t h e hydrogen bond.
tne
s i o n s c a n be measured by means of X'
the equations
These e x c u r -
q u a d r u p o l e c o u p l i n g t e n s o r , and
29
X
6, = a r c c o s
b
1 o
2 XHCl
aa
X
_ aa
+X
bb
+X
(1-43)
HCl.
X
*aa + -2 X°
*HC1
(1-44)
arccos
X
. aa
where 9
and 9
represent,
+X
cc
+X
HC1*
r e s p e c t i v e l y , t h e i n - p l a n e and o u t - o f - p l a n e
vibrationally-averaged bending angles,
x
» Xuu'
clcL
JD.D
and
are
X
t h e
diagonal
CC
elements of the c h l o r i n e q u a d r u p o l e c o u p l i n g t e n s o r , and Xum •LS ^he
of t h e c o u p l i n g c o n s t a n t i n free HCl.
va
^-ue
These e q u a t i o n s were a p p l i e d t o t h e
c o n s t a n t s in T a b l e 1-13 and t h e f r e e v a l u e s m Table 1-15 t o produce t h e
angles g i v e n in T a b l e 1-16.
In each i s o t o p i c s p e c i e s , 8
> 9 , implying
t h a t m o t i o n i s l e s s c o n s t r a i n e d i n t h e d i r e c t i o n p a r a l l e l t o t h e plane of
56
furan than in the direction perpendicular to it. This is consistent with
the kind of in-plane vibration that can produce the positive inertial
defect commented upon earlier. Also consistent with the proposed structure
is the fact that the angles are not seriously affected by substitution of
37
35
Cl for
Cl, while substitution of deuterium for hydrogen causes them
to decrease noticeably.
Analysis of centrifugal distortion effects can provide a comparative
measure of the strength of the interaction between the two subunits.
This
is done by exploiting a relationship between D and the hydrogen-bond
J
s t r e t c h i n g force c o n s t a n t , k , developed during the a n a l y s i s of benzene12
HCl.
Certain approximations are involved in t h i s approach, p r i n c i p a l l y
t h a t i n t e r n a l v i b r a t i o n s i n furan and HCl do not c o n t r i b u t e s i g n i f i c a n t l y
t o D and that t h e p r i n c i p a l axes of furan-HCl a t equilibrium coincide with
J
those of furan.
An attempt t o confirm t h i s assumption was made using the
force constants derived f o r ArClCN,
into consideration.
9
for which i n t e r n a l modes were taken
The force constants of the van der Waals modes alone
a r e used i n the equation
T
a6Y6-
4,
i a a V Y Y i 5 6 [ j J a3 £ x 3 Y* '
(1-45)
where a ,
3 , y, <S = a , b , c .
[J -1 = 91 „/3R. e v a l u a t e d a t e q u i l i b r i u m , and i t can be shown t h a t x , ,
a3 e
a3
I
aabb
d i f f e r s by ~17% o f t h e r e p o r t e d v a l u e , w h i l e t h e o t h e r nonzero x ' s a r e
reproduced to w i t h i n six p e r c e n t o r l e s s .
Kivelson-Wilson d e r i v a b l e x ' s :
D
J " " 37
(3T
52
D i n furan-HCl comes from t h e
J
hbbb+3T«ce+2Tbbcc)
(I
"46)
57
48
which are calculated by the Kirchhoff program mentioned e a r l i e r ,
using
p l a n a r i t y c o n d i t i o n s . The f a c t that t h e s e parameters (except x' , , )
bbbb
depend upon X
, which cannot be f i t t e d for furan-HCl, should cause
minimal e r r o r .
Calculations using the same model that produced t h e force
constant equation used in t h i s a n a l y s i s predict x
given the proposed equilibrium s t r u c t u r e .
12
is
Dj
=
= 0 for furan-HCl,
aaaa
The equation r e l a t i n g D to k
J
s
8TT3 (P pn R rM ) 2 [ (B2+C2) 2+2 (B4+C4) ]
C M _ _
(i_4?)
s
leading to k
= 0.0670(6) mdyn/A.
Using a well-established procedure
involving the assumption of a Lennard-Jones 6-12 potential, we arrive at
a well depth e = 883 cm
. This is compared with other weakly-bound sys-
tems involving HCl in Table 1-17.
The structure of furan-HCl has been shown to be planar, with the HCl
axis coincident with the a inertial axis of furan, giving the complex C
symmetry overall. A hydrogen bond is formed between the acid proton and
the lone pair of oxygen in furan.
The general features of this structure
are in agreement with a previous molecular orbital calculation, although
0
the observed bond length of 1.98A is significantly longer than the predicted
° 44
value of 1.783A.
This would seem to indicate that standard molecular-
orbital analyses are not as suitable for predicting detailed structures of
complexes of this sort as they are for free molecules.
The oxygen-chlorme separation is presented in Table 1-17 along with
analogous quantities for several HCl complexes.
In the series of hydro-
carbon-HCl complexes analyzed to date, the calculated well-depth seems to
vary inversely with the observed bond length.
HCN-HC1 fits this pattern
Table 1-17.
Bond Lengths and P o t e n t i a l Well Depths for Various HCl
Complexes
efcm" 1
R(A)
0C-HC1
3.70b
495
Ethylene-HCl
3.72C
575
d
Acetylene-HCl
3.69
614
Benzene-HCl
3.63°
720
Cyclopropane-HCl
3.57
855
Furan-HCl
3.26
883
HCN-HC1
3.40g
978
Calculated using force constants obtained using Eq. (1-47)
b
Ref. 40.
C
Ref. 10.
d
Ref. 29.
e
Ref. 12.
f
Ref. 30.
g
Ref. 53.
59
as well, while OC-HCl shows some departure from expected behavior.
However,
furan-HCl, which has the shortest bond length observed thus far, has an
estimated well-depth comparable to t h a t of cyclopropane-HCl, where one might
expect i t to be stronger even than HCN-HCl.
This apparent anomaly can be
p a r t i a l l y explained by considering t h a t no complexes had previously been
reported with 0 " ' C 1 hydrogen bonds.
The estimated van der Waals radius of
carbon i n the compounds studied averages a t about 1.6&, while, for oxygen,
i t is only 1.4&.
This smaller van der Waals radius implies that l e s s
force i s required t o hold the HCl a t a distance of 3.26A than would be r e quired i n the case of a C- # 'Cl bond.
This observation i s consistent with
54
t h e recently observed s t r u c t u r e of the l i n e a r CO -HCl complex,
i n which
a hydrogen bond a l s o forms to oxygen.
In t h i s complex, D(O-'-Cl) i s only
3.25A, y e t the p o t e n t i a l well depth, estimated using the published
spectro-
scopic d a t a and the method described above, i s ]ust 196 cm
The r e s u l t s of t h i s study have previously been published in a preliminary communication in the Journal of the American Chemical Society,
55
and
i n complete form m an a r t i c l e in t h e Journal of Chemical Physics.
D.
Argon-Carbonyl Fluoride
Argon-carbonyl fluoride is one of a s e r i e s of complexes involving the
binding of a rare gas atom t o a p o l a r molecule.
most l i k e l y has c
symmetry at equilibrium.
Ar-F CO i s nonplanar, and
The ArCO angle i s 100.3°,
placing t h e argon atom almost d i r e c t l y over the midpoint of the two fluorine
atoms.
This nonplanar s t r u c t u r e i s consistent with a trend noted f o r many
previously-studied r a r e - g a s - c o n t a i n m g van der Waals complexes, wherein the
r a r e gas atom appears to bind to t h e most e l e c t r o p o s i t i v e s i t e of t h e
companion molecule.
60
Ar-F CO was generated by preparing mixtures of ~3% F CO (Matheson, 97%)
in 20 psi of argon.
Thirty-six rotational transitions were measured for
Ar-F CO - seventeen c-dipole, Q-branch transitions; ten c-dipole, R-branch
transitions; and nine a-dipole, R-branch transitions - in the range between
18
4 and 17 GHz. Nine transitions of Ar-F C 0 were also measured,
six
b-dipole, Q-branch transitions; two b-dipole, R-branch transitions and one
a-dipole, R-branch transition.
The substituted carbonyl fluoride was syn-
thesized in situ by adding low concentrations of fluorine gas (Linde, 98%)
and
18
O-substituted carbon monoxide (Cambridge Isotope Laboratories, 90%)
in equal amounts to the holding tank, adding 20 psi of argon, and allowing
the components to react for a few minutes.
Ar-F CO is a nonplanar complex, with the argon atom located above the
plane of the carbonyl fluoride molecule.
This configuration of masses
leads to an "accidental" near-symmetry in Ar-F C
and K = -0.999996.
for which B-c = 8 kHz
This near-symmetry causes the unusual spectrum depicted
in Figs. 1-7 and 1-8.
i
16
0,
Fig. 1-7 shows the Q-branch series with |K| = 1
i
18
and |K'| = 2 for Ar-F C
O, which follows the pattern expected of b- and
c-dipole series, in prolate near-symmetric tops.
The splitting between
lines of equal J is due mainly to (B-C), while the splitting between adjacent lines of different J is caused by D . The pattern of all lines
JK
with J values up to seven extends over 400 MHz. The analogous pattern
16
exhibited by Ar-F C 0 is shown m Fig. 1-8. Here, transitions of equal
J are split by no more than 250 kHz, and the width of the entire pattern
is less than 25 MHz.
This set of transitions, the first observed in this
study, pointed out the unusually hiah symmetry of Ar-F CO.
Another unusual
result is the change in selection rules between isotopic species.
The
Figure 1-7. b-dipole Q-branch series (J=2 to 7, inclusive) for
18
Ar-F c 0, calculated from fitted rotational constants.
m
H
-3
II
II
~3
~3
tO
II
ro
ro
ii
(0
1^-
-3
II
~3
-3
CP
it
II
~3
"3
CM
CVJ
II
II
-3
II
-3
II
-3
12580 12635 12690 12745 12800 12855 12^10
12965 13020
v (MHz)
Ivj
U>
Figure 1-8.
Spectral pattern analogous to Figure 1-7, this time obeying c-dipole
selection rules, for Ar-F c
0.
The Lorentzians are an artifact of the
plotting program, and are not indicative of the observed linewidths,
which are on the order of 5-7 kHz.
64
CM
ro
ro
2=P
i-s;
ro
£=r
CD
CVJ
17=P
9=r
3:
ro
z=r
ro
oo
O
ro
65
transitions in Fig. 1-8 obey c-dipole selection rules, while those of
Fig. 1-7 obey b-dipole selection rules.
All of the transitions reported in this study are line centers, with
no resolvable hyperfine structure.
Some of the high-J, Q-branch transi-
tions of both isotopic species exhibited small splittings which are probably due to spin-rotation interactions of the fluorine nuclei, but these
were not assignable.
The spectra were fit to the distorted rotor Hamil-
57
toman in the near-symmetric limit, using D , D , and D .
J
JK
K
The complex
is sufficiently symmetric that a full asymmetric-top distortion treatment
was not only unnecessary, but unfeasible.
16
The observed and calculated frequencies for Ar-F C
are listed in Tables 1-18 and 1-19.
18
0 and Ar-F C
0
The rotational constants (A, B, and C)
and centrifugal distortion constants (D , D , and D ) for each isotopic
J
JK
K
species appear in Table 1-20.
The structure of Ar-F CO was fit using the measured rotational constants listed in Table 1-20, the known structural parameters of carbonyl
fluoride (see Table 1-21) , and the coordinate system shown in Fig. 1-9.
Here, R w is the distance from the center of mass of the F.CO molecule to
CM
2
the argon atom, cp is the angle between R
and the symmetry plane of car-
bonyl fluoride perpendicular to the F 2 c o molecule, always assumed to be
zero in the structural fits for reasons to be given below, and 8 is
the angle between R
and the c-inertial axis of carbonyl fluoride.
The
angle 9 is negative if the argon atom is tipped toward the midpoint between
the fluorine atoms, and positive if it is tipped toward the carbonyl group.
Our choice of cp is justified in the following manner.
A, is expected to be zero for a planar molecule.
The inertial defect,
In Ar-F CO, A = -84.2236
66
Observed and Calculated Rotational Transitions for Ar-F C16 0.
Table 1-18.
JK
-IKI *
3
2
03
02
4471.5270
-4.0
•*• 5
°15
4473.0651
4473.0686
-3.5
+ 4
4474.3517
4474.3533
-1.6
4475.3782
4475.3811
-2.9
4476.1488
4476.1519
-3.1
4476.6629
4476.6658
-2.9
4663.9254
4663.9282
-2.8
6093.2553
-18.1
6093.2849
6093.2719
13.0
6093.7645
6093.7691
-4.6
7523.6656
7523.6684
-2.8
7710.3436
7710.3516
-8.0
9137.0814
9137.0717
9.7
hi
6
1
11
11
1
14
13
•*• 2
12
hi
->• 3
-»• 2
03
12
-*• 2
1
10
11
01
-*• 2
02
°00
+
3
-*• 4
2
16
->• 3
^1 *
2
12
21
A(kHz)
4471.5230
06 -
04
Calculated (MHz)
-4.9
6
4
Observed(MHz)
4469.7284
07 *
05
:IK1
4469.7235
7
5
JK
x
io
-»• 3
04
22
6093.2372
v
2
h2
"+ 3J
13
9139.3196
9139.3343
-14.7
2
-»• 3
9139.3716
9139.3592
12.4
9140.1010
9140.1051
-4.1
10569.9451
10569.9460
-0.9
10944.3735
10944.3582
15.3
10944.6436
10944.6580
-14.4
12181.7459
12181.7382
7.7
12185.7842
12184.7827
1.5
2
1
7
7
3
3
3
11
02
01
26
25
21
22
03
12
•*• 3„„
03
•> 2
->• 8
-»• 8
->• 4
->• 4
-• 4
11
18
17
22
23
04
67
Table 1-18.
K
Continued
Observed(MHz)
Calculated(MHz)
A (kHz)
13410.8660
13410.8736
-7.6
7
+7
17
25
13411.1017
13411.1068
-5.1
6
-*• 6
15
25
13416.2135
13416.2112
2.3
6
16 "^ 624
13416.3895
13416.3860
3.5
5
14 * 524
13420.7876
13420.7862
1.4
5
-> 5
15
23
13420.9274
13420.9111
16.3
4
•> 4
13
23
13424.5964
13424.5987
-2.3
4
•*• 4
14
22
13424.6874
13424.6819
5.5
3
12 "* 322
13427.6421
13427.6487
-6.6
13 * 321
13427.6920
13427.6986
-6.6
2 „ •+• 3
13615.5420
13615.5361
5.9
5
14 * 6 06
13801.0861
13801.0915
-5.4
3
-*• 4
03
13
16660.2246
16660.2193
5.3
6
-»• 7
15
07
16844.9696
16844.9690
0.6
-1 K 1
7
16
3
02
K
-1 K 1
•*• 1
26
12
68
18
Observed and Calculated Rotational Transitions for Ar-F C 0.
K
i
Observed(MHz)
C a l c u l a t e d (MHz)
10246.2554
10246.2554
0.0
10797.6239
10797.6239
0.0
11994.0135
11994.0135
0.0
12962.6689
12692.6668
2.1
12733.9431
12733.9436
-0.5
12767.2339
12767.2375
-3.6
12792.3651
12792.3667
-1.6
12838.6555
12838.6481
7.4
12859.6709
12859.6746
-3.7
A(kHz)
69
T a b l e 1-20.
S p e c t r o s c o p i c C o n s t a n t s f o r A r - F CO, i n MHz.
Ar-F„C
0
Ar-F2C
18
0
A
6000.3169(30)
5771.5366(187)
B
1523.5196(5)
1507.3088(54)
C
1523.5113(5)
1490.8678(52)
D
J
D
JK
0.009138(6)
0.0089(1)
0.12639(5)
0.1201(1)
-0.1213(6)
-0.1202(48)
70
T a b l e 1-21.
M o l e c u l a r C o n s t a n t s of c a r b o n y l F l u o r i d e .
A(MHz)
11813.5381(18)
B(MHz)
11753.0547(18)
C(MHz)
5880.8992(18)
r
r
o
(C-F)(A)
1.315(19)
(C-O)(A)
1.170(35)
ZJ'CF (degrees)
*Ref. 58.
107.6(23)
71
Figure 1-9.
The s t r u c t u r e of argon-carbonyl f l u o r i d e .
72
73
amu K , c l e a r l y i n d i c a t i n g t h a t t h e complex i s n o n p l a n a r .
The p l a n a r
moment P
This quantity
i s g i v e n by a c y c l i c p e r m u t a t i o n of Eq. ( 1 - 1 6 ) .
d e s c r i b e s the mass l o c a t e d o u t of t h e ac p l a n e .
In the l i m i t that the
c - i n e r t i a l axis i s c o i n c i d e n t with t h e c a r b o n y l g r o u p of F CO, the s o l e
c o n t r i b u t o r s t o P, w i l l be t h e two f l u o r i n e atoms,
P
Since P,
b
=
2m
giving
FbF2 *
(1_48)
i s i n d e p e n d e n t of 9 i n Ar-F„CO, we can e s t i m a t e t h e v a l u e of P,
for cp = 0 from t h e c a r b o n y l f l u o r i d e p a r a m e t e r s m Table 1 - 2 1 .
o
42.7818 amu A .
p
h(0)
=
We t h u s e s t i m a t e t h e angle cp u s i n g t h e r e l a t i o n
P
= P (0)<cos2cp> .
(1-49)
The measured v a l u e of P . , d e r i v e d from the r o t a t i o n a l c o n s t a n t s , i s 4 2 . 1 1 3 6
amu A , which r e s u l t s i n a v a l u e of a r c c o s ( c o s cp)
=7.2°.
Model e r r o r s
in t h i s c a l c u l a t i o n undoubtedly p l a c e a l a r g e e r r o r on t h i s v a l u e , b u t
its
small magnitude l e d us t o b e l i e v e t h a t t h e e q u i l i b r i u m v a l u e of the a n g l e cp
i s t h e o n e s u g g e s t e d by symmetry, cp = 0, which p l a c e s t h e a r g o n atom d i r e c t l y
above t h e a - i n e r t i a l a x i s of F CO.
We w i l l l a t e r show t h a t t h e r o o t - m e a n -
2 1/2
square amplitude of v i b r a t i o n (Acp )
S e t t i n g cp t o zero and f i t t i n g R
is larger than 7.2°.
and 9 t o A, B, and C s i m u l t a n e o u s l y ,
we o b t a i n two s t r u c t u r e s t h a t are c o n s i s t e n t with t h e measured r o t a t i o n a l
c o n s t a n t s of Ar-F^C 0. We o b t a i n R ,. = 3.4016 A, and 9 e i t h e r +10.30° or
2
CM
-10.30°.
of t h e
18
To b r e a k t h i s i n d e t e r m i n a c y , we measured t h e r o t a t i o n a l
constants
O - s u b s t i t u t e d i s o t o p i c s p e c i e s of Ar-F 2 C0, r e p o r t e d i n Table
Again, two s t r u c t u r e s were c o n s i s t e n t with A, B, and C:
0 = - 9 . 5 7 ° ; and R = 3.4103&, 0 = + 1 0 . 8 2 ° .
1-20.
R = 3.3964A
H e r e , R i s t h e d i s t a n c e from
74
the argon atom to the coordinates of the center of mass of the principal
isotopic species of carbonyl fluoride, to provide direct comparison with
R
. The respective positive and negative values of 9 for the two isotopic
species agree almost equally well; for positive 0, R differs from R
by
CM
0.0087$, while in the latter case, the discrepancy is smaller.
0.0052JL.
If we assume that R and 9 are isotopically invariant, then the better
agreement in R should point out the actual vibrationally-averaged position
of the argon atom.
In this case, 9 should take on its negative value,
-10.30°, for the principal isotopic species.
This places the argon atom
closer to the fluorine atoms than to the carbonyl group.
It is important to note that if 9 is taken to be negative in the
above calculations, R < R .,, but R > R .. if 8 is taken to be positive. In
CM
CM
18
the heavier
O-substituted species, the vibrationally-averaged bond length
should be shorter, due to a lessening of vibrational motion.
This is only
true if we take 9 to be -10.30°, and provides an excellent argument for
assigning the negative value to this angle.
Another method of locating the argon atom comes from Kraitchman's
expression,
used m
the study of a similar complex, argon-furan:
2Ur2 = I '-I +1 '-I +1 '-I
,
xx xx yy yy zz zz
(1-50)
where r is the distance from the substituted atom to the molecular center
of mass, the primed moments of inertia are those of the
unprimed moments are those of the
where Am equals m(
18
0 species, the
o species, and
18
16
0)-m( 0\, and M is the mass of the principal isotopic
75
1 fi
s p e c i e s , Ar-F C O.
Using moments of i n e r t i a d e r i v e d from t h e r o t a t i o n a l
c o n s t a n t s of the t w o i s o t o p i c s p e c i e s , from Eq. (1-50) we f i n d
r = 1.8824A.
that
For a s t r u c t u r e with 9 = +10.30° and R .. = 3.4016A, r i s
CM
c a l c u l a t e d to be 1.6670A, w h i l e i n t h e c a s e where 9 = - 1 0 . 3 0 ° , we o b t a i n
r = 2.0089A.
A g a i n , the b e t t e r agreement r e s t s w i t h t h e n e g a t i v e value
o f 0.
The harmonic f o r c e c o n s t a n t s o f Ar-F CO can be o b t a i n e d from t h e
c e n t r i f u g a l d i s t o r t i o n c o n s t a n t s of the complex.
Force constants are
r e l a t e d t o the a s y m m e t r i c - t o p T ' S by Eq. ( 1 - 4 5 ) .
In a vibrational
a n a l y s i s of the ArOCS complex, t o b e d i s c u s s e d in S e c . I I - 3 , i t w i l l be
shown t h a t the v a l u e s of t h e force c o n s t a n t s for t h e van d e r Waals modes
a r e not s i g n i f i c a n t l y a l t e r e d by n e g l e c t of t h e i n t e r n a l modes of OCS.
T h i s i s assumed t o be t r u e h e r e , a s w e l l , s i n c e t h e harmonic force cons t a n t s of carbonyl f l u o r i d e
Waals modes in t h e complex.
are much g r e a t e r than t h o s e of t h e van der
This l e a v e s t h r e e van d e r Waals
c o o r d i n a t e s to be c h a r a c t e r i z e d ,
internal
t h e s t r e t c h between the a r g o n atom and
t h e c e n t e r of mass of c a r b o n y l f l u o r i d e (R_M) ; the bend p a r a l l e l t o t h e
c a r b o n y l group ( 9 ) ; and t h e bend p e r p e n d i c u l a r to t h e c a r b o n y l group (cp).
The T ' S are r e l a t e d t o t h e s y m m e t r i c - t o p d i s t o r t i o n c o n s t a n t s i n
46
Table 1-20 by Eq. (1-46) and the e q u a t i o n s :
D„ =
K
D
-<T
T " TtT
J
4
aaaa
U K + 2 T U U) " < T
aabb
JK
J
K
4
aacc
= >J »
(1-52)
acac
.
= - D - D - T T
D
abab
+2T
(1-53)
aaaa
E q s . ( 1 - 4 5 ) , ( 1 - 4 6 ) , ( 1 - 5 2 ) , and (1-53) a r e used t o f i t t h e d i a g o n a l
e l e m e n t s o f the i n v e r s e f o r c e c o n s t a n t m a t r i x t o t h e measured D_, D , „ , and
U
|JJ\
76
D„.
K
Since there are only three distortion constants available for Ar-F CO,
2
interaction force constants between van der Waals modes are neglected. The
force constants obtained in this manner are presented in Table 1-22.
The vibrational analysis of Ar-F CO was done in the same manner as
that used in the recent study of ArOCS, where the details of the calcula62
tion will be presented.
Briefly, we set up the B matrix,
forms Cartesian coordinates into internal coordinates.
which trans-
From this we cal-
culate the kinetic energy (G) matrix of terms of those internal coordinate.
The B and G matrices lead directly to the derivatives J „
needed in the
c*3
force constant determination. The G-matrix and the force constants allow
one to find the normal frequencies of vibration, which lead in turn to the
2
9
2
mean-square amplitudes of v i b r a t i o n , (AR ) , (A9 ) , and (Acp ) .
All of t h e s e
c a l c u l a t e d parameters appear i n Table 1-22.
Another useful quantity t h a t d e r i v e s from t h e force constant a n a l y s i s
i s e, the depth of t h e p o t e n t i a l well of Ar-F CO.
t h e s t r e t c h i n g force constant f
We c a l c u l a t e e using
and normal frequency \L in t h e same p r o RR
R
cedure used to determine the well depth of furan-HCl (see Sec. I-C). A
comparison of
values of several argon-containing complexes, including
Ar-F CO, is presented m Table 1-23, and is intended only to provide a
qualitative comparison of relative binding strengths.
A structure of the Ar-F„CO complex is nonplanar, with the argon atom
situated above the plane of the carbonyl fluoride molecule.
The line be-
tween the argon atom and the center of mass of F CO makes an angle of -10.3°
with the c-axis of the F„CO molecule; the argon is tipped in the direction
of the fluorine atoms.
striking.
Certain features of this complex are particularly
77
Table 1-22.
Structural and Vibrational Parameters of Ar-F CO.
R (A)
cm
3.4016
9 (degrees)
-10.30
f RR (mdyne/A)
0.02228
f eQ (mdyneA)
0.02005
f
(mdyneA)
cpcp
0.01016
v R (cm
)
36.102
V„ (cm
)
43.230
>
21.517
v
cp(cm
AR
(&)
0.1316
A0
(degrees)
8.12
Acp
(degrees)
rms
8.31
rms
rms
78
Table 1-23.
Bond Lengths and Potential Well Depths for Various Argon
Complexes.
R cm (A)
etcm"1)
ArSO
3.350
390
Ar-Furanc
3.54
236
Ar-ClFd
3.892
226
ArF CO
3.4016
178
ArOCS6
3.7064
176
ArClCNf
3.6490
168
3.325
159
ArC0„h
3.493
143
ATHCl1
3.979
125
ArHF3
3.5095
116
3.42
104
ArBF
ArO
g
k
ArHBr^
4.133
88
Structure and centrifugal distortion information taken from cited references.
b
Ref. 63.
h
Ref. 66.
C
Ref. 60.
^Ref. 6 7 .
d
Ref. 64.
3
Ref. 3 1 .
S
Sec. II-3.
k
Ref. 68.
f
g
Ref. 9.
Ref. 65.
*Ref. 6 9 .
79
It is interesting to note that the root-mean-square deviations in
Table 1-22 account for most of the fitted value of 0 and all of the cp value
determined from P..
This implies that the observed angles are mostly, if
not entirely, attributable to zero-point vibrations from the equilibrium
structure.
Although there is, as yet, no experimental determination of
the equilibrium structure, it is possible that the argon atom is situated
close to a point directly over the F CO center of mass at equilibrium.
A general trend of the complexes listed in Table 1-23 is the tendency
of argon to bind to the most electropositive site of the companion molecule.
The nonplanar structure of Ar-F„CO is consistent with this trend.
Blickensderfer, Wang, and Flygare
70
determined the molecular quadrupole
moments of carbonyl fluoride. They obtained Q = -3.7(7) DA, Q =
xx
yy
0
0
-0.2(5)DA, and Q
on Fig. 1-9.
= +3.9(11)DA, where x, y, and z are the axes shown
The large negative value of Q
is expected because of the
highly electronegative atoms located at either end of the molecule, measured
along the x-axis. Assuming van der Waals radii of 1.35, 1.5, 1.4, and
o
1.88 A for fluorine, carbon, oxygen, and argon, respectively, it is
apparent from Fig. 1-10 that the best approach of the argon atom to the
relatively electropositive carbon atom is from out of plane, rather than
from the side, midway between the oxygen and fluorine atoms. Blickensderfer,
et al, note that the positive sign for Q
indicates that the electronega*—— •
zz
tive oxygen and fluorine atoms effectively dominate the charge in the TT
bond of the carbonyl group.
The sign of the dipole moment of carbonyl fluoride has been calculated
71
using Flygare's atom-dipole model, which correctly reproduces the sign
and magnitude of the dipole moment of the structurally-similar molecule
80
Figure 1-10.
Top view of Ar-F CO, with van der Waals r a d i i
(see text) drawn in.
The dashed l i n e i n d i c a t e s
the van der Waals radius of argon.
81
82
formaldehyde.
71
The calculated dipole moment is + 0.64D, compared to the
experimental value of |0.95D|.
is determined to be +F CO-.
Thus, the polarity of carbonyl fluoride
The structure of Ar-F CO appears to be con-
sistent with this result, as the argon atom would be expected to tend
toward the less negative end of its binding partner.
In addition, the
argon atom experiences less steric hindrance when tipped toward the midpoint between the fluorine atoms than it would if tipped toward the carbonyl group. Thus the measured 0 of -10.3° is fully consistent with the
expected behavior of the argon atom upon complexation.
The results of this study have previously appeared as an article in
the Journal of chemical Physics.
E.
Propyne-HF:
72
Hindered Internal Rotation in a Hydrogen-Bound Complex
The rotational spectrum of the complex between propyne (methyl acetylene) and HF is reported, and the complex characterized, in this section.
The propyne-HF complex provides interesting comparisons with previouslystudied complexes involving hydrogen halides bound to simple hydrocarbons
(acetylene, ethylene, or benzene).
These latter species are all stabilized
by the attractive interaction between the electrophilic hydrogen halide
and the TT-electron density of the unsaturated hydrocarbon.
These previous
examples, involving hydrocarbons of high symmetry, are characterized as
having the HX center of mass located on the C„ or Cr axis of the complex,
with the hydrogen halide underoing a precession about the symmetry axis
as a result of orthogonal large-amplitude degenerate or near-degenerate
bending modes.
In this study, it will be shown that the HF subunit is
not located over the center of the ir-cloud; rather, it is displaced toward
83
the methyl group.
Moreover, the observed spectra exhibit torsional fine
structure characteristic of a low barrier (< 150 cm
) to internal rota-
tion of the methyl top relative to the propyne-HF frame.
As is observed in other HF complexes, the gas mixture is critical to
signal intensities.
Optimum signals were obtained with mixtures of ~1.5%
propyne (Chemicals Procurement Laboratories, 96%) and 0.05% HF (Linde,
99.9%) or DF (KOR Isotopes, 98%) in argon at 12 psi.
The J=0-1 and J=l-2 transitions of both isotopic species of propyne-HF
exhibit torsional splittings and nuclear hyperfine structure in addition
15
to the usual Doppler splittings.
The frequency-averaged line centers
of both the A and E symmetry torsional states along with their assignments
are reported in Table 1-24.
