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THE STUDY OF VARIOUS HYDROGEN-BONDED COMPLEXES USING PULSED, FOURIER-TRANSFORM FABRY-PEROT MICROWAVE TECHNIQUES

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Aldrich, Peter Douglas
THE STUDY OF VARIOUS HYDROGEN-BONDED COMPLEXES USING
PULSED, FOURIER-TRANSFORM FABRY-PEROT MICROWAVE TECHNIQUES
University of Illinois at Urbana-Champaign
University
Microfilms
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PH.D. 1983
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THE STUDY OF VARIOUS HYDROGEN-BONDED
COMPLEXES USING PULSED, FOURIER-TRANSFORM
FABRY-PEROT MICROWAVE TECHNIQUES
BY
PETER DOUGLAS ALDRICH
A . B . , U n i v e r s i t y of I l l i n o i s a t C h i c a g o , 1979
M . S . , U n i v e r s i t y o f I l l i n o i s a t U r b a n a - C h a m p a i g n , 1982
THESIS
Submitted i n p a r t i a l f u l f i l l m e n t of the r e q u i r e m e n t s
for the d e g r e e of Doctor o f P h i l o s o p h y m Chemistry
i n t h e Graduate C o l l e g e of t h e
U n i v e r s i t y of I l l i n o i s a t Urbana-Champaign, 1983
Urbana,
Illinois
UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN
T H E GRADUATE COLLEGE
MAY, 1983
W E HEREBY RECOMMEND THAT T H E THESIS BY
PETER DOUGLAS ALDRICH
RNfTTTTTT)
THE STUDY OF VARIOUS HYDROGEN-BONDED COMPLEXES USING PULSED,
FOURIER-TRANSFORM, FABRY-PEROT MICROWAVE TECHNIQUES
BE ACCEPTED IN PARTIAL F U L F I L L M E N T OF T H E REQUIREMENTS FOR
DOCTOR OF PHILOSOPHY
T H E DEGREE OF_
V
siuhud
Director of Thesis Research
Head of:Department
c
-
^
-
—
t
t Required for doctor's degree but not for master's
ill
THE STUDY OF VARIOUS HYDROGEN-BONDED
COMPLEXES USING PULSED, FOURIER-TRANSFORM,
FABRY-PEROT MICROWAVE TECHNIQUES
P e t e r D o u g l a s A l d n c h , Ph D.
D e p a r t m e n t o f Chemistry
U n i v e r s i t y of I l l i n o i s a t U r b a n a - C h a m p a i g n ,
A series
tained for
of s t u d i e s
is presented
v a r i o u s hydrogen-bonded,
i n which m i c r o w a v e s p e c t r a
The p u l s e d
small
Fourier-transform,
t e c h n i q u e i s u s e d a l l o w i n g nuclear q u a d r u p o l e c o u p l i n g
other v a r i o u s
hyperfine
normal r o t a t i o n a l
dated for
a r e ob-
g a s phase c o m p l e x e s b e t w e e n
h y d r o c a r b o n s a n d h y d r o g e n h a l i d e s o r HCN.
Fabry-Perot
1983
the
t i o n of t h e
interactions
spectra.
Details
t o be o b s e r v e d
of s t r u c t u r e
complexes from z e r o - f i e l d
rotational
Zeeman e f f e c t
in a d d i t i o n
to
a n d binding a r e
spectroscopic constants.
for complexes
involving
gives a d d i t i o n a l e l e c t r o n i c d i s t r i b u t i o n i n f o r m a t i o n
and i s s h o w n t o i n d i r e c t l y g i v e m a g n e t i c p r o p e r t i e s
The c o m p l e x e s d i s c u s s e d i n c l u d e c o m p l e x e s b e t w e e n
the
eluciObserva-
cyclopropane
for t h e
for
and
complexes
cyclopropane.
cyclopropane
a n d HC1,
HF, and HCN a n d c o m p l e x e s b e t w e e n e t h y l e n e or a c e t y l e n e and HC1 o r HCN.
Also, the e x t e n s i o n of t h e p u l s e d F o u r i e r - t r a n s f o r m ,
Fabry-Perot
wave t e c h n i q u e t o s t u d y e l e c t r o n i c a l l y e x c i t e d t r i p l e t
The f i r s t
and d i s c u s s
two c h a p t e r s d e a l w i t h complexes
the zero-field
and Z e e m a n microwave
states
involving
spectroscopic
the magnetic p r o p e r t i e s
t h o s e of t h e
c o m p l e x e s b y s u b t r a c t i n g o u t the v i b r a t i o n a l l y
of
t h e binding
Thp f o l l o w m q
constants.
of c y c l o p r o p a n e a r e o b t a i n e d
from
averaged
partners.
f o u r c h a p t e r s d e a l with t h e a c e t y l e n e - H C N ,
HC1, and e t h y l e n e - H C l
discussed.
cyclopropane
In a d d i t i o n ,
effects
is
micro-
c o m p l e x e s m o s t l y in t e r m s
of
their
acetylene-
zero-field,
IV
ground vibrational state rotational spectra.
Strength of binding,
vibrational motions in the complex, nuclear spin statistics, charge
rearrangement in the subunits, along with structural details are
discussed for the three complexes.
Electric field gradients at quadru-
polar nuclei are examined in terms of perturbations introduced upon
complexation in order to explain experimental anisotropics and inadequacies in projection models.
The final chapter discusses the combination of the pulsed Fouriertransform, Fabry-Perot microwave technique with electronic excitation
through flashlamps to achieve microwave spectra for electronically
excited triplet species.
The feasibility of having sufficient signal-
to-noise is discussed in detail for small carbonyls where the n ->- IT*
transition is excited prior to microwave excitation.
V
ACKNOWLEDGMENT
I express my indebtedness for having worked in a research group with
a tradition of competence and dedication.
I hope I have lent continuity
to these principles and am thankful to have spent four years in such an
environment.
I express my thanks to the School of Chemical Sciences for giving
all necessary assistance and support and also thank the various professors
of Physical Chemistry who have lent their time for helpful discussions.
I also thank Lynette for having proofread this thesis so carefully.
vi
TABLE OF CONTENTS
CHAPTER
I.
PAGE
STUDY OF THE CYCLOPROPANE-HCl COMPLEX FROM ITS
ZERO-FIELD ROTATIONAL SPECTRA
A.
B.
C.
D.
E.
II.
D.
E.
F.
G.
H.
I.
Introduction
Experimental
Determination of S p e c t r o s c o p i c Constants f o r
Cyclopropane-H
CI a n d C y c l o p r o p a n e - H C ^ N
C o n s i d e r a t i o n of V i b r a t i o n a l A v e r a g i n g E f f e c t s
Molecular G-values
Magnetic S u s c e p t i b i l i t y Anisotropy
M o l e c u l a r Q u a d r u p o l e Moments
Discussion
M a t r i x Elements i n t h e Uncoupled Basis
29
34
36
49
54
65
68
70
76
THE ACETYLENE-HCN COMPLEX
A.
B.
C.
D.
E.
IV.
. . .
1
3
6
17
27
THE MOLECULAR PROPERTIES OF CYCLOPROPANE AS DETERMINED
FROM ROTATIONAL ZEEMAN STUDIES OF THE CYCLOPROPANE-HCl
AND CYCLOPROPANE-HC15N COMPLEXES
A.
B.
C.
III.
Introduction
Experimental
Assignment and A n a l y s i s of t h e R o t a t i o n a l S p e c t r u m
M o l e c u l a r Geometry a n d B i n d i n g
Conclusion
Introduction
Experimental
Determination of Molecular C o n s t a n t s
Structure
I n t e r p r e t a t i o n of the Nuclear Quadrupole
Constants
THE ACETYLENE-HC1 COMPLEX.
COUPLING ANISOTROPY
A.
B.
C.
D.
86
87
87
98
Coupling
116
A CASE OF NUCLEAR QUADRUPOLE
Introduction
E x p e r i m e n t a l Method and D e t e r m i n a t i o n
Molecular Constants
Molecular Structure
Nuclear Quadrupole Coupling
125
of
126
135
138
VI1
CHAPTER
V.
PAGE
THE ETHYLENE-HC1 COMPLEX
A.
B.
C.
D.
E.
VT.
148
151
151
167
172
PERTURBATION IN THE ELECTRIC FIELD GRADIENTS IN
ACETYLENE-DC1 AND ETHYLENE-DC1
A.
B.
C.
D.
VII.
Introduction
E x p e r i m e n t a l Method a n d D e t e r m i n a t i o n o f
Molecular Constants
Molecular S t r u c t u r e
Vibrational Effects
Discussion
Introduction
Results
Nuclear Quadrupole Coupling
Nuclear Spin-Rotation
176
176
182
186
THE USE OF THE FOURIER-TRANSFORM, FABRY-PEROT MICROWAVE
METHOD FOR THE EXAMINATION OF PARAMAGNETIC TRANSIENT SPECIES
A.
B.
C.
D.
Introduction
Experimental
E x a m i n a t i o n of E l e c t r o n i c a n d V i b r a t i o n a l P r o c e s s e s
I n v o l v e d i n the T r i p l e t S t a t e Experiment
I n t e r a c t i o n s t o be C o n s i d e r e d i n P a r a m a g n e t i c
Systems
188
190
191
201
REFERENCES
206
VITA
215
1
CHAPTER I
STUDY OF THE CYCLOPROPANE-HCl COMPLEX FROM
ITS ZERO-FIELD ROTATIONAL SPECTRA
A.
Introduction
In the following two chapters is presented a comprehensive study
of the cyclopropane-HCl and cyclopropane-HC
tion of their rotational spectra.
N complexes through observa-
A zero-field study
is conducted to
provide structural details, rotational constants, and nuclear quadrupole coupling constants.
served
2
The rotational Zeeman effect is also ob-
by applying an external magnetic field and provides detailed
information regarding electronic distributions in the complexes.
It is
shown that study of these complexes indirectly gives information about
the nature of cyclopropane which connot itself be studied directly by
microwave techniques because of the absence of a permanent dipole moment.
Cyclopropane has been observed to e>hibit certain properties associated with ethylenic compounds.
Ease of hydrogenation
addition of HX to substituted cyclopropanes
for fr-bond character in cyclopropane.
4
3
and Markovnikov
has been used as evidence
The con^ugative ability of cyclo-
propane has been evidenced by consideration of the dipole moment of
cyclopropyl chloride
and various spectroscopic evidence to be discussed
in the next chapter.
Two of the most prominent models for the chemical
S 7
bonding in cyclopropane ' have the electrons involved in carbon-carbon
bonding with their peak density not coinciding with the carbon-carbon
mternuclear axis.
The Coulson-Moffitt model
for cyclopropane has bent
2
carbon-carbon bonds with the a r e a of peak electron density displaced
7
outwaid from the midpoint of the bond. The Walsh model brings t o 2
gether three sp
hybridized carbon atoms with the carbon-carbon bonds
formed from pure p o r b i t a l s and a l s o being b e n t . The carbon-hydrogen
2
bonds contain sp hybridized o r b i t a l s from the carbon atoms leaving the
2
molecule with 3 sp hybridized o r b i t a l s overlapping i n the center of
the r i n g .
The common p r e d i c t i o n of both models, namely, the e l e c t r o n
density displaced outside the ring, i s confirmed experimentally by an
electron density difference map from an X-ray d i f f r a c t i o n study of
8
tricyanocyclopropane
9
and t h e o r e t i c a l l y by an ab i n i t i o SCF c a l c u l a t i o n .
Given t h a t t h i s e l e c t r o n d i s t r i b u t i o n feature i s c o r r e c t i t is reasonable
for the e l e c t r o p o s i t i v e hydrogen atom of HC1, or other hydrogen h a l i d e s ,
to seek t h i s e l e c t r o n rich region forming an e l e c t r o s t a t i c - l i k e hydrogen
bond with cyclopropane.
I t i s also conceivable t h a t i f the Walsh model
were to be a c o r r e c t description of the e l e c t r o n i c d i s t r i b u t i o n in cyclopropane, the hydrogen bond could be formed between the hydrogen atom
and e l e c t r o n density predicted in the center of the ring as a r e s u l t
2
of the carbon atoms' sp
hybridized o r b i t a l o v e r l a p .
The existence of
hydrogen-bonded complexes involving s u b s t i t u t e d cyclopropanes and pfluorophenol has been e s t a b l i s h e d i n the l i q u i d phase through i n f r a r e d
spectroscopy
and from t h i s work the preferred s i t e for bonding of the
proton appears to be the edge of the cyclopropane r i n g .
Clearly, un-
ambiguous s t r u c t u r a l information for the cyclopropane-HCl complex is
d e s i r a b l e i n confirming t h i s region of l i k e l y binding for the hydrogen
atom and might b e s t be obtained in the gas phase i n the absence of
l a t t i c e or s o l v e n t e f f e c t s .
Furthermore, high r e s o l u t i o n work where the
3
effects of nuclear quadrupole coupling of the CI nucleus and centrifugal
d i s t o r t i o n of the complex due to molecular rotation can be observed*can
give i n s i g h t i n t o the nature of the weak binding i n the complex. The use
11-12
of pulsed, Fourier-trans form spectroscopy
where gas is pulsed i n t o
a high vacuum, tuned Fabry-Perot cavity is ideal for meeting these objectives.
The a d i a b a t i c expansion of the gas mixture kept a t .5 to
2.5 atm i n t o a high vacuum through a pulsed, supersonic nozzle generates
large numbers of these complexes with i n t e r n a l temperatures of 1-10K.
This leads to observation of the complex i n i t s ground v i b r a t i o n a l
s t a t e with g r e a t e r population of the lower r o t a t i o n a l l e v e l s .
The
resolution is enhanced as a r e s u l t of low c o l l i s i o n a l l i n e broadening
effects as the complexes are observed i n almost c o l l i s i o n l e s s expansion.
A d e t a i l e d analysis of the r o t a t i o n a l spectra for the three i s o t o p i c
species of cyclopropane-HCl along with information regarding the analagous
13
cyclopropane-HF complex
shows unambiguously t h a t the complex i s on average
with the HC1 hydrogen-bonded to the edge of the cyclopropane ring with
HC1 on the C symmetry axis of the complex.
(See Fig. 1-1).
The spec-
t r a l analysis leads to a description of the hydrogen bond between the
e l e c t r o p h i l i c hydrogen atom and the region of high e l e c t r o n d e n s i t y ,
both i n terms of binding strength and dynamics.
B.
Experimental
The d e t a i l s of the spectrometer employed for t h i s work have been
given in g r e a t d e t a i l previously.
11 12
'
The complexes were generated by
expanding a gas mixture of ~2% of both monomers i n argon a t room temperature and .5-2.5 atm through a solenoid valve with a .5 mm diameter nozzle
•c
Figure 1 - 1 .
M o l e c u l a r geometry and i d e n t i f i c a t i o n o f t h e p r i n c i p a l
i n e r t i a l a x e s ( a , b , c) i n c y c l o p r o p a n e - h y d r o g e n
chloride.
The o r i e n t a t i o n chosen f o r c y c l o p r o p a n e d e f i n e s t h e a n g l e
<>
j = 0 f o r r o t a t i o n a b o u t t h e l o c a l c_ a x i s .
6
opening into a Fabry-Perot cavity which i s a t -10
Torr.
All r o t a -
t i o n a l t r a n s i t i o n s within the cavity bandwidth (~1 MHz) were then
p o l a r i z e d by a s u i t a b l y delayed 3.0 ys microwave power p u l s e .
The
r e s u l t i n g coherent molecular emission time domain s i g n a l i s subsequently
d i g i t i z e d a t a r a t e of .5 ys per point for 256 p o i n t s .
Approximately
20 s i g n a l s are then taken a t a r a t e of ~1 Hz with every a l t e r n a t e s i g n a l ,
which i s taken with no gas in the cavity, subtracted from the average to
eliminate any coherent n o i s e .
The averaged signal i s then Fourier
transformed t o give the power spectrum which c o n s i s t s of 256 p o i n t s a t
3.9 kHz per p o i n t r e s o l u t i o n .
A c h a r a c t e r i s t i c Doppler doubling i s
p r e s e n t in the frequency spectrum varying from 5-30 kHz with the actual
molecular resonance l o c a t e d a t the midpoint of the two Doppler components.
This phenomenon i s well understood and has been described i n d e t a i l
elsewhere.
C.
12
The half-widths a t h a l f h e i g h t are t y p i c a l l y ~6 kHz.
Assignment and Analysis of the Rotational Spectrum
The r o t a t i o n a l s p e c t r a of three i s o t o p i c species of cyclopropane-HCl
are t h a t of a near p r o l a t e asymmetric top (K = - . 9 9 3 ) with an accompanying
hyperfme s t r u c t u r e due to the nuclear quadrupole i n t e r a c t i o n of a CI
nucleus .
The nuclear quadrupole coupling constants of CI i n the complex,
given by
eQ q
j ^ 2 2 - (g=a,b,c)
CI
where Q i s the nuclear quadrupole moment of the CI nucleus and q
is
gy
the e l e c t r i c f i e l d gradient a t the CI nucleus along the g a x i s , couples
the angular momentum of CI (I = 3/2) to t h a t of the nuclear framework (J)
7
to give the resultant angular momentum F = I + J.
sitions was made in the nearly diagonal basis
is not necessary for the zero-field study.
Assignment of tran-
|jKIF) where M dependence
Excited vibrational states
were not observed presumably because these states are insufficiently
populated at the low temperature of the gas.
Even in the ground vibra-
tional state rotational transitions involving levels with K_, ^ 2 were
weaker than expected because such levels are ~3 cm
higher m energy
35
than K
= 0 states.
The spectra of the cyclopropane-D
CI species in-
volved the complication of a deuterium quadrupole moment, which causes
a small s p l i t t i n g in each hyperfme component.
The major portion of the
intensity however does not move appreciably from a zero deuterium quadrupole prediction and thus this interaction was ignored in the analysis.
The hyperfme components for the rotational transitions of the various
isotopic species of cyclopropane-HCl are listed in Table 1-1.
in Table 1-1 was reduced by the following two-step process.
The data
First, ob-
served frequencies were corrected for second order nuclear quadrupole
effects in the symmetric top basis.
This is done with available tables
14
where a tabulated result for the corresponding symmetric top limit transi2
-3
tion is multiplied by an approximate value for 2\
/(B+C) x 10 . Due
3.3.
to the estimated accuracy of the measurements of ~3 kHz, second order
effects, where the nuclear quadrupole interaction is treated as a perturbation to the pure rotational Hamiltonian, are significant and range
from 0-20 kH<s.
X
and XUK'
an(
The two independent nuclear quadrupole coupling constants,
* the zero-quadrupole rotational frequencies, V , were then
related to the observed quadrupole components, V
V
ob "
A
2nd -
C
a*aa
+ C
b*bb
+ V
o
, by the expression
{l
~1]
8
Table
Observed and C a l c u l a t e d F r e q u e n c i e s
1-1
(MHz) of R o t a t i o n a l
Transitions
i n t h e Ground S t a t e of I s o t o p i c S p e c i e s of (V, HC1)
Transition
I s o t o p i c Species
35
J
K
•*" J ' i i
K
-1 1
-1K1
K
3
13 *" 2 12
F
•*• F'
obs
5a
7/2 + 7/2
8820.620
b
5/2 «- 3/2
8827.297
7/2 -s- 5/2
-*- 2
obs
obs
8592.948 - 0 . 0 0 2
8815.648 - 0 . 0 0 2
Q.003
8598.233
0.001
8822.589
0.002
8827.382
0.001
8598.279 - 0 . 0 0 2
8822.680
0.002
9/2 «- 7/2
8830.800
0.001
8600.970
8826.230
0.003
5/2 -(-5/2
8832.138
b
3/2 •*- 1/2
8830.677-0.005
7/2 -f- 7/2
0.000
8602.032 - 0 . 0 0 2
3/2 -*- 3/2
3
(V, D 35 C1)
(V, H 37 C1)
(V, H CI]1
8600.911
8827.620 - 0 . 0 0 4
0.006
8606.244 - 0 . 0 0 1
8917.326 - 0 . 0 0 1
5/2 •*- 3/2 >
>8927.550
3/2 *• 1/2J
0.002
—
—
8912.127
0.013
8693.410 - 0 . 0 0 0
8922.738 - 0 . 0 1 7
8696.074
8926.275
0.001
8932.899
0.00 3
9 / 2 +• 7/2*
y
'89 30.925-0.00 2
7/2 <- 5 / 2 . '
3
•*• 2
5/2 f- 5/2
8937.290
b
3/2 <- 3/2
8941.145
0.001
9/2 •*• 7/2
8934.144
7/2 •*• 5/2
5/2 •*• 3/2
8930.30 7
b
3/2 *• 1/2
8943.928
b
0.000
b
8692.512 - 0 . 0 0 1
b
8687.893
0.001
9
Table 1-1
(Continued)
Transition
I s o t o p i c Species
(V, H35C1)
J,, v *• J ' , ,,,
K
K ,K
llKl
3
<- 3
F
<- F'
v ,
(V, H37C1)
6a
o b s
V.
(V, D35C1)
6
o b s
9/2 +• 7/2
8934.935
0.005
7/2 «- 5/2
8921.339 -0.001
V.