Since the E symmetry torsional states are of
higher energy than A symmetry states, symmetry assignments were made on
the basis of observed intensities, i.e., lines assigned as transitions
between E states were of markedly lower intensity than those assigned as A
symmetry transitions.
We were unable to confidently assign K-prolate/
K-oblate quantum numbers to the J=l-2 E symmetry lines.
It is of interest
to qualitatively compare the observed propyne-HF spectrum with the corresponding transitions in methanol, which may be regarded as a well characterized near-prolate top which also exhibits a low C, barrier to internal
rotation (see Fig. I-ll).
An accurate description of internal rotation must include coupling
with the vibrational modes that affect the interaction of the methyl top
with neighboring atoms.
It has been shown
73
that a rigid internal rotor
Hamiltonian which neglects this coupling fails to reproduce the quantitative torsional splittings in methanol. Moreover, an accurate determination
84
e 1-24.
v
K
l
Frequency-Averaged Line C e n t e r s for Propyne-HF and -DF (MHz).
"*" J i i v i
K K
1 -1
r
<D?)
3
_
Propyne-HF
Observed
0
•*• 1
Calculated
Propyne-DF
Observed
Calculated
6639.57
A
6714.25
E
6755.28
A
12224.82
12252.47
12121.96
12146.27
hi - 202
A
13242.91
13214.04
13126.02
13099.93
Ho - 2 n
A
14525.41
14536.21
14402.87
14411.93
E
13164.73
13066.36
E
13186.98
13092.56
E
13199.55
13148.63
0
00
00
\ l
•+ 1
*
1-2
1-2
1-2
2
01
01
12
6697.19
6652.25
6724.79
00
in
Figure I-ll.
Comparison of methanol (a), propyne-DF (b), and propyne-HF
(c) spectra. Frequencies are m GHz.
J=0 — I
J= l-2
2 Lines
(I T
a)
48.25 48.50 95.75
b)
i
6.50
11
•r
i
7.00
i—•—»
1
p
1""
12.50
13.00
12,00
12.50
13.00
T
7.00
1
96,75
96.75
12.00
c)
6.50
r
T
96.25
96,73
i
i
i
13.50
11
97.75
97.25
13.50
i
14.00
T
r—i
14.00
14.50
r
14.50
J/(GHz)
co
87
of the internal rotor potential requires the observation of b-dipole,
Q-branch transitions.
Kirtman
74
has developed the theory of interaction
of hindered internal rotation with ordinary vibration.
However, this
treatment requires the determination of 8 parameters to describe a-dipole,
R-branch transitions and 12 parameters to describe b-dipole, Q-branch
transitions.
Lees and Baker
75
have succeeded in fitting all 20 of these
parameters to several hundred methanol lines.
In view of the large amplitude vibrational modes common to weakly
bound complexes, the need for including the interaction discussed above
in describing propyne-HF is apparent.
However, no b-dipole transitions
have been identified and only two a-dipole R-branches have been observed
in our experimentally accessible region.
Thus, following Herschbach,
75
we will employ a rigid internal rotor-rigid frame Hamiltonian to determine
inertial constants and to qualitatively characterize the V
barrier from
the observed line centers.
X = 3-Cr + F(p-P)
2
V
3
+ -j- (l-cos3a)
(1-54)
where 3€ is the usual rigid rotor Hamiltonian involving inertial constants
in the principal frame, F is the reducec. rotational constant of the internal
rotor, p-P is the operator describing the relative angular momentum of the
top and the frame, V
is the barrier height, and a is the relative angle
of the top with the frame (see Fig. 1-12).
The second term represents the
kinetic energy of the top relative to the frame and the third term is the
potential energy of the top written as appropriate for a force field with
C, symmetry, i.e., periodic in 2Tf/3.
Since a low barrier was expected m
this case, the Hamiltonian matrix
elements were derived in the prolate symmetric top - free rotor basis
CO
CO
Figure 1-12.
Definition of a and plot of barrier potential.
09
90
|jKMm).
The n o n - z e r o m a t r i x elements of Eq. (1-54)
are:
<JKMm|3C|jKI>lm) = [ (B+C+F32+Fy ) / 2 ] [ J ( J + 1 ) - K 2 ]
(1-55)
2
2
2
+ (a F+A)K +Fm -2FmaK+v / 2 ,
<JKMm|3<:| JKMm±3) = - V 3 / 4 ,
(1-56)
<JKMm|3<:|jK±lMm> = (1/2)F [ a ( 2 K ± l ) - 2 m ] ( $ ± i y ) [ J ( J + 1 ) - K ( K ± 1 ) ] 1 / 2
<JKMm|3C|JK±2Mm> = (1/4) [C-B+F (0+ry) 2 ] [J(J+1)-K(K±1) ]
,
(1-57)
1 / 2
(1-58)
X[J(J+1)-(K±1)(K±2)]
1/2
,
where
F = !l2/2rl
(1-59)
a
r = 1 - I l^gAg
a
and I
g = *,y,z
(1-60)
- KVxz ' B - W 1 , '
Y=
VA
i s t h e moment of i n e r t i a of the t o p about i t s symmetry a x i s , I
(1_61)
is
the moment of i n e r t i a of t h e molecule about the g - p r i n c i p a l a x i s , and \ ,
A , and X a r e the d i r e c t i o n cosines of t h e top a x i s with the x, y and z
y
z
axes r e s p e c t i v e l y .
Although the exact matrix r e p r e s e n t a t i o n of the i n t e r n a l r o t o r Hamiltonian is i n f i n i t e i n the m space, we find that the eigenvalues converge t o
~1 kHz p r e c i s i o n for b a r r i e r s < 150 cm
and truncation in m = ±18.
Diagonalization is g r e a t l y f a c i l i t a t e d by factoring the matrix i n t o the
usual A and E symmetry blocks.
Since propyne-HF has a plane of symmetry
91
(see Fig. 1-13), the A block may be further factored into Al and A2 blocks.
All c a l c u l a t i o n s were c a r r i e d out in double precision on an IBM 4341 or a
VAX 11/780 d i g i t a l computer.
As expected, the A symmetry lines were least s e n s i t i v e to t h e b a r r i e r
height with t y p i c a l 9v/9 (V,) ~ 2MHz/cm
spectrum.
, and e x h i b i t a pseudo r i g i d rotor
However, only a t b a r r i e r heights >150 cm
do t h e E symmetry
l i n e s exhibit a corresponding pseudo-rigid-rotor spectrum giving r i s e to
A and E doublets.
At lower b a r r i e r s , t h e l ( l , l ) - 2 ( 1 , 2 ) E and 1(1,0)-2(1,1)E
lines move i n t o the J=l-2 band o r i g i n .
The view of the observed spectra
(Fig. I - l l ) , we may regard V = 150 cm
as un upper l i m i t to the r o t a -
tional barrier.
Due to t h e neglect of v i b r a t i o n - t o r s i o n coupling and the
f a i l u r e to observe any b-dipole t r a n s i t i o n s , i t i s not possible t o f i t V
to the observed spectrum.
However, we can crudely estimate the b a r r i e r by
f i t t i n g a V t o each p o s s i b l e A-E symmetry pair s p l i t t i n g using a fixed
s e t of optimized r i g i d r o t o r i n e r t i a l constants f o r both i s o t o p i c species.
Averaging the b a r r i e r height over a l l possible p e r n u t a t i o n s of t h e J=l-2
E symmetry assignments y i e l d s V = 100 ± 50 cm .
Since the Hamiltonian matrix elements are s e n s i t i v e t o the d i r e c t i o n
cosines of the top axis with the p r i n c i p a l axes which are in turn dependent on the s t r u c t u r e , i t i s convenient t o f i t the s t r u c t u r a l parameters
d i r e c t l y to t h e spectrum r a t h e r than to f i t the r o t a t i o n a l c o n s t a n t s . We
make the usual assumption t h a t t h e monomer s t r u c t u r e s of Tables 1-6 and
1-25 remain unchanged upon complexation.
A l e a s t squares f i t of the mea-
sured A-symmetry t r a n s i t i o n s of a given isotopic species t o those calculated by the diagonalization of t h e Hamiltonian matrix was carried out
with the c o n s t r a i n t s t h a t V_ = 100 cm
and that t h e HF a x i s b i s e c t s but
92
Figure 1-13.
The p r i n c i p a l i n e r t i a l axes and s t r u c t u r a l parameters
of propyne-HF.
Orthogonal zero-point bending modes
r e s u l t in a precessional motion and a v i b r a t i o n a l l y averaged quadrupole projection operator corresponding
t o the operationally-defined angle y (see Eq. 1-24).
93
94
Table 1 - 2 5 .
M o l e c u l a r S t r u c t u r e and C o n s t a n t s of Propyne.
Z.HCH ( d e g ) a
108.42
^HCC ( d e g ) a
110.50
R(C-H,Me)
(A) a
R(C-H, Acyl)
(&) a
1.4577
R(C=C) ( A ) a
1.2073
B (MHz)b
o
I
Ref. 77.
b
Ref. 78.
1.0602
(A)3
R(C-C)
a
1.1124
a
(Amu & 2 ) C
C a l c u l a t e d from t h e s t r u c t u r e .
8545.8691
3.2822
95
i s not n e c e s s a r i l y perpendicular to the propyne t r i p l e bond.
I t was found
t h a t the c o n s t r a i n t on the HF axis direction d i d not introduce any new
m e r t i a l l y - e q u i v a l e n t s t r u c t u r e s , and, since t h e r o t a t i o n a l constants are
not very s e n s i t i v e t o the l o c a t i o n of the hydrogen atom, t h i s c o n s t r a i n t
has l i t t l e effect on the optimized structure of propyne-HF.
The s t r u c t u r a l
parameters a r e defined in F i g . 1-13 and are g i v e n for both isotopic species
i n Table 1-26.
Table 1-24.
The observed and calculated frequencies are reported in
Reported u n c e r t a i n t i e s in the s t r u c t u r a l parameters are one
standard deviation i n the f i t .
A s i m i l a r s t r u c t u r e may be derived by f i t t i n g the same s t r u c t u r a l
parameters t o effective r o t a t i o n a l constants derived from a pseudo-rigidr o t o r treatment of t h e A symmetry l i n e centers a s i l l u s t r a t e d in Table 1-26.
Since the r i g i d r o t o r treatment t o t a l l y neglects the projection of t h e
methyl top zero point angular momentum on the p r i n c i p a l i n e r t i a l axes, the
corresponding r o t a t i o n a l constants must be regarded as effective c o n s t a n t s .
I t should be noted t h a t the r o t a t i o n a l constants are c o n s i s t e n t with two
p o s s i b l e s t r u c t u r e s , one in which t h e acid p r o t o n is located between the
F-atom and t h e propyne t r i p l e bond and another i n which t h e hydrogen i s
on the opposite side of the F-atom, making i t t n e farther atom of the two
from the t r i p l e bond.
Table 1-27 c l e a r l y i l l u s t r a t e s t h a t only the former
s t r u c t u r e i s consistent with t h e r o t a t i o n a l c o n s t a n t s of both propyne-HF
and propyne-DF.
Only t h e J=0-1 t r a n s i t i o n s e x h i b i t fully resolved nuclear hyperfine
s t r u c t u r e (see Table 1-28).
However, we are o n l y able t o f i t a pseudo-
r i g i d r o t o r , spin-spin and quadrupole Hamiltonian of the form of Eq.
(I-l)
t o the propyne-DF spectrum in which the nuclear quadrupole coupling i n t e r a c t i o n due t o the 1=1 deuterium atom of DF dominates t h e hyperfine s p l i t t i n g .
96
Table 1-26.
S p e c t r o s c o p i c and S t r u c t u r a l P a r a m e t e r s of Propyne-HF.
H i n d e r e d I n t e r n a l Rotor
Propyne-HF
Propyne-DF
P s e u d o - R i g i d Rotor
Propyne-HF
Propyne-DF
A(MHz)
8722(9)
8644(12)
8657
8747
B(MHz)
3919(3)
3886(6)
3932
3896
C(MHz)
2753(1)
2728(2)
2782
2756
v&)
3.07(3)
3.08(2)
3.07(1)
3.06(1)
3(deg)
82(3)
81(3)
81(1)
82(1)
D (kHz)
aa
-23(6)
Y (kHz)
*aa
Y (deg)c
163(6)
Y (deg)
37(1)
34(6)
Values i n p a r e n t h e s e s r e p r e s e n t one s t a n d a r d d e v i a t i o n in t h e
b
c
Effective
constants.
Determined from D
aa
Determined from Y
A
aa
fit.
97
Table 1-27.
D e t e r m i n a t i o n of HF Vector
Assumed S t r u c t u r e
Directionality.
F i t t e d Dis t a n c e
t o F (A)
Propyne-HF
2.97
Propyne-DF
2.97
Propyne-FH
2.88
Propyne-FD
2.80
For t h i s p u r p o s e the HF v e c t o r was assumed to be p e r p e n d i c u l a r t o and
b i s e c t i n g the p r o p y n e t r i p l e b o n d .
98
Table 1 - 2 8 .
N u c l e a r Hyperfine S t r u c t u r e of the 0 Q O -+ 1 Q 1 T r a n s i t i o n s .
Propyne-HF
Propyne-DF
F-+ I 1
F'
Observed(MHz)
C a l c . (MHz)
6714.1762
3 / 2 3/2+3/2
3/2
6652.1558
6652.1560
1
6714.2204
1/2 1/2+1/2
3/2
6652.2229
6652.2258
l-a
2
6714.3025
3/2 3/2->-3/2
5/2
6652.2354
6652.2321
l+l
0
6714.3277
3 / 2 3/2-*-3/2
3/2
6652.2746
6652.2735
1/2 1/2-KL/2
1/2
6652.2895
6652.2908
I
F-+I' F '
1
1->1
1
0
0-^0
1
1
Observed(MHz)
I
99
The hyperfine components of the 0(0,0) - 1(0,1) line of propyne-DF
were f i t allowing the l i n e center, t h e quadrupole coupling constant x
/
33
and the spin-spin coupling constant D
to vary independently.
These
33
transitions are essentially independent of v, -y
, D, ,-D
rt
bb *cc
the off-diagonal elements of the coupling t e n s o r s .
bb
and all of
cc
These calculated
hyperfine components are reported along with the measured l i n e s in
Table 1-28.
The f i t t e d Y
and D
33
a r e reported in Table 1-26.
To i n t e r -
33
p r e t the measured spin-spin and deuterium quadrupole coupling constants,
2
Eq. (1-24) i s invoked, l e t t i n g Y = arccos((cos Y'))
values of Y a r e reported in Table 1-26.
1/2
, as before.
These
The f a i l u r e of the Hamiltonian of
Eq. ( I - l ) to properly reproduce the corresponding spin-spin hyperfine
s t r u c t u r e in propyne-HF may suggest t h e need to include a coupled v i b r a t i o n - t o r s i o n i n t e r a c t i o n term in the Hamiltonian.
Unfortunately, t h e small
number of observed t r a n s i t i o n s precludes such a treatment m t h i s c a s e .
Since propyne-DF is w e l l - c h a r a c t e r i z e d by t h e pseudo-rigid-rotor treatment,
i t seems t h a t such coupling effects are negligible i n this c a s e .
a
borne out by t h e fact t h a t the Y values obtained from x
"d D
33
This is
agree
33
within the stated uncertainties.
The molecular structure of propyne-HF has been determined.
The fitted
structure has the acid proton of HF forming a hydrogen bond with the TTelectron density of propyne and the F-atom displaced from a line perpendicular to and bisecting the propyne triple bond. We feel that the displacement of F towards the methyl group is indicative of a weak hydrogen bonding
interaction between F and the methyl protons.
This idea is further
strengthened when one considers the van der Waals radii of fluorine and
the methyl protons.
As shown in Fig. 1-14 the calculated coordinates for
o
o
Figure 1-14.
Van der Waals contours of the propyne-HF subunits.
101
102
F place it in a position such that its van der Waals radius is nearly in
contact with that of the nearest methyl proton, i.e., in the attractive
region of the Lennard-Jones potential.
The direction of the F displace-
ment may further suggest that the anisotropy of the torsional potential
is dominated by attractive interactions resulting in potential minima
when the methyl protons are eclipsed with the F.
This study may represent the first example of rotational spectra
which exhibit clear evidence of internal rotation in a van der Waals molecule.
Rather large uncertainties in the spectroscopic constants are
primarily due to the model defects discussed above and cannot be improved
upon without a significantly larger data set.
However, the residuals of
the calculated line centers are of the same magnitude as other internal
rotor molecule calculations done at this level of sophistication.
79 80
'
The distance from the H of HF to the center of the triple bond of
propyne fits well in the series R-HF, where R = acetylene, ethylene
and benzene and X = F or Cl, as shown in Table 1-29.
If shorter bond
lengths are taken to indicate higher gas phase Lewis acidity, these complexes demonstrate the expected trend of HF > HCl.
The results of this study have previously appeared as an article
in the Journal of Chemical Physics.
82
Table 1-29. Comparison of Bond Lengths of Propyne-HF and Some Other
Weakly Bound Complexes.
R(H)(A)a
Propyne-HF
2.18
Acetylene-HF
2.19
Ethylene-HFC
2.22
d
Benzene-HF
2.25
Acetylene-HCl
2.41
Ethylene-HCl
2.44
Benzene-HCl g
2.35
a R(H) i s d i s t a n c e from H of HX t o t h e c e n t e r of t h e ir-bond o r
benzene c e n t e r of mass
b
Ref. 1 1 .
C
Ref. 4 3 .
d
Ref. 8 1 .
e
Ref. 29.
f
Ref. 10.
g
Ref. 12.
104
CHAPTER I I
The Rotational Zeeman Effect i n Weakly-Bound Complexes
A.
Introduction
The range of molecular p r o p e r t i e s t h a t could be measured using the
Fourier-transform microwave technique was expanded by the development
of a spectrometer employing a Fabry-Perot cavity placed inside the bore
83 84
of a superconducting solenoid magnet. '
With t h i s instrument, i t b e came p o s s i b l e to measure the r o t a t i o n a l Zeeman e f f e c t i n weakly-bound
complexes, examining the behavior of the r o t a t i o n a l magnetic dipole
moment and the magnetic s u s c e p t i b i l i t y anisotropy upon complexation, as
well as the behavior of those p r o p e r t i e s , e s p e c i a l l y the molecular
quadrupole moment and the second moment of the e l e c t r o n i c charge d i s 85
t r i b u t i o n , which can be derived from them.
The various one-electron
2
p r o p e r t i e s ( ( r ) , ( r ) , e t c . ) and multipole moments are useful in t h e o r e t i cal c a l c u l a t i o n s , both as a i d s in p o t e n t i a l surface modeling,
as a check a g a i n s t the accuracy of the c a l c u l a t i o n .
86 87
'
and
Knowing the behavior
of these p r o p e r t i e s w i l l provide an i n s i g h t i n t o the nature of the weak
binding in these complexes.
Of p a r t i c u l a r i n t e r e s t i s the p o s s i b i l i t y of using the Zeeman e f f e c t
in van der Waals complexes as a means of determining p r o p e r t i e s of nonpolar molecules.
If we can confidently p r e d i c t the g-value, magnetic
s u s c e p t i b i l i t y anisotropy, and quadrupole moment of a complex from knowledge
of these p r o p e r t i e s in the i n d i v i d u a l subunits, then i t follows t h a t we
should be able to determine these p r o p e r t i e s in a nonpolar molecule—which
105
could not be measured by conventional microwave Zeeman spectroscopy—
by complexing it with a polar molecule, and taking the Zeeman spectra
of the complex.
This would provide for interesting comparisons with
go
quantities measured by birefringence techniques
and those determined
from theoretical models. These projection equations will be presented
in both the linear molecule and asymmetric top cases, in Sections B
and C, respectively.
Aside from the complexes to be discussed in this chapter, the rotaQ-}
QA
QA
t i o n a l Zeeman e f f e c t h a s been s t u d i e d i n Ar-HF,
Ar-DF,
Ar-HCl,
89
89
89
90
91
OC-H(D)F,
OC-HC1,
N -H(D)F,
Ar-HBr,
cyclopropane-HCl,
ethylene92
93
94
95
HCl,
acetylene-HCl,
Ne-HCl,
and Ar-HCN.
The s p e c t r o m e t e r ,
intro-
duced i n Ref. 8 3 , and d e s c r i b e d i n d e t a i l i n R e f s . 84 and 9 6 , c o n s i s t s
of a s u p e r c o n d u c t i n g s o l e n o i d magnet w i t h a 1 2 - i n c h b o r e , i n t o which
i s p l a c e d an e v a c u a t e d F a b r y - P e r o t c a v i t y , whose m i r r o r a x i s l i e s
per-
p e n d i c u l a r t o t h e magnetic f i e l d .
is
The p o l a r i z i n g microwave p u l s e
o r i e n t e d i n such a way t h a t i t s e l e c t r i c f i e l d i s p e r p e n d i c u l a r t o t h e
external field,
c a u s i n g s e l e c t i o n r u l e s of |AM| = 1 .
Gas i s p u l s e d i n t o
t h e c a v i t y t h r o u g h a p i e z o e l e c t r i c v a l v e , which sends t h e a x i s o f t h e gas
expansion p a r a l l e l to the magnetic f i e l d .
Large numbers of
c o l d complexes a r e formed i n t h e a d i a b a t i c gas e x p a n s i o n .
p o l a r i z e d by the microwave p u l s e .
rotationally
These a r e
The s u b s e q u e n t c o h e r e n t e m i s s i o n i s
d e t e c t e d by a s u p e r h e t e r o d y n e r e c e i v e r a n d d i g i t i z e d a t 0 . 5 usee p e r
point.
The r e s u l t s of s e v e r a l such p u l s e s a r e a v e r a g e d t o produce a
time-domain s i g n a l , which i s t h e n F o u r i e r t r a n s f o r m e d t o g i v e t h e power
spectrum.
The Zeeman s p l i t t i n g s a r e measured a t more t h a n one m a g n e t i c
f i e l d s t r e n g t h , t o ensure consistency.
These f i e l d s t r e n g t h s a r e
calibrated
106
a g a i n s t t h e J = 0 -*• 1 t r a n s i t i o n of OCS, and c a r r y an u n c e r t a i n t y of
a b o u t 60 G a u s s .
In each c a s e , t h e r o t a t i o n a l t r a n s i t i o n s a r e a l s o
measured on t h e same s p e c t r o m e t e r a t z e r o f i e l d ,
for any s m a l l s y s t e m a t i c s h i f t s
t o properly account
i n t h e frequency measurement.
I n t h i s c h a p t e r , r o t a t i o n a l Zeeman measurements w i l l be d e s c r i b e d
for t h e l i n e a r hydrogen-bound complexes OCO-HF, OCO-DF, OCO-HCl, and
SCO-HF ( S e c . I l - B ) , and t h e van d e r Waals complex ArOCS ( S e c . I I - C ) .
A d d i t i o n a l measurements needed t o augment t h e
analyses—additional
i s o t o p i c s p e c i e s in t h e former c a s e , a d e t a i l e d v i b r a t i o n a l a n a l y s i s
of t h e van d e r Waals modes i n t h e l a t t e r — w i l l a l s o be d i s c u s s e d .
B.
L i n e a r Hydrogen-Bound Complexes: OCO-HF, OCO-DF, OCO-HCl, and SCO-HF
The r o t a t i o n a l Zeeman e f f e c t i n t h e l i n e a r hydrogen-bound complexes
OCO-HF, OCO-DF, OCO-HCl, and SCO-HF i s r e p o r t e d .
34
f i e l d r o t a t i o n a l s p e c t r a of SCO-DF,
13
18 18
0
CO-HCl, and
In a d d i t i o n ,
13
SCO-HF, 0
18
CO-HF,
zero-
18
OC O-HF,
OC O-HCl were t a k e n t o o b t a i n needed i n f o r m a t i o n
t h e m o l e c u l a r s t r u c t u r e s of t h e s e complexes.
about
Klemperer and coworkers
have p r e v i o u s l y r e p o r t e d r o t a t i o n a l s p e c t r o s c o p i c c o n s t a n t s and e l e c t r i c
97
97
97
35
54
37
54
d i p o l e moments f o r OCO-HF,
OCO-DF,
SCO-HF,
OCO-H C l ,
OCO-H C l ,
35
54
and OCO-D C l .
No complexes i s o t o p i c a l l y s u b s t i t u t e d on t h e OCO o r OCS
54 97
s u b u n i t were r e p o r t e d m t h a t e a r l i e r work.
'
The s t u d y of OCO-H(D)F, OCO-HCl, and SCO-HF i s a l o g i c a l
t o t h a t of OC-HF, N„-HF, and OC-HCl.
follow-up
These s i m p l e l i n e a r complexes
p r o v i d e a s t r a i g h t f o r w a r d t e s t of t h e p r o j e c t i o n e q u a t i o n s .
We w i l l show
t h a t t h e r e i s e x c e l l e n t a g r e e m e n t between e x p e r i m e n t and t h e o r y for t h e
molecular g-value.
The m a g n e t i c s u s c e p t i b i l i t y a n i s o t r o p y and m o l e c u l a r
107
quadrupole moment p r o j e c t remarkably well in OCO-HF and OCO-HF. OCO-DF
and SCO-HF behave more e r r a t i c a l l y , but s t i l l within previously e s 89
tablished limits.
Each complex was measured a t magnetic f i e l d strengths
of 25103 and 30098 Gauss, except OCO-HCl, which was measured a t 28113 and
30098 Gauss.
13
13
18 18
18 18
The r o t a t i o n a l spectra of O CO-HF, O CO-HCl,
OC O-HF,
OC 0-HCl,
34
SCO-DF, and
SCO-HF were measured on the Balle-Flygare Fourier-transform
13
microwave spectrometer.
1 Q
13
The sample of O CO (98%) used was obtained
1 Q
from KOR Isotopes;
OC O (90%) came from Stohler Isotope Chemicals.
34
spectrum of
SCO-HF was measured in n a t u r a l abundance.
The
The t r a n s i t i o n s measured in t h i s study were f i t using the following
Hamiltonian:
K =
VV^ss " IT WZ " 7 ?T5 " "F X g iii* (i"2i} '5 •
(II 1)
"
57
3C, i s the r o t a t i o n a l Hamiltonian.
Eqs. (1-6) and (1-35). K
3<L i s the quadrupole Hamiltonian of
i s the spin-spin Hamiltonian of Eqs. (1-4) and
bb
(1-5) .
- •=-D
(Note that the i n t e r a c t i o n constant used here, S , i s equal to
aa
, as defined i n Eq. (1-5).)
These three terms c o n s t i t u t e the
" z e r o - f i e l d " Hamiltonian, and are s u f f i c i e n t t o describe the z e r o - f i e l d
r o t a t i o n a l spectra i n t h i s study.
The r o t a t i o n a l Zeeman effect i s described by the remaining three
terms of Eq. ( I I - l ) .
The f i r s t of these describes the i n t e r a c t i o n of
the r o t a t i o n a l magnetic dipole moment with the e x t e r n a l magnetic f i e l d .
This i n t e r a c t i o n i s characterized by the molecular g tensor, g, which
85 98
is the sum of nuclear and e l e c t r o n i c c o n t r i b u t i o n s :
'
108
g = g
+ ge
(11-2)
0
1
g = m [}z (r 1 - r r ) ] • !
«n
p L a a~
~a~a
«
2m
(II-3)
'
v
<o|L|k>(k|L|o)
3* "1^,1
]
W
'i
(II 4>
•
"
Here, Za i s the atomic number of nucleus a, r~a is the vector Jnoininq
-s
nucleus a to the center of mass of the molecule, m and m are the masses
P
e
of the proton and the electron, respectively, I
i s the inverse moment
of i n e r t i a tensor, L is the t o t a l electronic angular momentum about the
center-of-mass frame, and e
and e, are the energies of the ground
electronic state and the k
electronic excited s t a t e , respectively.
In a linear molecule, the only component of the g tensor that affects
the observed spectrum is g
= (g ht +9
C V2.
The next term in Eq. ( I I - l ) describes the magnetic susceptibility
of the molecule.
X is the magnetic susceptibility tensor, composed of
paramagnetic and diamagnetic p a r t s :
'
X = Xd + XP
d
X
(H-5)
2
e j<0|2rl - rr.|0>
4m c
i
e
2
f'-rrsl 2m c
e
(n-6)
<0|L|k><k|L|0>
k>0
\ o-ek ~
(n-7)
Here, r is the vector joining electron i to the molecular center of
-i
mass, c i s the velocity of l i g h t , and e i s the electronic charge.
Since
the bulk magnetic susceptibility i s rotationally invariant, i t can be
109
f a c t o r e d o u t , l e a v i n g the t r a c e l e s s magnetic s u s c e p t i b i l i t y a n i s o t r o p y
t e n s o r , which has o n l y one i n d e p e n d e n t element i n a l i n e a r m o l e c u l e ,
X | | ~ X , ' where X
an
^ XlI
a r e
tne
magnetic s u s c e p t i b i l i t i e s
perpendicular
t o , and p a r a l l e l t o , t h e p r i n c i p a l a x i s .
The f i n a l term o f Eq. ( I I - l ) d e s c r i b e s t h e i n t e r a c t i o n of t h e
magnetic d i p o l e moment of n u c l e u s 1 w i t h t h e e x t e r n a l magnetic
a.
field.
i s the n u c l e a r s h i e l d i n g t e n s o r , which c h a r a c t e r i z e s t h e e f f e c t s
of
e l e c t r o n i c s h i e l d i n g o f t h e n u c l e u s , and i s a l s o composed of d i a m a g n e t i c
and p a r a m a g n e t i c p a r t s , as i s d e s c r i b e d e l s e w h e r e .
'
In the
analyses
t o f o l l o w , a was h e l d f i x e d , s i n c e i t can only be f i t t e d i n c a s e s of
s t r o n g c o u p l i n g between t h e n u c l e a r s p i n and t h e o v e r a l l
rotational
a n g u l a r momentum of t h e m o l e c u l e .
Using t h i s H a m i l t o n i a n , t h e observed Z e e m a n - s p l i t s p e c t r a were
f i t t e d with a n o n l i n e a r l e a s t - s q u a r e s procedure.
Hyperfine
constants
Cl
such as S , xA , e t c . were h e l d f i x e d a t v a l u e s e s t a b l i s h e d i n p r e v i o u s
aa
aa
54 97
z e r o - f i e l d measurements. '
I n t h i s way, v a l u e s of g and X ~X|| were
o b t a i n e d f o r OCO-HF, OCO-DF, OCO-HCl, and SCO-HF.
Energy l e v e l s for t h e
HF and DF complexes were c a l c u l a t e d by s e t t i n g up t h e H a m i l t o n i a n m a t r i x
i n t h e uncoupled b a s i s and d i a g o n a l i z i n g .