(
o b s
8699.27 3 - 0 . 0 0 4
8688.559
0.004
5/2 «- 3/2
3
«- 2
4.,, «- 3 , ,
14
13
3/2 +• 1/2
8944.660-0.004
7/2*-
7/2
9023.352
5/2 •*- 3/2
9030.065
0.001
8790.472
7/2 •<- 5/2
9030.164
0.001
8790.551-0.002
3/2 •<- 1/2
9033.453 -0.004
8793.154
0.006
9/2 *• 7/2
9033.573
8793.240
0.000
5/2 •*• 5/2
90 34.945
8794.320 -0.002
3/2 «- 3/2
9040.291
8798.541 - 0 . 0 0 1
7/2 *- 5/2 11770.765
'
'
8785.175 -0.002
0.001
0.000 11465.041 - 0 . 0 0 1 11764.558 - 0 . 0 0 1
9/2^- 7/2 11771.470 -0.003 11465.596
5/2 f- 3/2 11772.124
11/2 <- 9/2 11772.836
4„„ •<- 3„„
04
03
0.001
0.000 11765.292 - 0 . 0 0 1
0.001 11466.109 -0.002 11765.970 -0.002
0.002 11466.673
0.002 11766.713
0.004
7/2 •*- 5/2 11904.784 -0.001 11592.176 -0.004 11898.488 - 0 . 0 0 1
'
'
5/2+
3/2 11904.793
0.005 11592.186
9/2 «- 7/2 11906.345 -0.022
11/2 •*- 9/2 11906.386
0.018 11593.427
0.004 11898.502 - 0 . 0 0 3
11900.153
0.004
0.000 11900.160
0.001
10
Table 1-1
(Continued)
Transition
Isotopic
(V, H 3 5 C1)
J T , „ -<-J', „ ,
K • ,K,
1 1 K' - 1KL1
4
3 2 "*" 3 3 1
4
F
•<- F '
9//2
"*"
7 / 2
v .
obs
1 1 8 9 7
-703
b
1 1 / 2 *• 9 / 2 1 1 9 0 9 . 9 7 8
b
21
v .
obs
9 / 2 «- 7 / 2 1 1 9 0 3 . 2 4 3 - 0 . 0 0 2 1 1 5 9 0 . 9 9 4
5
9 / 2 •<- 7 / 2 1 1 9 0 5 . 1 1 9
1 1 / 2 «- 9 / 2 1 1 9 1 0 . 5 4 7
<- 3
(
-0.009
0.002 11595.287 - 0 . 0 0 1 11902.567
0.009
b
—
0.002
7 / 2 •*- 5 / 2 1 2 0 4 1 . 1 0 5
0.000
11721.373
0.000
9 / 2 <- 7 / 2 1 2 0 4 1 . 8 1 4 - 0 . 0 0 2 1 1 7 2 1 . 9 3 3
0.000
5 / 2 «- 3/2 1 2 0 4 2 . 4 6 3
11722.443
0.002
0.001 11723.009
0.002
1 1 / 2 •*- 9 / 2 1 2 0 4 3 . 1 7 8
11898.744
-0.005
11900.748
O.005
0.002 11597.191
5 / 2 -<- 3 / 2 1 1 9 1 2 . 4 4 5
5 is the difference
V,
obs
0.001 11896.890
7 / 2 *• 5 / 2 1 1 9 0 7 . 0 0 9 - 0 . 0 0 4 1 1 5 9 4 . 1 6 2
4
D 3 5 C1)
11905.164
1 1 / 2 «- 9 / 2 1 1 9 0 8 . 6 9 4
3
(V,
b
9 / 2 -<- 7 / 2 1 1 8 9 7 . 7 3 1
7 / 2 f- 5 / 2
22 *
6a
b
4 2 3 -<- 3 2 2
4
(V, H 3 7 C 1 )
1 1 / 2 «- 9 / 2 1 1 9 0 9 . 9 6 3
•<- 3
Species
0.000
v-v
,
between v the observed frequencies
corrected
calc
for small second order e f f e c t s and the frequencies V .
o b t a i n e d from
i X., a n < * v
values.
aa
bb
c
l e a s t square analysis for x
and
the l e a s t squares analysis
Not i n c l u d e d m
the
for x
Xhh•
11
where x
an L
^ Xv,>, a
r e t n e
^ nuclear quadrupole coupling constants along
the a_ and b principal axes, A_ . is the second order nuclear quadrupole
correction and C and C. are given by
c
l r j , 2 j ' + 3 , 2' 2'.
2 ,,
c 2J+3, 2
-, = rt f —77~to -a ) - f — — a -a )]
a h
J'
ciz cz
J
az cz
n
S
=
lr^,2J'-f3, 2'
2'
^ 2J+3. 2
]
(I
3/4C(C+l)-I(I-fl)j(J+l)
21(21-1)(2J-1)(2J+3)
C = F(F+1)-I(I+1)-J(J+1)
a
2 .,
hIf -7-<BbB-ac«} " f -5Hab«-a0«)
1
fi-2)
*'
KX
"3)
(I
.
~4'
(1-5)
is the direction cosine between the z-axis and the g_ principal axis
averaged over the appropriate asymmetric top wavefunction.
Using this equa-
tion and applying the least squares method to the observed frequencies in
Table 1-1 leads to the zero-quadrupole rotational frequencies in Table 1-2
and the nuclear quadrupole coupling constants in Table 1-3.
The results in Table 1-2 were f i t as described below with centrifugal
distortion being treated in the symmetric top limit.
This is justified by
the near prolate value of K and the limited number of transitions in the
range of our spectrometer.
Though exact analysis would employ nine T distor-
tion constants, the frequencies of only seven zero-quadrupole rotational
transitions, a l l of which are AK = 0, R-branch, y
available precluding this exact treatment.
dipole type are presently
In the symmetric top limit, the
centrifugal distortion contribution to each transition i s given by
-4DJ(J+1)3 - 2{J+1)K21DJK
where
(T-6)
12
Table
1-2
Unperturbed R o t a t i o n a l T r a n s i t i o n F r e q u e n c i e s
(MHz)
I s o t o p i c S p e c i e s of (V, HCl)
Transition
I s o t o p i c Species
(V, H 35 C1)
(V, H 37 C1)
(V, D 35 C1)
12
8829.335
8599.825
8824.708
3
<- 2
03
02
8930.278
8695.562
8925.597
4-2
^21
8930.300
8695.546
89 31.040
8696.209
9032.110
8792.087
11772.028
11466.037
11765.872
11905 .954
1159 3.102
11899.718
11906.710
11593.726
11900.506
11908.563
11595 .385
11902.357
12042.370
11722.371
3
13 *
3
22
2
3
21 *
2
20
3
12 *
2
11
14
J
13
4
4- 3
J
03
4
4- 3
J
32
31
04
4
4
30
•*- 3
23
4
11906.0 34
•+• 3
31
11906 .012
22
+-3
J
22
21
4
-+-3
J
13
12
E s t i m a t e d a c c u r a c y 0 . 0 0 3 MHz.
13
Table
1-3
Ground S t a t e S p e c t r o s c o p i c
of I s o t o p i c S p e c i e s of
Spectroscopic
Constant
Constants'
(V, HCl)
( 7 , H35C1)
(V, H 3 7 C 1 )
(V, D 3 5 C1)
A (MHz)
200 3 4 ( 4 4 )
20043(36)
20035(52)
B (MHZ)
1522.332(1)
1481.4477(7)
1521.531(2)
C (MHz)
1454.744(1)
1417.3625(7)
1453.978(1)
D T (kHz)
1.87(2)
1.92(3)
1.79(4)
J
29.8(2)
28.4(1)
29.0(3)
-54.41(2)
-42.91(3)
-56.65(3)
27.25(7)
21.49(8)
2B.47(5)
X CC (MH Z )
27.16(7)
21.42(8)
28.18(5)
P. (amu & )
20 . 3 2 5
20.320
20.328
P (amu A )
c
4.901
4.895
4.896
DjK(kHz)
X a a (MH Z )
X b b (MHz)
Figures in parentheses
are standard deviations
calculated in the
squares analyses .
b
P , = - 1/2
b
'
(I - I - I ) = Z.m.b 2 ; P
b
a c
1 1 1 c
= - 1/2 ( I - I - I . ) = I m c 2
' c a b
1 1 1
n
C o n v e r s i o n f a c t o r BI = 5 0 5 3 7 9 . 0 amu A
MHz.
least
14
D
h4
="^r
J
4
T
T
(1-7)
'
v
xxxx
.4
D w = - 2 D , - ^ {x
+2T
}
JK
J
2
xxzz
xzxz
(1-8)
'
v
This follows from t h e Kive I s on-Wilson t r e a t m e n t i f we assume K
= (p ) and
-1
z'
i f terms i n v o l v i n g R , RR , and
c a n be n e g l e c t e d where
a n d 66
5' 6'
J
R c = - 1/32 [T
-T
-2(x
+2T
) +
5
xxxx yyyy
xxzz
xzxz
2(T
) lh
+2T
yyzz
4
yzyz
R. = 1/64 [T
+x
-2(T
+2T
) ]h 4
6
xxxx yyyy
xxyy
xyxy "
^ ^ ^ ^ ^ x x x x - V y y ^
(I
'
"9)
R c , R., and 6 , a r e c l e a r l y e q u a l t o 0 f o r a t r u e symmetric top and t h e terms
b o
J
i n v o l v i n g t h e s e q u a n t i t i e s a r e e x p e c t e d t o make m i n o r c o n t r i b u t i o n s t o cent r i f u g a l d i s t o r t i o n for t h e t r a n s i t i o n s c o n s i d e r e d h e r e .
Also, s i n c e AK . =
0 , D need n o t be c o n s i d e r e d as i t s c o e f f i c i e n t w i l l always be 0 i n t h e above
approximation.
This i n t u i t i v e l y c o r r e c t t r e a t m e n t was t e s t e d f o r a c c u r a c y
w i t h d a t a f o r a molecule w i t h a s i m i l a r K, v i n y l b r o m i d e , where D a n d D
u
JK
were c a l c u l a t e d e x a c t l y from t h e T ' s which were i n t u r n c a l c u l a t e d from a
l a r g e number of d i f f e r e n t
y
and a
transitions.
Comparison o f t h e e x a c t
D and D w i t h t h o s e o b t a i n e d through our s y m m e t r i c t o p l i m i t a n a l y s i s
J
JK
showed no d i f f e r e n c e o u t s i d e of e x p e r i m e n t a l
error.
Using t h i s symmetric t o p c e n t r i f u g a l d i s t o r t i o n a n a l y s i s , the
zero-
quadrupole r o t a t i o n a l frequencies were f i t i n the following i t e r a t i v e
fashion.
Approximate g u e s s e s a r e made for A, B, and C.
frequencies
Next, r i g i d
are c a l c u l a t e d by e v a l u a t i n g t h e m a t r i x r e p r e s e n t a t i o n i n
symmetric t o p b a s i s f o r t h e r i g i d r o t o r , asymmetric t o p Hamiltonian
rotor
the
15
, 2
H==
2TTA ,
, 2 2TTB ,
+
~ ?A 1 T ? B
, 2
2TTC
1O,
/T
+ J
(I 10)
IT ~C IT
-
The m a t r i x i s t h e n d i a g o n a l i z e d t o give t h e r i g i d r o t o r asymmetric e n e r g y
l e v e l s and s u b s e q u e n t asymmetric t r a n s i t i o n f r e q u e n c i e s .
lowing e q u a t i o n may be used i t e r a t i v e l y
Next, the
fol-
t o improve the v a l u e s of A, B,
and C and t o o b t a i n v a l u e s for D and D_ .
J
JK
Av
= v ,
ob
- Dj 4 ( J + 1 ) 3 - D J K 2(J+1)K 2 L
Here v
(1-11)
RR
i s t h e r i g i d r o t o r frequency o b t a i n e d from t h e g r a d u a l l y improved
°
.RRv
v a l u e s of A, B , and C, [TT— )
(Gn = A,B,C) i s a n u m e r i c a l d e r i v a t i v e
VGlJG2'G3
1
which may e a s i l y be e v a l u a t e d , a n a AG i s an unknown which i s s o l v e d
for
by a p p l y i n g t h e l e a s t s q u a r e s p r o c e d u r e and i s t h e n added t o t h e r o t a t i o n a l c o n s t a n t , G, t o improve i t s a c c u r a c y each c y c l e .
of A, B , C, D , and D
J
a r e g i v e n i n Table 1 - 3 .
The f i n a l
values
The r e s i d u e s i n Table 1-2
ulv
r e f l e c t t h e s l i g h t e r r o r i n t r o d u c e d when n o t u s i n g t h e terms which a r e def i n e d i n Eq. ( 1 - 9 ) .