In t h e c a s e of OCO-HCl, w i t h
i t s l a r g e q u a d r u p l e c o u p l i n g , a c o u p l e d b a s i s was u s e d , w i t h t h e Hamiltoni a n c o n s t r u c t e d i n b l o c k s o f M , where
F = I
+ J
.
(II-8)
The Zeeman p a r a m e t e r s a r e r e p o r t e d i n Table I I - l and t h e observed s p e c t r a
f o r t h e above complexes a r e l i s t e d i n Tables I I - 2 - I I - 5 .
In a l l of the
Zeeman f i t s , t h e t r a n s l a t i o n a l S t a r k e f f e c t was n e g l e c t e d , s i n c e i t s c o n 8 3 89
t r i b u t i o n t o our o b s e r v e d s p e c t r a h a s been d e m o n s t r a t e d t o be s m a l l .
'
110
Table I I - l .
S p e c t r o s c o p i c C o n s t a n t s and M o l e c u l a r P r o p e r t i e s
of
OCO-HF, OCO-DF, OCO-HCl, and SCO-HF.
OCO-HF
OCO-DF
1951.16963
1935.99593
D_(MHz)
J
X a a (MHz)
0.010693
0.011213
S
0.10473
B(MHz)
aa
0.26385a
(MHz)
X(10" 9 MHZ/G 2 )°
X
| |(10 _ 9 MHZ/G 2 ) d
X (10"°MHZ/G 2 ) d
1109.886b
1307.4623
0.0046 3 b
0.00246a
-49.573b
0.l05a
0.01384(12) -
0.005808(32) -
0.01002(14)
-1.39(19)
-1.16(10)
-1.45(4)
-2.53(17)
2.2465a
2.30243
1.4509
3.20853
U(D)
Q | I CD*)
SCO-HF
0.01739a
- 0.01393(27) Xl |-X x (10" 9 MHz/G 2 )
OCO-HCl
-11.1(9)
-12.0(5)
-6.3(2)
-7.4(8)
-7.38(4)
-7.38(4)
-10.77(13)
-10.26(4)
-8.30(14)
-8.16(8)
-11.74(13)
-11.94(12)
-6.92(8)
-6.99(5)
-10.29(13)
-9.42(7)
X?|(10" 9 MHz/G 2 )
0.93(68)
0.96(68)
1.15(85)
0.89(85)
137.76(59)
138.62(59)
242.67(74)
206.94(74)
-9.24(69)
-9.12(68)
-12.89(86)
-12.83(86)
- 146.38(60)
-145.62(59)
-259.96(74)
-216.36(74)
(M2> - u 2 > a2)
129.00(92)
128.38(91)
225.80(113)
191.43(114)
<||2>
133.34(65)
132.68(64)
231.86(81)
197.47(80)
4.34(65)
4.30(64)
6.06(81)
6.04(80)
y^dO^MHz/G2)
Xd,(10"9MHz/G2)d
Xd(10_9MHz/G2)d
(X 2 >
(&2)d
(A2)d
'Ref. 97.
Ref. 54.
'Estimated (see t e x t )
Property i s dependent upon the estimated value of \.
Table I I - 2 .
Observed and Calculated Rotational Zeeman T r a n s i t i o n s for
OCO-HF, J=2-K3.a
Observed
(MHz)
F i e l d (G)
M
±Aj
ML
—J
25104
-l
-2
11705.5415
11705.5659
-24.4
-2
-3
11705.5964
11705.5937
2.7
1
0
11705.6234
11705.6438
-20.4
1
2
11706.0802
11706.0988
-18.6
2
3
11706.1284
11706.1267
1.7
-1
0
11706.1492
11706.1768
-27.6
-1
-2
11705.4733
11705.4946
-21.3
-2
-3
11705.5425
11705.5 346
7.9
1
0
11705.5852
11705.6066
-21.4
1
2
11706.1121
11706.1336
-21.5
2
3
11706.1833
11706.1736
9.7
-1
0
11706.2246
11706.2456
-21.0
30098
Calculated
(MHz)
The z e r o - f i e l d t r a n s i t i o n was measured a t 11705.8779(55) MHz.
A (kHz)
Table I I - 3 .
Observed and Calculated Rotational Zeeman T r a n s i t i o n s
for
OCO-DF, J=2-r3. a
Field(G)
M
4J
25104
-1
-2
30098
—J
"I
Observed (MHz)
C a l c u l a t e d (MHz)
A (kHz)
11614.4980
11614.4903
7.7
11615.0221
11615.0201
2.0
- 3 /
1
2
2
3j
^
}
0
-1
11614.4180
11614.4160
2.0
-2
-3
11614.4418
11614.4328
9.0
1
0
11614.5045
11614.5013
3.0
0
1
11615.0497
11615.0512
2
3
11615.0787
11615.0680
10.7
11615.1461
11615.1367
9.4
-1
0
-
1.5
A AF = +1 z e r o - f i e l d t r a n s i t i o n was measured a t 11614.7684(29) MHz.
113
Table I I - 4 .
Observed and C a l c u l a t e d R o t a t i o n a l Zeeman T r a n s i t i o n s
for
OCO-HCl, J=3->4. a
F i e l d (G)
F
28113
9/2
Mr,
-F
p.
—F
Observed (MHz)
C a l c u l a t e d (MHz)
5/2
-
5/2
8875.5188
8875.5263
-
7/2
8876.4092
8876.4070
A(kHz)
-
7.5
7/2
-- 53 // 22
9/2
9/2
1/2
7/2
3/2
8876.6048
8876.6083
-
3.5
9/2
-1/2
11/2
1/2
8876.7031
8876.7091
-
6.0
5/2
3/2
7/2
5/2
8876.9744
8876.9733
1.1
7/2
-3/2
9/2
-
5/2
8877.0697
8877.0644
5.3
7/2
-1/2
9/2
-
3/2
8877.2698
8877.2693
0.5
9/2
-1/2
11/2
-
3/2
8877.3678
8877.3668
1.0
5/2
5/2
7/2
7/2
8877.4425
8877.4493
9/2
3/2
11/2
5/2
8877.5394
8877.5311
5/2
-5/2
7/2
-
7/2
8877.5994
8877.6008
-
7/2
-7/2
9/2
-
9/2
8877.6895
8877.6985
- 9.0
9/2
7/2
11/2
9/2
8877.7332
8877.7224
10.8
9/2
-9/2
11/2
-11/2
8878.1432
8878.1433
-
0.1
5/2
-3/2
7/2
-
5/2
8878.2453
8878.2479
-
2.5
7/2
3/2
9/2
1/2
8878.3257
8878.3284
-
2.7
9/2
9/2
11/2
11/2
8878.3915
8878.3921
- 0.6
5/2
-1/2
7/2
-
3/2
8878.4944
9978.4970
-
2.6
9/2
-7/2
11/2
-
9/2
8878.5602
8878.5643
-
4.1
3/2
1/2
5/2
3/2
8878.8745
8878.8750
- 0.5
9/2
-5/2
11/2
7/2
8878.9273
8878.9297
-
2.4
7/2
7/2
9/2
8879.0376
8879.0377
-
0.1
-
9/2
2.2
-
6.8
8.3
1.4
114
Table I I - 4 ,
30098
Continued
MJ.
Observed (MHz)
C a l c u l a t e d (MHz)
A (kHz)
1/2
8879.7274
8879.7274
0.0
3.1
9/2
1/2
5/2
9/2
1/2
11/2
-
1/2
8879.8212
8879.8181
9/2
-3/2
7/2
-
5/2
8875.5572
8875.5610
7/2
-5/2
9/2
-
7/2
8876.3928
8876.3913
1.5
9/2
1/2
7/2
3/2
8876.5957
8876.5925
3.2
5/2
3/2
7/2
5/2
8876.9674
8876.9661
1.3
7/2
-1/2
9/2
3/2
8877.2361
8877.2290
7.1
5/2
5/2
7/2
7/2
8877.4662
8877.4660
0.2
5/2
-5/2
7/2
7/2
8877.5796
8877.5765
3.1
3/2
3/2
5/2
5/2
8877.9073
8877.9137
-
6.4
9/2
-9/2
11/2
-11/2
8878.1312
8878.1329
-
1.7
5/2
-3/2
5/2
-
5/2
8878.2486
8878.2486
9/2
9/2
11/2
11/2
8878.3986
8878.3992
7/2
1/2
7/2
- V2
8878.5266
8878.5190
7/2
7/2
9/2
9/2
8879.0612
8879.0653
3/2
-1/2
5/2
1/2
8879.7232
8879.7214
1.8
9/2
1/2
11/2
8879.7660
8879.7665
0.5
-
-
-
1/2
Two AF=+1 z e r o - f i e l d t r a n s i t i o n s were measured:
and a t 8878.2794(19) MHz.
a t 8876.8375(19) MHz
-
3.8
0.0
-
0.6
7.6
-
4.1
Table I 1 - 5 .
o b s e r v e d and C a l c u l a t e d R o t a t i o n a l Zeeman T r a n s i t i o n s
for
SCO-HF, J=3->4. a
Field(G)
25104
M'
—J
^
-1
-2
:;}
-3
-4
1
2
:}
3
30098
3
-4
;}
Observed (MHz)
Calculated (MHz)
A(kHz)
10458.8288
10458.8359
-7.1
10458.8768
10458.8694
7.4
10459.2126
10459.2193
-6.7
10459.2592
10459.2528
6.4
10458.7775
10458.7760
1.5
10458.8332
10458.8242
9.0
10459.2335
10459.2357
-2.2
10459.2971
10459.2839
13.2
The z e r o - f i e l d t r a n s i t i o n was measured a t 10459.0772(51) MHz.
116
I n o r d e r t o p r o p e r l y a n a l y z e the r e s u l t s of t h e Zeeman e x p e r i m e n t s ,
d e t a i l e d s t r u c t u r a l i n f o r m a t i o n about t h e complexes had t o be known.
As
97
97
54
mentioned e a r l i e r , p r e v i o u s s t u d i e s of OCO-HF,
OCO-DF,
OCO-HCl,
and
97
SCO-HF
c o n t a i n e d no measurements of complexes w i t h i s o t o p i c s u b s t i t u t i o n
on t h e h e a v i e r component (OCO o r SCO).
T h u s , t h e a n g l e between t h i s sub-
u n i t and t h e a - a x i s i n each complex was i n d e t e r m i n a t e .
This a n g l e
is
e s s e n t i a l f o r p r o p e r c a l c u l a t i o n of p r o j e c t e d Zeeman p a r a m e t e r s , as w i l l
be s e e n i n t h e f o l l o w i n g s e c t i o n .
s p e c t r a for O 13 C0-HF, O 1 3 C0-HCl,
We h a v e measured z e r o - f i e l d
18
18
0C
O - H F , and
34
SCO-HF.
we o b t a i n e d r o t a t i o n a l c o n s t a n t s and h y p e r f i n e c o n s t a n t s .
rotational
From t h e s e ,
We c o n s t r u c t e d
a H a m i l t o n i a n c o n s i s t i n g of t h e f i r s t t h r e e terms i n Eq. ( I I - l ) i n t h e
c o u p l e d b a s i s , I . + l „ = I , I + J = F, i n b l o c k s o f F and d i a g o n a l i z e d .
A l e a s t - s q u a r e s f i t t i n g p r o c e d u r e was l i n k e d t o t h i s c a l c u l a t i o n r o u t i n e ,
e x t r a c t i n g t h e needed c o n s t a n t s , which a p p e a r i n T a b l e I I - 6 .
The measured
l i n e p o s i t i o n s for a l l i s o t o p i c s p e c i e s a p p e a r i n T a b l e s I I - 7 - I I - 1 0 .
Now, t h e r e s u l t s o f the Zeeman e x p e r i m e n t s , and t h e r e l a t i o n between
t h e measured Zeeman p a r a m e t e r s i n the complexes and t h o s e of t h e
s u b u n i t s , w i l l be d i s c u s s e d .
individual
The complexes are a l l assumed t o be l i n e a r
a t e q u i l i b r i u m , with e a c h s u b u n i t u n d e r g o i n g w i d e - a m p l i t u d e b e n d i n g about
i t s equilibrium position.
the e a r l i e r s t u d i e s .
56 97
'
The hydrogen h a l i d e a n g l e s a r e a v a i l a b l e
from
The d e t e r m i n a t i o n of t h e OCO and SCO a n g l e s
w i l l be d i s c u s s e d b e l o w , a f t e r w h i c h t h e s e r e s u l t s w i l l be i n c o r p o r a t e d
i n t o t h e a n a l y s i s of t h e Zeeman d a t a .
The f i r s t
z e r o - f i e l d measurement was t h a t of SCO-DF.
T h i s was done t o
s p e c t r o s c o p i c a l l y c o n f i r m the a t o m i c o r d e r p o s t u l a t e d by B a i o c c h i , e t
The measured l i n e s a p p e a r in T a b l e I I - 7 , a n d the d e r i v e d s p e c t r o s c o p i c
al.
97
Table II-6.
Spectroscopic Constants of SCO-DF, 0
13
18 18
13
18 18
CO-HF,
OC O-HF, 0 CO-HCl,
OC O-HCl, and
34
SCO-HF, all in MHz.
B
SCO-DF
i-a
O CO-HF
1 8 1 R
OC O-HF
~\ 3
O CO-HCl
1290.2167(28)
1939.7749(5)
1870.85244(5)
1099.7833(2)
1059.5772(1)
1277.59298(3)
0.004577(3)
0.004288(2)
0.0023040(7)
-49.586(4)
-49.65(4)
D^
0.0022(2)
X„
0.249(16)
0.01052(2)
0.010031(2)
Tftlfl
OC O-HCl
34.
SCO-HF
O.O.
S
0.101(4)
aa
^i
118
1-7.
Observed and Calculated Zero-field Rotational Transitions
34
for SCO-DF and SCO-HF.
SCO--DF
I_
J'
pi
3/2
3/2
2
3/2
5160 . 6 6 7 4
5160.6698
-2.4
5/2
1/2
2
5/2
5160.7879
5160.7855
2.4
3/2
3/2
2
7/2
5160.7959
5160.7907
5.2
1/2
3/2
2
3/2
5160 . 8 4 6 0
5160.8512
-5.2
7/2
3/2
3
9/2
7741.0548
7741.0578
-3.0
3/2
1/2
3
5/2
7741.0752
7741.0722
3.0
34„„„
-HF ( l i n e
SCO
centers)
7665.3090
0.1
10220.1539
10220.1540
-0.1
12774.7778
12774.7778
0.0
F
•+
O b s e r v e d (MHz) C a l c u l a t e d
7665 . 3 0 9 1
(MHz)
A (kHz)
119
Table I I - 8 .
Observed and C a l c u l a t e d Z e r o - f i e l d R o t a t i o n a l
13
for 0
18
CO-HF and
0
+
i_" J '
13
18
OC O-HF.
CO-HF
Observed (MHz)
pi
I
J
F
0
1
1
0
2
2^
1
1
1
1
2
2 >
1
1
2
1
2
3w
1
1
1
1
2
1
1
2
1
1
3
2"*
0
2
2
0
3
3
1
7758.7643
1
7758.8648
<
Transitions
C a l c u l a t e d (MHz)
A (kHz)
7758.7630
1.3
7758.7630
1.3
7758.7673
-3.0
7758.8638
1.0
11637.5032
7.2
11637.5132
-2.8
11637.5104
1
2
2
1
3
3
11637.5132
-2.8
1
2
3
1
3
4
11637.5156
-5.2
1
3
2
1
4
3*^
11515.5018
2.8
1
3
3
1
4
4
15515.5061
-1.5
>
15515.5046
0
3
3
0
4
4
15515.5061
-1.5
1
3
4
1
4
5
15515.5076
-3.0
18
18
OC
-*•
O-HF ( l i n e
centers)
J'
1
2
7483.0889
7483.0888
0.1
2
3
11224.0312
11224.0313
-0.1
3
4
14964.2517
14964.2517
0.0
120
Table I I - 9 .
Observed and Calculated Zero-field R o t a t i o n a l Transitions
f o r 0 CO--HCl.
J
F
3
9/2
3
5/2
-»•
F'
Observed (MHz)
4
9/2
8785.0764
4
7/2>
J'
>
3
3/2
4
5/2J
3
7/2
4
9/2^
C a l c u l a t e d (MHz)
A(kHz)
8785.0770
-0.6
8796.0279
2.6
8796.0 320
-1.5
8797.4709
2.7
8797.4717
1.9
8796.0 305
8797.4736
3
9/2
4
H/2/
3
7/2
4
7/2
8801.8314
8801.8306
0.8
3
5/2
4
5/2
8808.4224
8808.4201
2.3
4
7/2
5
9/2 -\
10994.9519
-0.8
10994.95 36
-2.5
10995.8050
0.3
10995 .8055
-0.2
•
4
5/2
5
4
9/2
5
10994.9511
7/2 J
11/2^
13/2 J
10995.805 3
4
1/2
5
4
9/2
5
9/2
10999.3116
10999.3117
-0.1
4
7/2
5
7/2
11007.3432
11007.3458
-2.6
5
9/2
6
ll/2*\
13193.0680
0.6
1319 3.0689
-0.3
13193.6361
2.9
1319 3.6 365
2.5
13193.0686
5
7/2
6
9/2/
5
11/2
6
13/2-^
13193.6390
5
13/2
6
15/2/
121
Table 1 1 - 1 0 .
Observed and C a l c u l a t e d Z e r o - f i e l d R o t a t i o n a l
for
J
p
3
5/2
+
J'
4
OC
F'
Transitions
O-HCl.
Observed (MHz)
7/2*\
C a l c u l a t e d (MHz)
A(kHz)
8474.4516
2.3
8474.4558
-1.9
8475.8966
1.1
8475.8975
0.2
10593.0 347
0.3
1059 3 . 0 364
-1.4
10593.8890
-0.4
1059 3.8895
-0.9
12710.8441
0.9
12710.8450
0.0
12711.4130
0.2
12711.4134
-0.2
8 4 7 4 . 4 5 39
3
3/2
4
5/2 J
3
7/2
4
9/2>
8475.8977
3
9/2
4
11/2 J
4
7/2
5
9 / 2 "S
10593.0350
4
5/2
5
7/2 J
4
9/2
5
11/2-N
10593.8886
4
11/2
5
13/2 J
5
9/2
6
ll/2>
12710.8450
5
7/2
6
9/2 /
5
11/2
6
1 3 / 2 >»
12711.4132
5
13/2
6
15/2 J
122
c o n s t a n t s , in Table I I - 6 .
The r o t a t i o n a l constant thus determined was
c l e a r l y more c o n s i s t e n t with the atomic order SCO-H(D)F than H(D)F-SCO,
the only other s t r u c t u r e consistent with the previously-measured dipole
4.
9
7
moment.
Next, we measured the z e r o - f i e l d r o t a t i o n a l spectra of complexes
involving the d i f f e r e n t i s o t o p i c a l l y - s u b s t i t u t e d forms of OCO and OCS
whose s p e c t r a l lines are l i s t e d in Tables I I - 7 - I I - 1 0 , and whose s p e c t r o scopic constants appear in Table I I - 2 .
This was done in order t o obtain
the vibrationally-averaged angle t h a t OCO (or OCS) makes with the p r i n c i p a l
axis.
This information i s necessary for proper comparison of predicted
and measured Zeeman parameters, as w i l l be seen below.
The coordinate
system used in t h i s analysis i s presented in Figure I I - l .
parameters t h a t were f i t are R
and 6.
The s t r u c t u r a l
The expression of B i n terms of
cm
o
a s e r i e s expansion, used in previous s t u d i e s ,
'
proved inappropriate
h e r e , as the heavier OCO and OCS subunits caused the s e r i e s t o converge
much too slowly for p r a c t i c a l a n a l y t i c a l evaluation of a l l the needed
terms.
Instead, moments of i n e r t i a were calculated in a convenient
frame, assuming p l a n a r i t y of v i b r a t i o n a l motion:
2
2
I
= I . s i n 9 + I „ s i n cp
xx
1
2
^
I
= I
yy
+ I 1 cos 2 9 + I„cos2cp
PD
1
2
^
I
= I
zz
II
PD
+ I . + I„
1
2
=
= -I,sin6cos8
-i.sinfjcostj +
+ I„sincpcoscp
l2sincpcoscp
I
=1
xz
= 0
yz
,
(11-10)
(11-11)
(11-12)
(11-13)
(11-14)
H
to
Figure II-l. Coordinate system used to characterize the
structures in this Section.
Y = 0 or S.
/
-Center of Moss
of HX
t
Center of Moss
of Complex
:
CM
125
where I . and I
a r e t h e moments of i n e r t i a of OCO(OCS) and HX, r e s p e c -
t i v e l y , and I
i s d e f i n e d a f t e r Eq. ( 1 - 2 2 ) .
The moment of i n e r t i a
t e n s o r i s d i a g o n a l i z e d by r o t a t i n g by t h e a n g l e a , w i t h t h e r e s u l t :
I
aa
=
T^l3*11
0
+
I
2 s i n °^ ^
+
) +
-
/l+z
( - I . s i n 6 c o s 9 + I-siKpcoscp)
A+z
+ j ( I p D + I 1 c o s 2 9 + I 2 cos 2 cp) (1 - — ^ - )
•kz
I. . = j d - j S i n 6 + I j S i n <p) (1 "
) )/l+Z
+ J^pD-*-1!0032
,
(11-15)
2
•
( - I 1 s i n 9 c o s 9 + I 2 sincpcoscp)
A+z
+ I 2 cos 2 cp) (1 + — — )
,
(11-16)
/l+z
and
^C "
X
PD
+
+
h
h
•
(II
~17)
Here,
z = t a n 2a
- 2 l j S i n 9 c o s 9 + 2I 2 sirepcoscp
2
2
2
2
I., ( s i n 9 - c o s 0) + I_ ( s i n cp-cos cp) - I
(XT-18)
Since
B =
and
^
!
C
=
^
'
ttW9)
126
B Q = j(B+C)
,
(11-20)
the rotational constant is readily determined.
For OCO-HF, the structural determination proceeded as follows: rotational constants were obtained for OCO-HF, O
13
18 18
CO-HF, and
OC O-HF.
Since
structural parameters should be isotopically invariant (the differences
»
in bending amplitudes among the various C0 2 isotopic species should be
small), a single set of R
and 9 values was fitted to the three B values.
cm
o
No corrections were applied to R , as the OCO center of mass is located
cm
on the carbon atom for a l l three s p e c i e s .
cp was held fixed i n t h i s f i t
54 97
a t the value obtained from hyperfine measurements. '
I t s value was
corrected by the determined angle a, and the f i t was run again.
pected, B was r e l a t i v e l y i n s e n s i t i v e t o t h i s parameter.
derived from available spectroscopic measurements.
As ex-
I. and I
were
Known constants for
OCO and OCS which are p e r t i n e n t to t h i s analysis are l i s t e d i n Table 11-11;
the constants of the hydrogen halides appear in Table 11-12.
Structural
parameters of OCO-HF determined in t h i s manner appear in Table 11-13, where
reported e r r o r s c o n s t i t u t e one standard deviation in the f i t .
A similar
procedure was followed for SCO-HF, with the following exceptions-
since
34
the centers of mass of OCS and OC S are not the same, an appropriate
0-dependent correction had t o be added to the f i t t i n g r o u t i n e ; the reported
R i s t h a t of
cm
32
SCO-HF.
Also, no e r r o r s are available for the s t r u c t u r a l
parameters, as the f i t consisted of two unknowns to two equations.
was f i t in the same manner as OCO-HF, but with d i f f e r e n t r e s u l t s .
dependence of B upon R
OCO-HCl
The
and 9 in t h i s case was weak enough t h a t the l e a s t -
squares program was unable t o f i t the parameters.
Iterative calculations
Table 11-11.
Molecular Properties of Isotopic Species of CO- and OCS.
o 13 co
OCO
B(MHz)
11698.2(12)
-0.05508 (5 ) d
XI I-Xx < 1 0 9 MHz/G 2 )
-1.561 (45)
y(D)
0(D£)
f
11698.2(12)
18 18
OC 0
10395.4(11)
OCS
oc 34 s
6081.4949
5932.8354
-0.028839 ( 6 ) 6
-0.028242(10)'
-2.348(3)e
-2.342 ( 5 ) e
0.71521 (20)g
0
- 4 .-3(2)"
-0.786(14)e
a 11 (A3)
3, . 9 5
1
7.691
a x (A 3 )
1 .92 X
3.791
X(10~9MHZ/G2)
Ref. 1 0 1 .
Calculated from
C
Ref. 102.
d
Eef. 103.
e
Ref. 104.
f
Ref. 105.
g
Ref. 106.
h
Kef. 8 8 .
^ e f . 107.
D
Ref. 1 0 8 .
- 5 .23(2)D
B(OCO)
-8.11(2):l
-0.858(23)
128
Table
11-12.
E l e c t r i c a n d M a g n e t i c P r o p e r t i e s o f HF, DF, a n d H C l .
HF
g
l
9
2
X||-XX(10~ MHZ/G )
DF
HCl
0.74104(11
0.3695(50)
0.45935(9)
0.132(6)a
0.132(6)°
-0.048(18)a
740a
<T avg (ppm>
(ff
l|-°A
^H-VH/D
108 ( 9 ) a
1 0 8 (9)
24(9)a
24(9)'
d
300{24)a
21(5)a
P(D)
1.8265d
1.8188
0(DA)
2.36(3)a
2.21(5)"
n(DA2)
1.699g
a,,(A3)
1 1
0.99h
0.99
2.811
0.77h
0.77
2.501
aA (ft3)
X(10"9MHz/G2)
a
Ref. 109.
b
Ref. 110.
- 2 . 1 5 (3)D
'Assumed t o b e t h e same a s i n HF.
Ref. 26.
e
Ref. 50.
f
Ref. 97.
g
Ref. 111.
h
Ref.
112.
Sef.
113.
3
Ref. 114.
1.1086s
3.74(12)a
2.446g
-2.15(3)
•5.54 (13)
j
129
Table 1 1 - 1 3 .
cm
S t r u c t u r a l P a r a m e t e r s o f t h e Complexes i n This
OCO-HF
OCO-DF
OCO-HCl
SCO-HF
3.9620(7)
3.9083b
4.5605b
4.4978
12.0(6)
12.0°
12.0C
8.9
1.9
1.8
1.0
1.9
10.1
10.2
11.0
7.0
25.10s
22.28e
24.95f
6 (deg)
a (deg)
Y
Study.
(deg)d
0C0(S) '
THX(deg)
25.06
R(A)d
2.7234
2.6449
2.5087
3.3726
r(A)d
1.2386
1.2634
2.0518
1.1252
E r r o r s u n a v a i l a b l e J on R
and 9 .
cm
Best R
f o r g3 i v e n 9,
cm
"Assumed (see t e x t ) .
Determined from g i v e n R , 9 ,
3
cm'
"Ref. 9 7 .
Ref.
54.
and Y.
HX"
'
130
showed t h a t the sum of squared residues was smallest a t 9 = 0 , but the
standard deviation on 9 a t t h i s point was very l a r g e .
As a best R
cm
was f i t t o each of the number of possible 6 values, t h i s standard dev i a t i o n was never l e s s than 18°, reaching a minimum a t 6 - 18°.
It
should be noted t h a t the c o r r e l a t i o n c o e f f i c i e n t between R and 9 a t
cm
8
= 0 was very nearly unity, i n d i c a t i n g that these two parameters were
not f i t t i n g independently.
Apparently, t h i s method of determining
from moments of i n e r t i a i s breaking down for OCO-HCl, forcing us t o
estimate t h i s angle by other means. In the study of OC-HF and 0C-HC1,
89
the angles 9 were found to be equal within e r r o r .
We assumed t h a t
t h i s would hold true for OCO complexes, a s w e l l , and s e t 9 equal t o 12.0°
i n OCO-HCl. We then f i t a b e s t R t o 9 and the measured r o t a t i o n a l
cm
c o n s t a n t s , and used t h i s R
H>, to get the angle a.
along with 0 and the previously determined
Thus, we obtained the s t r u c t u r a l parameters of
Table 11-13.
Now we w i l l combine the s t r u c t u r e s derived above with the measured
Zeeman parameters in an attempt to explain these p r o p e r t i e s in terms of
those of the individual subunits.
All equations w i l l be expressed in
terms of the coordinate system presented an Fig. I I - l .
In assessing the contributions of the g values of the two subunits
t o the o v e r a l l r o t a t i o n a l magnetic moment of the hydrogen-bound complex,
c e r t a i n assumptions must be made.
F i r s t , we assume t h a t the wavefunction
of the complex can be factored i n t o separate c o n t r i b u t i o n s from OCO(S)
and HX.
Second, we assume t h a t the molecular properties—both e l e c t r o n i c
and s t r u c t u r a l — of the two subunits are unchanged upon complexation, an
assumption common to work on weakly-bound complexes.
Given these
131
a s s u m p t i o n s , t h e m o l e c u l a r g - v a l u e of t h e complex can be e x p r e s s e d i n
the semi-rigid limit
89
as.
HXTHX,_
2^ .
g x I (1+cos y H X )
gxI =
J
+
OCO(S),OCO(S),. ,
2
.
9X
I
<l+cos y o c o ( s ) >
2
2m
2m
- - ^ pHX<R
,
HX
where g
COSYHX>
OCO(S), ,,HX
, g
' \i
+
. ,,OCO(S)
, and U
T a b l e s 11-11 and 1 1 - 1 2 .
nnnta\
- r ^ y°C0(S)<r cosYoco(s)>
.,
. .
,
(H-21)
-
,
,
a r e the a p p r o p r i a t e f r e e v a l u e s
The e q u a t i o n i s d e f i n e d s u c h t h a t a l l
and d i p o l e moments a r e e n t e r e d as p o s i t i v e n u m b e r s .
from
distances
this
89
e q u a t i o n i n p r e d i c t i n g t h e p r o p e r t i e s of o t h e r hydrogen-bound complexes
e n c o u r a g e s i t s use h e r e .
Since t h e s i g n of g
The s u c c e s s of
i s indeterminate in molecules
w i t h o u t s t r o n g c o u p l i n g of n u c l e a r s p i n t o r o t a t i o n a l a n g u l a r momentum,
t h i s e q u a t i o n i s a s t r a i g h t f o r w a r d way t o d e t e r m i n e t h e s i g n of g
t h e complexes s t u d i e d h e r e .
measured and c a l c u l a t e d g
for
T a b l e 11-14 p r e s e n t s a comparison of
v a l u e s , and shows t h a t t h e r e i s good agreement
between e x p e r i m e n t and t h e o r y i n a l l c a s e s .
S i n c e OCO-HCl h a s a l a r g e
q u a d r u p o l e c o u p l i n g c o n s t a n t , t h e s i g n of g
i s determined d i r e c t l y
t h e Zeeman d a t a .
significant,
g
x
from
T h i s makes t h e good agreement i n OCO-HCl p a r t i c u l a r l y
as i t i n d i c a t e s t h a t t h e s i g n s p r e d i c t e d f o r t h e o t h e r t h r e e
v a l u e s s h o u l d a l s o be c o r r e c t .
The s t r u c t u r e r e p o r t e d i n Table 11-13 and d e s c r i b e d above p r o v i d e d
t h e b e s t agreement i n g
f o r OCO-HCl.
By c o m p a r i s o n , u s i n g t h e
structure
of 9 = 0 and R
= 4 . 5 5 5 6 ^ l e a d s t o a g v a l u e of - 0 . 0 0 6 0 6 , which i s
cm
'l
i n p o o r e r agreement w i t h e x p e r i m e n t .
(More d r a m a t i c a l l y , t h i s
-9
p r o d u c e s a magnetic s u s c e p t i b i l i t y a n i s o t r o p y of - 1 . 6 0 x 10
structure
2
MHz/G ,
Table 11-14.
Comparison Between Measured and Calculated g Values.
g
(expt)
g
J.
(calc)
*Ws)(D)
A
g(calc)
A
OCO-HF
-0.0139(3)
-0.0140
0.0001
0.074
0.3337
-0.0130
-0.0009
OCO-DF
-0.0138(1)
-0.0141
0.0003
0.078
0.359
-0.0130
-0.0008
OCO-HCl
-0.00581(3)
-0.00597
0.00016
0.116
0.191
-0.00597
SCO-HF
-0.0100(1)
-0.0099
0.037
0.419
-0.0095
-0.0001
0.00016
-0.0005
Calculated using Eq. (11-21).
Calculated using Eq. (11-23) or Eq. (11-24).
"Same as a, but with induced dipole effects upon each subunit included.
to
133
which i s a l s o f a r t h e r from the o b s e r v e d v a l u e than t h a t o b t a i n e d from
the assumed s t r u c t u r e . )
assumed 9 .
For OCO-DF, g
was a l s o c a l c u l a t e d from an
The s l i g h t changes i n the DF bond l e n g t h and angle cp
a r e n o t e x p e c t e d t o cause a s i g n i f i c a n t e f f e c t in t h e v a l u e of 9.
Eq. (11-21) d o e s not take induced d i p o l e s i n t o a c c o u n t i n c a l c u l a t i n g
t h e e f f e c t of t r a n s l a t i n g d i p o l e moments upon the m o l e c u l a r g v a l u e .
This
e q u a t i o n o p e r a t e s i n the l i m i t t h a t t h e t o t a l d i p o l e moment of, f o r e x ample, OCO-HF i s e q u a l t o the v e c t o r sum of c o n t r i b u t i o n s from OCO and HF.
Using t h e s t r u c t u r e s of Table 1 1 - 1 3 , t h i s v e c t o r sum i s c a l c u l a t e d
to
be
U = U H F ( C O S Y H F > = 1.654D
The measured d i p o l e moment of OCO-HF
97
(11-22)
i s 2.246D.
Induced d i p o l e moments
were e s t i m a t e d u s i n g a m u l t i p o l e expansion which a c c o u n t s f o r backp o l a r i z a t i o n s from each s u b u n i t onto t h e o t h e r :
HX
md
HXL ,->„„/„*
OCO(S)
o OC0(S)JHX'
2ot
'E
cm
HX 0C0(s)
E
uoco(s)
= a oco(s) [~HX
E x+ 2a -3
ind
) + aHX,( s i n y
z a b i l i t y of HX and a 0 C 0 C S = ^ °
(S)
R
cm
HX
R 6 - 4 a o c o ( s ) 0! J
L. cm
cm
R6_4a0CO(S)
• cm
cm
where a HX = aiHXi<cos y
'"
HX
v i b r a t i o n a l l y - a v e r a g e d p o l a r i z a t o i l i t y o f 0C0(S).
is
+
(11-23)
(11-24)
a J
> , the v i b r a t i o n a l l y - a v e r a g e d
<cos\C0(s)>
due t o OCO(S) a l o n g t h e p r i n c i p a l a x i s
'
polari-
a f ° ( S ) < s i n 2 Y o c o ( s ) ) , the
The e l e c t r i c f i e l d a t HX
134
^C°'S)<-W,>
Eocc,s,
^ ' ^ W s , ^
B
„„,
_
2R*
cm
R
cm
(11-25)
and
EHX
2u H X <cosy
>
HX_
+
30HX(3cos2YHX-l)
HX
R
cm
+
2P. H X <5cos 3 Y
-3cosY p v >
_HX
HX_
2R*
cm
i s the e l e c t r i c f i e l d a t OCO(S) .
_26)
R
cm
y, 0 , and Q, a r e t h e d i p o l e , q u a d r u p o l e ,
and o c t u p o l e moments, r e s p e c t i v e l y .
The i n d u c e d d i p o l e moments
c a l c u l a t e d by t h i s method appear i n Table 1 1 - 1 4 .
t h e z e r o - o r d e r d i p o l e moments ( e . g . , \i
Eq. (11-24) t o g i v e g
(II
b
These were added t o
HX
( c o s Y „ v ) ) , and i n s e r t e d i n t o
HX
values, a l s o l i s t e d i n Table 11-14.
Note t h a t
agreement between t h e o r y and e x p e r i m e n t became p o o r e r i n e v e r y case
where i n c l u s i o n of i n d u c e d d i p o l e s had a s i g n i f i c a n t e f f e c t .
However,
agreement i n a l l c a s e s , w i t h or w i t h o u t i n d u c e d d i p o l e s , i s w i t h i n 0 . 0 0 1 ,
which i s b e l i e v e d t o be t h e l i m i t imposed by a p p r o x i m a t i o n s i n h e r e n t i n
89
the model.
An i m p o r t a n t c o n s i d e r a t i o n h e r e i s the f a c t t h a t induced
d i p o l e moments do n o t completely a c c o u n t for t h e t o t a l d i p o l e moment
o f the complex.
Again u s i n g OCO-HF as a t e s t c a s e , t h e i n d u c e d d i p o l e
moments of OCO and HF from Table 11-14 sum t o 0.411D.
Add t h i s t o
ncn-HP
Eq. (11-22) and y
becomes 2.065D, s t i l l s h o r t of t h e measured v a l u e .
I n t h e i r s t u d y of OCO-HCl,
54
Altman, e t al_., c a l c u l a t e d t h e d i p o l e moment
o f the complex u s i n g a p u r e l y e l e c t r o s t a t i c m o d e l .
f e l l s h o r t of the e x p e r i m e n t a l number by 0.25D.
Their calculated value
They c o n c l u d e d t h a t more
s o p h i s t i c a t e d c a l c u l a t i o n s , p e r h a p s i n c l u d i n g c h a r g e t r a n s f e r , were n e e d e d
135
to account for the observed dipole moment enhancement. In our calculation,
we used the values in Table 11-14, since induced dipoles on the individual
subunits were needed for Eq. (11-21).
The other quantity that we measure in this experiment is the magnetic
susceptibility anisotropy Xl|"X.• Like the molecular g value, we can express this as a sum of projections of the free values of the two subunits:
X| |-XX - |(X| \-XL)m^os\x-l)
+
i( X , |-X x ) O C O ( S ) <3cos 2 Y o c o ( s ) -l>
(11-27)
Again, we assume t h a t the s u s c e p t i b i l i t y a n i s o t r o p i e s of t h e subunits are
unperturbed upon complexation.
Table 11-15 l i s t s observed and c a l c u l a t e d
s u s c e p t i b i l i t y anisotropies for the complexes discussed i n t h i s paper.
P l a i n l y , the agreement between experiment and theory in these cases i s
much more e r r a t i c than i t was for the molecular g value:
m the b e s t
case, OCO-HF, the two agree e x a c t l y , while SCO-HF e x h i b i t s a discrepancy
-9
2
of -0.33 x 10 MHz/G , comparable in magnitude t o t h a t exhibited by Ar-HF
83 84
and Ar-DF. ' The worst agreement previously observed in a hydrogen—9
2
89
bound complex was -0.12 x 10
MHz/G , i n OC-HF.
A l i k e l y source of
e r r o r m the c u r r e n t case i s t h e fact t h a t magnetic s u s c e p t i b i l i t y
anisotropies for t h e H(D)F complexes i n t h i s paper carry standard deviations roughly five times as large as those observed i n OC and N_ complexes.
The molecular
quadrupole moment f o r a l i n e a r molecule can be e x 85
pressed as
II
.
2
4m c
2| i • v - ^ 1 ^ ! i^w - -[fr (x i rxx) '
(II 28)
-
where giii
aa is the product of the molecular g value and moment of inertia
II
along the principal axis. This can be estimated as
136
Table 1 1 - 1 5 .
Comparison Between Measured and C a l c u l a t e d
Susceptibility
Anisotropies for Several
-9
C o m p l e x e s , i n U n i t s o f 10
X[|-Xx(expt)
Magnetic
Weakly-bound
2
MHz/G .
Xu-X^calc)
OCO-HF
-1.39(19)
- 1 .39
0.00
OCO-DF
-1.16(10)
- 1 .38
0.22
OCO-HCl
-1.45(4)
- 1 .51
0.06
SCO-HF
-2.53(17)
- 2 .20
-0.33
OC-HF a
-1.95(5)
- 1 .81
-0.12
OC-DF 3
-1.84(3)
- 1 , .78
-0.06
OC-HCl 3
-1.94(3)
- 1 , .93
-0.01
N -HFa
-1.89(4)
- 1 .88
-0.01
N2-DFa
-1.92(2)
- 1 , .88
-0.04
Ar-HF
-0.26(17)
+ 0 , .05
-0.31
-0.26(15)
+ 0 , .07
-0.33
Ar-HClC
-0.1(1)
- 0 . .02
-0.08
Ar-HBr
-0.13(9)
- 0 . ,05
-0.08
Ar-DF
c
Ref. 8 9 .
Ref. 8 3 .
'Ref.
84.
Ref. 90.
137
g
||raa "
g
HX..HX, , 2
v
OCO(S)„OCO ( S ) , . 2
.
i x < s i n YHX> + 9X
* 'I
' < • « Y0C0(S)>
,
(H-29)
which i s analogous t o the p r o j e c t i o n e q u a t i o n used t o c a l c u l a t e g .
c o n t r i b u t i o n of the g i i i
The
t e r m to t h e c a l c u l a t e d q u a d r u p o l e moment i s
s m a l l i n a l l of the c a s e s s t u d i e d h e r e , making up no more t h a n 4.1% of
Qi I .
The e x c e l l e n t performance of E q . (11-21) encourages t h e b e l i e f
Eq. (11-29) i s a l s o v a l i d .
Combining Eqs. ( 1 1 - 2 1 ) ,
y i e l d s a p r o j e c t i o n e q u a t i o n for Qi
1 JHX.
Q||
=
I Q | |
2
<3COS
- 2UHX<R
Y H X
,.
-1>
COS Y H X >
1
+
that
( 1 1 - 2 8 ) , and (11-29)
89
OCO(S),.,
2
,.
l
'OeoB Yooo(s)-l>
2-Q,|
+ 2u0CO(S)<r c°sY0C0(s)>
•
(""30)
Table 11-16 p r e s e n t s t h e r e s u l t s of a p p l y i n g E q s . (11-28) a n d
(11-29)
the e x p e r i m e n t a l d a t a , along with p r o j e c t e d q u a d r u p o l e moments.
to
I t should
come as no s u r p r i s e t h a t t h e p o o r e s t agreement between the t w o o c c u r s on
OCO-DF and SCO-HF, t h e complexes whose m a g n e t i c s u s c e p t i b i l i t y
p r o j e c t e d most p o o r l y .
dipole e f f e c t s :
anisotropies
Quadrupole moments w e r e a l s o c a l c u l a t e d w i t h induced
t h e q u a l i t y of agreement i n OCO-HF and OCO-HCl was v i r -
t u a l l y unchanged; OCO-DF showed p o o r e r agreement, w h i l e SCO-HF showed improved agreement.
I n a l l c a s e s , the c a l c u l a t i o n w i t h induced d i p o l e s gave
a l e s s n e g a t i v e Q, , t h a n t h e c a l c u l a t i o n w i t h o u t t h e s e
effects.
The quadrupole moment c a n now be combined with known s t r u c t u r a l
formation t o give t h e a n i s o t r o p y of t h e second moment of t h e
distribution:
charge
in-
Table 11-16.
Comparison Between Measured and Calculated Q.i Values, All in D»A.
Q, I (expt)
Qi I ( c a l c )
A
Qi I ( c a l c )
A
OCO-HF
-11.1(9)
-11.4
0.3
-10.9
-0.2
OCO-DF
-12.0(5)
-11.3
-0.7
-10.8
-1.2
OCO-HCl
- 6.3(2)
- 6.5
0.2
-
6.1
-0.2
SCO-HF
- 7.4(8)
- 8.6
1.2
- 7.9
0.5
Calculated using Eq.
(11-30).
Same a s a , b u t w i t h i n d u c e d d i p o l e e f f e c t s
upon e a c h
subunit.
03
139
<a 2 > - ( b 2 ) = V z ( a 2 - b 2 ) + — [ g i i l
a
p
4m c
+ —^~
where a
and b
a
Cx
l |~xi]
-g I ]
'
(n-31)
r e p r e s e n t t h e a- and b - c o o r d i n a t e s of atom a , and g i i l
*|I aa
a
comes from Eq. (11-29).
For a nearly linear molecule, we express this
anisotropy as
<||2> - <X2> = | [ « a 2 ) - <b2>) - «c 2 > - <a2))]
(11-32)
2
2
where ( c ) - ( a ) i s o b t a i n e d from a c y c l i c p e r m u t a t i o n o f Eq.
The e l e m e n t s of the p a r a m a g n e t i c s u s c e p t i b i l i t y t e n s o r a r e
from t h e m o l e c u l a r s t r u c t u r e and g - v a l u e s :
2
9
P
X<
„ "= -~ —
^aa
4m c
e
2
a a aa
m
P
+
»* Kb W - v 4 - <
available
85
r _ , , 2 , 2,
) Z (b + c )
^ a a
a
a
with cyclic permutations for X ? Ka n a X
CD
(11-31).
•
We
CC
and X =
(x
(11-33)
take g
+
= gi| and
clcl
I I
I l b b 4» •
i n o r d e r t o o b t a i n i n d i v i d u a l s e c o n d moments, o r d i a m a g n e t i c s u s c e p t i b i l i t i e s , i t i s n e c e s s a r y t o know t h e bulk s u s c e p t i b i l i t y of
m o l e c u l e , x«
the
T h i s has not b e e n measured f o r weakly-bound s y s t e m s , b u t
can be e s t i m a t e d a s
x0COHF = X 0C0 +
since x i s r o t a t i o n a l l y invariant.
c e s s of Eq. (11-31)
XHF
^
(II
_34)
T h i s e q u a t i o n i s j u s t i f i e d by t h e s u c -
in p r e d i c t i n g magnetic s u s c e p t i b i l i t y a n i s o t r o p i e s
t h e s e and o t h e r s y s t e m s ,
x = 3 ( X a a +X b b +X c c >
= ytX] | + 2 X X ) > so i t c a n be
in
140
combined with the measured magnetic s u s c e p t i b i l i t y anisotropy t o get
X|I and x / which y i e l d the diamagnetic s u s c e p t i b i l i t y tensor elements
when combined with Eq. ( n - 5 ) .
The second moments of the charge d i s -
t r i b u t i o n can then be found by using appropriate l i n e a r combinations of
Eq. ( I I - 6 ) .
All of t h e s e p r o p e r t i e s appear in Table I I - l , with e r r o r s
determined by the standard deviations in measured q u a n t i t i e s , and i n herent e r r o r s in other parameters ( e . g . , molecular s t r u c t u r e ) .
The r o t a t i o n a l Zeeman s p e c t r a of OCO-HF, OCO-DF, OCO-HCl, and SCO-HF
have been presented.
From t h e s e , we have obtained the r o t a t i o n a l magnetic
dipole moment and magnetic s u s c e p t i b i l i t y anisotropy of these complexes.
By measuring r o t a t i o n a l spectra of the i s o t r o p i c species 0 O-HF,
18 18
13
18 18
34
OC O-HF, O CO-HCl,
OC O-HCl, SCO-DF, and
SCO-HF, improved
s t r u c t u r e s for the complexes were obtained.
This allowed the use of
projection equations t o determine whether g
and Xl |"X c °uld be p r e d i c t e d
on t h e basis of the p r o p e r t i e s of the i n d i v i d u a l s u b u n i t s .
Quadrupole
moments were obtained f o r each complex, along with elements of t h e paramagnetic s u s c e p t i b i l i t y tensor.
Using an estimated value of x» the bulk
magnetic s u s c e p t i b i l i t y , we obtained diamagnetic s u s c e p t i b i l i t i e s and
second moments of the e l e c t r o n i c charge d i s t r i b u t i o n .
Some discussion o f the p r o j e c t i o n equations i s in order a t t h i s
point.
In a l l cases, agreement between experiment and theory for g
good,
whether or not induced dipole e f f e c t s are taken i n t o account.
is
Consideration of C o r i o l i s coupling terms proved t o be of c r i t i c a l importance in obtaining good agreement between measured and calculaged g values
84 90
in t h e rare gas-hydrogen halide systems, '
where the HX subunit exhibits
much wider amplitude bending motion than i s the case for the systems
141
studied here. The Coriolis correction takes the form of a factor of
2
(f(cos Y )) in each of the f i r s t two terms of Eq. (1-21), where y equals
YflX
or Y0C0(S) •
Thl S
-
r e s u l t s of Ref. 9 0 .
<f(cos
2
Y „_))
lit
f a c t o r can be e s t i m a t e d for OCO-HF, u s i n g t h e
2
( f ( c o s Y n r r . ) > i s u n i t y t o two s i g n i f i c a n t f i g u r e s w h i l e
^OCO
i s equal to 0.98.
These corrections are negligible and have
been omitted from our g analyses.
The good performance of the g
equa-
tion lends credence t o the b e l i e f t h a t we can e x t r a c t elements of the
g-tensor for nonpolar molecules by complexing them with p o l a r molecules
and studying the Zeeman spectra of the complexes.
Prediction of Xi|"X, proved t o be a b i t more e r r a t i c ; however, t h i s
i s probably due t o problems in the experimental data, r a t h e r than a breakdown i n Eq. (11-27) .
In both OCO-DF and OCO-HF, hyperfine
effects—
deuterium quadrupole coupling and/or nuclear spin-nuclear spin coupling—
which were unresolvable in the Zeeman spectrometer, caused t h e magneticf i e l d - s p l i t l i n e s t o broaden t o the point where d i f f e r e n t |AM | = 1
t r a n s i t i o n s were i n d i s t i n g u i s h a b l e , despite the fact t h a t they are nondegenerate.
In f i t t i n g t h i s d a t a , we had t o assume t h a t we were seeing
an intensity-weighted average of the overlapping l i n e s , those which are
joined by brackets m Tables I I - 3 and I I - 5 .
t a i n t y of the l i n e p o s i t i o n s .
This increases the uncer-
This uncertainty w i l l have l i t t l e or no
effect upon g which i s determined by the s p l i t t i n g s between ±AM
t r a n s i t i o n s ( e . g . , between M = - 1 •*• -2 and M = 1 -»• 2 ) , but i t w i l l
cause e r r o r s in the determination of X||-X » which depends on the t r a n s i tion frequencies r e l a t i v e to zero f i e l d .
Further support for t h i s argu-
ment comes from a comparison of the observed and predicted s u s c e p t i b i l i t y
anisotropies of OCO-HF and OCO-DF.
As the magnetic s u s c e p t i b i l i t y
142
a n i s o t r o p y i s known t o be o r i g i n - i n d e p e n d e n t ,
t i a l l y unchanged between i s o t o p i c s p e c i e s .
Xl |"X, s h o u l d be e s s e n -
The c a l c u l a t e d v a l u e s
Table 11-15 r e f l e c t t h i s ; t h e only d i f f e r e n c e between t h e v a l u e s
caused by t h e s m a l l change i n
Yuv,
going from OCO-HF t o OCO-DF.
in
is
The
HX
measured v a l u e s , however, a r e s u b s t a n t i a l l y d i f f e r e n t :
f a l l s w i t h i n t h e e r r o r b a r s of t h e o t h e r .
neither value
I t should a l s o be n o t e d t h a t ,
d e s p i t e the e r r o r s mentioned h e r e , t h e d i s c r e p a n c i e s between t h e o r y and
e x p e r i m e n t s t i l l s t a y w i t h i n ±3 x 10
Eq. (11-27) s h o u l d p r e d i c t Xi|~X
holds.
t o
MHz/G , so the a s s e r t i o n t h a t
89
t h a t d e g r e e of a c c u r a c y
still
Problems w i t h the q u a d r u p o l e p r o j e c t i o n e q u a t i o n s u r e l y
In
from t h o s e w i t h Xl |~X •
OCO-HF and OCO-HCl, the c a l c u l a t e d q u a d r u p o l e
moment i s l e s s n e g a t i v e t h a n t h e o b s e r v e d v a l u e , which i s
with p r e v i o u s o b s e r v a t i o n s .
arise
89
consistent
I f we assume t h a t the monomer s t r u c t u r e s
are e s s e n t i a l l y unchanged upon c o m p l e x a t i o n , t h e n t h i s b e h a v i o r must be
caused by an enhancement of the a n i s o t r o p y i n t h e second moment o f charge
2
n
d i s t r i b u t i o n , ( | | ) - ( j . ) , over t h e value p r e d i c t e d from the v i b r a t i o n a l l y
averaged v e c t o r sum of c o n t r i b u t i o n s of the two s u b u n i t s .
Given t h e r e p r o d u c i b l e b e h a v i o r of Eqs. (11-21) and (11-31)
for
hydrogen-bound complexes, we are encouraged t o b e l i e v e t h a t they c a n be
used t o d e r i v e t h e magnetic p r o p e r t i e s of n o n p o l a r m o l e c u l e s .
This
t r e a t m e n t i s e x t e n d e d i n t o t h e more g e n e r a l c a s e of asymmetric t o p comp l e x e s i n t h e t r e a t m e n t o f ArOCS, i n Section C, which f o l l o w s .
The r e s u l t s o f t h i s s t u d y have p r e v i o u s l y appeared a s an a r t i c l e
117
in t h e J o u r n a l of Chemical P h y s i c s .
143
C.
ArOCS
In t h i s s e c t i o n , t h e r o t a t i o n a l Zeeman e f f e c t
Waals complex ArOCS i s d e s c r i b e d .
i n the v a n der
The d i a g o n a l e l e m e n t s o f t h e r o t a -
t i o n a l m a g n e t i c d i p o l e moment t e n s o r a r e o b t a i n e d , along w i t h the two
i n d e p e n d e n t magnetic s u s c e p t i b i l i t y a n i s o t r o p i e s .
In a d d i t i o n ,
zero-field
r o t a t i o n a l s p e c t r a of ArOCS were t a k e n t o obtain d e t a i l e d s t r u c t u r a l
v i b r a t i o n a l i n f o r m a t i o n a b o u t t h e complex.
and
H a r r i s , e t a l . , have p r e -
v i o u s l y measured r o t a t i o n a l c o n s t a n t s and e l e c t r i c dipole moments f o r
ArOCS.
work.
118
No c e n t r i f u g a l d i s t o r t i o n i n f o r m a t i o n was i n c l u d e d in t h a t
The t r a n s i t i o n s r e p o r t e d i n the p r e s e n t s t u d y were combined w i t h
t h o s e i n Ref. 118 and o t h e r s measured by t h e Klemperer r e s e a r c h group
t o f i t a complete s e t of c e n t r i f u g a l d i s t o r t i o n c o n s t a n t s .
119
These w e r e
used t o d e t e r m i n e the harmonic force c o n s t a n t s r e l a t e d t o t h e van d e r
Waals bond, w h i c h , i n t u r n , allowed c a l c u l a t i o n o f t h e mean-square
a m p l i t u d e s o f v i b r a t i o n of t h e van der Waals modes and the
r o t a t i o n c o u p l i n g c o n s t a n t s of t h e s e modes.
vibration-
The l a t t e r c o n s t a n t s , once
s u b t r a c t e d from the moments of i n e r t i a , p r o v i d e a s e t of r o t a t i o n a l
c o n s t a n t s from which we d e r i v e a s i n g l e , c o n s i s t e n t p l a n a r s t r u c t u r e .
ArOCS i s t h e f i r s t r a r e gas van der Waals complex for which a l l
components o f t h e m o l e c u l a r g - t e n s o r have been m e a s u r e d .
120 lr
'
three
I n f o r m a t i o n on
g i I i s needed i n t h e l i n e a r r a r e g a s - h y d r o g e n h a l i d e systems m o r d e r
t o o b t a i n Qi i , t h e m o l e c u l a r quadrupole moment, b u t g i i i s
i n a c c e s s i b l e i n these complexes.
experimentally
Since ArOCS i s a n asymmetric t o p ,
it
a f f o r d s t h e o p p o r t u n i t y t o t e s t p r o j e c t i o n e q u a t i o n s in t h r e e d i m e n s i o n s .
I n the a b s e n c e of induced e f f e c t s ,
the magnetic p r o p e r t i e s o f the complex
s h o u l d be t h e r e s u l t of c o n t r i b u t i o n s from the OCS molecule a l o n e .
144
Thus we have an i n d i r e c t v e r i f i c a t i o n of the formulas used t o study the
rare gas-hydrogen h a l i d e s .
We w i l l show t h a t there i s good agreement
between experiment and theory for a l l p r o p e r t i e s , p a r t i c u l a r l y the
molecular quadrupole moments, which p r o j e c t e x t r a o r d i n a r i l y w e l l .
The Zeeman spectra of ArOCS were measured a t f i e l d strengths of
28113 and 29036 G, using the 0 - 1
transitions.
and 1 0 1 - 2 1 2 b-dipole R-branch
These two t r a n s i t i o n s , measured a t two fields apiece,
provided s u f f i c i e n t information to allow us to f i t the three components
of the molecular g-tensor, and the two independent magnetic susceptibility anisotropies.
Fifteen r o t a t i o n a l t r a n s i t i o n s of ArOCS were measured a t zero f i e l d
on the Balle-Flygare Fourier-transform microwave spectrometer. 14 ' 15
measured t r a n s i t i o n s consist of a variety of types:
The
a-dipole R-branch,
b-dipole R-branch, and b-dipole Q-branch.
The t r a n s i t i o n s were f i t using the Hamiltonian of Eq. ( I I - l ) ,
without the hyperfine terms, as ArOCS i s a complex whose nuclei are a l l
spinless .
Since ArOCS i s an asymmetric t o p , a l l three diagonal elements
of the molecular g-tensor—g
aa
, g.. , and g — affect the observed s p e c t r a .
=
c
br>
cc
Ihere a r e also two independent elements of the magnetic s u s c e p t i b i l i t y
anisotropy t e n s o r , 2 X a a -X b b -X c c and 2x b b -X c c -X a a Using t h i s Hamiltonian, t h e observed Zeeman-split spectra were f i t t e d
with a nonlinear least-squares procedure.
The z e r o - f i e l d t r a n s i t i o n s ,
measured on the Zeeman spectrometer, were used as l i n e c e n t e r s .
way, values of g^,
In t h i s
g b b , g c c , 2x a a "X b b -X c o / and 2 X b b -X c c fX a a were obtained
for ArOCS. Energy levels were obtained by s e t t i n g up the Hamiltonian
matrix and diagonalizing.
The Zeeman parameters are reported in
145
Table 11-17, and the observed Zeeman s p e c t r a are l i s t e d i n Table 11-18.
83 89
The t r a n s l a t i o n a l Stark e f f e c t was neglected. '
To supplement the Zeeman a n a l y s i s , we performed an analysis of
the centrifugal d i s t o r t i o n of ArOCS. F i f t e e n r o t a t i o n a l t r a n s i t i o n s
were measured.
These were combined with previously reported l i n e s 118 ' 119
and f i t to the determinable d i s t o r t i o n parameters e s t a b l i s h e d by Watson 47A", B», C", T A , T 2 , T ^ a a a , T » b b b , and T » c c c - using a program w r i t t e n by
48
Kirchhoff.
Since ArOCS is p l a n a r , T could be determined from p l a n a r i t y
c o n d i t i o n s , and was held fixed in the f i t .
T
The four p l a n a r T ' S — b h h b f
i T , , , and T . , — were derived from the determinable parameters,
cccc
aabb
abac
These were used t o perform an analysis of the force field in ArOCS.
The
q u a l i t y of the f i t shows t h a t q u a r t i c c e n t r i f u g a l d i s t o r t i o n terms are
s u f f i c i e n t to c h a r a c t e r i z e ArOCS.
To confirm t h i s , a second f i t was run,
t h i s time including s e x t i c terms in the Hamiltonian.
The quality of the
f i t was not noticeably improved, nor were the previously determined cons t a n t s s i g n i f i c a n t l y changed.
The r o t a t i o n a l t r a n s i t i o n s of ArOCS appear i n Table 11-19.
The
spectroscopic constants determined from t h e s e t r a n s i t i o n s are l i s t e d in
Table 11-17.
To i n t e r p r e t the Zeeman parameters of ArOCS p r o p e r l y , we needed the
most complete s t r u c t u r a l and dynamical information p o s s i b l e .
To obtain
t h i s information, the analysis of ArOCS was conducted in three s t e p s .
F i r s t , we f i t t e d a complete s e t of asymmetric-top d i s t o r t i o n parameters
t o the available r o t a t i o n a l t r a n s i t i o n s , including those obtained i n
118 119
e a r l i e r studies.
'
This procedure i s described below. This cent r i f u g a l d i s t o r t i o n information was then used to e x t r a c t t h e force constants
146
Table
11-17.
Spectroscopic
Constants and Molecular P r o p e r t i e s
of
ArOCS.a
A" (MHz)
6786.4429(12)
B"
(MHz)
1509.9867(4)
C"
(MHz)
1226.9832(3)
T1
(MHz)
-0.3512(2)
T2
(MHz)
-0.0632(1)
T3b
(MHz)
T
aaaa
T
(MHz)
-1.2152(8)
{ m z )
-0.05739(3)
(MHz)
-0.02181(2)
bbbb
T
1.8965(13)
CCCC
3
aa
3
bb
-0.02483(21)
-0.00086(23)
-0.00558(11)
cc
aa-xbb-XCc(10"9MHz/G2)
1.313(32)
Xbb-Xcc-Xaa(10~9MHz/G2)
-3.762(26)
2x
2
Ua(D)C
^
0.2146(10)
0.669(2)
(D)'
1.0(2)
Qaa(DA)
-0.7(4)
2bb(DA)
-0.3(3)
2cc(DA)
X(10~9MHZ/G2)d
X
(10'9MHZ/G2)S
8L3L
-12.95(3)
-12.51(3)
-14.20(3)
Xbb(10"9MHz/G2)e
-12.13(3)
X c c (D
_9
MHZ/G 2 )
Table 11-17, Continued
XL (10"9MHZ/G2)
42.11(102)
aLa.