F i n a l l y , i f we assume t h a t t h e c y c l o p r o p a n e geometry
formation, we can r e p r o d u c e t h e o b s e r v e d B
and C
s u r v i v e s complex
values w i t h the v a l u e s
of t h e c e n t r o i d t o CI d i s t a n c e g i v e n for each i s o t o p i c s p e c i e s i n
17
Table 1-4. We a l s o assume t h a t r(H-Cl) i s as i n t h e free molecule
but
the r e s u l t i s r e l a t i v e l y i n s e n s i t i v e to this assumption.
These r
of t h e c e n t r o i d t o CI d i s t a n c e a r e e s s e n t i a l l y i s o t o p i c a l l y
values
invariant
and imply a d i s t a n c e of 3.57 A from the m i d p o i n t of t h e C-C bond t o the
16
Table 1-4
Molecular Geometries and Quantities Measuring Strength
of Binding for I s o t o p i c Species of (V, HCl)
Quantity
(V, H 3 5 C 1 )
37
(V , H J / C 1 )
(V , D 3 5 C 1 )
r(centroid-•-CI)(A)
4.004b
4.004b
4.001b
y(deg.)
21.15(1)
21.14(1)
19.03(1)
k (mdyn A )
s
0 .087
0.085
0.095
V (cm )
s
e(cm
)
87
85
90
959
9 38
1025
See t e x t for d e f i n i t i o n of q u a n t i t i e s and method of c a l c u l a t i o n .
Mean of two values obtained by independently f i t t i n g B and C under the
assumption of unchanged monomer geometries.
±0.001 A i n each case.
The range about the mean i s
17
Cl atom in the edge-on model but 3.13 A from the axial carbon atom t o
Cl i f the corner-on model is assumed.
in 0C---HC1
18
Given t h a t r ( C - - ' C l ) = 3.69 A
and t h a t the sum of the van der Waals r a d i i of C and Cl i s
~3.6 A, t h i s provides evidence in favor of t h e complex being edge-on.
Due to zero-point v i b r a t i o n a l e f f e c t s , a s l i g h t l y d i f f e r e n t distance
is obtained by f i t t i n g B and c.
Thus the d i s t a n c e given in Table 1-4
i s an average obtained using
+ c 2 )} _
V m a. 2+c
= TI.
L
i
l
0-12)
ii
I
2,
2.,
7 m (a 2+b 2 ) = I
L
1 1
i
cc
(1-13)
and u t i l i z i n g the center of mass condition
y ma
L
l
D.
l
i
= 0
.
(1-14)
Molecular Geometry and Binding
The spectroscopic constants obtained i n the previous section now
allow d e t a i l e d statements regarding the s t r u c t u r e and binding of the
cyclopropane-HCl complex to be made.
From t h e fact t h a t B and C are
unequal we can rule out the p o s s i b i l i t y of the complex being a symmetric
top with the HCl lying on the C symmetry a x i s of the r i n g .
Comparison
of the A r o t a t i o n a l constant for the three i s o t o p i c species with the
A = B = 2009 3 for free cyclopropane
19
shows t h a t the Cl atom of HCl
must l i e on the a-axis of the complex, thus making no c o n t r i b u t i o n t o
the moment of i n e r t i a about t h a t a x i s , and t h a t cyclopropane seems to
18
have s u r v i v e d complexation u n p e r t u r b e d s t r u c t u r a l l y .
P, and P
The v a l u e s of
f o r the complex d e f i n e d and r e p o r t e d i n Table 1-3 l e a d t o
s i m i l a r c o n c l u s i o n s when compared t o t h e f r e e c y c l o p r o p a n e v a l u e s of
20.179 and 4.973 amu A
respectively.
'
That the hydrogen atom of
HCl i s c l o s e t o c y c l o p r o p a n e r a t h e r than away from i t i s
demonstrated
by the s m a l l s h i f t i n the B and C r o t a t i o n a l c o n s t a n t s f o r t h e complex
35
i n going from cyclopropane-H
35
Cl t o cyclopropane-D
Cl.
I f the hydrogen
atom were away from c y c l o p r o p a n e and n o t hydrogen-bonded then a r e l a t i v e l y l a r g e s h i f t would be e x p e c t e d .
The hydrogen-bonded model how-
e v e r f i n d s t h e hydrogen atom c l o s e t o t h e c e n t e r of mass of the complex
c a u s i n g s h i f t s of o n l y -1 MHz i n B
and C .
I t i s a consequence of t h e l o c a l C a x i s of c y c l o p r o p a n e i n t h e
complex t h a t any o r i e n t a t i o n of c y c l o p r o p a n e a b o u t t h i s a x i s w i t h
r e s p e c t t o HCl (see F i g . 1-1)
g i v e s t h e same v a l u e s f o r t h e
rotational
c o n s t a n t s . 1,1-d - c y c l o p r o p a n e was used t o b r e a k the symmetry of t h e
13
cyclopropane r i n g i n t h e analagous cyclopropane-HF complex
(see F i g .
1-2) so t h a t d i f f e r e n t values o f <f>, d e f i n e d i n F i g . 1 - 2 , g i v e
values for t h e r o t a t i o n a l c o n s t a n t s .
different
If the limiting p o s s i b i l i t i e s
are
taken t o be an edge-on or c o r n e r - o n model t h e n each model f o r t h e
complex w i l l have a COTr and C_ i s o t o p i c s p e c i e s for
1,l-d_-cyclopropane-HF
which depend upon w h e t h e r the carbon atom on the c
a x i s o r a n o t h e r carbon
atom i s d e u t e r a t e d .
This w i l l l e a d t o four r e s u l t a n t s e t s of p o s s i b l e
r o t a t i o n a l constants
(see Table 1 - 5 ) .
Three t r a n s i t i o n s of b o t h t h e
C_,r and C J = 1 -*• 2 R-branch were o b s e r v e d (see Table 1-6) .
2V
s
Two of
t h e s e t r a n s i t i o n s a r e i n d e p e n d e n t of A and thus B and C can be e x t r a c t e d
for both i s o m e r s .
As shown i n Table 1-5 t h e s e match v e r y c l o s e l y t o t h e
VD
Figure 1-2.
Molecular geometry and i d e n t i f i c a t i o n of the principal
axes i n the cyclopropane hydrogen fluoride complex.
20
21
Table
1-5
C a l c u l a t e d and Observed B and C Values f o r t h e C„„ and C
2V
s
Isomers of the Edge-On and Corner-On Models
Observed
B = 2560.3 MHz
Edge-On
Calculated
B = 2554.5 MHz
C = 2388.5 MHz
C = 2394.0 MHz
B = 2727.2 MHz
B = 2724.6 MHz
C = 2498.6 MHz
C = 2504.4 MHz
<J
HF
<L
HF
'2V
Cc
Corner-On
None Observed
B = 2725.3 MHz
D2HF
C = 2543.4 MHz
None observed
C2V
>
B = 2634.9 MHz
HF
C = 2429.7 MHz
>
C
22
Table 1-6
Observed F r e q u e n c i e s
\ ± *
+ 1
" ^
x
f o r C H.D.-HP
C 2V
C
2V
Cs
1 1 1 -»• 2
9725
9 7 2 5. 5 6 1 7
10222.8562
1 „ . -*• 2 „ „
01
02
99891
891.1735
10448.7767
10069
1 0 0 6 9. 1 5 8 4
10679.9295
1
-»• 2
23
B and C v a l u e s c a l c u l a t e d for t h e two i s o m e r s of the d e u t e r a t e d edge-on
model w i t h r i g i d models.
The n a t u r e of the weak b i n d i n g i n t h e complex can b e d i s c e r n e d from
the s t r u c t u r e and s p e c t r o s c o p i c c o n s t a n t s .
F i r s t l y , the structure
is
i n d i c a t i v e of hydrogen bonding w i t h t h e e l e c t r o p h i l i c hydrogen atom of
HCl p o i n t i n g midway between t h e c a r b o n - c a r b o n bond, a p p a r e n t l y bound
t o the h i g h e l e c t r o n d e n s i t y p r e d i c t e d t h e r e by the
model.
A l s o , t h e value of x
Coulson-Moffit
measured f o r t h e Cl n u c l e a r 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 i s r e d u c e d from the f r e e HCl value x
presumably as
a r e s u l t of z e r o - p o i n t bending v i b r a t i o n s of HCl i n t h e complex.
Values
o b t a i n e d i n C h a p t e r I I f o r t h e m o l e c u l a r q u a d r u p o l e moment of c y c l o p r o p a n e
indicate that the e l e c t r o s t a t i c effects
of c y c l o p r o p a n e on charge r e -
a r r a n g e m e n t i n H C l a r e s m a l l and t h a t 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 t h e
Cl n u c l e a r s i t e i s r e l a t i v e l y u n p e r t u r b e d by complex f o r m a t i o n .
t h i s a s s u m p t i o n we have
Under
that
X
aa
=
1 / 2
X0<3cos2y-l)
(1-15)
where y i s t h e i n s t a n t a n e o u s a n g l e between t h e HCl a x i s and t h e a - a x i s
t h e complex.
From the v a l u e s o f x
and x
an
can be o b t a i n e d and i t i s g i v e n i n Table 1-4.
o p e r a t i o n a l v a l u e of y
180-y can also be obtained
from the v a l u e s of X
and AY y e t i s i n c o n s i s t e n t w i t h t h e s t r u c t u r e
A
aa
o *
o b t a i n e d from c o n s i d e r a t i o n of t h e r o t a t i o n a l c o n s t a n t s .
Though the
average v a l u e o f y , ( y ) , i s 0 , t h e v a l u e of y o b t a i n e d h e r e
represents
t h e v i b r a t i o n a l l y a v e r a g e d a m p l i t u d e o f the b e n d i n g motion of t h e HCl
molecule a b o u t i t s c e n t e r of mass i n t h e ground v i b r a t i o n a l s t a t e of
t h e complex.
of
The value o b t a i n e d i s much s m a l l e r than t h o s e o b t a i n e d i n
24
rare gas-hydrogen h a l i d e complexes as shown i n Table 1-7 and can be
a t t r i b u t e d to stronger binding in the present case.
From arguments
presented m Chapter IV xt is shown t h a t the equality of X,_w
and
bb
X
within experimental error i n d i c a t e s that t h e bending motion of
HCl i n the b and c_ d i r e c t i o n s i s i s o t r o p i c .
The attenuation of y in
35
going from c y c l o p r o p a n e - H
35
Cl t o c y c l o p r o p a n e - D
Cl i s
consistent with
e x p e c t e d b e h a v i o r for HCl b e n d i n g m o t i o n i n g o i n g t o a l a r g e r HCl moment
of i n e r t i a .
The strength of binding of the hydrogen bond can be described i n
terms of the force constant of the bond and t h e dissociation energy, e .
There i s c l e a r l y information regarding these q u a n t i t i e s in the centrifugal
d i s t o r t i o n constant D which measures the s t r e t c h i n g of the hydrogen bond
j
in h i g h e r J s t a t e s .
I n the many cases of loosely bound complexes where
only the ground v i b r a t i o n a l s t a t e has been measured, i t has often been
useful to use a diatomic model which t r e a t s t h e monomers as point masses.
The diatomic model for such complexes owes i t s legitimacy to the f a c t
t h a t t h e v i b r a t i o n a l frequencies of t h e monomers are considerably higher
than the s t r e t c h i n g and bending frequency of the van d e r Waals bond.
This i s especially v a l i d where the monomers a r e diatomics and rare
gases as the s t r e t c h i n g modes of the monomers are e s p e c i a l l y high i n
frequency and q u i t e unlikely t o couple strongly with the van der Waals
bond.