X^ b (10" 9 MHz/G 2 )
169.39(102)
X^ c (lO _9 MHz/G 2 )
211.37(144)
X = a (10" 9 MHz/G 2 ) e
-54.68(102)
aa
X^ b (10 _ 9 MHz/G 2 ) e
-183.59(102)
x!L(10" 9 MHz/G 2 ) e
-223.50(144)
<a 2 >-<b 2 )
(A2)
121.3(14)
<b 2 >-<c 2 )
(A2)
37.5(10)
<c 2 >-<a 2 >
(A2)
-158.8(10)
<a2>
(A2)S
165.8(10)
<b2> ( £ 2 ) 6
44.5(10)
<c 2 > ( A 2 ) 6
6.9(10)
a.Errors in parentheses constitute one standard deviation m the fit.
b
Held fixed in the fit to rotational data.
C
Ref. 118.
d
E s t i m a t e d (see t e x t ) .
P r o p e r t y i s d e p e n d e n t upon t h e e s t i m a t e d v a l u e of x-
148
Table 1 1 - 1 8 .
o b s e r v e d and C a l c u l a t e d R o t a t i o n a l Zeeman T r a n s i t i o n s
for
ArOCS.
J„
„ -MA. „ .
0
0O^ll
Field(G)
M_
M'
Observed (MHz)
28113
0
-1
8012.4760
8012.4765
-0.5
0
-1
8013.2055
8013.2053
0.2
0
-1
8012.4580
8012.4579
0.1
0
1
8013.2100
8013.2106
-0.6
-1
-2
10465.8756
10465.8784
-2.8
1
2
10466.4737
10466.4775
-3.8
0
-1
10466.2316
10466.2357
-4.1
0
1
10466.6021
10466.6043
-2.2
-1
-2
10465.8622
10465.8601
2.1
1
2
10466.4801
10466.4789
1.2
0
-1
10466.2377
10466.2373
0.4
0
1
10466.6206
10466.6180
2.6
-1
0
10466.435 3
10466.4373
-2.0
29036
1
0l"202
28113
29036
Calculated(MHz)
A(kHz)
Observed and C a l c u l a t e d Z e r o - f i e l d R o t a t i o n a l
Transitions
for ArOCS.
Observed(MHz)
C a l c u l a t e d (MHz)
A(kHz)
7836.3862
7836.3838
2.4
a
8012.9382
8012.9412
-3.0
a
8165.2806
8165.2823
-1.7
a
8956.0769
8956.0746
2.3
a
9324.1778
9324.1818
-4.0
a
10 350.1880
10 350.1924
-4.4
a
10466.3023
10466.3045
-2.2
a
10835.2809
10835.2810
-0.1
a
12441.0161
12441.0274
-11.3
a
12782.0668
12782.0620
4.8
a
14118.9 306
14118.9245
6.1
a
14334.1175
14334.1024
15.1
a
14553.1189
1455 3.1150
3.9
a
14974.4204
14974.4205
-0.1
a
15532.6795
155 32.6936
-14.1
a
Source
0.269
0.269
0
b
1.881
1.880
1
b
7.504
7.503
1
c
11.056
11.055
1
b
22.425
22.424
1
c
150
Table 11-19, Continued
jK K J
-i r ^i K i
3
22
- J3
21
A(kHz)
Source
55.146
55 .146
0
b
282.994
282.994
0
b
11 "
1
10
5
25 "
6
24
748.740
748.740
0
c
12
- 2
"'ii
848.875
848.877
-2
c
13
- 3
22
3919.764
3919 .764
0
c
oi " ho
5559.158
5559.161
-3
b
ho ' hi
5756.015
5756.020
-5
b
2
02 -
2
11
5852.922
5852.925
-3
b
6
16 "
6
15
5912.977
5912.984
-7
c
3
- J3
03
12
6313.939
6313.944
-5
b
4
14 "
3
21
6801.370
6801.373
-3
c
7
25 "
6
34
6887.305
6887.305
0
b
4
04 "
4
13
6965.600
6065.603
-3
c
3
12 "
2
21
7198.725
7198.726
-1
c
8252.066
8252.069
-3
b
10963.287
10963.311
-24
b
11043.852
11043.853
-1
b
4
x
2
20
- J3
21
3
30 "
4
31
3
21 "
4
22
T h i s work.
Ref. 118.
C
C a l c u l a t e d (MHz)
1
2
b
Observed(MHz)
Ref. 1 1 9 .
151
and normal f r e q u e n c i e s of t h e van d e r Waals modes o f ArOCS.
Finally,
t h e r e s u l t s of t h e s e a n a l y s e s were i n c o r p o r a t e d i n t o t h e a n a l y s i s of
t h e Zeeman d a t a .
The s t r u c t u r e of ArOCS was i n i t i a l l y d e t e r m i n e d from t h e d i s t o r t i o n f r e e r o t a t i o n a l c o n s t a n t s p r e s e n t e d i n Table 1 1 - 2 0 .
The d e t e r m i n a b l e
p a r a m e t e r s A", B " , C", T , , T„, T_, T" , T" . , and x"
are fit to
1
2' 3
aaa
bbbb
cccc
t h e o b s e r v e d t r a n s i t i o n s . These a r e used t o d e t e r m i n e t h e K i v e l s o n Wilson p a r a m e t e r s A ' , B ' , C ' , T'
, T' , . , T'
, X' . . , T1
, which
aaaa
bbbb
cccc
aabb
aacc
a r e t h e n used t o o b t a i n t h e d i s t o r t i o n - f r e e r o t a t i o n a l c o n s t a n t s by
standard techniques.
46
.
In the f i t ,
T
I S fixed a t a value determined
by i t s l i n e a r dependence upon t h e o t h e r x's.
(For a g e n e r a l asymmetric
top m o l e c u l e , a t most f i v e o f t h e s i x T ' s a r e l i n e a r l y i n d e p e n d e n t . )
a d d i t i o n , T"
, , T , and T
CCCC
tions.
X
a r e r e l a t e d i n ArOCS due t o p l a n a r i t y
In
condi-
&
As a r e s u l t , t h e f i n a l d i s t o r t i o n - f r e e
rotational constants w i l l
vary a c c o r d i n g t o which two of t h e s e t h r e e T ' s a r e t a k e n a s i n d e p e n d e n t
parameters.
The r e s u l t s of t h i s a n a l y s i s a p p e a r in Table 1 1 - 2 0 .
The m o l e c u l a r s t r u c t u r e was d e r i v e d u s i n g t h e c o o r d i n a t e system i n
F i g u r e I I - 2 and t h e f o l l o w i n g e q u a t i o n s f o r t h e e l e m e n t s of the moment
of i n e r t i a
tensor:
I
= I
xx
X
xy
=
+ l__„ cos cp
OCS
^
PD
I
= I„«
yy
PD
r
zz "
X
zx
=
+
,
(11-35)
!„„«.
OCS
'
(11-36)
OCS sin 2 cp
,
(II-37)
Z
- X 0CS
cosl
^incp
,
(H-38)
152
Table 11-20.
D e r i v e d M o l e c u l a r C o n s t a n t s of ArOCS.
T. and x 2
T
l
and
T
cccc
T* and x
2
cccc
A (MHz)
6786.297
6786.308
6786.310
B (MHz)
1509.885
1509.896
1509.898
C (MHz)1
1226.991
1226.974
1226.970
-1.2152(8)
-1.2152(8)
-1.2152(8)
T
aaaa(MHz)
T
bbbb
(MHZ)
-0.05739(3)
-0.05739(3)
-0.05739(3)
T
aabb
(MHZ)
0.1444(9)
0.1176(4)
0.1176(4)
T
abab
(MHZ)
-0.2587(7)
- 0 . 2 5 38(3)
-0.2317(4)
Al°(amu ft2)
f j ^ (mdyne/A)
f
cpp(mdyne ^ ) _
f^(mydne)"1
2.701
59(38)
35.3(9)
-15(6)
2.709
58(4)
35.0(1)
-11.7(6)
2.711
57.2(5)
34.94(1)
-11.93(7)
Errors in parentheses are one standard deviation in the fit.
This represents the T-free rotational constant.
\
153
Figure I I - 2 .
Coordinate system used t o c h a r a c t e r i z e ArOCS.
154
.M/ArOQS)
C,M.(OCS)
155
I
i s the "pseudodiatomic" moment of i n e r t i a of Eq. (1-22).
For the
purpose of these equations, z l i e s along R, while y i s out-of-plane.
This tensor i s diagonalized to y i e l d values for A, B, and C.
means we f i t R and cp t o p a i r s of A, B, and C.
By t h i s
No s t r u c t u r e was consistent
with A, B, and C simultaneously, due to the large i n e r t i a l defect, about
2.7 amu ft , which i s caused by Coriolis coupling between the van der
Waals vibrations and the o v e r a l l r o t a t i o n of the complex, and w i l l be
d e a l t with below.
The value of R derived from the (A,C) p a i r agrees with
t h a t obtained for the (B,C) p a i r , while the cp values from (A,C) and (A,B)
were equal.
For t h i s reason we chose t o s e t R and cp a t the values obtained
from the (A,C) p a i r .
Thus, R° = 3.7027 ft and cp° = 73.53°.
study, Harris, e t a l . ,
used t r a n s i t i o n s of ArOC
In t h e i r ArOCS
S to confirm t h a t the
s t r u c t u r e with the argon atom closer to the oxygen atom than t o the sulfur
atom i s c o r r e c t .
This molecular s t r u c t u r e was used in the force f i e l d
analysis t h a t follows.
Centrifugal d i s t o r t i o n constants are d i r e c t l y r e l a t e d to the i n t r a molecular force field of the molecule.
Thus, we can obtain the harmonic
force constants of ArOCS from the T's determined above using Elq. (1-45).
For a nonlinear molecule, i and j are summed over a l l 3N-6 v i b r a t i o n a l
degrees of freedom.
In ArOCS, these i n t e r n a l coordinates a r e :
the van
der Waals s t r e t c h between the argon atom and the OCS center of mass (R),
the van der Waals bend along the axis of the OCS molecule (cp) , the CS
s t r e t c h (r ) , the CO s t r e t c h (r ) , the OCS in-plane bend ( 8 , ) , and the OCS
out-of-plane bend ( 6 2 ) .
Many of the techniques i n t h i s analysis are
similar to those used by Keenan, e t a l . , to analyze the ArClCN complex,
but are s e t up in a d i f f e r e n t set of i n t e r n a l c o o r d i n a t e s .
156
Certain assumptions had to be made to carry out this calculation.
We assume that the internal motions of OCS are unchanged upon complexation, and that force constants describing the interactions between them
and van der Waals modes can be neglected.
three parameters (fjy,, f
This leaves us with a f i t of
/ and f" ) to the four equations defined by
the four independent planar T's.
evaluated at equilibrium.
In theory, the J ' s are only valid if
Since the equilibrium structure of ArOCS i s
unknown, we used the vibrationally-averaged structure obtained previously,
along with moments of inertia derived from the rotational constants in
Table 11-20 and OCS force constants in Table 11-21.
If J D is the vector containing the derivatives of component ce$ of
the moment of inertia tensor, then we can write,
J
Q
~0'P
= 2G - 1 Bi a i | 3 X
X
12 3 124
'
,
(11-39)
XX X ~
~8
S
where I i s t h e t r a n s p o s e o f t h e m a t r i x I .
X i s a vector containing
p o s i t i o n v e c t o r components of a l l atoms i n ArOCS.
The B m a t r i x t r a n s f o r m s
C a r t e s i a n c o o r d i n a t e s i n t o i n t e r n a l c o o r d i n a t e s by t h e r e l a t i o n
R = BX
I
62
.
(11-40)
is an auxiliary matrix originally established by Meal and Polo.
(The
x, y, and z axes must be defined consistently throughout this calculation.
To properly relate the J's to the T's, they must also be coincident with
the principal axes of the molecule.)
G
is the kinetic energy matrix in
a
62
terms of the internal coordinates and is defined as
G _1 = g-'W"1
,
(11-41)
157
Table 11-21.
Structure and Force Constants of OCS.
r C Q (A) a
1.5651(9)
r c s (A) a
1.1561(12)
(mdyne/ft)b
f
r
l 1
f
r
7.443(40)
b
(mdyne
ft)
16.14(11)
ft)
1.040(65)
2r2
f
(mdyne
ir2
f (mdyne/ft)
r
,C
0.6513(4)
Fitted to B-values of various isotopic species reported in Ref. 102.
b
Ref. 122.
c
a is the OCS bending angle.
158
where M i s a 3Nx3N matrix whose diagonal elements are the atomic
masses.
Once we have c a l c u l a t e d the J ' s , we can use Eq. (1-45) to f i t the
three inverse van der Waals force constants to the four planar T ' s .
As
we mentioned e a r l i e r , t h e r e are three s e t s of planar x's from the f i t
to the r o t a t i o n a l spectrum.
Thus, we f i t a s e t of inverse force constants
to each s e t of centrifugal d i s t o r t i o n c o n s t a n t s , with the r e s u l t s l i s t e d
in Table 11-20.
We took t h e final inverse force constants to be averages
over the three s e t s , weighted by t h e appropriate standard d e v i a t i o n s .
These appear in Table 11-22.
At t h i s p o i n t , the s i g n i f i c a n c e of t h e OCS i n t e r n a l modes i n the
v i b r a t i o n a l c a l c u l a t i o n s was t e s t e d .
In Section I-C, i t was a s s e r t e d
t h a t inclusion of the force field of furan would not have seriously
affected the determined force constants of the hydrogen bond in furan-HCl.
A second s e t of f i t s for ArOCS were run, t h i s time neglecting contributions of a l l force constants but the van der Waals.
None of the inverse
force constants in t h i s second s e t of f i t s differed from i t s counterpart
in the f i r s t s e t by as much as the s t a t e d uncertainty of the parameter.
Thus we can conclude t h a t v i b r a t i o n s of a r i g i d l y bound subunit have
l i t t l e e f f e c t upon the determination of force constants associated with
a van der Waals bond.
In other words, the vibrations of the covalent
bonds make a negligible c o n t r i b u t i o n to t h e centrifugal
distortion
constants.
Now t h a t we have the force constants of ArOCS, we need to define
the transformation from normal t o i n t e r n a l coordinates
R = LQ
(11-42)
Table 11-22.
V i b r a t i o n a l Force Constants, Normal Frequencies, MeanSquare Amplitudes, and Average Structure of ArOCS.
f R R (mdyne/A)
0.01879
fjpp (mdyne ft)
0.03081
f
0.00642
Hp (mdyne)
^(cm-1)
37.996
V (cm - 1 )
cp
AR
(A)
rms
25.970
0.1406
AJO
(degrees)
^rms
^
5.54
I * (amu ft )
aa
75.0703
I * b ( a m u ft )
337.4323
I * (amu A )
cc
412.5652
R* (A)
3.7064
cp* ( d e g r e e s )
74.17
0* ( d e g r e e s )
110.61
Aa (A)
1.4770
*b <*>
0.1236
6 a (A)
2.2164
6b
0.1855
(ft)
160
s o t h a t we can o b t a i n t h e normal f r e q u e n c i e s of v i b r a t i o n .
t a i n e d by s o l v i n g t h e s e c u l a r e q u a t i o n
L i s ob-
62
GfL = LA
.
(11-43)
The e i g e n v a l u e m a t r i x , A, c o n t a i n s d i a g o n a l e l e m e n t s
A . = X = rt2ch
11
co
1
2
(II
•
"44)
1
i s t h e frequency o f v i b r a t i o n of normal mode i , e x p r e s s e d i n cm
.
The
normal f r e q u e n c i e s o f van der Waals m o t i o n s , o b t a i n e d by s o l u t i o n of
Eq.
( I I - 4 3 ) , appear i n Table 1 1 - 2 2 , and are compared t o those of
complexes i n Table 1 1 - 2 3 .
similar
Table 11-2 3 a l s o p r e s e n t s a comparison of van
d e r Waals w e l l d e p t h s , £ , c a l c u l a t e d u s i n g t h e Lennard Jones 6-12 p o t e n t i a l
method employed e l s e w h e r e m t h i s
thesis.
The normal v i b r a t i o n s can now be used t o c a l c u l a t e the mean-square
a m p l i t u d e s of v i b r a t i o n in t h e i n t e r n a l c o o r d i n a t e scheme by t h e t r a n s formation
<ARAR) = L6£
,
(11-45)
127
where 5 i s a d i a g o n a l m a t r i x whose elements a r e d e f i n e d as
6
**= 6*(0)
=
7JT
•
(I1 46)
"
87T CO
Eq.
(11-46) i s d e f i n e d a t a t e m p e r a t u r e of 0 K, and t h e r e f o r e
t o the v i b r a t i o n a l g r o u n d s t a t e f o r a l l the normal v i b r a t i o n s .
corresponds
The r o o t -
m e a n - s q u a r e a m p l i t u d e s of v i b r a t i o n ,
AR
= <ARAR>1/2
v
rms
*
(11-47)
161
Table 11-23.
Comparison of Force Constants and Normal Frequencies in
ArOCS, ArCO_, and ArClCN.
Ar-OCS
Ar-CO,
Ar-ClCN
f^
(mdyne/A)
0.01879
0.0174b
0.018O7
f
(mdyne A)
0.03081
0.01649C
0.02818
cpcp
fj^p (mdyne)
0.00642
~ (cm
/ " I N)
V
R
37.996
37.5b
35.911
V (cm" )
cp
e(cm )
25.790
38.9 C
26.351
176
143 d
0.00250
168
Calculated using the experimental results of Ref. 9, in the coordinate
system of Fig. II-2 for comparative purposes.
3
Ref. 66.
3
Ref. 126.
Calculated using the results of b and c.
162
are reported i n Table 11-22.
The coupling between the v i b r a t i o n a l and r o t a t i o n a l energies of
the molecule i s described by the Coriolis coupling constants, t,. , (a =
x,y, or z) , which, in t u r n , can be used t o determine the average
s t r u c t u r e of ArOCS, and to estimate the v i b r a t i o n a l contribution to the
i n e r t i a l defect.
To determine the C o r i o l i s constants, we f i r s t define
a transformation from normal coordinates to mass-weighted Cartesian
coordinates
q = M1/2X = X.Q ,
(11-48)
where
X = vrl/2%G-h
•
(11-49)
Given t h i s transformation, the Coriolis matrices are defined by the expres. 125
s i on
Sa = ; f t a *
.
(11-50)
We can now c a l c u l a t e the average moments of i n e r t i a
a
h
=1
o l
3N 6
a "2
I
'
~
V>ar>
•
(11-51)
5
The E are harmonic contributions to the v i b r a t i o n - r o t a t i o n parameters of
s
ArOCS, and d i s the degeneracy of normal mode s .
These v i b r a t i o n - r o t a t i o n
parameters depend only upon harmonic force c o n s t a n t s , molecular geometry,
and atomic masses:
163
j
ir.
V-
\
6h
(har) =
Lao.
4
r,
a ,2
t
1
A
- Z2— I -B - 3 I <W JTZrA
*t */ s
8TTft)c l_
t
,
(H-52)
sJ
where
92I
„aa
A
=
N
aa
_
r ,,-a . 2
— = I - I #7>
3$T
1=1 1 S
. „ _,.
(11-53)
.
The v i b r a t i o n a l c o n t r i b u t i o n t o t h e i n e r t i a l d e f e c t , Al ., , can a l s o
vib
128—130
be c a l c u l a t e d from t h e normal f r e q u e n c i e s a n d t h e C o r i o l i s c o n s t a n t s :
Ai
vib = T V { * i I^ s
2TT C V.s=l
S S'7
2
s'
2 2
(ft) -<0 )
[c^'OXs.-2]*^}Here, M refers to the out-of-plane bending coordinate of OCS.
Al
(11-54)
For ArOCS,
. = 2.65 amu ft , as compared with the experimental value of Al° = 2 . 7 1
s2
amu A
.
Vibration-rotation coupling thus accounts for a l l but 2% of the
measured inertial defect of ArOCS.
For this reason, the average moments
of inertia are the preferred source from which to derive the molecular
structure.
Since Al
= 0.06 amu A , a single planar structure can be f i t
to the I* values, removing the structural indeterminacies introduced by
fitting R andcp to pairs of rotational constants.
The I* values, as well
as the structural parameters derived from them, appear in Table 11-22 and
provide a l l of the i n e r t i a l and structural information used in the analysis
of the Zeeman parameters.
164
We a r e now ready t o a n a l y z e t h e measured Zeeman p a r a m e t e r s o f ArOCS
i n terms of t h e m a g n e t i c p r o p e r t i e s o f OCS, u s i n g t h e s t r u c t u r e
deter-
mined a b o v e , a n d the c o o r d i n a t e system of F i g . I I - 2 .
To d e t e r m i n e t h e c o n t r i b u t i o n o f g
of OCS t o t h e measured g t e n s o r
elements of ArOCS, we must assume t h a t t h e w a v e f u n c t i o n o f ArOCS c a n be
f a c t o r e d i n t o s e p a r a t e c o n t r i b u t i o n s from Ar and OCS, and t h a t t h e e l e c t r o n i c a n d s t r u c t u r a l p r o p e r t i e s of OCS a r e unchanged upon c o m p l e x a t i o n .
Given t h e s e a s s u m p t i o n s , we c a n d e r i v e e x p r e s s i o n s f o r t h e m o l e c u l a r
g - t e n s o r e l e m e n t s in t h e s e m i - r i g i d l i m i t
90
b y a method a n a l o g o u s t o
t h a t u s e d t o show t h e dependence of g on t h e m o l e c u l a r e l e c t r i c d i p o l e
. 131
moment:
Ay
9 I
3
aa a a
g^r.1^.
o
3
0CS
m OCS ,< s i.n 29>n . -,
p
p
g
^b^b
m
p
g
g
c c cc
-£i~=
P
flAr
a
m
=
=
2
A
s nar
e p
Ar
QCSI0CS /
20v ^ 2 A b
<COS
8; +
:
N
m
' m m
p
e p
2 A.
26. .
' '
' '
e)p
b
" I TDT ,< s i. n oX
o c s +, lejb V
2A
a/
e
• '
fiv„
-i—r \COSO>U,.__
A
OCS
a
e
«0| Laf|n>) 2
'
e -e
n>0
o n
.
-
a
Ar
(11-56)
+ -I—r- pU
'
Ar
0CS OCS
c
OCS,. ,
„\. » /
^\ x 2 , b ,,
a « .
(A <sine +A
cose )+
»
'mm - - | I 1 ~ b
> a<
> ]el^ArV^ArSa)
1
1
p
e
p
V
(11 55)
,__
•
(II
c_.
"57)
(1I_5Q)
and m a r e t h e p r o t o n and e l e c t r o n m a s s e s , r e s p e c t i v e l y . A and Ab a r e
d i s t a n c e s along t h e a a n d b a x e s s e p a r a t i n g t h e ArOCS c e n t e r of mass from
t h a t o f OCS, w h i l e <S a n d 5, s e p a r a t e t h e Ar n u c l e u s from t h e c e n t e r of
a
D
mass o f t h e complex. The e q u a t i o n s a r e d e f i n e d such t h a t a l l t r a n s l a t i o n s
Ar
and u „ a a r e e n t e r e d a s p o s i t i v e numbers. L
i s t h e e l e c t r o n i c angular
165
momentum centered about the Ar nucleus.
Note that Eq. (11-58)
refers to argon as it exists in the complex, not in its free state.
OCS
g
ocs
and y
and u
ocs
are the free
values
'
whi e
are induced dipole moments.
i
i
a
= h/4irB0CS.
yAr
In t h e absence of strong coupling
between a nuclear spin and the molecular r o t a t i o n a l angular momentum,
only t h e r e l a t i v e signs of the g-tensor elements can be determined using
plane-polarized r a d i a t i o n .
Eqs. (11-55)-(11-57) can then be used t o fix
the absolute signs of g , g,, , and g .
aa
DD
cc
Table 11-24 presents a comparison of the measured g-values with
those c a l c u l a t e d from Eqs. (11-55)- (11-57) , neglecting terms involving
Ar
A and u . All s t r u c t u r a l parameters were obtained from the average
(I*) s t r u c t u r e as l i s t e d i n Table 11-22.
Both g
•.
aa
and g
exhibit
3
cc
projected values t h a t f a l l within the s t a t e d e r r o r s of the experimental
numbers, while g
shows a discrepancy of about two standard d e v i a t i o n s .
I t is l i k e l y t h a t much of t h i s discrepancy is due to an induced dipole
moment on the argon atom.
This e f f e c t w i l l be discussed a f t e r the
presentation of the projection equations i s complete.
Table 11-24 a l s o contains comparisons between the measured magnetic
susceptibility anisotropies,
2
X a a -X b b -X c c and ^X^-X^X^
and those
calculated by the following equations, which a r i s e when (xi |~X, ) n r q i s
rotated through 9, the angle between the OCS molecule and the a - m e r t i a l
axis of ArOCS:
2X -X bb -X cc = ( X ||-X x ) ocs <3cos 2 e-1>
(11-59)
2
(II
Xbb-Xcc-Xaa * <*| | - V o c S < 3 s i n 2 " ^
2
X cc fX aa -X bb = -CXjl-Xjoca
"60)
C11-61'
Table 1 1 - 2 4 .
Comparison Between Measured and C a l c u l a t e d Magnetic
P r o p e r t i e s of ArOCS.
aa
3
bb
cc
E x p t ' l . Value
C a l c . Value
-0.02843(21)
- 0 .02843
0 .00000
-0.00086(23)
- 0 .00042
- 0 .00044
-0.00558(11)
-0.00552
-0.00006
2
Xaa-Xbb-XCc(10"9MHz/G2)
1.313(32)
1.459
- 0 .146
2
Xbb-Xcc-Xaad0"9MHz/G2)
-3.762(26)
-3.782
0.020
Q a a <° *>
Qbb(D
&)
2cc(D&)
1.0(2)
1.0
0.0
-0.7(4)
-0.8
0.1
-0.3(3)
-0.2
0.1
167
Again, i t i s assumed t h a t (X|i~X ) o c s i s unperturbed upon complexation.
As has generally been the case with weakly bound complexes, the s u s c e p t i b i l i t y a n i s o t r o p i e s e x h i b i t l e s s c o n s i s t e n t agreement between
observed and c a l c u l a t e d values than i s the case for g - v a l u e s .
2xOJ3
K. ~Xcc ~Xaa agrees with i t s c a l c u l a t e d value within e r r o r , while the
-9
observed and c a l c u l a t e d 2x ~XVK"X
values d i f f e r by - 0 . 1 5 x 10
aa OD cc
2
MHz/G . The l a t t e r agreement i s poorer than t h a t observed in a l l
83
hydrogen-bound molecules except OCO-DF and SCO-HF. Only ArHF
and
84
ArDF
show poorer agreement among rare gas-hydrogen h a l i d e s . The
agreement i s nonetheless s t i l l within 11% for 2x
noting that the measured value of 2x
•
-XL.V.~X
I t i s worth
aa DD cc
is more negative than
~Xi.v.~X
3
aa "•bb ^cc
the c a l c u l a t e d v a l u e , which i s c o n s i s t e n t with the phenomenon observed
in a l l rare gas-hydrogen h a l i d e s studied thus f a r .
The molecular
quadrupole moments of an asymmetric top molecule can
132
be expressed as
2
2m c
I I
2aa - - f f r ' W X c c ^ X a a *
1
'
+
S T (Wbb^ao1«f29aa1aa)
P
and c y c l i c permutations for Q . and Q .
(II
"62)
Projection equations for quadru-
pole moments can be obtained by combining Eqs. (11-55)-(11-62), ignoring
induced e f f e c t s :
Q
2
Q
cc
aa = j 2 0 C S < 3 c o s 2 e - 1 > - 2 V s A a < C O s 6 >
bb
=
=
" \
j2ocs<3sin2e-1> " 2»Wb<Bin9>
Q
0CS
+
^OCS <Aa<cos9>
+
Vsin9>)
(II
'
(II
'
•
(II
"63)
"64)
"65)
168
Table 11-24 p r e s e n t s comparisons of ArOCS q u a d r u p o l e moments c a l c u l a t e d
u s i n g Eq.
(11-62) w i t h p r o j e c t e d v a l u e s .
I n a l l c a s e s , agreement
falls
within e r r o r .
Now t h e quadrupole moments can be combined w i t h t h e known s t r u c t u r e
of ArOCS t o c a l c u l a t e the a n i s o t r o p i e s of t h e second moment of t h e e l e c t r o m c charge
distribution:
85
N
<a 2 >-<b 2 > = I Z ( a 2 - b 2 ) + — [g
I -g, , I . . ]
> ' ^ '
*• a a a
m a a a aa y b b bb J
4m c
+
and cyclic permutations.
Z
-TJ2 [Xaa-Xbb]
(II
'
~66)
is the atomic number of a, and x a ~XV,K
can
be calculated from a linear combination of the known magnetic susceptibility anisotropies.
The elements of the paramagnetic susceptibility tensor are
available from the molecular structure and g-values, as seen in
P
Eq. (11-33), with cyclic permutations for yf
and x
p
• To obtain
diamagnetic susceptibilities, or individual second moments of charge
distribution, it is necessary to know the bulk magnetic susceptibility
of the molecule, Ax= T (AX +AX, ,+X )•
3 aa bb ^cc
Tnl
s has not been measured for weakly-
bound systems, but can be estimated as
ArOCS
Ar ^ OCS
+
X
= X
X
/
,
.__ _,,
(11-67)
169
Air
where x
~9
= -4.842 x 10
Table 11-11.
2
MHz/G
nn^
(Ref. 1 3 3 ) , and x
can b e found in
T h e simple addition o f properties occurs because X is
rotationally invariant.
This equation is justified by the success o f
projection equations, such as E q s . (11-59)-(11-61), in this w o r k , i n
X I s combined with the measured
predicting susceptibility anisotropies.
susceptibility anisotropies to get x » X K K »
aa
ijij
and
X » which yield the
cc
diamagnetic susceptibiliity tensor elements w h e n combined with E q . (II-5) .
The second moments of the charge distribution can then be found by using
appropriate linear combinations of Eq. (II-6).
All of these properties
appear in Table 11-17 with errors determined by the standard deviations
in measured quantities, and by uncertainties inherent in other parameters,
such a s molecular structure.
The rotational Zeeman spectrum o f ArOCS has been presented, allowing
determination o f the rotational magnetic dipole moment tensor elements
and the magnetic susceptibility anisotropies.
N e w zero-field rotational
transitions were measured to obtain both an improved structure and centrifugal distortion information.
This led to a calculation of the van
der Waals force constants, normal frequencies, and mean-square amplitudes
of vibration.
From t h i s , w e calculated the Coriolis coupling constants,
which resulted i n an average structure for ArOCS.
This structure w a s
used with a set o f projection equations to determine whether g , g.,,.
a a DD
g
cc'
2
X a a"Xbb"X C c' " ^
2x
bb"Xcc" X aa
COuld
b e
Predicted
from
t h e
properties
of OCS. Molecular quadrupole moments and elements of the paramagnetic
susceptibility tensor were calculated.
Using an estimated value of X/
the bulk magnetic susceptibility, we obtained diamagnetic susceptib i l i t i e s and the second moments of the electronic charge distribution.
170
E a r l i e r , we mentioned t h a t Eqs. (11-55)-(11-57) were derived in
the semi-rigid l i m i t .
This means t h a t the dependence of the g-tensor
elements upon the v i b r a t i o n a l motion of OCS has been neglected.
Con-
s i d e r a t i o n of such effects i s c r i t i c a l l y important i n obtaining good
agreement between measured and calculated g values in the rare g a s 84 90
hydrogen halide systems, '
where the HX subunit e x h i b i t s wide
amplitude bending motions.
For a l i n e a r molecule, t h i s correction takes
the form of a factor of ( f (cos Acp)) (Ref. 90) in the g
of the projection equation for g .
-dependent term
The function f ranges from zero in
the l i m i t i n which HX (or OCS) i s a free r o t o r , to unity in the r i g i d
limit.
In the rare gas-hydrogen halides studied so f a r , Acp ranges from
35 t o 40°, r e s u l t i n g m f values t h a t d i f f e r s i g n i f i c a n t l y from u n i t y .
In ArOCS by c o n t r a s t , the root-mean-square amplitude of vibration of
the OCS subunit from i t s equilibrium configuration has already been e s timated to be 5 . 5 ° .
For the ArHX systems, a 5.5° amplitude corresponds
to an f value t h a t d i f f e r s from unity by l e s s than 0.001 (See Fig. 3,
Ref. 90).
Although the exact form of the Coriolis correction w i l l be
d i f f e r e n t i n the ArOCS system, t h i s comparison does provide a r e l i a b l e
estimate of i t s importance in ArOCS, making i t s correction t o the projection equations n e g l i g i b l e .
analysis.
Thus, t h i s e f f e c t has been omitted from the
The good performance of Eqs. (11-55)-(11-57) supports t h i s
conclusion.
The f a c t t h a t the g-values can be predicted accurately using
Eqs. (11-55)-(11-57) has another important implication.
l i n e a r weakly-bound complexes,
quantity g . . 1
In studies of
83 84 89 90 117
' ' ' '
the operationally-defined
had to be estimated in order to c a l c u l a t e the molecular
171
q u a d r u p o l e moment.
This was done u s i n g t h e e q u a t i o n
RHX—RHX
HX^HX, , 2 A \
giil
= g I < s i n 9>
g
and I
,
_,-.*
(11-68)
a r e t h e m o l e c u l a r g - v a l u e and moment o f i n e r t i a ,
respectively,
J*
of t h e f r e e hydrogen h a l i d e , w h i l e 6, i n t h i s c a s e , d e s c r i b e s t h e
motion o f t h e HX s u b u n i t .
RHX
gii
i s an o p e r a t i o n a l l y - d e f i n e d
chosen f o r i t s u t i l i t y i n c a l c u l a t i n g Q i i •
off-axis
quantity,
Since no e x p e r i m e n t a l l y
determinable g i | I
was a v a i l a b l e , t h e v a l i d i t y o f t h e c a l c u l a t e d v a l u e
had t o be assumed.
With ArOCS, we now s e e t h a t g
of a l i n e a r molecule
j.
does i n d e e d p r o j e c t p r o p e r l y i n a l l t h r e e d i m e n s i o n s , so t h a t our a l g o r i t h m
for c a l c u l a t i n g q u a d r u p o l e moments of l i n e a r weakly-bound complexes
is
correct.
When H a r r i s , e t a l . , measured t h e a and b components of t h e d i p o l e
118
moment of ArOCS,
t h e y found t h a t t h e s e d i d n o t a g r e e w i t h t h e v a l u e s
o b t a i n e d by simple p r o j e c t i o n o f u
_.
This was a t t r i b u t e d t o a combina-
t i o n of z e r o - p o i n t o s c i l l a t i o n a b o u t t h e e q u i l i b r i u m a n g l e and i n d u c e d
d i p o l e s on t h e argon atom.
Since induced dipoles a f f e c t the g-values
of t h e complex, we a t t e m p t e d t o e x t r a c t t h i s i n f o r m a t i o n from E q s .
(11-57).
g
aa
(11-55)-
To t h e number of d i g i t s c a r r i e d i n t h e c a l c u l a t i o n , t h e o b s e r v e d
agrees exactly with the p r e d i c t e d v a l u e .
This suggests t h a t the dipole
moment i n d u c e d on Ar i n t h e b - d i r e c t i o n i s v e r y s m a l l , which i s
by t h e f a c t t h a t t h e e x p r e s s i o n ]j
( s m 9 ) , where 9 i s t h e I
1 1 0 . 6 1 ° , e x a c t l y r e p r o d u c e s t h e measured | i , 0.669D.
supported
v a l u e of
The p o o r e r agreement
of g. . i m p l i e s t h a t t h e induced d i p o l e i n t h e a d i r e c t i o n i s
significantly
l a r g e r . To b r i n g o b s e r v e d and c a l c u l a t e d v a l u e s i n t o e x a c t a g r e e m e n t ,
a
y = - 0 . 1 6 D i s needed. The same c a l c u l a t i o n u s i n g g , assuming
172
b
V.
a
= 0, yields u
= -0.03D.
Plainly, a quantitative determination of
the induced dipole moments is not possible here, but it seems reasonable
to conclude that there is probably a significant dipole moment induced
on argon in the a direction, which is nearly parallel to R, and that it
is aligned along the negative a-axis, pointing toward the OCS molecule.
118
The measured y or ArOCS is 0.2146D,
which is smaller in magnitude
a
than y
(cos9).
It is likely that part of this discrepancy is due to
zero-point oscillation of the OCS molecule from its equilibrium position.
The magnitude of this oscillation can be taken from the mean-square amplitude, Ca>
i which is 5.5°. However, no simple calculation can
r
^rms
presently account for the observed y . First, the equilibrium angle
a
between the OCS molecule and the a-axis is unknown, although it probably
falls between 9*-Acp
(105.1°) and 9*+Acp
(116.1°). Second, Acp
T
rms
rms
rms
is too small to account for a change of more than 1% in y . This is cona
s i s t e n t with the e x c e l l e n t agreement between measured and p r o j e c t e d values
Ar
of y , . Third, the magnitude of the induced y
i s unknown, since the
multipole expansion of t h e moments of OCS f a i l s t o converge a t R = 3.7064
Ar
and 9 = 110 .61°, and the determination of y
from the molecular g-values
a
is inconsistent.
Since charge transfer is not included in these calcula-
tions, and the effect of oscillation along the van der Waals stretch
(AR
=0.14A)
upon the molecular dipole moment is unknown, further conclu-
sions about the cause of the discrepancy in y are not feasible at this
a
time.
I t has been noted t h a t the magnetic s u s c e p t i b i l i t y a n i s o t r o p i e s agree
l e s s well than molecular g-values i n r a r e gas complexes, a trend which
173
continues in this study.
Attempts have been made to explain this dis-
crepancy in terms of contributions from the quadrupole polarizability of
84
argon,
and from a susceptibility anisotropy induced on the argon atom
by an interaction of the argon electrons with the squared electric field
99 134
of its binding partner. '
These effects are both small; combined,
they are expected to contribute less than 15% of the observed difference
between projected and experimental values.
It is important to note that
the molecular quadrupole moments calculated using this anisotropy are in
excellent agreement with the results of Eqs. (II-63)-(II-65), discrepancies in g . and 2x
~Xhb~X
notwithstanding.
It seems that the
enhancement in the quadrupole moments observed in hydrogen-bound
systems
90 117
'
and attributed to perturbations upon the anisotropies of
the second moments of charge distribution are not significant in this
case.
The r e s u l t s of t h i s study have previously appeared as an a r t i c l e
in the Journal of Chemical Physics.
129
174
CHAPTER III
Rotational Spectra and Molecular Structures of
Mercury-Containing van der Waals Complexes
Using a High-Temperature Molecular Source
A.
Introduction
In order to expand the range of species that may be studied using
the Fourier-transform microwave technique, a high-temperature nozzle
system has been developed.
Prior to this, the apparatus was limited to
the study of materials which were gases (or high-vapor-pressure liquids)
at room temperature.
The heated nozzle system allows study of weakly-
bound complexes involving low-boiling liquid substances.
The motivation
for adding high-temperature capability to the Fabry-Perot, Fouriertransform spectrometer was partly provided by the thesis work of Dr.
»
1 O
I
3 5
Paul Soper.
The experiments in Chapter III were carried out in the large136
throughput cavity originally developed for Stark-effect measurements,
which has a higher pumping speed than the original Balle-Flygare instrument.
The pulsed-nozzle system was modified as follows.
The standard General
Valve model 8-14-900 pulsed solenoid valve was modified to incorporate
a new valve stem and reservoir, as shown in Fig. III-l.
The reservoir is
wrapped with heating tapes that are controlled by Variac transformers outside the cavity, allowing heating to temperatures of approximately 250°C.
We set this as an upper limit to ensure that the Viton seal at the nozzle
orifice would be able to maintain a gas tight seal.
The temperatures of
of the reservoir and valve were monitored using chormal-alumel thermocouples.
175
Figure III-l.
High-temperature pulsed molecular source used in this
study.
(1) General Valve model number 8-14-900
solenoid valve body; (2) Copper tubing to carry cooling
water; (3) Extended plunger; (4) Varian flange, sealed
by a copper O-ring; (5) Liquid mercury within the
heated reservoir; (6) Nozzle opening.
The Viton plug
at the end of the plunger forms a vacuum seal with a
raised lip around this opening.
wrapped with heating tape.
The reservoir is
Ar, HX Gas Inlet
177
At 250°C, enough mercury i s in the vapor phase that complexes can form
with the HCl introduced through the normal gas-handling system.
Cold
water i s passed through the copper tubing wrapped around the upper valve
stem, preventing mercury vapor from reaching the General valve, and
allowing us t o use t h i s valve body without high-temperature modification.
The valve stem, plunger, and r e s e r v o i r are a l l constructed of type 302
s t a i n l e s s s t e e l , and the length of the plunger was corrected to account
for the thermal expansion of t h i s m a t e r i a l .
Once we have added mercury l i q u i d to the r e s e r v o i r , heating t h e
reservoir t o roughly 250°C, and allowed the system t o e q u i l i b r a t e , we can
take spectra in the manner described i n Section I-A.
The study of HgHCl
d i f f e r s from those i n Chapter I—and from t h a t of HCNHg—in t h a t a data
averaging system designed by Mr. D. B. Wozniak 137 and interfaced with an
LSI-11 minicomputer was used in place of the system i n t e r f a c e d with the
Chemistry Department's VAX-11/780 computer.
The s t u d i e s of HgHCl and HCNHg, in Sections I I I - B and I I I - C , respect i v e l y , mark the f i r s t pure r o t a t i o n a l spectra of weakly-bound complexes
involving a metal atom.
The mercury atom possesses
completely-filled
atomic o r b i t a l s , and the element behaves much like a r a r e gas in t h e vapor
phase.
Thus, i t w i l l be i n t e r e s t i n g t o compare the behavior of mercury
upon complexation w i t h polar molecules with t h a t of r a r e gases such as
argon and krypton.
I t w i l l also be p o s s i b l e to determine, from the measure-
201
ment of
Hg quadrupole coupling c o n s t a n t s , t o derive an empirical e s -
timate of t h e Sternheimer shielding constant
not p r e v i o u s l y measured.
of mercury, a quantity
This a n a l y s i s w i l l appear a s Section I I I - D .
F i n a l l y , in Section I I I - E , there w i l l be a discussion of other p o s s i b l e
uses for the heated nozzle system.
178
B.
HgHCl
The rotational spectra of sixteen isotopic species of the van der
Waals complex between mercury and hydrogen chloride have been assigned.
Complexes of
and
Hg (10% abundance),
Hg (17%),
Hg (23%),
Hg (30%),
204
35
35
Hg (7%) with H Cl and D Cl have been studied, as have complexes
204
37
of the above mercury isotopes (except
the J = 3 -+• 4 rotational transitions for
Hg) with H
Cl. In addition,
HgH
HgD
Cl and
Cl have
been measured, in order to determine the nuclear quadrupole coupling
201
constant of
Hg for these complexes. Four J -*- J + 1 transitions have
been measured for each mercury complex with H
Cl except for
Two transitions each were measured for
Cl and
HgH
HgH
HgH
Cl.
Cl.
The
isotopic assignments of these transitions were confirmed by measuring the
198
37
199
37
J = 6 ->- 7 transitions of
HgH Cl and
HgH Cl. Three J ->• J + 1
35
transitions were measured for each mercury complex with D Cl, with the
. 201 u 35„,
exception of
HgD Cl.
HgHCl is similar m
Waals complexes ArHCl,
structure to the previously reported van der
KrHCl, '
and XeHCl.
'
Given these
similarities, we will compare several properties of HgHCl with those of
rare gas-hydrogen halide complexes, including the harmonic force constants
describing the stretch of the weak bond and the bending motion of the HX
subunit, and the effective van der Waals radius for the rare gas or
mercury atom.
Moreover, it will be shown that an angular potential model
previously developed to analyze angular information in the rare gas144
hydrogen halide systems
does a good job of predicting angular expectation values for both HgHCl and HgDCl.
179
The t r a n s i t i o n s measured i n t h i s study were f i t using t h e following
Hamiltonian:
3C = JCR + K^ 1 + K g g
.
'
(III-l)
KDx\ i s t h e r o t a t i o n a l Hamiltonian for a l i n e a r molecule, including c e n t r i f ugal d i s t o r t i o n . 57 K Cl i s the quadrupole Hamiltonian of Eq. (1-6).
Due
to the r e l a t i v e l y large values of the r o t a t i o n a l quantum number, J , for
the measured t r a n s i t i o n s , deuterium quadrupole coupling and nuclear spinnuclear spin coupling i n the HCl subunit did not have a measurable effect
upon the observed s p e c t r a .
Calculated t r a n s i t i o n frequencies were obtained by diagonalizing the
Hamiltonian matrix in blocks of F, where
; • i c i + hg
F = I + J
(II1
'
,
~2)
(III-3)
and I „ , and I „ a r e t h e r o t a t i o n a l a n g u l a r momenta of t h e c h l o r i n e and
~C1
~Hg
*
mercury n u c l e i , r e s p e c t i v e l y .
The observed t r a n s i t i o n s were f i t
using
t h i s p r o c e d u r e coupled w i t h a l e a s t - s q u a r e s f i t t i n g program t h a t f i t s
the
r o t a t i o n a l c o n s t a n t i , t h e c e n t r i f u g a l d i s t o r t i o n c o n s t a n t D_, and t h e
o
Cl
J
chlorine nuclear quadrupole coupling constant x • In the case of the
201
Cl
Hg species, D and X
were held fixed at values estimated from the
J
behavior of these parameters in the other isotopic species, and B and
Ha
X
were determined in the fit.
The observed transitions of all isotopic species of Hg-HCl are listed
in Table III-l except for the
separately in Table III-2.
201
Hg-substituted species, which appear
In both tables, frequencies calculated
180
Table I I I - l .
Observed and C a l c u l a t e d T r a n s i t i o n F r e q u e n c i e s for HgHCl.
Isotopic Species
198
HgH35cl
J •+ JJ_
3
5
6
7
199
HgH 3 5 Cl
3
5
6
7
200„ ,,35,,.
HgH Cl
3
5
6
4
6
7
8
4
6
7
8
4
6
7
2F -> 2F'
Observed (MHz)
C a l c u l a t e d (MHz)
A (kHz)
5,3
7,5
8006.4365
8006.4366
-0.1
7,9
9,11
8007.6088
8007.6099
-1.1
12008.8624
12008.8639
-1.5
11,13 13,15
12009.3238
12009.3261
-2.3
11,9
13,11
14009.1350
14009.1333
1.7
13,15 15,17
14009.4695
14009.4645
5.0
13,11 15,13
16008.7351
16008.7403
-5.2
15,17 17,19
16008.9932
16008.9899
3.3
9,7
11,9
5,3
7,5
8000.2921
8000.2922
-0.1
7,9
9,11
8001.4660
8001.4659
0.1
11999.6520
11999.6520
0.0
11,13 13,15
12000.1139
12000.1143
-0.4
11,9
13,11
13998.3889
13998.3894
-0.5
13,15 15,17
13998.7207
13998.7207
0.0
13,11 15,13
15996.4620
15996.4659
-3.9
15,17 17,19
15996.7207
15996.7156
5.1
9,7
11,9
5,3
7,5
7994.2165
7994.2179
-1.4
7,9
9,11
7995.3904
7995.3907
-0.3
11990.5399
11990.5412
-1.3
11,13 13,15
11991.0037
11991.0032
0.5
11,9
13,11
13987.7619
13987.7610
0.9
13,15 15,17
13988.0925
13988.0922
0.3
9,7
11,9
181
Table I I I - l .
Continued
Isotopic Species
J •*• J '
7
2 0 2 „ „35„,
HgH Cl
3
5
6
7
204
HgH35cl
3
5
6
7
198
199
37
HgH Cl
HgH37Cl
6
8
4
6
7
8
4
6
7
8
7
2F ->• 2 F '
Observed (MHz)
C a l c u l a t e d (MHz)
A (kHz)
13,11 15,13
15984.3205
15984.3206
-0.1
15,17 17,19
15984.5691
15984.5702
-1.1
5,3
7,5
7982.2356
7982.2378
-2.2
7,9
9,11
7883.4083
7983.4099
-1.6
11972.5753
11972.5757
-0.4
11,13 13,15
11973.0380
11973.0374
0.6
11,9
13,11
13966.8064
13966.8052
1.2
13,15 15,17
13967.1360
13967.1362
-0.2
13,11 15,13
15960.3743
15960.3764
-2.1
15,17 17,19
15960.6249
15960.6258
-0.9
9,7
11,9
5,3
7,5
7970.4859
7970.4886
-2.7
7,9
9,11
7971.6584
7971.6604
-2.0
11954.9558
11954.9551
0.7
11,13 13,15
11955.4182
11955.4166
1.6
11,9
13,11
13946.2539
13946.2504
3.5
13,15 15,17
13946.5844
13946.5811
3.3
13,11 15,13
15936.8896
15936.8884
1.2
15,17 17,19
15937.1345
15937.1377
-3.2
11,9
13,11
13380.2079
13,15 15,17
13380.4690
11,9
13,11
13369.4659
13,15 15,17
13369.7289
9,7
11,9
182
Table I I I - l .
Continued
I s o t o p i c Species
2F -*• 2F'
200„ „37_.
HgH Cl
202
HgH
3
6
7
199„ „ 3 5 _
HgD Cl
C a l c u l a t e d (MHz)
A (kHz)
13,11
13358.8405
13358.8389
1.6
13,15 1 5 , 1 7
13359.0997
13359.1005
-0.8
13,11 15,13
15265.6920
15265.6931
-1.1
15,17 17,19
15265.8925
15265.8902
1.3
11,9
13,11
13337.8842
13337.8835
0.7
13,15 15,17
13338.1442
13338.1425
1.7
1 3 , 1 1 15,13
15241.7553
15241.7516
3.7
15,17 17,19
15241.9459
15241.9467
-0.8
11,9
37 ,
Cl
198„ „ 3 5 „
HgD Cl
Observed (MHz)
J
3
6
7
4
7
8
4
7
8
5,3
7,5
7867.9867
7867.9836
3.1
7,9
9,11
7869.4092
7869.4178
-8.6
11,9
13,11
13767.4368
13767.4300
6.8
13,15 15,17
13767.8453
13767.8349
10.4
13,11 15,13
15732.6663
15732.6826
3.5
15,17 17,19
15732.9952
15732.9880
7.2
9
9
7851.0066
7851.0071
-0.5
5,7
3,5
7861.8309
7861.8275
3.4
7,9
9,11
7863.2518
7863.2522
-0.4
11,9
13,11
13756.6599
13756.6611
-1.2
13,15 15,17
13757.0632
13757.0633
-0.1
13,11 15,13
15720.3788
15720.3824
-3.6
15,17 17,19
15720.6887
15720.6856
3.1
183
Table III-l.
Continued
Isotopic Species
200rr „35on
HgD Cl
J -»• J_]_
3
6
7
202
HgD 35 Cl
3
6
7
204tT ,,35^,
HgD Cl
3
6
7
2F -»• 2F' Observed (MHz)
8
7,5
7855.7365
7855.7342
2.3
7,9
9,11
7857.1570
7857.1578
-0.8
11,9 13,11 13746.0012
13746.0002
1.0
13,15 15,17 13746.4012
13746.4021
-0.9
13,11 15,13 15708.1961
15708.2004
-4.3
15,17 17,19 15708.5040
15708.5033
0.7
5,3
7,5
7843.7200
7843.7191
0.9
7,9
9,11
7845.1408
7845.1384
2.4
7
7
7849.4303
7849.4304
-0.1
11,9 13,11 13724.9815
13724.9782
3.3
13,15 15,17 13725.3794
13725.3790
0.4
13,11 15,13 15684.1812
15684.1798
1.4
15,17 17,19 15684.4818
15684.4818
0.0
4
7
8
5,3
7,5
7831.9319
7831.9294
2.5
7,9
9,11
7833.3533
7833.3518
1.5
11,9 13,11 13704.3637
13704.3636
0.1
13,15 15,17 13704.7645
13704.7653
-0.8
13,11 15,13 15660.6299
15660.6278
2.1
15,17 17,19 15660.9300
15660.9304
-0.4
4
7
8
A (kHz)
5,3
4
7
Calculated (MHz)
a
198 37
Spectroscopic constants were not fit to the data for
HgH Cl and
199
37
HgH Cl. One r o t a t i o n a l t r a n s i t i o n f o r each i s o t o p i c species was
measured in o r d e r to confirm t h e i s o t o p i c assignments of the s t r o n g e r
200
t r a n s i t i o n s , belonging t o
37
202
37
HgH Cl and
HgH C l .
184
Table III-2.
Observed and calculated Transition Frequencies for
Isotopic Species
201
HgH 35 Cl
J -> Jj_
3
4
!_ = I'
3
F -*• F'
4
Observed (MHz)
5
201
HgHCl
Calculated (MHz) A (kHz)
7988.0735
-5.5
7988.0751
-7.1
7988.3584
8.5
7988.3609
6.0
7988.0680
2
1
2
3
2
3
7988.3669
3
3
4
3
5
6
7989.2730
7989.2708
2.2
3
6
7
7989.3308
7989.3204
10.4
1
3
4
7989.3645
1.4
7989.3694
-3.5
7989.3659
201
HgD 35 Cl
3
4
2
5
6
2
4
5
7989.4182
7989.4282
-10.0
1
4
5
7989.4654
7989.4589
6.5
2
3
4
7989.5104
7989.5138
-3.4
0
3
4
7849.4875
7849.4973
-9.8
3
4
5
7849.5396
14.6
7849.5401
14.1
7849.9060
-0.2
7849.9099
-4.1
7851.0559
2.8
7851.1117
1.9
7851.1192
-5.6
7849.5542
2
1
2
3
2
3
7849.9058
3
3
4
3
6
7
1
3
4
2
5
6
2
4
5
7851.1899
7851.1955
-5.6
1
4
5
7851.2397
7851.2332
6.5
2
3
4
7851.3103
7851.3100
0.3
7851.0587
7851.1136
185
according to the fitting procedure above are listed alongside the measured
values and quantum number assignments.
eluding those of the
All spectroscopic constants, in-
201
Hg species, appear in Table III-3.
lines of the J = 3 -»• 4 transition of
HgD
The observed
Cl - along with two
F = 0
lines belonging to other isotopic species - are shown in Fig. III-2.
Mercury-hydrogen chloride is a linear, or near-linear, van der Waals
complex, with wide-amplitude bending exhibited by the HCl subunit. The
structural parameters of Table III-4 were obtained by using a set of equations developed for a similar analysis
117
with the rotational constants of
Table III-3, the known structural parameters of HCl and DC1 (R (HCl) =
o
2^
1.28387&; R (DCl) = 1.28124A*),
and the coordinate system shown in
Fig. Ill-3.
(Note that 0, which does not appear in Fig. III-3, is the
angle between the HCl figure axis and the a-inertial axis of the complex,
and differs from y by no more than a few tenths of a degree.)
As in the
studies of rare gas-hydrogen halide systems, we assume that the structural
and electronic properties of HCl are unchanged upon complexation.
To
derive the structure of each isotopic species of HgHCl, we defined the
angle 9 by the expression
C1
X
Cl
where X H r l
ls t n e
= 1/2 X ^ !
<3COS29-1>
(III-4)
chlorine nuclear quadrupole coupling constant in free HCl,
and the brackets indicate an expectation value in the vibrational ground
state.
This value of 9 is used in Eqs.
(11-10)-(11-20), which are
used to fit R
to the measured B value. From 9 and R O M the angles
y and«a
3
cm
o
CM
^
and the distance between the heavy atoms were determined using simple geometry.
Since both acute and obtuse values for 9 satisfy Eq. (III-4), it is
necessary to establish the atomic order of Hg-HCl using isotopic substitution.
186
Table I I I - 3 .
Spectroscopic Constants for HgHCl.
Isotopic Species
i
o
(MHz)
DT(kHz)
C1
x
Hg
(MHz)
x
198
HgH35Cl
1001.0319(4)
3.718(4)
-40.364(162)
199
HgH35Cl
1000.2636(3)
3.709(3)
-40.382(120)
200
HgH 35 cl
999.50413(9)
3.7060(8)
-40.350(38)
201
HgH35Cl
998.7508(3)
3.700b
-40.338 b
202
HgH35Cl
998.0062(1)
3.695(1)
-40.326(58)
204
35
HgH Cl
996.5373(3)
3.688(3)
-40.312(124)
5.993(165)
200
HgH37Cl
954.5455(7)
3.375(6)
-31.894(398)
202
HgH 37 ci
953.0469(8)
3.358(7)
-31.578(417)
198rT ,35,,,
HgD Cl
983.7390(16)
3.394(15)
-49.318(620)
199rT ,,35,,,
HgD Cl
982.9681(3)
3.378(3)
-48.991(13)
982.2062(3)
3.374(3)
-48.951(110)
HgD35ci
981.4507(4)
3.370b
-48.921 b
202
35 ,
HgD Cl
980.7036(2)
3'.364(2)
-48.805(20)
204r, ^35,,.,
HgD Cl
979.2297(2)
3.349(1)
-48.914(62)
2
°°HgD35Cl
201
Errors in parentheses a r e one standard d e v i a t i o n in the
Held fixed in the f i t .
(MHz)
J
7.789(165)
fit.
H
CO
-J
Figure III-2.
Observed spectrum of the J = 3 -+ 4 transition of
HgD
along with two AF = 0 lines arising from other mercury
isotopic species. The envelope shown is calculated.
Cl,
7849.4303
7849.4875
7849.5542
7849.9058
7851 ,0066
7851 .0587
7851 .1136
7851 .1899
7851 .2397
7851 .3103
88T
189
Table I I I - 4 .
S t r u c t u r a l Constants for HgHCl.
Isotopic Species
R
o
cm (A)
6(deg)'
198„ u 3 5 _
HgH Cl
4.0666
199„ „35„n
HgH Cl
y(deg)
cp(deg)
R(Hg-Cl) (&)
31.22(10)
31.30
31.04
4.0974
4.0666
31.21(8)
31.29
31.03
4.0974
200
35 .
HgH Cl
4.0666
31.23(2)
31.31
31.05
4.0974
201„ „35^,.c
HgH Cl
4.0666
31.24
31.32
31.06
4.0974
202
35 .
HgH Cl
4.0666
31.25(4)
31.33
31.07
4.0974
204
35 ,
HgH Cl
4.0665
31.26(8)
31.34
31.08
4.0973
200„ „ 3 7 _
HgH Cl
4.0677
31.16(32)
31.24
30.99
4.0969
202
37 ,
HgH Cl
4.0677
31.41(33)
31.49
31.24
4.0968
198„ „35_
HgD Cl
4.0490
25.01(54)
25.14
24.73
4.1123
199„ n35_..
HgD Cl
4.0490
25.26(1)
25.39
24.97
4.1121
200„ „35^n
HgD Cl
4.0490
25.28(8)
25.41
24.99
4.1121
201„ „35„-C
HgD Cl
4.0490
25.30
25.43
25.02
4.1121
202„ „35„.
HgD Cl
4.0490
25.33(1)
25.46
25.04
4.1121
204„ ^35^,,
HgD Cl
4.0490
25.31(5)
25.44
25.02
4.1121
a
Cl
Angle obtained from X • Reported error is solely due to error in that
quantity.
See Fig. III-3.
202.
'Distances and angles interpolated from 200.Hg and
Hg isotopic species
VO
o
Figure III-3. Coordinates used to describe the structure of HgHCl.
R
CM
R(Hg-CI)
C.M.(HCI)
*l
Cl
VD
192
The distances R(Hg-Cl) in Table III-4 were calculated assuming the acute
0
values for 9.
These distances differ by 0.0147A between the HCl and
DC1 complexes.
that in
in
If we take the appropriate obtuse values for 9, we find
HgHCl, R(Hg-Cl) is 4.0361A, whereas this distance is 3.9861A
HgDCl, a difference of -0.0500A.
This indicates that the acute
values of 6 are preferred, and that the proton must lie between the heavy
atoms. The same conclusion is reached when comparing the rotational con35
37
stants of the HgH Cl and HgH Cl isotopic forms. It is interesting to
note that the value of 0.0147A is almost identical to the analogous
quantity in KrHCl, 0.0145A.
This similarity underscores the fact that
HgHCl is behaving like a rare gas-hydrogen halide complex.
The heavy-atom separations listed in Table III-4 can be used to
estimate an effective van der Waals radius for the mercury atom.