However, as the monomers become increasingly complex the diatomic
model becomes l e s s and less v a l i d .
This is t h e case w i t h the present
complex especially as t h e hydrogen bond stretching frequency of 87 cm
p r e d i c t e d from the diatomic model begins to approach some of the low
frequency bending modes of cyclopropane.
Even so, i t i s s t i l l
useful
25
Table
1-7
Comparison of y f o r Cyclopropane-HCl and Some
Rare Gas-Hydrogen Halide Complexes
y(degrees)
C,H r -HCl
3 6
21
ArDF a
32
1_
KrHCl
38
XeHCl
35
M. R. Keenan, L. W. Buxton, E. J . Campbell, A. C. Legon, and W. H.
F l y g a r e , J . Chem. P h y s . 74_, 2133 ( 1 9 8 1 ) .
E . j . Campbell, L. W. Buxton, M. R. Keenan, a n d W . H. F l y g a r e , J . Chem.
P h y s . 74, 2133 ( 1 9 8 1 ) .
26
t o c a r r y o u t t h e d i a t o m i c model c a l c u l a t i o n - and use the v a l u e s
for
a p p r o x i m a t e comparison p u r p o s e s with i t k e p t i n mind t h a t i n c a s e s
where one of the monomers i s a s v i b r a t i o n a l l y complex as c y c l o p r o p a n e ,
the values are approximations.
In t h e diatomic model the r a d i a l i n t e r a c t i o n between t h e monomers
i s d e s c r i b e d by an e f f e c t i v e
mode.
r a d i a l p o t e n t i a l averaged o v e r the bending
The 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 i s then r e l a t e d t o t h e
s t r e t c h i n g frequency, V , of t h e hydrogen bond by t h e r e l a t i o n
DT
J
4B 3
= —fV
(1-16)
2
s
where
Be =
&—j
4iTy R
s e
(1-17)
and
M M
1IC1CH
C H
3 6
Here R i s the e q u i l i b r i u m s e p a r a t i o n of the c e n t e r s of mass of t h e monomers
b u t w i l l be a p p r o x i m a t e d by t h e same d i s t a n c e i n t h e ground v i b r a t i o n a l
state.
F u r t h e r m o r e , i n the d i a t o m i c model, t h e s t r e t c h i n g frequency of
t h e hydrogen bond i s t h e n r e l a t e d t o t h e f o r c e c o n s t a n t , k , by t h e usual
harmonic o s c i l l a t o r
relationship
v
s
V/2
= Li^l)
(1-19)
27
We can express the p o t e n t i a l i n terms of a Lennard-Jones 6/12
p o t e n t i a l given by
V(R) = e
r -#
(1-20)
Next we expand t h i s in a Taylor s e r i e s about the equilibrium d i s t a n c e ,
Re , to obtain
V(R) = -e + ^ |2 ( R - R
J2 - - ^
e
r,
r,
R
e
R
3
( R - Re J 3 . . .
•
(1-21)
e
Since the force constant, k , i s generally twice the coefficient of the
term quadratic i n (R-R ) , we can r e l a t e £, the w e l l depth of the p o t e n t i a l ,
to the force constant and the equilibrium d i s t a n c e by the r e l a t i o n
kR
2
e =-*£- .
d-22)
The values of e , k , and V are l i s t e d i n Table 1-4 for the cyclopropaneHCl i s o t o p i c s p e c i e s .
E.
Conclusion
This study has e s t a b l i s h e d the existence of a gas phase complex be-
tween cyclopropane and HCl where the edge of cyclopropane acts as a
proton acceptor and the acidic HCl proton acts a s a proton donor.
The
HCl has the proton pointing on average midway between the carbon-carbon
bond and l i e s on the C symmetry axis with the C l atom 3.57 A away from
the carbon-carbon bond.
The HCl undergoes an i s o t r o p i c bending motion
away from i t s average position on the a-axis w i t h HCl making a
28
v i b r a t i o n a l l y averaged angle of -21.1° with the a-axis.
The well depth
for the hydrogen bond a t t r a c t i v e i n t e r a c t i o n i s ~2 kcal/mole as determined from the centrifugal d i s t o r t i o n constant D . Consideration of the
J
r o t a t i o n a l constants and l i n e a r combinations of these p, and P seem
b
c
to i n d i c a t e t h a t the cyclopropane molecule undergoes complexation r e l a t i v e l y unperturbed.
However comparison of these values for P, and P
with free cyclopropane values quoted e a r l i e r a l s o imply t h a t the zeropoint bending modes introduced upon complexation and involving cyclopropane are r e l a t i v e l y small i n amplitude.
That weak complexation can be a method for probing areas of high
e l e c t r o n density in a nucleophile has been supported by a large amount
21
22
of experimental evidence, in the furan-HCl,
oxirane-HF,
and
23
oxetane-HF
complexes the a c i d i c proton of the hydrogen h a l i d e bonds
24
to lone pairs of an oxygen molecule. In the acetylene-HCl,
ethyleneHCl,
acetylene-HCN
and ethylene-HCN
complexes the a c i d i c proton
binds to IT electron density i n the nucleophile i n a p r e d i c t a b l e and
i n t u i t i v e manner.
In the p r e s e n t case then the s t r u c t u r e i s i n d i c a t i v e
of the hydrogen atom of HCl binding t o the e l e c t r o n density outside
the edge of the cyclopropane r i n g .
This is c o n s i s t e n t with the model
for cyclopropane given by Coulson and Moffit and does not s u b s t a n t i a t e
2
the electron density formed from sp overlap i n the center of the ring
predicted by the Walsh model.
29
CHAPTER I I
THE MOLECULAR PROPERTIES OF CYCLOPROPANE AS DETERMINED
FROM ROTATIONAL ZEEMAN STUDIES OF THE CYCLOPROPANE-HCL
AND CYCLOPROPANE-HC
A.
N COMPLEXES
Introduction
Microwave Zeeman e x p e r i m e n t s have b e e n shown t o be q u i t e
i n t h e d e t e r m i n a t i o n of c e r t a i n m o l e c u l a r i n f o r m a t i o n .
effective
The m o l e c u l a r
q u a d r u p o l e moment, m o l e c u l a r g - v a l u e s , m a g n e t i c s u s c e p t i b i l i t y
aniso-
t r o p i e s , and t h e s i g n and m a g n i t u d e of t h e e l e c t r i c d i p o l e moment c a n
a l l be o b t a i n e d by t h i s means.
28 29
'
The m o l e c u l a r q u a d r u p o l e moment
and e l e c t r i c d i p o l e moment give i m p o r t a n t i n f o r m a t i o n r e g a r d i n g c h a r g e
distribution.
The m o l e c u l a r g - v a l u e s can be combined with 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 , s t r u c t u r a l information,
and bulk
susceptibility
t o g i v e t h e second moments of t h e e l e c t r o n i c c h a r g e d i s t r i b u t i o n a s w e l l
a s t h e d i a m a g n e t i c and p a r a m a g n e t i c c o n t r i b u t i o n s t o the m a g n e t i c s u s c e p tibilities.
I n t h e c a s e of r i n g compounds, the m a g n e t i c
susceptibilities
can be compared t o l o c a l i z e d s e m i e m p i r i c a l models t o givp a
f o r a r o m a t i c i t y and d e r e a l i z a t i o n .
criterion
Obtaining t h i s information
from
microwave Zeeman e x p e r i m e n t s i s however c o n t i n g e n t upon t h e molecule
h a v i n g a permanent e l e c t r i c d i p o l e moment, thus a l l o w i n g r o t a t i o n a l
s i t i o n t o be o b s e r v e d .
tran-
In t h e c a s e of a n o n p o l a r molecule i t i s c o n c e i v a b l e
t h a t weak c o m p l e x a t i o n with a d i p o l a r m o l e c u l e m i g h t however
indirectly
g i v e i n f o r m a t i o n a b o u t t h e n o n p o l a r b i n d i n g p a r t n e r through Zeeman s t u d i e s .
The development of p u l s e d , F o u r i e r - t r a n s f o r m microwave s p e c t r o s c o p y w i t h
g a s pulsed i n t o a F a b r y - P e r o t c a v i t y ,
a n d more r e c e n t l y ,
Zeeman microwave
30
31-33
studies under the same conditions
make this sort of experiment feasible. Recently, Zeeman studies of many linear hydrogen-bound complexes
have been conducted with the aim of determining the effects of weak
complexation upon the molecular properties of the substituent molecules.
33
The results have shown that if proper account is taken of changes in
centers of mass and bending modes introduced upon complexation, the molecular quadrupole moments, magnetic susceptibility anisotropies, and
g-values are all to a good approximation resultants of the corresponding
properties in the substituent molecules.
It then seems plausible to
study the aforementioned molecular properties of cyclopropane by obtaining
the same molecular properties for cyclopropane complexed with a dipolar
binding partner and subtracting out the effects of the binding partner.
By complexmg cyclopropane with two very magnetically different molecules,
35
15
H Cl and HC N, the ability of the projection equations to subtract out
the effects of the binding partners can be tested.
Cyclopropane has been the object of much study and speculation.
Values are not known for the molecular quadrupole moment.
In addition.
proton shieldmgs by cyclopropyl groups have pointed to cyclopropane as
having an unexpectedly large magnetic susceptibility amsotropy possibly
arising from the presence of ring currents.
Bulk susceptibility
39
measurements of cyclopropane have caused similar speculations.
currents have been attributed to many aromatic compounds
though there is disagreement
42-44
'
'
Ring
and
it is thought that many ring compounds
not traditionally thought of as aromatic have some degree of electron
45 46
derealization and thus ring current. '
The Coulson-Moffit theory
of cyclopropane predicts a certain amount of o electron derealization
31
as a result of resonance
and the conjugative ability of the cyclopropyl
group has been evidenced by various spectroscopic means. The electronic
absorption of carbonyl groups occurs at longer wavelengths with the
attachment of cyclopropyl groups as is the case with conjugation.
'
Similar bathochromic shifts occur in the absorption spectrum of double
49 50
bonds conjugated with cyclopropyl groups. '
NMR spectra of phenyl
protons of phenylcyclopropane have been interpreted as giving this molecule an optimum conformation for conjugation with the benzene ring.
51
Other works have shown that while cyclopropyl groups can extend conjugation, they are unable to serve as central transmitters of conjuga47 ^9 ^*^
tion.
'
ization m
'
Because of the ambiguous understanding of electron dereal-
cyclopropane it becomes important to obtain an accurate value
for the magnetic susceptibility amsotropy.
This coupled with a value
for the bulk susceptibility can then give the out-of-plane susceptibility
tensor element which is strongly influenced by the presence of ring currents due to electron derealization.
The zero-field rotational spectra for various isotopic species of
cyclopropane-HCl have been presented in the previous section and the
structure is well determined.
Structural information as well as zero-
field spectroscopic parameters will be used freely in this section
The
14
54
zero-field spectrum of cyclopropane-HC N has been recently studied,
15
however the cyclopropane-HC N rotational transitions are presented here
as well as the rotational constants for this isotopic species.
Both com-
plexes are shown in Fig. II-1 with respect to their principal axes.
In
both complexes the HX{X=C1,CN) subunit lies on the a principal axis of
the complex on averaqe where this axis is also a C
symmetry axis.
In
this section the g-values for cyclopropane-HCl are reported along with
32
Figure I I - l .
Equilibrium s t r u c t u r e for t h e cyclopropane-HCl and
15
cyclopropane-HC N complexes with respect t o t h e i r
p r i n c i p a l axes and center of mass s e p a r a t i o n .