R(Hg - Cl) = R(Hg) + R(HC1)
,
We let
(III-5)
where R(Hg) is the effective van der Waals radius of mercury, and R(HC1)
(or R(DC1)) is the effective van der Waals radius of HCl (or DC1).
This
latter quantity is obtained from bond lengths for complexes of argon,
krypton, and xenon with HCl, using van der Waals radii of 1.90A, 2.00A, and
2.20A1 for these respective rare gas atoms. We have R(HC1) = 2.11 (2)A.
If we take the HgHCl value for R(Hg-Cl), 4.0974A, we find that R(Hg) =
1.99(2)&.
Using the HgDCl separation, 4.1121& R(Hg) = 2.00(2)A.
A self-
consistent van der Waals radius for the mercury atom is thus obtained by
this method.
The best previous determination of this quantity was the
range of 1.7 to 2.0A proposed by Canty and Deacon
on the basis of
mercury contact distances for various organomercury compounds.
193
90
2
It should be noted that the Coriolis coupling function,
f((cos 9)),
was neglected in all derivations of the molecular structure of Hg-HCl from
its rotational constants.
This approach is valid because we believe that
f is nearly unity, for reasons which will be described in the discussion
below.
Contributions from this term are in any case very small.
Mercury-hydrogen chloride exhibits the spectrum of a linear complex,
with the HCl subunit making wide-amplitude excursions from its equilibrium
configuration.
Information regarding the intermolecular potential, internal
dynamics, and equilibrium structure of Hg-HCl can be derived from the centrifugal distortion constants and the vibrationally-averaged structure of the
complex.
We take the pseudodiatomic expression
D T = 4B 3 /V 2 ,
J
O s
(III-6)
where V i s the harmonic s t r e t c h i n g frequency of the complex:
V
s-F(W
, 1 / a
The pseudodiatomic reduced mass of Hg-HCl, y
Eq. (1-22).
(I11 7)
•
"
, is defined analogous to
In Table III-5 we present the stretching force constants, k ,
and normal frequencies of vibration calculated by the method above, as well
as the related parameters R
k
and e to be explained below.
Note that the
values for the Hg-DCl isotopic forms are larger than those for the
corresponding HCl complexes by about 0.014 mdyn/A.
This is consistent
with the behavior of this constant observed in rare gas-hydrogen halides,
and probably results in part from coupling between bending and stretching
modes in the complexes.
The potential well depths, e, and equilibrium
heavy-atom separations, R , are calculated by invoking a well-established
Table III-5. Stretching Force Constants and Frequencies, and iennard-Jones
Parameters for HgHCl.
Isotopic Species
s (mdyn/A)
~ , ~lv
V (cm )
s
R (A)
e
e (cm )
198
HgH 35 Cl
0.0215
34.60
4.0304
244
199
HgH 35 Cl
0.0215
34.61
4.0304
244
200
HgH 35 Cl
0.0215
34.58
4.0304
244
202
HgH 35 ci
0.0215
34.55
4.0304
244
VH35CI
0.0215
34.51
4.0303
244
20
200
HgH 37 cl
0.0215
33.82
4.0324
244
202
HgH 37 cl
0.0216
33.83
4.0324
245
198
HgD 35 Cl
0.0228
35.23
4.0141
257
199„ „35„.
HgD Cl
0.0229
35.28
4.0142
258
200„ ^S^,.
HgD Cl
0.0229
35.26
4.0142
258
202„ „350.
HgD Cl
0.0228
35.22
4.0142
257
204„ ^35,,.,
HgD Cl
0.0229
35.23
4.0143
258
195
procedure
involving the assumption of a Lennard-Jones 6-12 p o t e n t i a l .
We compare these t o values for other weakly bound complexes in Table I I I - 6
Turning our a t t e n t i o n to the bending motion, we note t h a t t h e v i b r a 35
tionally-averaged angle y drops from 31.31(2)° for HgH Cl to 25.37(11)°
35
for HgD c l .
If we assume t h a t HgHCl i s l i n e a r a t equilibrium, and take
as our model a two-dimensional harmonic o s c i l l a t o r for the HCl bending
motion, the HCl angle would be expected t o drop by a f a c t o r of (I
i n going from HgHCl to HgDCl, or from 31.31° to 26.54°.
agreement with the measured r e s u l t .
. / I n)
DCi HCl
This i s in good
This behavior is e n t i r e l y analogous
t o t h a t observed for the r a r e gas-hydrogen halide complexes, and supports
a l i n e a r equilibrium s t r u c t u r e for HgHCl.
Given the p o t e n t i a l
V(cp) = 1/2 kbcp2 ,
(III-8)
2
the expectation value (cp ) is related to the normal bending frequency,
V, , by the equations
<*2> - afihr
(III 9)
-
b b
and
V i W
V J
We choose t h e bending reduced mass, y, , to be
b
"b " MHgRHgCl V L
^
(III 10)
-
"
69,146
^ " V^
'
Using Eqs. (III-8)-(III-ll), we can calculate the bending frequency and
bending force constant of each isotopic species of HgHCl.
The results of
196
Table III-6. Bond Lengths and Potential Well Depths for Various
Weakly-bound Complexes.
R„m(A)
e(cm_1)
NeHCla
3.794
31
ArHBrb
4.133
88
ArHFc
3.510
116
ArHCld
3.979
125
KrHBr
4.243
163
KrHCle
4.083
177
XeHClf
4.246
234
HgHCl
4.067
244
a
b
Ref. 86.
Ref. 69.
C
Ref. 31.
d
Ref. 67.
e
Ref. 6.
f
Ref. 143.
197
these calculations can be found in Table III-7.
Once again, the force
constants for the DC1 species markedly exceed their HCl counterparts, in
this case by almost 20%. This is probably due in part to our assumed
separation of the bending and stretching motions, and also to our assumed
harmonic bending potential.
We have measured rotational spectra of sixteen isotopic species
of the mercury-hydrogen chloride van der Waals complex.
We have obtained
spectroscopic constants for fourteen of these isotopic species and thus
have determined the vibrationally-averaged structure of the complex in
its vibrational ground state.
The structure and properties of HgHCl
are very analogous to those of rare gas-hydrogen chloride complexes
previously studied.
Using this analogy, we have determined an effective,
self-consistent mercury van der Waals radius of 1.99 (2)A, by methods
used m
144
the study of rare gas-hydrogen halides.
The similarity of the
difference in KrHCl and KrDCl, encourages us to believe that the effective
van der Waals radii of Hg and Kr have the same meaning in complexes with
HCl.
In Table III-8 we have listed the bending force constants for four
atom-HCl complexes, including HgHCl. We find that the Hg*•"HCl interaction is the most anisotropic of the four systems listed.
It will be use-
ful to examine the anisotropy in the Hg*• 'HCl interaction using a longrange polarization model previously developed and applied to the rare gas144
hydrogen halide systems.
Specifically, we wanted to know whether the
increased anisotropy in HgHCl could be explained by the greater polarizability of the Hg atom.
We refer the reader to Ref. 144 for the develop-
ment and application of the long range model to the rare gas-hydrogen
Table III-7.
Bending Force Constants and Frequencies for HgHCl.
Isotopic Species
198
HgH 35 Cl
k,xlO (mdvnA1)
V (cm" )
4.74
70.12
Cl
4.75
70.17
200
HgH 35 Cl
4.74
70.08
202
HgH 35 Cl
4.73
69.98
204
HgH 35 Cl
4.72
69.93
199
35
HgH
200
37
HgH Cl
4.77
70.31
202
HgH 37 Cl
4.62
69.18
198
HgD 35 Cl
6.00
56.28
199
HgD 35 Cl
5.78
55.22
200
HgD 35 Cl
5.76
55.13
202
HgD 35 Cl
5.71
54.90
204
HgD 35 Cl
5.73
54.98
199
Table III-8.
Atomic Polarizabilities and Atom-diatom Bending Angles
and Harmonic Bending Force Constants for Several Weakly
Bound Complexes.
a (atom)(A* )
a (atom)(A )
9(deg.)C
ArHCl
1.6
2.0
41
0.0016
KrHCl
2.5
3.8
38
0.0022
XeHCl
4.0
8.2
35
0.0031
HgHCl
5.1
10.0
31.3
0.0047
a
Ref. 147.
Quadrupole polarizabilities calculated in Ref. 148.
-.
2 \ 1/2
'Obtained as arc cos ((cos Q))
k (mdynA)
200
halide systems.
The barrier to internal rotation of the HX subunit is
described by a multipole expansion comprised of induction and dispersion
terms:
144
V(9) =
I
Pj(cos9)
[c(n,Jl,ind) + C(n,£,dis)] -^—-
.
(111-12)
cm
Expressions for the coefficients c are summarized in Table III-3 of
149-152
Ref. 144.
The value of R
is fixed at its vibrationally-averaged
value in the ground state, and angular-radial interactions are ignored.
144
The anisotropy in the repulsive potential is assumed to be small compared
to the anisotropy in the attractive potential. V(9) was calculated using
the HCl parameters given in Table III-9 and the following mercury parameters:
U(the first ionization energy) = 16.73 D /A
electric dipole polarizability) = 5.1A
quadrupole polarizability) = 10.06A
(Ref. 153); a(the
(Ref. 147); and a (the electric
(Ref. 148). The potential barrier for
HgHCl is shown in Fig. III-4, and is given by
V(9) = 146.7 - 66.4 P (cos9) - 32.6 P (cos8) - 36.4 P (cos8)
X
^
—
(111-13)
- 7.5 P4(cos9) - 3.7 P5(cos8)
This potential was used to generate wavefunctions that allowed us to calculate expectation values for P (cos0), as shown in Table 111-10.
This
calculation reproduces the measured values of (p (cos9)) remarkably well
202
for all three
HgHCl isotopic species.
The success of the multipole
model in correctly predicting the different HCl and DC1 bending angles
lends strong support to the assumption of a linear equilibrium geometry
for this system.
201
35
Table III-9. Properties Used in the Multipole Expansion of H Cl
ai,(A 3 ) a
2.81
ax (A 3 ) a
2.50
U(D 2 /A 3 ) b
20.124
A,,<* 4 )°
1.066
A^ < A V
0.192
2)
a
b
Ref. 153.
C
d
Ref. 113.
Ref. 154.
Ref. 151.
df (AV
0.010
d^(A2)d
0.032
to
o
to
Figure III-4.
Angular potential for HgHCl, calculated using Eq. (JEII-13)
After Figure III-2 of Ref. 144.
203
(ft
a>
0)
a>
•o
CD
(.J^HflJA
204
Table 111-10.
Expectation Values Generated from the P o t e n t i a l of
Eq. (111-13), Compared w i t h Experimental Values, when
Available.
202
HgH 3 5 Cl
202
HgH 37 Cl
202
35
HgD Cl
<P 2 (cos9)>ex p t
0.596
0.593
0.724
<Vcos9»calc
<Pl(cos9)>calc
0.629
0.629
0.749
0.853
0.853
0.907
Ct(deg)
31.25
31.41
25.39
9
29.83
29.81
24.15
0.958
0.958
0.981
calc
(de
*>
<f(cos29)>calc
a
Cl
Derived from X
Derived from ( P 9 ( c o s 6 ) )
205
The m u l t i p o l e e x p a n s i o n , Eq.
( 1 1 1 - 1 2 ) , has p r e v i o u s l y been used t o
p r e d i c t t h e v i b r a t i o n a l l y - a v e r a g e d bending a n g l e 9 for s e v e r a l r a r e g a s hydrogen h a l i d e complexes w i t h good s u c c e s s .
both 9
2
( ( c o s 9))
and 0
144
I n Table I I I - 1 1 we l i s t
for t h e s e complexes, where 9 r e p r e s e n t s ax„ cos
1/2
, and 0
.
was d e t e r m i n e d u s i n g t h e g r o u n d - s t a t e b e n d i n g wave-
f u n c t i o n g e n e r a t e d by t h e p o t e n t i a l of Eq. ( 1 1 1 - 1 2 ) .
The w o r s t agreement
i n 9 i s s e e n for HgHCl, where t h e d i s c r e p a n c y i s only 2 . 4 ° , o r 8%.
It
is
i n t e r e s t i n g t o n o t e t h a t HgH (D)Cl follows t h e p a t t e r n s e t by t h e r a r e g a s hydrogen h a l i d e s i n t h a t 9
i s XeHCl.)
> 9
.
(The o n l y e x c e p t i o n t o t h i s t r e n d
This phenomenon h a s been a t t r i b u t e d t o a n i s o t r o p y i n t h e r e p u l -
s i v e part of the angular p o t e n t i a l .
144
While t h e r e s u l t s of t h i s s i m p l e model c a n n o t be t a k e n a s
definitive,
i t s s u c c e s s i n p r e d i c t i n g t h e a n g u l a r p r o p e r t i e s of t h e atom-HX systems
l i s t e d i n d i c a t e s t h a t l o n g - r a n g e a t t r a c t i v e i n t e r a c t i o n s p l a y an i m p o r t a n t
r o l e in d e t e r m i n i n g t h e a n g u l a r p r o p e r t i e s of t h e s e s y s t e m s , i n c l u d i n g t h e
merucyr c o m p l e x e s .
In t h e c a s e of mercury, no chemical arguments based on
o r b i t a l geometry a r e needed t o e x p l a i n t h e g r e a t e r a n i s o t r o p y of t h e
H g ' • "HCl i n t e r a c t i o n .
One need o n l y invoke t h e g r e a t e r p o l a r i z a b i l i t y of
t h e mercury atom r e l a t i v e t o t h e r a r e gas atoms.
157
The C o r i o l i s c o u p l i n g f u n c t i o n
t h e multipole p o t e n t i a l .
2
f ((cos 9 ) ) can be e s t i m a t e d u s i n g
As s e e n i n Table I I I - l l , i t s p r e d i c t e d v a l u e i s
0 . 9 6 (0.98) for HgH(D)Cl. These v a l u e s a r e m good agreement w i t h t h e
90
p r e d i c t i o n s of a s e m i - e m p i r i c a l c u r v e g e n e r a t e d p r e v i o u s l y
for the r a r e
gas-hydrogen halide systems.
We conclude t h a t t h e f - v a l u e s f o r t h e s e
mercury complexes a r e s u f f i c i e n t l y
c l o s e t o u n i t y t h a t t h e i r e f f e c t on
t h e s t r u c t u r a l d e t e r m i n a t i o n f o r HgHCl i s n e g l i g i b l e .
206
2
Table III-ll. Angles 9= arccos ((cos 0))
"L/1?
for Several Complexes
Calculated Using the Potential of Eq. (111-12) after
Table III-4 of Ref. 144.
ArHF
41.6
40.5
1.1
KrHF
39.3°
37.5
1.8
XeHF
35.7
35.1
0.6
NeDCl
47.0S
45.9
1.1
ArHCl
41.7 f
40.7
1.0
KrHCl
38.lg
37.8
0.3
XeHCl
34.8h
35.4
-0.6
HgHCl
31.2
29.8
2.4
HgDCl
25.4
24.2
1.2
Ref. 144. (HgH(D)Cl values from this work.)
b
Ref. 31.
C
d
Ref. 8.
Ref. 155.
Ref. 156.
f
g
h
Ref. 67.
Ref. 6.
Ref. 143.
207
The remaining interesting feature in HgHCl is the
201
Hg quadrupole
coupling constant, from which information about the quadrupolar shielding
in the mercury atom can be derived.
in the HCNHg complex.
This phenomenon was also observed
Thus, discussion of
201
Hg quadrupole coupling in
both complexes will be undertaken in Section D, after the presentation of
the HCNHg findings, in the following section.
This study of HgHCl has previously appeared as a preliminary communi158
cation in the Journal of Chemical Physics,
and as a full article in
that same publication.
C.
159
HCNHg
In order t o further examine t h e p r o p e r t i e s of mercury-containing
complexes, the r o t a t i o n a l spectra of twenty-two i s o t o p i c species of a
complex between mercury and hydrogen cyanide have been assigned.
We
wished to see whether t h i s complex would e x h i b i t behavior analagous to
KrHCN
and ArHCN,
in an attempt to c h a r a c t e r i z e systematic behavior
among mercury-containing complexes.
In c o n t r a s t to HgHCl, in which the mercury atom binds to the e l e c t r o p o s i t i v e proton of HCl, we find that the atomic order of the mercuryhydrogen cyanide complex i s HCNHg, with the mercury atom apparently favoring
the more electronegative end of t h e HCN molecule.
In t h i s s e c t i o n , the
p r o p e r t i e s of HCNHg w i l l be compared with those of HgHCl, and with those of
r a r e gas-hydrogen cyanide complexes.
Three J -*• J + 1 t r a n s i t i o n s have been measured for each of the isotopes
198
Hg,
DC14 N.
199
Hg,
2
°°Hg,
202
Hg, and
204
Hg complexes w i t h HC14N, HC15N, and
Two t r a n s i t i o n s were measured for each of t h e complexes of the
15
above mercury isotopes with DC N.
A fourth t r a n s i t i o n was also measured
208
14 199
for HC N
14 200
Hg, HC N
t r a n s i t i o n s of DC N
14 209
Hg, and HC N
Hg, and t h e J = 3 + 4 and 4 + 5
Hg, were measured, i n order to e x t r a c t the
quadrupole coupling c o n s t a n t s .
Hg
These t r a n s i t i o n s were f i t using t h e
Hamiltonian of Eq. ( I I I - l ) , with an H
term s u b s t i t u t i n g for the H
C1
term, using t h e same f i t t i n g techniques employed m the previous s e c t i o n .
The observed t r a n s i t i o n s for a l l i s o t o p i c species of HCNHg are l i s t e d in
Table 111-12—except for the 201Hg-substituted s p e c i e s , which appear
separately in Table 111-13—along with the frequencies calculated from
the spectroscopic constants i n Table 111-14.
Since the signs of the nitrogen and mercury quadrupole coupling
constants are c r u c i a l t o the discussions t h a t follow, a word about the
determination of these signs i s in order a t this p o i n t . The magnitude
* N
„ 14„202TI
„014 200TT
, „„14 202„
... , .
..
and s i g n of x
m HC N
to t h e observed s p e c t r a .
Hg, HC N
Hg, and DC N
Hg were f i t d i r e c t l y
Any p o s s i b l e sign ambiguity was eliminated by
the observation of a J = 2 + 3 , AF = 0 t r a n s i t i o n m each case.
magnitude and sign of x
in HC N
Hg and DC N
The
Hg were also f i t d i r e c t l y ,
but, s i n c e no AF = 0 t r a n s i t i o n s were observed for these i.sotopic s p e c i e s ,
the s i g n had t o be confirmed by other means.
For HC N
Hg, x
was
held
fixed a t -5.97 MHz, and B and D, were f i t , giving I = 1234.9642 MHz and
3
o
J
o
D = 18.94 kHz, the values in Table 111-14. A second f i t was run, with an
J
appropriate r e v e r s a l of F quantum-number assignments, with x
+5.97 MHz,
giving B = 1234.8908 and D_ = 16.98 kHz. Table 111-14 shows that D_ undero
J
"J
15 198
goes a gradual, monotonic decrease i n the isotopic series from HC N Hg t o
HC15N204 Hg—a p h y s i c a l l y reasonable trend—with a l l values between 18.84 and
18.97 kHz.
Only the D corresponding to x**9 = "5-97 MHz coincides with t h i s
trend, while t h a t which corresponds t o x
9
- +5.97 MHz l i e s e n t i r e l y out-
side t h e i s o t o p i c r a n g e , by over 25 standard deviations i n the f i t .
This
209
Table 111-12.
Observed and Calculated Transition Frequencies for HCNHg.
Isotopic Species
HC
HC
14 198„
N
Hg
14 199
N
Hg
tJlr,14„200„
HC
N
Hg
„^l4„202tT
HC N
Hg
J_+_J'
F + F'
14 204
N
Hg
Calculated(MHz) A(kHz)
3+4
10143.4872
10143.4879
-0.7
4 + 5
12675.6186
12675.6176
0.1
5+6
15205.2520
15205.2524
-0.4
2 + 3
7604.9004
7604.8968
3.8
3 + 4
10137.5305
10137.5346
-4.1
4+5
12668.1781
12668.1777
0.4
5 -v 6
15196.3276
15196.3271
0.5
3 + 3
7600.2494
7600.2524
-3.0
2 + 3
7600.4740
7600.4687
5.3
2 -> 2
7600.7692
7600.7714
-2.2
3+4
10131.6348
10131.6354
-0.6
4+5
12660.8120
12660.8113
0.7
5+6
15187.4982
15187.4984
-0.2
3 + 3
7591.5144
7591.5209
-4.6
+
3
7591.7481
7591.7441
4.0
2 + 2
7592.0521
7592.0567
-4.6
3+4
10120.0151
10120.0105
4.6
4+5
12646.2965
12646.2927
3.8
5+6
15170.0919
15170.0946
-2.7
3+4
10108.6169
10108.6169
0.0
4+5
12632.0523
12632.0523
0.0
5+6
15153.0085
15153.0085
0.0
2+3
2+3
2
HC
Observed(MHz)
210
Table 111-12,
Continued
Isotopic Species
HC15N198Hg
HC15N199Hg
HC
15 200
N
Hg
„ „ 1 5 „202 T T
HC N
Hg
„^15„204„
HC N
Hg
„r,14„198„
DC N
Hg
„„14„199„
DC N
Hg
J + J'
F + F'
Observed(MHz)
Calculated(MHz)
A(kHz)
2 "+ 3
7421.1080
7421.1083
-0.3
3 •*• 4
9892.6866
9892.6863
0.3
4 •*• 5
12362.4429
12362.4430
-0.1
2 + 3
7416.6090
7416.6090
0.0
3 + 4
9886.6899
9886.6900
-0.1
4+5
12354.9521
12354.9521
0.0
2 + 3
7412.1532
7412.1535
-0.3
3+4
9880.7520
9880.7517
0.3
4+5
12347.5329
12347.5330
-0.1
2+3
7403.3720
7403.3723
-0.3
3 + 4
9869.0479
9869.0475
0.4
4+5
12332.9093
12332.9094
-0.1
2+3
7394.7584
7394.7588
-0.4
3+ 4
9857.5694
9857.5689
0.5
4+5
12318.5705
12318.5707
-0.2
3+4
9632.1820
9632.1820
0.0
4 + 5
12036.3807
12036.3807
0.0
3+4
9626.3619
9626,3619
0,0
4+5
12029.1184
12029.1184
0.0
211
Table 111-12, Continued
Isotopic Species
r,„14„200„
DC
DC
N
Hg
14 202
N
Hg
„„14 204„
DC N
Hg
DC
15 198
N
Hg
DC 1 5 N 1 9 9 Hg
DC 1 5 N 2 0 0 Hg
DC 1 5 N 2 0 2 Hg
DC 1 5 N 2 0 4 Hg
J + J'
F + F'
Observed(MHz)
Calculated(MHz)
A (kHz)
2+3
7217.2363
7217.2371
-0.8
3+4
9620.6008
9620.5997
1.1
4+5
12021.9194
12021.9198
-0.4
3+3
7208.4639
7208.4715
-7.6
2+3
7208.7184
7208.7119
6.5
2+2
7209.0431
7209.0485
-5.4
3 + 4
9609.2486
9609.2400
8.6
4+5
12007.7286
12007.7316
-3.0
3+4
9598.1149
9598.1149
0.0
4+5
11993.8096
11993.8096
0.0
3+4
9409.8995
9409.8995
0.0
4 + 5
11758.8687
11758.8687
0.0
3+4
9404.0375
9404.0375
0.0
4 + 5
11751.5422
11751.5422
0.0
3 + 4
9398.2355
9398.2355
0.0
4 + 5
11744.2940
11744.2940
0.0
3+4
9386.7930
9386.7930
0.0
4+5
11730.0043
11730.0043
0.0
3+4
9375.5734
9375.5734
0.0
4+5
11715.9878
11715.9878
0.0
2+3
212
Table 111-13. Observed and Calculated Transition Frequencies for HCN
Isotopic Species
15 201
HC N
Hg
F'
2 + 3
Observed(MHz)
3/2 + 5/2
Calculated(MHz)
201.
201
Hg
A(kHz)
7407.4406
-1.9
7407.4408
-2.1
7407.8103
1.8
7407.8103
1.8
9874.7360
3.7
9874.7360
3.7
9874.9092
-4.1
9874.9092
-4.1
9392.3527
-2.2
9392.3528
-2.3
9392.5274
2.1
9392.5274
2.1
11737.0443
3.5
11737.0443
3.5
11737.1476
-3.5
11737.1476
-3.5
7407.4387
1/2 + 3/2
5/2 + 7/2
7407.8121
7/2 + 9/2
3 + 4
5/2 + 7/2
9874.7397
3/2 + 5/2
7/2 + 9/2
9874.9051
9/2 +11/2
15 201
DC N
Hg
3+4
5/2 + 7/2
9392.3505
3/2 + 5/2
7/2 + 9/2
9392.5295
9/2 +11/2
4+5
7/2 + 9/2
11737.0478
5/2 + 7/2
9/2 +11/2
11737.1441
11/2 +13/2
Table 1 1 1 - 1 4 .
S p e c t r o s c o p i c C o n s t a n t s f o r HCNHg.
Isotopic Species
o(
z
'
D,(kHz)
XN(MHz)
HC 1 4 N 1 9 8 Hg
1268.6013(3)
20.790(5)
HC 1 4 N 1 9 9 Hg
1267.8568(6)
20.781(11)
HC 1 4 N 2 0 °Hg
1267.1181(4)
20.739(9)
-0.673(7)
„„14„202r,
HC N
Hg
1265.6627(7)
20.669(14)
-0.695(12)
14 204 b
HC N
Hg
1264.2382
20.660
1237.1928(1)
18.971(2)
„„15„199TT
HC N
Hg
1236.44253(2)
18.9464(4)
„„15 „200rl
HC N
Hg
1235.6696(1)
18.925(3)
HC
15 198
N
Hg
HC
15 201
N
Hg
1234.9642(19)
18.944(68)
HC
15 202
N
Hg
1234.2354(1)
18.889(3)
15 204
HC N
Hg
1232.7988(2)
18.835(4)
DC 1 4 N 1 9 8 Hg b
1204.7066
21.371
DC 1 4 N 1 9 9 Hg b
1203.9768
21.300
DC 14 N 20 °Hg
1203.2558(3)
21.277(8)
DC 1 4 N 2 0 2 Hg
1201.8338(16)
21.213(45)
DC 1 4 N 2 0 4 Hg b
1200.4460
21.300
„„15 198TT b
DC N
Hg
1176.8607
19.476
15 199 b
DC N
Hg
1176.1277
19.470
„_15 200tI b
DC N
Hg
1175.4017
19.446
„^15„201TT
DC N
Hg
1174.6800(17)
19.368(37)
„^15„202„ b
DC N
Hg
1173.9690
19.372
„„15„204„ b
DC N
Hg
1172.5652
19.328
-0.748(19)
214
Table 111-14, Continued
Errors in parentheses are one standard deviation in the fit.
Errors unavailable for these isotopic species.
215
is convincing evidence that the negative value for X
fits were run for DC
N
is correct.
Hg, using values of +6.02 MHz for x**3'
suiting in D 's of 19.37 and 19.01 kHz, respectively.
Similar
and
re
~
While the discrepancy
is not as dramatic in this case, the D corresponding to the positive value
J
for x
again falls well outside the range exhibited by the other mercury
isotopic species, showing that the negative value is correct in DC
N
Hg,
as well.
Mercury-hydrogen cyanide exhibits the microwave spectrum of a linear
van der Waals complex. The structure of the complex was obtained from
the spectroscopic constants of Table 111-14, the known properties of the
various isotopic species of HCN (see Table 111-15)—which are taken to
be unchanged upon complexation—and the coordinate system shown in
Fig. III-5, using the same equations used to characterize HgHCl.
The
structural parameters thus determined are presented in Table 111-16.
As usual, we assume that the properties of HCN are unchanged upon complexation, and that the angle between the HCN figure axis and the a-axis of the
N
complex can be derived from Eq. (III-4), applied to x •
Once R
and 9 are fit, using Eqs. (11-10)- (11-20), the angles y and
cp and R(Hg-N) are easily determined.
Since both acute and obtuse values for 9 satisfy Eq. (III-4), it is
necessary to establish the atomic order of HCN-Hg using isotopic substitution.
The coordinates of the four atoms in HC
from the R
cm
obtained from the procedure outlined above, assuming both
obtuse and actute values of y,
axis.
14 202
N
Hg were calculated
the angle between R
and the HCN figure
For the purposes of this calculation, these coordinates were
assumed to be isotopically invariant.
Using them, B
values were calcu-
lated for the HC 1 4 N 2 0 2 Hg, HC 1 5 N 2 0 2 Hg, DC 1 4 N 2 0 2 Hg, and DC 15 N 202 Hg.
These
216
Table 111-15.
B (MHz) 3
o
Molecular Properties of HCN.
14
HC N
HC15N
DC14N
44315.9757
43027.69
36207.4627
35169.85
~
-4.70396(47)
—
rg(H-C)(A)b
1.06317
rg(C-N)(K)b
1.15538
X N (MHz) a
y(D)a
-4.70789(8)
2.984594
DC15N
2.990198
2m ( D A )
3.1°
3.3(6)d
2.9°
3.0C
a (DA 2 )
6,4e
6.6f
5.9f
6.1f
a
Ref. 162.
b
Ref. 1 6 3 .
c 15
HC N value, corrected for change in center-of mass.
Ref. 160.
"Ref. 164.
f
14
HC N v a l u e , c o r r e c t e d f o r change i n c e n t e r - o f - m a s s .
to
r-"
Figure III-5.
Coordinates used to describe the structure of HCNHg.
2ir
219
Table 111-16.
Structural Constants for HCNHg.a
Isotopic Species
9(deg)b
cm
Y (deg) °
cp(deg)
R(Hg-N)(A)
14 202
HC N
Hg
4.0522(4)
131.08(10)
130.25
123.18
3.6952
15 202
HC N
Hg
4.0384(5)
131.08(10)
130.24
123.42
3.6932
14 202
DC N
Hg
4.0849(6)
131.52(10)
130.55
122.81
3.6931
„o15„202„
DC
N
Hg
4.0700(6)
131.52(10)
130.54
123.06
3.6907
For each HCN isotopic species, a ll mercury isotopes exhibit the same
structure.
b
Thus, only the
N
14
14
Angle obtained from X of HC N and DC N species.
14
15
0(H(D)C
N) = 0(H(D)C
the text.)
C
202
Hg species are presented here.
See Fig. ITI-5.
It is assumed that
N) within the limit of this determination. (See
220
calculated values appear in Table 111-17, along with the measured rotational constants.
Examination of this table clearly shows that the
obtuse value of y,
130.25°, is the correct one, giving an atomic order of
HCNHg.