33
CM,
3.97 A
4.49 A
34
the two independent magnetic susceptibility anisotropies, 2X
and 2X, .-X
0<O
33
-
X
~Xhh~X
• Using other information the individual magnetic
CC
susceptibility tensor elements are also obtained along with the paramagnetic and diamagnetic contributions, and the second moments of the
electronic charge distribution. For the cyclopropane-HC N complex
q
+a
and 2va a -y, -Y
are obtained along with the rotational confab cc
"b cc
stants.
Projection equations are also presented to give the Zeeman
parameters of a general asymmetric top complex in terms of the corresponding values of the substituent molecules.
These equations are then
used to derive the Zeeman parameters of cyclopropane from those of the
complexes and the binding partners.
The values obtained are shown to
be internally consistent, as, for example, the magnetic susceptibility
amsotropy of cyclopropane, Xi |~X > c a n °e determined from any of the
three anisotropies obtained for the complexes.
In addition, the mag-
netic susceptibility tensor elements and the second moments of the charge
distribution of cyclopropane are compared with various ab initio and
semi-empirical calculations as well as rough experimental determinations.
B.
2
Experimental
The rotational Zeeman effect was observed for the 2„„ •*• 3„„ and
02
03
-»• 3
nuclear quadrupole-split rotational transitions of the cyclo-
propane-H
35
Cl complex and also the 2
the cyclopropane-HC
15
N complex.
-* 3
rotational transition of
For cyclopropane-HCl, transitions were
observed at field strengths of 25104G and 30098G while the cyclopropaneHC N Zeeman transitions were observed at 30098G where the field is
determined by calibrating the solenoid current using the Zeeman splitting
35
of the J = 0 -> 1 transition of OCS and known Zeeman parameters.
Also
six zero-field rotational transitions were observed for cyclopropane-HC
to establish the rotational constants of this complex.
15
N
Zeeman spectra
were obtained using a pulsed, Fourier-transform microwave spectrometer
with a Fabry-Perot cavity located in the bore of a superconducting solenoid
31-33
magnet.
This spectrometer was built and described previously.
Zero-
field spectra were obtained using the original pulsed, Fourier-transform
spectrometer developed by T. J. Balle and W. H. Flygare described briefly
in the last section.
With both spectrometers a mixture of ~ 2 % cyclopro-
pane and ~2% of either HCl or HC
15
N with argon is pulsed into a tuned
Fabry-Perot cavity kept under high vacuum by a diffusion pump. All
transitions within the ~2MHz cavity bandwidth are then polarized by
~1.50-3.0 Usee power pulse from a phase-locked microwave oscillator.
The
free induction decay is then detected by a superheterodyne detector,
mixed down to near DC, and digitized at .5 Usee per point, 20-30 signals
are taken at a rate of 1 Hz with every alternate signal, which is taken
with no gas in the cavity, subtracted from the average to eliminate any
coherent noise.
The signal is then Fourier transformed to give a .5 MHz
or 1 MHz spectrum with half-widths at half-height from 5-15 kHz representing the offset of molecular resonances from the excitation frequency.
Observed transitions then consist of 6-10 measurements taken at different
excitation frequencies. All transitions lie in the 8-11 GHz region.
With the Zeeman spectrometer gas is pulsed through a piezoelectric valve
with the axis of the gas flow approximately parallel to the static field.
The microwave polarization pulse is oriented perpendicular to the static
field in the present experiment to allow A M = ±1 transitions.
36
C.
Determination of Spectroscopic Constants for Cyclopropane-H
and Cyclopropane-HC15N
35
Cl
The Hamiltonian describing the interactions present in the rotational
Zeeman experiment is given by
K =3C
rot
V
V
- T - H - g ' J - 1/2 H'X'H - r~ 1 g . l
+ J" Q :V
, ~1 ~1
1 ~
H ~ B J ~
~ as ~
-tl
1
3~1
" ( 1 - 0 )'H .
SJ
s-1
(II-l)
~
The first term is the rotational energy term described in terms of the
rotational and centrifugal distortion constants. The second term is the
nuclear quadrupole interaction and is necessary for the Cl nucleus in
cyclopropane-HCl.
and V
Q
is the nuclear quadrupole tensor for the I
is the electric field gradient tensor.
nucleus
The third term describes
the interaction of the external magnetic field vector, H, with the rotaUQ
tionally induced magnetic dipole moment, -r— g*J, where g is the molecular
XI ~ ~
—
g-value tensor and J is the rotational angular momentum vector for the
molecule.
The fourth term takes into account the response of the electrons
to an external magnetic field leading to an induced magnetic dipole moment
proportional to the field strength.
X
xs
the magnetic susceptibility
tensor describing this response and has both paramagnetic and diamagnetic
The rotationally invariant trace of x c a n b e factored
2
out to give an energy contribution of -Tr(x)H
which is of course
contributions.
z
unobservable with rotational transitions.
For an asymmetric top then,
this term is parameterized by the two independent susceptibility anisotropies, 2 X a a -X b b -X c c and 2 X b b -X a a -X c c -
The last term in Eq. (II-l)
is the nuclear Zeeman interactions whereby an electronically shielded
nuclear moment interacts with the external magnetic field.
This term
involves a summation over all nuclei with I > 0 however in the present
work only the Cl nucleus is coupled to the molecular rotation and thus
37
other nuclei need not be considered,
o is the nuclear shielding
tensor and is made up of a diamagnetic contribution involving ground
state electronic wavefunctions and a paramagnetic contribution involving
ground and excited state wavefunctions.
The Zeeman splitting of the 2
•> 3
UJ
and 2 _ -»• 3
UJ
J."
transitions of
J. *3
cyclopropane-HCl was observed at two field strengths with 55 lines being
observed.
Initial assignments were made using matrix elements (presented
later) of the Hamiltonian in Eq. (II-l) calculated in the uncoupled
IJKM IM ) basis with matrix elements off-diagonal in J being neglected.
J I
This proved to be computer efficient in deconvoluting the extremely rich
spectrum (see Fig. II-2) and gives transition frequencies differing from
an exact treatment by less than 5 kHz in almost all cases.
Final fitting
involved correcting the observed frequencies by the difference between
the above first order treatment and an infinite order treatment and improved the fit slightly.
As the chlorine nucleus is expected to have
its nuclear spin strongly coupled to the angular momentum of the nuclear
framework, the observed frequencies for cyclopropane-HCl are reported
in Table II-l in the coupled |JKI
FM ) basis.
The rotational and nuclear
quadrupole parameters from the previous zero-field study were adjusted
so that they exactly reproduced the measured zero-field frequencies.
The
effects of shielding of the chlorine nucleus on the spectrum are slight,
only amounting to 2 kHz or less for 0
ranging from 0 to 1000 ppm.
Furthermore the effect of the magnetic susceptibility amsotropy of cyclopropane on the chlorine nuclear shielding can be shown to be less than .1%
using the McConnell equation presented later.
For this reason the chlorine
nuclear shielding anisotropics were set equal to their free HCl value
given in Table II-2 and projected into the axis system of the complex
Figure II-2. Transitions observed for cyclopropane-HCl
in the 8927-8933 MHz frequency range at a
field strength of 25 kG.
i-l
27.00
27.75
28.50
29.25
30.00
FREQUENCY
30.75
31.50
32.25
33.00
OO
40
Table
II-l
Measured Zeeman T r a n s i t i o n s
• K * JK< K>
- I +1
-1%-1
f o r Cyclopropane-H
F M -*• T?I M«
_ _ L _ _ _ Z
F i e l d (G)
35
Cl
Measured
Frequency (MHz)
obs"
(kH
3 / 2 , - 3 / 2 -* 5 / 2 , . - 5 / 2
8927.2271
7/2, -5/2
8927.7657
1
- 3/2,-- 3 / 2
-
2
7/2, -1/2 + 9/2,
1/2
8 9 2 8 . 3 0 78
5
7 / 2 , 1 / 2 "»• 5 / 2 ,
3/2
8928.6471
4
3/2,
3/2 + 5 / 2 ,
5/2
8929.1232
- 2
7/2,
3 / 2 -* 9 / 2 ,
5/2
8929.3277
-
3 / 2 , 1 / 2 "*• 5 / 2 , - - 1 / 2
8929.4647
1/2,
1 / 2 -• 3 / 2 ,
3/2
8929.6403
7/2, 5/2 + 9 / 2 ,
7/2
8929.9730
8
5 / 2 , . - 5 / 2 •+ 7 / 2 , •- 7 / 2
89 3 0 . 3 2 2 8
7
5 / 2 , - - 3 / 2 "»- 7 / 2 , - - 5 / 2
89 3 0 . 3 6 3 7
2
5/2,
3 / 2 •* 7 / 2 ,
5/2
89 30 . 7 7 9 3
-
7/2,
7 / 2 "»• 9 / 2 ,
9/2
8930.8579
-
7 / 2 , . - 7 / 2 •»• 9 / 2 , - - 9 / 2
8931.0226
5 / 2 , • - 5 / 2 + 5 / 2 ,-- 3 / 2
8931.2086
-
5/2,
-
7
3
3
3/2 + 7 / 2 ,
1/2
89 3 1 . 6 1 7 2
-
5 / 2 , 1 / 2 •* 7 / 2 ,
1/2
89 3 1 . 6 6 1 4
-
7 / 2 , .- 5 / 2 + 9 / 2 , - - 7 / 2
8931.7324
-11
5 / 2 , 5 / 2 ->• 7 / 2 ,
7/2
8931.7808
2
7 / 2 , - - 3 / 2 •»• 3 / 2 , - - 1 / 2
89 3 2 . 0 1 4 4
6
7 / 2 , - -3/2">- 9 / 2 , - - 5 / 2
89 3 2 . 1 1 7 2
1
1 / 2 , - - 1 / 2 •»•
89 3 2 . 3 3 9 8
-12
3/2,
1/2
1
41
Table I I - l
K
-1 K +1
K
(Continued)
-1K+1
Field(G)
30098
]
•+
1/2
8928.2506
7 / 2 , 1/2 -*- 5 / 2 ,
3/2
8928.5342
1.8
7/2,-3/2
8929.0610
5.7
- > •
5/2,
5/2
8929.1275
-10.8
-+•
7/2,
3/2
8929.1675
6.0
7 / 2 , 3 / 2 -*- 9 / 2 ,
5/2
8929.26 30
1.1
5/2,-1/2
8929.5520
3/2, 3/2
5 / 2 , 1/2
3 / 2 , 1/2
-+
- * •
1 / 2 , 1/2 ->- 3 / 2 ,
3
13
251
°4
-
-
2.3
3.8
3/2
8929.8149
6.8
7 / 2 , 7 / 2 -*• 9 / 2 , 9/2
89 30.8560
5.1
7/2,- - 7 / 2 -*• 9 / 2 , - 9 / 2
89 31.0393
5/2,--5/2
8931.2531
1.0
1/2
8931.6275
2.8
7/2,-7/2
8827.3879
5 / 2 , - - 3 / 2 ->• 5 / 2 , - 5 / 2
8827.9165
3 / 2 , 3/2
- » •
5/2,-3/2
5 / 2 , 3 / 2 ->- 7 / 2 ,
12 -
obs
calc
(kHz)
9/2,
7 / 2 , --1/2
3 / 2 , - -1/2
2
Measured
Frequency (MHz)
F',M^
5/2,--5/2
•+•
-
-
1.0
6.8
1.8
5/2,
5/2
8827.9999
-
.2
7/2,
7/2
8828.9068
-
5.0
9/2,
5/2
8829.1328
3.4
9/2,
7/2
8829.2133
1.1
5/2,-1/2
8820.3281
5.4
7/2,-3/2
8829.3606
-11.1
3/2 ,•- 1 / 2 -> 5 / 2 , - 3 / 2
8829.4139
-
7 / 2 , 1/2 -»- 7 / 2 , - 1 / 2
8829.5881
0
9/2,-3/2
8829.8681
7.8
5/2, 5/2
7 / 2 , 3/2
- * •
-y
- * •
7/2, 5/2
-h
5 / 2 , 1/2
- * •
5 / 2 , .-1/2
•+
7/2,- - 1 / 2
- > •
.4
42
Table I I - l
J
(Continued)
->• J '
K
- 1 K + 1 K -1 K +1
•y
Measured
Frequency (MHz)
V . -v .