It should be noted that in Table 111-16 the angles 9 for the HC
15
and DC
N
14
N isotopic species are taken from their respective
N counter-
parts, assuming that the angles are equal within the limits of this determination. We justify this assumption by pointing out that the observed
difference in 0 between HC NHg and DC NHg, where the difference in
14
15
HCN moments of inertia is 20%, in only 0.4°. Since HC N and HC N have
moments of inertia that differ by only 3%, it is reasonable to believe
that the difference in bending angle between HC
14
15
NHg and HC NHg will be
small.
Table 111-18 contains the r e s u l t s of applying Eq. (1-47), and the
well-depth analysis outlined in the previous s e c t i o n , to HCNHg.
low e values i n d i c a t e t h a t t h i s complex i s q u i t e weakly bound.
The
These
numbers should be i n t e r p r e t e d with some c a u t i o n , however, as Eq. (1-47)
operates under t h e assumption t h a t the moments of i n e r t i a of the subunits
are c o l l m e a r with those of the complex, and t h a t supposition may not be
t r u e in t h i s c a s e .
The equilibrium s t r u c t u r e of HCNHg i s a matter of some i n t e r e s t .
The only other known Hg atom-molecule complex i s HgHCl, discussed in
the preceding s e c t i o n , where we concluded t h a t HgHCl i s most l i k e l y l i n e a r
(or nearly so) a t equilibrium, f o r reasons t h a t are worth summarizing h e r e :
(1)
Although the d i r e c t spectroscopic evidence was inconclusive on
t h i s p o i n t , with only K = 0 t r a n s i t i o n s being observed, t h e s e observations
were at l e a s t c o n s i s t e n t with a l i n e a r equilibrium c o n f i q u r a t i o n .
221
Table 111-17.
Comparison of Measured vs. Predicted B Values for Various
o
Isotopic Species of HCNHg, Assuming Both Obtuse and Acute
Values for Y-
Species
Measured B
o
Obtuse
A
Acute
A
HC 1 4 N 2 0 2 Hg
1265.6627
1265.7119
-0.0492
1265.7147
-0 .0520
HC 1 5 N 2 0 2 Hg
1234.2354
1234.2480
-0.0126
1217.8533
16,.3821
DC 1 4 N 2 0 2 Hg
1201.8338
1198.8102
3.0236
1243.5602
-41,.7264
DC 1 5 N 2 0 2 Hg
1173.9690
1170.9466
3.0224
1197.6033
-23,.6343
aB
calculated using Y = 130.25°,
b=
B
calculated using Y = 49.75°.
222
Table 111-18.
S t r e t c h i n g F o r c e C o n s t a n t s and F r e q u e n c i e s ,
Jones Parameters
isotopic Species
k
s(mdyn/&)
and Lennard-
f o r HCNHg.
V cm
)
Re(A)
e (cm
HC14N198Hg
0.00600
20 .69
3.9722
66
HC14N199Hg
0.00599
20 .68
3.9722
66
HC14N200Hg
0.00600
20 .68
3.9721
66
HC14N202Hg
0.O0600
20 .68
3.9722
66
HC14N204Hg
0.00599
20 .65
3.9722
66
HC15N198Hg
0.00629
20 .86
3.9614
69
HC15N199Hg
0.00629
20 .86
3.9614
69
HC15N2°°Hg
0.00629
20 .85
3.9614
69
HC15N201Hg
0.00628
20 .82
3.9614
69
HC15N202Hg
0.00629
20 .83
3.9615
69
HC15N204Hg
0.00629
20 .83
3.9615
69
14 1 9 8 t ,
DC N
Hg
0.00514
18 85
4.0003
58
0.00515
18 87
4.0005
58
0.00515
18 86
4.0005
58
14 2 0 2
DC N
Hg
0.00515
18. 86
4.0006
58
14 2 0 4
DC N
Hg
0.00512
18 79
4.0003
57
^15„198 ,
DC N THg
0.00542
19. 07
3.9888
60
DclV"
g
0.00542
19. 05
3.9887
60
DC15N2°°Hg
0.00542
19. 05
3.9888
60
„„15„201„
DC N
Hg
0.00543
19. 07
3.9889
60
0.00542
19. 05
3.9889
60
0.00542
19. 04
3.9889
60
rv,14„199„
DC N
Hg
14 2 0 0
DC N
Hg
H
15 2 0 2
DC N
Hg
„ 15„204„
DC N
Hg
)
223
(2)
The bending angle f o r HgHCl i s small:
for HgDCl.
These values are smaller than corresponding angles for HCl
complexes with argon,
krypton, '
believed to be linear a t equilibrium.
(3)
31° for HgHCl; 25°
and xenon,
86
'
a l l of which a r e
The observed change i n bending angle upon deuteration of the
HCl subunit i s approximately p r e d i c t e d by a two-dimensional harmonic
bending model, which assumes l i n e a r i t y at equilibrium.
This model p r e -
d i c t s a drop i n angle of 4.77°, compared to t h e experimentally-observed
r e s u l t of 5.94(11)°.
(4)
A hindered-rotor model, developed f o r and applied t o rare g a s 144
hydrogen halide systems,
which a l s o assumes a l i n e a r equilibrium con-
f i g u r a t i o n , accurately p r e d i c t s the observed bending angles for both
HgHCl and HgDCl, using no adjustable parameters.
We now consider the a p p l i c a b i l i t y of t h e s e arguments to HCNHg:
(1)
The d i r e c t spectroscopic evidence i s again inconclusive, as
no K T= 0 s t a t e s were observed, t h i s despite an extensive search over a
frequency region equal to 2B .
As i n the case of many other l i n e a r or
n e a r l y - l i n e a r atom-molecule systems, t h i s might be due to the r e l a t i v e l y
high temperatures needed to populate K ^ 0 s t a t e s .
For an assumed r i g i d
0
HCNHg s t r u c t u r e with R
= 4.0522A and y~ 1 3 0 . 2 5 ° , t h e 1 , , s t a t e has an
cm
'
11
energy of ~4K. The t e m p e r a t u r e expected in t h e n o z z l e expansion i s g i v e n
v. 165
by
T
T =
,
(111-14)
1+1/2 (y-l)M
where T
i s t h e temperature o f t h e g a s in t h e valve r e s e r v o i r , y = 5 / 3
t h e argon c a r r i e r g a s , and M = 133 (P D) '
for argon.
P
i s the
for
224
r e s e r v o i r p r e s s u r e in a t m o s p h e r e s , and D i s t h e d i a m e t e r of t h e n o z z l e
o p e n i n g in cm.
T ~ 0.3K.
Using T
= 523K, P
= 2 . 5 atm, and D = 0.1 cm, we o b t a i n
T h u s , d e s p i t e t h e m o d e r a t e l y h i g h t e m p e r a t u r e s i n our g a s
r e s e r v o i r , t h e K = 1 s t a t e s would n o t be e x p e c t e d t o be s i g n i f i c a n t l y
p o p u l a t e d in t h e m o l e c u l a r beam.
The e f f e c t of n o n - l i n e a r i t y on K = 0
s t a t e s has b e e n d i s c u s s e d in d e t a i l e l s e w h e r e .
160
F o r HCNHg, as f o r
KrHCN, t h e s e e f f e c t s a r e small a n d i n c o n c l u s i v e .
(2)
The o b s e r v e d b e n d i n g a n g l e in HCNHg i s e x t r e m e l y
large—a
d e v i a t i o n of ~ 5 0 ° from l i n e a r i t y — c o m p a r e d t o 27° f o r KrHCl,
KrHCN. 1 6 0
In NeHCl, t h e r e s u l t 8 6 ' 1 6 6 a r c c o s ( ( c o s 2 9 > ^ 2 )
and 3 1 °
for
= 39.7° h a s been
i n t e r p r e t e d i n terms of n e a r l y f r e e r o t a t i o n of t h e HCl s u b u n i t , r e s u l t i n g
from t h e low HCl moment o f i n e r t i a , and t h e v e r y low p o l a r i z a b i l i t y
neon.
of
Given t h e r e l a t i v e l y l a r g e moment of i n e r t i a of HCN (seven t i m e s
t h a t of HCl), a n d the h i g h p o l a r i z a b i l i t y of m e r c u r y , i t i s d i f f i c u l t
i n t e r p r e t the o b s e r v e d v a l u e of ( P
n e a r l y free r o t a t i o n .
to
(cos9)) i n HCNHg a s r e s u l t i n g from
Comparing t h e o b s e r v e d b e n d i n g a n g l e s i n HgHCl
and HCNHg, u s i n g the t w o - d i m e n s i o n a l harmonic b e n d i n g model, the r a t i o
in
t h e b e n d i n g f o r c e c o n s t a n t s , k , f o r t h e s e two s y s t e m s would be g i v e n by
k (HCNHg)
_£
kjHgHCl)
a
( J 1 " ! );
M9.75
Such a v a r i a t i o n would b e d i f f i c u l t
4
— = 0u u02
7
' ^
l (111-15)
LJ L 1 3 ;
- "
t o u n d e r s t a n d i n c h e m i c a l terms.
Even
i n g o i n g from KrHCl t o KrHCN, t h e b e n d i n g f o r c e c o n s t a n t i n t h i s approximat i o n d r o p s by o n l y a f a c t o r of t w o .
HCN-CO„,
167
I n t h e hydrogen-bound complex
w h e r e the n i t r o g e n end of t h e HCN m o l e c u l e b i n d s t o the c a r b o n
atom of CO , g i v i n g a s t r u c t u r e w i t h a p p a r e n t C
a n g l e i s only 1 7 ° .
symmetry, t h e HCN b e n d i n g
225
14
14
(3) In going from HC NHg to DC NHg, a drop of 0.3° in Y i s
observed. The two-dimensional harmonic model would predict a drop of
(1 - (v 6 ^?!) 1 ^ 4 ) 49.75° = 2.45°, based on the r o t a t i o n a l constants of
44315
14
14
HC N and DC N.
This prediction e r r s by 2.15°, a factor of e i g h t .
In
HgHCl and HgDCl, t h e same model p r e d i c t s the measured r e s u l t to within
a f a c t o r of 0.8.
(4)
The hindered rotor model cannot be applied in i t s present form
to HCN complexes, as i t i s physically unreasonable to t r e a t HCN as
144
spherical in shape, a requirement of t h a t model.
From these observations, we conclude that HCNHg is l i k e l y to be nonl i n e a r i n i t s equilibrium configuration, probably with an equilibrium
angle y t h a t i s g r e a t e r than 130.25°, as evidenced by the increase in y
going from HCNHg t o DCNHg.
The most f a s c i n a t i n g aspect of the structure of HCNHg i s the f a c t
that the mercury atom appears to bind t o the e l e c t r o n e g a t i v e end of i t s
partner molecule, while, in HgHCl, i t binds to t h e e l e c t r o p o s i t i v e end.
In r a r e gas-molecule complexes, the r a r e gas atom invariably tends toward
the most e l e c t r o p o s i t i v e s i t e on the companion molecule.
(A possible
exception to t h i s trend i s the argon-acetylene complex, which i s asserted
to be T-shaped.
However, as only one r o t a t i o n a l t r a n s i t i o n was observed
168
for t h i s complex,
i t i s d i f f i c u l t t o accept t h i s conclusion without
a d d i t i o n a l spectroscopic evidence.)
This is often taken to mean t h a t
the r a r e gas atom a c t s as a Lewis b a s e , i . e . , a donor of e l e c t r o n i c
charge density.
Since mercury vapor resembles a r a r e gas in many ways,
i t was thought t h a t mercury complexes would follow t h i s t r e n d .
The
assignment of HgHCl, which e x h i b i t s behavior c h a r a c t e r i s t i c of rare
226
gas-hydrogen halide complexes, seemed to bear out t h i s b e l i e f .
However,
the mercury atom i n HCNHg seems to b e acting a s a Lewis acid, accepting
charge d e n s i t y from the lone pair of electrons on the nitrogen atom,
the iT-electron cloud on t h e cyano group, or b o t h .
(See Fig. I I I - 6 . )
This arrangement i s not without precedent, as studies of HgX complexes
169
with ethylene in argon matrices
apparently exhibit electron donation
from the 2pir molecular o r b i t a l of ethylene i n t o the vacant 6p o r b i t a l
of mercury.
170
Conversely, i t seems that, i n HgHCl, electron density
i s being donated from the atom's f i l l e d 6s s h e l l .
Experiments which may
better c h a r a c t e r i z e the Lewis acid-base behavior of t h e mercury atom in
van der Waals complexes w i l l be suggested in Sec. I I I - E .
201
Hg quadrupole coupling effects upon the
In HCNHg, as i n HgHCl,
r o t a t i o n a l t r a n s i t i o n s have been measured.
An analysis of t h e s e effects
will be presented in the following section.
The r e s u l t s of t h i s study are currently being prepared f o r publication. 171
D.
201Hg Quadrupolar Coupling in HgHCl and HCNHg
The mercury atom has t h e e l e c t r o n configuration [Xe]4f
14
5d
10 2
6s .
These
completely-filled s h e l l s give the atom a spherically-symmetric e l e c t r o n i c
charge d i s t r i b u t i o n in i t s free s t a t e , with t h e r e s u l t that t h e e l e c t r i c
field g r a d i e n t a t t h e nucleus, and t h u s the nuclear quadrupole coupling constant, are identically zero.
have been determined for
201
Nonzero mercury quadrupole coupling constants
HgH 35 Cl,
as seen i n Tables I I I - 3 and 111-14.
20l
HgD 3 5 Cl, HCL5N201Hg, and DC15N201Hg,
This c o n s t a n t a r i s e s from the i n t e r -
action between the quadrupole moment of the
201
Hg nucleus (I = 3/2) and an
to
to
Figure III-6.
Structure of HCNHg, with van der Waals radii
of the atoms drawn in.
(R(Hg) is taken to be
2.Oil, the value ascertained in Section III-B.)
228
229
e l e c t r i c f i e l d g r a d i e n t caused by t h e p r e s e n c e o f t h e p o l a r m o l e c u l e ,
which d i s t o r t s t h e s p h e r i c a l symmetry of t h e mercury atom.
v i o u s l y measured q u a d r u p o l e c o u p l i n g c o n s t a n t s f o r
131
83
We have p r e -
7 160 172
Kr, '
'
and
143 172
Xe,
'
and have d e m o n s t r a t e d t h a t t h e magnitude of t h e o b s e r v e d
q u a d r u p o l e c o u p l i n g c o n s t a n t s can be accounted f o r by q u a d r u p o l a r
shield-
i n g e f f e c t s i n t h e r a r e - g a s atom i n t h e p r e s e n c e o f the i n d u c e d e l e c t r i c
field gradient.
83
131
Kr and
'
we s h a l l a p p l y t h e same methods u s e d to a n a l y z e
201
Xe t o a n a l y z e t h e
Hg c o u p l i n g c o n s t a n t , and t h u s d e r i v e
an e m p i r i c a l e s t i m a t e for t h e S t e r n h e i m e r s h i e l d i n g c o n s t a n t
"
of
m e r c u r y , a q u a n t i t y n o t p r e v i o u s l y measured, t o o u r knowledge.
201
The measured s p e c t r a for t h e
Hg i s o t o p i c forms a r e p r e s e n t e d i n
Ha
T a b l e s I I I - 2 and 1 1 1 - 1 3 . The X
v a l u e s i n T a b l e s I I I - 3 a n d 111-14 were
Her s
o b t a i n e d by t h e method d e s c r i b e d i n s e c . I I I - B . x
i d e f i n e d as
X H9 = - e q Q H 9 / h
,
(111-16)
where e i s t h e p r o t o n c h a r g e , and h i s P l a n c k ' s c o n s t a n t .
Q
The v a l u e of
, o b t a i n e d from n u c l e a r h y p e r f i n e s p e c t r a w i t h small c o r r e c t i o n s
173
for Sternheimer e f f e c t s ,
-24
i s +0.455(40) x 10
(<11%)
2
cm .
T h u s we n e e d only
d e t e r m i n e q, t h e e l e c t r i c f i e l d g r a d i e n t a t the s i t e of t h e mercury
nucleus.
i n t h e absence of charge t r a n s f o r or o r b i t a l o v e r l a p t h e r e
be a d i r e c t p r o p o r t i o n a l i t y between q and q , t h e d i r e c t f i e l d
172
due s o l e l y t o t h e p r e s e n c e of HCl:
q
Here, y
= q o ( l - YM) •
will
gradient
(111-17)
i s t h e S t e r n h e i m e r s h i e l d i n g f a c t o r , which i s s p e c i f i c t o a
g i v e n c l o s e d - s h e l l atom o r i o n .
We c a l c u l a t e q
using a simple expansion
of t h e m u l t i p o l e moments of t h e c y l i n d r i c a l l y - s y m m e t r i c HCl or HCN m o l e c u l e :
230
_§U_ ,„ ,
,v _ " ^ n /„ .
, _ 20fi
q o = - ^f- (P^cosy)) - -—• (P2(cosY)>v - ~
(P3(cosY)> - . . .
cm
cm
Here, y, Q,
(111-18)
cm
and Q are, respectively, the dipole, quadrupole, and octupole
moments of HCl or HCN.
The moments of HCl are listed m Table 11-12, while
those of HCN appear in Table 111-15.
Values of R
and
cm
from Tables III-4
and HI-16 were used to carry out this calculation; (p (cosy)) and
(P_(COSY))
were generated algebraically from Y.- as Stark data is not
presently available to determine (p..) , and (p.) cannot be determined experimentally.
The hexadecapole moment of HCl is known, but fourth-order terms
were not included in q , as (P.) < 0 when calculated algebraically from Y,
which is physically unreasonable for a complex that is linear at equilibrium.
The reasons for the expected rapid convergence of Eq. (111-18) for linear
172
systems have been discussed elsewhere.
was applied to the calculation of q
rapid convergence was also observed,
For consistency, the same method
for HC
N
Hg and DC
N
Hg, where
The results of Eq. (111-18) are:
q (HgHCl) = -4.79(39) x 10 2 SC«cm"3
q (HgDCl) = -5.77(65) x 10 1 2 SC«cm~3
q (HCNHg) = +2.99(97) x 10 1 2 SC«cm~3
q (DCNHg) = +3.04(86) x 10
SC.cm"
The errors in parentheses are taken as the sum of the uncertainty in the
second term due to the estimated error in the experimental determination of
0 , and the entire contribution from the third term, which gives some m d i m
cation of the rate at which the series is converging.
If we combine Eqs. (111-16) and (111-17), we get the expression
231
X
9
=
j;
(111-19)
which establishes a direct proportionality between q and x
•
In the
absence of significant charge transfer, orbital overlap, or electric
dipole polarization contributions to q, a plot of x
versus (-eq /h) should
be a straight line with slope Q(l - y ) and y-intercept a t the origin.
This plot appears as Fig. III-7.
units of MHz/b, are:
The calculated values of
0.347(28) for
(-eq / h ) , in
201
HgH35Cl, 0.418(47) for
-0.216(70) for HC15N201Hg, and -0.220 (.62) for DC15N201Hg.
201
HgD35Cl,
(Note:
lb =
,„-24
2 .
10
cm .)
A best-fit straight line is determined from the three available data
points.
Since the (-eqQ/h) values for HC N
Hg and DC N
within error, only the former was used in this analysis.
Hg are equal
The slope of the
line is 21.5 (27)b, and i t s y-mtercept i s -1.39(80) MHz, where the numbers
in parentheses represent one standard deviation of uncertainty.
viously,
172
Pre-
the y-intercepts of graphs of this kind were used to obtain
estimates of the amount of charge transfer in Kr and Xe complexes, using
arguments of the kind developed by Townes and Dailey,
valence p-orbitals of the rare gas atoms.
174
applied to the
Such a calculation is not appli-
cable to HgHCl, as the electric field gradient at the mercury nucleus due
to charge transfer would be zero for the spherically-symmetric mercury
6s orbital.
In the case of HCN-Hg, any charge transfer would be expected
to occur into the normally empty mercury 6p orbitals.
A second complica-
tion in the interpretation of the y-intercept of Fig. III-7 is the fact
that contributions of electric dipole distortions of the mercury atom to
the electric field gradient may not be entirely negligible for the three
232
Figure III-7.
Plot of (.-eq /hi vs. x
f° r
H
9" complexes.
The slope of this line is related to the quadrupolar shielding constant, y , of mercury.
233
-ecg[calc)/h (MHz/b)
234
systems here, as they were estimated to be for the krypton- and xenon143
containing complexes.
This results in part from the greater polariza-
bility and smaller van der waals radius of the Hg atom, relative to Kr
or Xe, and also from the fact that, in the HCl-contaming systems, HgHCl
is more nearly linear, on average, than KrHCl or XeHCl.
Using the one-
143
electron model discussed for the particular case of XeHCl,
the most
important electronic excitation contribution to x(
to be the 6 S
+ 6 P
dipole-allowed transition.
201
Hg) would be expected
We calculate contributions
to x( ° Hg) of -0.9 MHz for HgHCl, -1.3 MHz for HgDCl, and -0.8 MHz for
HCNHg.
It is important to note that since electric dipole distortions of
the mercury atom contribute to q in second order, these contributions
201
would have the same sign for all three Hg systems studied. Because x(
Hg)
changes sign in going from HgHCl to HCNHg, a change characteristic of an
odd-order interaction such as that described by Eq. (111-19), electric
dipole distortion cannot be the predominant contribution to x(
these systems.
201
Hg) in
However, such distortion will be expected to produce a
difference from zero in the y-mtercept of Fig. III-7 on the order of
1 MHz or less.
Since the measured intercept of -1.4(8) MHz is already zero
within less than three standard deviations of uncertainty, we conclude that
charge transfer in HCNHg probably amounts to less than a few thousandths of
an electron, using a conversion of 780 MHz per electron estimated for the
175
6p mercury orbital by Dehmelt, Robinson, and Gordy,
with no evidence
z
that any charge transfer actually occurs.
Using the Hg quadrupole moment quoted above and Eq. (111-19), we
arrive at a value of -4.72 (.70) for the quadrupolar shielding constant of
mercury.
The quoted error includes both the uncertainty in the slope of
235
I I I - 7 , and the u n c e r t a i n t y in Q 9 of roughly 9%.
Fig.
t i o n s of Y
1
Previous c a l c u l a -
include a r e l a t i v i s t i c Hartree-Fock-Slater free-ion c a l c u l a -
00
148
++
tion,
giving a value of -88.73 for neutral mercury (-60.20 for Hg ) ,
and a nonrelativistic HFS calculation, which separates effects from the
176
Xe-like core and the 5d electrons,
resulting in a value of -50.82.
The discrepancy between the y
of Ref. 148 and our effective number is
much large than was observed in Kr and Xe, both of which showed agreement
to within 15%. The agreement between the experimental value and the nonrelativistic calculation is better.
Because the Sternheimer shielding
constant is only defined for the situation in which the perturbing charge
lies entirely outside the radius of the atom or ion in question, it is
best to consider the shielding constant obtained here to be an effective
value in these complexes, albeit an experimentally well-established one.
The bulk of the material in this section is drawn from Ref. 159,
incorporating results from Ref. 171. It should be noted at this point
that the value of Y given here differs slightly from that reported in
the abstract of a paper given at the 1983 Fall Meeting of the American
Physical Society.
177
That value, -39, was based solely on HgHCl and HgDCl
data.
E.
Other Possible Uses for the Heated Nozzle System
The heated-nozzle system used in t h i s study expands the range of
m a t e r i a l s which can be studied using the pulsed Fourier-transform technique.
For example, weakly-bound complexes involving the aromatic heterocycle
furan have been studied by t h i s group.
'
I t would be i n t e r e s t i n g to
c o n t r a s t t h e behavior of furan with t h a t of o t h e r , s i m i l a r aromatic h e t e r o cycles ( e . g . , p y r r o l e and pyridine) whose vapor p r e s s u r e s might make i t
236
difficult or impossible to perform rotational spectroscopy using a roomtemperature molecular source.
It is also possible that low-melting
organic solids may now be studied using this technique.
Several more complexes of interest involving mercury remain to be
studied.
A search for a weakly-bound complex between mercury and hydrogen
fluoride has been conducted, thus far without success.
Determination of
the atomic order of this complex (HgHF or HFHg) would tell us much about
the nature of the binding of mercury in these complexes.
In particular,
it would provide an interesting test of the Lewis acid/base model in
describing weakly-bound complexes. From the structures of the complexes
ArHCN, 161 KrHCN, 160 ArCO , 6 6 HCN-C0 2 , 167 OCO-HF,97 OCO-HCl,54 HF-HC1, 178
HCN-HC1,53 HCN-HF,
9
and HCN-HBr,180 a qualitative table of Lewis basicities
can be drawn up, with Ar, Kr > HCN > CO
> HF > HCl > HBr. With the study
of HgHF (or HFHg), mercury could be placed on this table.
Moreover, it
would be possible, with the study of additional complexes such as HgCO ,
to ascertain whether the Lewis acid/base model can reliably predict gross
structures of weakly-bound complexes.
In addition, there has been much interest in mercury-rare gas com181
plexes, due to their possible application in excimer lasers.
Interac-
182
tion potentials from absorption spectra have been studied for HgAr,
183
HgKr,
184
and HgXe.
The heated nozzle system would be well suited to the
study of the structures of these complexes, provided they possess a sufficient induced dipole moment to be detected.
To study other more refractory
metals, the pulsed Fourier-transform technique can perhaps be adapted for
use with a laser vaporization system, as in recent work by Smalley and
coworkers on the copper dimer.
237
Eq. (111-14) shows that the effective temperature of the molecular
beam goes linearly as the source temperature.
Since hotter beams result
from hotter nozzles, it is possible that a sufficiently hot nozzle might
produce a beam in which excited vibrational states of weakly-bound complexes are significantly populated.
Structural studies of such excited
states would provide a direct link to the equilibrium structures of these
complexes, as well as a wealth of information on intermolecular potentials.
A. C. Legon and coworkers have measured excited-state transitions for
179
HCN-HF,
186
CH CN-HF,
187
(CH ) CCN-HF,
gas microwave spectrometer.
188
and H O-HF
in a cold, static-
The nature of these experiments is such that
only strongly-bound complexes (such as those involving HF) can be studied.
The heated nozzle opens the possibility of determining excited-state
structures for more weakly-bound species, such as rare gas complexes, whose
pg 189
potentials have been studied in great detail in recent years. '
A
search for such excited-state species is currently underway, conducted
by S. B. O'Brien, under the direction of J. M. Lisy.
238
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7
x
20
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3
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VITA
James Arthur shea was horn on October 2, 1957, in Stoneham, Massachusetts.
He attended Medford High School in Medford, Massachusetts,
where he was a member of the National Honor Society.
He obtained a
diploma in 1975. He pursued undergraduate studies at Tufts University,
majoring in Chemistry.
He received an award by the Massachusetts Chapter
of the American Institute of Chemists in 1979, and graduated from Tufts
with a B.S. degree in June of that year. He attended graduate school at
the University of Illinois, working under the late Professor W. H. Flygare,
and will receive a Ph.D. in physical chemistry in May, 1984. He is a
member of the American Chemical Society and the American Physical Society.
During his graduate work, he presented papers at the Thirty-Eighth Symposium on Molecular Spectroscopy at the Ohio State University, Columbus, Ohio
and at the 1983 Fall Meeting of the American Physical Society in San
Francisco, California.
He is coauthor of the following publications:
"The Rotational Spectrum and Molecular Geometry of the Cyclopropane-HF
Dimer", L. W. Buxton, P. D. Aldrich, J. A. Shea, A. C. Legon, and
W. H. Flygare, J. Chem. Phys. 75_, 2681 (1981).
"The Rotational Spectrum and Molecular Structure of the Ethylene-HF Complex", J. A. Shea and W. H. Flygare, J. Chem. Phys. 7<5_, 4857 (1982).
"The Microwave Spectrum and Molecular Structure of the Furan-HCl Complex",
J. A. Shea and S. G. Kukolich, j. Am. Chem. Soc. 104, 4999 (1982).
"The Microwave Spectrum and Molecular Structure of the Furan-Argon Complex", S. G. Kukolich and J. A. Shea, J. Chem. Phys. 77_, 5242 (1982).
"The Electric Dipole Moments of OCHF and OCDF", E. J. Campbell, W. G.
Read, and J. A. Shea, Chem. Phys. Lett. 94, 69 (1983).
"The Rotational Spectrum and Molecular structure of the Furan-HCl Complex", J. A. Shea and S. G. Kukolich, J. Chem. Phys. 78, 3545 (1983).
249
"The Rotational Zeeman Effect in the OCO-HF, OCO-DF, OCO-HCl, and SCO-HF
Complexes", J. A. Shea, W. G. Read, and E. J. Campbell, J. Chem. Phys.
79_, 614 (1983) .
"The Rotational Zeeman Effect in the ArOCS van der Waals Complex", J. A.
Shea, W. G. Read, and E. J. Campbell, J. Chem. Phys. 79, 2559 (1983) .
"Molecular Beam Microwave Spectroscopy on Complexes", S. G. Kukolich,
J. A. Shea, P. D. Aldrich, E. J. Campbell, and W. G. Read, 186th
National Meeting of the American Chemical Society, Fall, 1983.
"Measurements of Molecular g-values, Magnetic Susceptibility Anisotropics,
and Quadrupole Moments for the Acetylene-HCl Complex", S. G. Kukolich,
W. G. Read, J. A. Shea, and E. J. Campbell, J. Am. Chem. Soc. 105, 6423
(1983).
"Rotational Spectroscopic Constants and Structure of the Mercury-Hydrogen
Chloride van der Waals Complex", E. J. Campbell and J. A. Shea, J. Chem.
Phys. 79, 4082 (1983).
"The Rotational Spectrum and Molecular Structure of the Argon-Carbonyl
Fluoride Complex", J. A. Shea and E. J. Campbell, J. Chem. Phys. 79_,
4724 (1983).
"Rotational Zeeman Effect and Coriolis Coupling in NeHCl and KrHCl",
E. J. Campbell, W. G. Read, and J. A. Shea, Mol. Phys. 51, 0000 (1984) .
"The Microwave Spectrum and Properties of the Propyne-HF Complex", J. A.
Shea, R. E. Bumgarner, and Giles Henderson, J. Chem. Phys. 80, 0000 (1984).
201
"The Rotational Spectra, Molecular Structures and
Hg Quadrupole Coupling
Constants of HgHCl and HgDCl", J. A. Shea and E. J. Campbell, J. Chem.
Phys. (submitted for publication).
"The Rotational Spectrum and Molecular Structure of the HCN-Hg Complex",
J. A. Shea and E. J. Campbell (in preparation).
"The Rotational Zeeman Effect in ArHCN", E. J. Campbell, J. A. Shea, and
W. G. Read (in preparation).
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