obs c a l c
(kHz)
3 / 2 , - 3 / 2 ->• 3 / 2 , - 1 / 2
8830 .1339
11.4
F,M p
Field(G)
-*•
9/2,
9/2
8830 .7700
- 2.7
7/2,-7/2
•+
9/2,-9/2
8830.9073
2.9
1/2,
1/2
•+
3/2,
3/2
8831.3783
-
1.5
3/2,
3/2
-y
5/2,
5/2
8827.9623
-
3.8
7 / 2 , - 1 / 2 -*- 9 / 2 , - 3 / 2
8828.8150
-
3.3
-
1.2
7/2,
30098
7/2
3/2,-1/2
•y
5/2,-3/2
8829.66 35
7/2,
-y
9 / 2 , 9/2
8829.7805
1.9
7/2,-7/2
•y
9/2,-9/2
8830 .9424
5.7
1/2,
-y
3/2,
8831.3516
5.3
7/2
1/2
3/2
43
Table I I - 2
Molecular P r o p e r t i e s of t h e Substituent Molecules
H35C1
Cyclopropane
A(MHz)
20093(5)a
B(MHz)
20093(5)a
C(MHz)
12522(9)a
„ ,
°2,
P, (amuA )
b
4.97(1)
P (amuA )
20.17(1)
HC 15 N
312989.297b
43027.7°
d
2.985e
y(debye)
1 . 1 0 8 6 (3)
a. , ( A ) 3
2.81f
3.1g
g
.45935 ( 9 ) h
-0.0904(3 J1
x
2
X l l - X , ( e r g / G mole)
1 1 •*•
2
X ( e r g / G mole)
a
(ppm)
avg
"^
a|i-o
a
-.19(7)xl0_€
-39.2(8)xl0
-6 ^
-22.1(5)xlo"
7.2(4)xl0~6
.6k
740(24)h
300(200)
(ppm)
S e e Ref. 16 and Ref.
;*
19.
F . C. DeLucia, P . H e l m i n g e r , and W. Gordy, P h y s . Rev. A 3 , 1849 (1971)
C
B . S e n i t z k y , J . Chem. P h y s . 45_, 409
(1966).
E . U. K a i s e r , J . Chem. P h y s . 5_3, 1686 ( 1 9 7 0 ) .
e
A . G. Maki, J . Chem. P h y s . Rev. D a t a _3»
221
(1974).
N. J . Bridge and A. D. Buckingham, P r o c . Roy. S o c . 295A, 334 (1966) .
g
1
K . G. Denbigh, T r a n s . Faraday S o c . 36_, 9 36 ( 1 9 4 0 ) .
See Ref.
57.
S e e Ref.
58.
•'see Ref. 6 2 .
k
V . P . E h r l i c h , Z. Anorg. A l l g e n . Chem. 249, 219 ( 1 9 4 7 ) .
44
taking into account v i b r a t i o n a l averaging e f f e c t s .
This p r o j e c t i o n ,
which i s completely analogous t o the p r o j e c t i o n of HCl magnetic suscept i b i l i t y amsotropy into the p r i n c i p a l a x i s system of the complex t h a t
i s discussed l a t e r , gives 2a -a, , -a
= 484 ppm and 2a, -a -a
=
aa bb cc
bb aa cc
242 ppm while 0
is unaffected by projection.
Including these shield-
ing values led to a slightly better fit without addition of new parameters.
Final values for the Zeeman parameters for cyclopropane-HCl are reported
in Table II-3. The sign of the molecular g-values are determined relative
to the nuclear g-value of Cl
leading to positive values for all three.
For the zero-field study of cyclopropane-HC
N only the first term
of Eq. (II-l) was necessary and is given explicitly by
Km* " If ^
where K
W
^ - DT(J+1)2 - DJ(J+1)K_J
tH-2)
represents the K quantum number in the prolate limit. As indi-
cated by Eq. (II-2), centrifugal distortion was treated in the symmetric
top limit as the asymmetry parameter < is -.994 and D
necessary for a-dipole type transitions.
dependence is not
The six zero-field transitions
in Table II-4 were used to obtain the rotational parameters given in
Table II-5. These rotational parameters were used to form the rotational
part of the Zeeman Hamiltonian to study cyclopropane-HC
15
N at 30 kG.
Matrix elements for the three necessary terms of Eq. (II-l) were calculated
in the |JKM ) basis. The four Zeeman lines in Table II-6 were then fit
J
to g, , + g and 2x _X,, "X • Analysis showed that these transitions are
DD
cc
aa aa cc
essentially independent of g , g., -g , and 2x,,_ X ~X j
aa
ob cc
bb aa cc
Attempts to
fit any or all of these parameters had little effect on the values of
g
bb
+ g
rc a n d
2
*
"Xbb~Xcc
that are re
P°rted
in
Table II-5. The sign of
45
Table I I - 3
Molecular Zeeman Constants for Cyclopropane-H
.0301(8)
aa
J
.0011(2)
bb
.0071(1)
cc
2
Xaa-Xbb-X C c ( e r g / G n i o l e )
2
Xbb-Xaa _ Xcc ( e r g / G 2 i n o l e )
8.77(28)xl0 - 6
10. 39(61) xlo"
-1.83(26) xlo' •26
aa
.06(47)xlo' •26
*bb
1.77(44)xlO
•cc
bb
2
(erg/G mole)
-58(1)xlO - 6 a
2
-68(l)xl0"
Xcc (erg/G mole)
Xaa
Xbb
• a,b
2
!erg/G mole)
74(1)xlO
2
(erg/G mole)
762(1)xlO
2
-6a,b
788(1)xlO
2
!erg/G mole)
-132(1) xlO'
d
xda a
2
(erg/G mole)
Xbb
d
(erg/G mole)
X
cc
<a2>(A2)
a
_ 6 a,b
cc (erg/G mole)
A
-26
-58(l)xl0 _ (
Xaa (erg/G mole)
X
35
Cl
-820(l)xl0
.ga,b
•6a'b
-855(l)xl0"
;a,b
,a,b
181.9(3)
<b2)(i£2)
19.8(3)
<c 2 >(A 2 )
11.4(3)
a,b
a,b
—^7—HCl
—6
2
Calculated using x
= -61.3x10 erg/G mole.
Calculated using s t r u c t u r a l information or rotational constants for
cyclopropane-HCl from Ref. 16 and Ref. 19.
46
Table I I - 4
Measured R o t a t i o n a l T r a n s i t i o n s
Cyclopropane-HC
J
K
K
-1+1
+
J
K- K'
-1+1
for
15
N
°bS
Measured(MHz)
CalC
(kHz)
2
1 2 "* 3 13
7827.2659
-3.0
2
0 2 * 3 03
7906.9763
-0.0
2
-y 3
7986.8621
2.8
3
-y 4
10436.0688
2.1
3 0 3 + 404
10541.9475
.1
3
10648.8516
-2.1
-> 4
47
Table I I - 5
15
Molecular Constants f o r Cyclopropane-HC N
A(MHZ)
20081(468)
B(MHz)
1344.529(2)
C(MHz)
1291.332(2)
D(kHz)
J
DjK(kHz)
1.42(7)
49(2)
°2
P (amuA )
371.04(29)
P, (amuS )
20.32(29)
P (amuA1 )
c
4.84(29)
R
CM ( & )
4.495(3)
g
bb
b
2x
+
g
-.01283(2)
cc
aa" X bb" X cc
(10
—6
2
erg/G mole)
-4.31(6)
48
Table
II-6
Measured Zeeman T r a n s i t i o n s f o r the 2 „ -y 3
R o t a t i o n a l T r a n s i t i o n of Cyclopropane-HC
30 kG
Measured (MHz)
V , -V ..
obs
calc
(kHz)
3
7906.820 3
.0
M'
J
J
2 -y
15
N
-1
-*•
-2
7907.1007
-.3
-2
-y - 3
7907.1173
.5
0
7907.1438
-.2
1 -y
49
g
+ g
for cyclopropane-HC
15
N was determined by arguments to be given
later.
D.
Consideration of Vibrational Averaging Effects
In order to calculate the contribution of each of the substituent
molecules to the Zeeman parameters of the complex, it is necessary to
account for the effects of zero-point bending motions introduced upon
complexation.
Motions involving cyclopropane can be safely ignored.
Comparison of P
and P
for cyclopropane-HCl, cyclopropane-HC
15
N, and for
free cyclopropane where
r
2
P = I m,g
g
I i
i
g = a,b,c
(II-3)
shows these values to be equal within experimental error indicating that
bending motions involving cyclopropane in the complex are small. The
zero-point bending motions of H
Cl from its average position in the
complex is however relatively large m
noticeable decrease of the
the complex from free H
amplitude as indicated by the
35
Cl nuclear quadrupole coupling constant in
35
Cl.
Similar conclusions can be made regarding
15
14
N motion by consideration of the cyclopropane-HC N isotopic
54
15
species
where
N isotopic substitution is expected to have only a
the HC
slight effect on the amplitude of the bending motions.
effects at the
If small electronic
35
14
Cl and
N nuclear sites which occur upon complexation
eQq
are ignored, the nuclear quadrupole coupling c o n s t a n t s , —r5-9- (g = a , b , c ) ,
h
35
14
in the cyclopropane-H Cl and cyclopropane-HC N complexes are given by
50
eQq
eQq
aa
2
2
c
— - — = ( 3 / 2 c o s Scos a - 1 / 2 ) —r—
n
n
e
Q ^
h
o
e
o
= < 3 / 2 s i n Bcos a - l / 2 >
*'
'
' '
Q<L
h
eQq^
,
eQq
° c = <3/2sin <3-l/2> -r-2h
21
(H-4)
eQq
o
as can be shown by arguments in Chapter IV. Here — - — is the nuclear
quadrupole coupling constant of
35
14
35
14
Cl or
N in free H Cl or HC N, Q
is the nuclear quadrupole moment, q
(g = a,b,c) is the electric field
yy
gradient at the quadrupolar nuclei, and e and h have their usual meaning.
35
14
a and 6 are the Euler angles required to project H Cl or HC N from
their instantaneous displacement off the a-axis of the complex first into
the ab plane and then onto the a-axis (see Fig. II-3), and the brackets
indicate averaging over the zero-point motion.
Information regarding the
angle, 6, that the HCl or HCN subunit makes with the a-axis of the complex
is contained in the first of Eq. II-4 as cos8 = coscccosS.
35
Small perturbations at the
14
Cl and
N nuclear sites upon complexa-
tion are ignored in the present treatment. As the molecular quadrupole
moment of cyclopropane is later shown to be small, calculations described
in Chapter 5 show that if higher molecular moments are less important,
the nuclear quadupole coupling constants are better than 99% determined by
projection.
From the measured values of the
35
14
Cl and
N nuclear quadrupole cou-
pling constants in cyclopropane-HX (X =
H
35
14
C1,C N) along with the free
35
14
Cl and HC N values, all given in Table II-7, operational values of
a, (3, and A can all be assigned and are given by
<J1
Figure II-3. Euler angles describing the mstaneous displacement
of HCl in the cyclopropane-HCl complex.
52
53
Table I I - 7
O p e r a t i o n a l Angles 0, a , and 0 f o r Cyclopropane-H
and Cyclopropane-HC
35
Cl
15
N
9(degrees)
a (degrees)
3(degrees)
Cyclopropane-H 3 5 C1
21.15 ( l ) b
15.35(5)b
15.25(5)b
Cyclopropane-HC 1 5 N
12.4(1)°
8.9(6)°
8.9(6)°
eQq
eQq
aa
2
o
Angle o b t a i n e d from — - — = ( 3 c o s 0-1)
.
i_
25
O b t a i n e d from eQq / h and eQq . / h i n T a b l e 1-3 for cyclopropane-H
Cl
35
and eQq / h = - 6 7 . 6 1 8 MHz for H Cl i n Ref. 2 0 .
a
° 0 b t a i n e d from eQq
cyclopropane-HC
14
/ h = - 4 . 3 8 ( 1 ) MHz and eQq , / h = 2.19(3)
N i s o t o p i c s p e c i e s i n Ref.
for the
59 and eQq / h = - 4 . 7 0 9 ( 1 )
14
for HC N i n F . DeLucia and N. W. Gordy, P h y s . Rev. 187, 58
(1969).
54
arctan
B = arccos
9 = arccos
-"-=? + 1/3
(II-5)
These operational values for a, B and 8 are given in Table II-7 for the
two complexes and will be used in projection equations for the Zeeman
parameters of the complexes.
The distance between the centers of mass of the subunits, R„ „ ,
CM.
in cyclopropane-HC
N, can be determined from the rotational constants
of the complex and subunits and consideration of vibrational averaging
effects.
By redefining P for the complex in terms of displacements of
EL
the atoms from the centers of mass of the subunits we have
15
p V"HC15N
= p
15
V + T HC 15 N
V HC N
2 e >+ M _ M ! 1 ^ _
2
#
M +M
V
HC N
where M and M
are the masses of the substituents. Using values P
a
15
15
HP N
V—HC N
and I
m Table II-2 along with P
in Table II-5 and 6 from
a
o
Table II-7 we obtain R„„ = 4.495(3)A.
CM
determination are small with R
The effect of errors in 8 in this
changing by .004A for 8 ranging from 0°
to 13°.
E.
Molecular G-values
33
Recent studies by Read, et al.
indicate that for weakly bound
linear complexes of similar binding strength as the present ones, certain
molecular properties of the complex, such as g-values, magnetic susceptibilities, and molecular quadrupole moments, are to a good approximation,
55
resultants of the corresponding properties in the substituent molecules.
In these studies, unlike the present one, the properties of the substituent molecules were known while those of the complex were determined.
The success of using projection equations which relate the molecular
property of the complex to those of the substituent molecules could then
be determined by taking into account vibrational effects which are introduced upon complexation and changes of centers of mass.
The intuition
that weak complexation would little alter these properties in the substituent molecules was shown to be correct for these linear, hydrogenbound complexes. A similar approach will be taken with the present
asymmetric tops to obtain g-values for cyclopropane.
The molecular g-values of the complexes are a sum of nuclear and
electronic terms and are given by
29
g - M, j Z (r 2l-r r )-I~1 + ^ l"1 • J <0 11, |fc><g|fc10>
m
=
% a a ' ~a~a *
*
k>0
VEk
The first summation is over all nuclei in the complex, I
is the inverse
moment of inertia tensor of the complex and the summation in the electronic
term involves matrix elements of the angular momentum operator between
ground and excited molecular electronic states of the complex where
L = l r
~
~i
* p .
Angular momentum and displacements are defined in terms
~i
1
of the centers of mass of the complex.
The displacements of the nuclei
and electrons of the complex can now be redefined in terms of the centers
of mass of the substituent molecules they are associated with.
From
Fig. II-4 we have that
r
~i
V
= R
~
+ r
V
~i
(II-8)
(Jl
Figure II-4. Translation of the coordinates of a cyclopropane electron
from the center of mass frame of the complex to the
center of mass frame of cyclopropane.
57
u
a.
m
•-C
II
58
where r
V
is the vector from the center of mass of the cyclopropane
V
molecule to the ith electron and R is the vector from the center of
mass of the complex to the center of mass of cyclopropane.
considerations apply to HCl electrons and all nuclei.
Similar
The nuclear
term of Eq. (II-7) is then easily broken up into two summations over
cyclopropane and HCl nuclei to give for the x component of the nuclear
term
nuc
XX
—
,VV9
XX _
<? „
V_
= (Y 2+z 2)
"p
V r-
I Z + 2[Y I
a(V) a
a(7)
V
a y
a a
V r
+
z
V
I
ZzM
a(V) a a
a(V)
+ (YHCl2+ZHCl2)
Z+2[YHC1
I
a(HCl)
V
+
„ , HCl 2
a
I
ZvHC1+ZHC1
a(HCl)
I
a(HCl)
HCl2,
I V ^ a+2 a
a (HCl) a
a
]
ZZHC1]
a
a
,„
n.
(II 9)
'
"
a
The electronic term requires a few assumptions to be separated conveniently.
The electronic wavefunction of the complex must be approximated as a product of the electronic wavefunctions of the substituent molecules in
an uncomplexed state. Thus we have
<k| = <k V |<k HCl |
k=0,l,2,... ,
Furthermore, the energy of interaction (~500 cm
(11-10)
) must be neglected in
comparison to the much larger electronic excitation energies
(>30,000 cm ) . Under these approximations m the coordinate system of
the complex we have that
59
gGlI
|<0V|L l * V
xx xx _
2
M
.
'm
r
I
KV>0
x
V V
E
o "\
|<0HC1|L | k H C 1 ) | 2
+ 2/m
J,
(II
HCl *HC1
k^1 0
E
- U)
o "Ek
We now switch to the coordinate systems of the substituent molecules
using the definition of L
x
L = I y P 1 - z.P1 .
u J
x
I z
ly
(11-12)
However P1(g=x,y,z) is irrespective of the center of mass giving
ell
g xx
xx
M
P
_
2^
m
e
V
'K O
' x'
y
V V S 'O V
V ) !' 2
Jy '
'. Jz P ^ Z
. V
l
V
V
k >0
l
V
E -E
0 k
+ HCl term
(11-13)
V .
where the HCl term is analogous and L is with respect to the center of
mass of cyclopropane.
Using
<0|pjk>* = <k|p*|o)
(11-14)
<0|P |k> = mi/ll(E -E )<0|x|k)
X
O
Px - - * £
leads to
geli
XX XX
M
P
= „2/m
Ir
,
' J-
k, v\
>0„
|<o v |L V |k V >| 2
'
' X'
V V
E
E
o~ k,
' '
(11-15)
JC
(H-16)
60
+ 12A
Y W | L > V X k V | y Z > V > - < 0 V | I z> V ><k V |LV|0 V >]
I
V
k
,
i
„ V r / „ V | V Vi, V W l V,
Vi Vv
/„V|TV|. V
+ z [<o I).y ± Ik >(k | L J O >-<O
y2
+ i/n j
Y
w
,V|r
Vi.V.,
|L x |k )<k 12, y i | o )]
[-co v n pziikv><kviF -ri°v>
V
k
1
>0
i
i
>0
+ <0 |E z, |k ><k \l P z |0 )]
l
l
2
V
+ z
v
/ V i r
i i V v / V i r
V i V \
[ - ( o v H P |k v ><k v |£ yj[|k v >
i
i
.^IF/I.'X.'IIP/IO7)]
r
- i2/il
V V
, Vir
V
£YV[-<O |}
n
V. , V i r
Vi V,
v
p/|k ><k 17 V . I 0 >
V
k >o
-Vir
Vi.Vv,, V
+ <o V IIv> V ><^ II *
B
»]
+ HCl Term
(11-17)
r-,2
„2
V
V
where the Y
and Z
terms were broken up into two equal parts prior to
using Eq. (11-15).
The first summation is clearly equal to the electronic
contribution in free cyclopropane.
The other summations can be made
into summations including the k=0 state by the following reasoning.
che second summation the k=0 term is clearly zero.
For
For the third and
fourth summation the k=0 states are clearly zero by noting that (o|p |0)
(g = x,y,z) is zero from Eq. (11-15)o
The closure property
61
J |k><k| = 1
k>0
V
can next be used along with L
n
VI
I
L
i(V) X
=
X
elx
(11-18)
to give
Vel^
P
P
X
• i(V)
+ 2/itlzV|l I
L*\
x
I(V)
i(V)
1
J
YW>
i(V)
V
V
+ Terms q u a d r a t i c i n Y and Z
+ HCl t e r m .
•
(11-19)
Using
r
[ I
Vi
l/\
X
i(V)
[ I
i(V)
I*1,
X
r
V
. ^ V
J" z j ] = i h J V
i(7)
I
(II-20)
x
"•
y*] = -ill J *\
i(V)
(11-21)
x
we have
el
Vel 7
!x^x_=!xx_JSx_
M
P
M
2y V <0 V,
P
y
ar Y|o
i(V)
V
>-a Z V <0 V | J
x
i(V)
z V >
x
V
V
+ Terms q u a d r a t i c i s Y and Z
+ HCl term
.
(11-22)
V
V
The terms quadratic in Y and Z can now be obtained from Eq. (11-17)
using the closure property and
I I P! 1 * I *!] = -*k I
i(V) g
i(V) l
i(V)
1
g - x,y,z
(11-23)
62
I J * S I Y.l = 0
i(V) z i(7)
(11-24)
giving
!sks-£j^-»Wl I Y > V » V | 1 .J|0»>
P
P
i (7)
i(V)
- (Y V2 + ZV2) I
1
i(V)
+ HCl term
.
(11-25)
Combining this term with the nuclear terms in Eq. (II-9) and realizing the
HCl electronic term is totally analogous to the cyclopropane electronic
term gives
V
h°L™
=
V
HCl HCl
I**J£* + Z*x **
p
P
V
+ 2Z [
[ y z y v - < o v | Y y V |o v >]
P
P
a(V)
V , Vl r
(o
£ Vcf
a
a(V)
,
V
+ 2Y
n„HClr
a(HCl)
or,HClr
+ 2Z
[
r
)
Vl Vv
)]
I ? J°
a
v
Z
i(V)
i(V)
„
H
1
C1 / „ H C l i
a
HCl,
HCl V l
i(HCl)
„ HCl , „ H C 1 |
Z z
-<0
|
a (HCl) a
v
v
I
i(HCl)
HCli^HClv,
z
|0
)]
„^v
(11-26)
/TT
X
where everything is defined in the coordinate system of the complex and
cyclical permutations apply to g I
and g I
. Zero-point vibrational
motions must however be accounted for in relating the free substituent
properties to the g-values measured in the complex.
63
C o n s i d e r a t i o n of t h e s e v i b r a t i o n a l a v e r a g i n g e f f e c t s d i s c u s s e d i n
Chapter I I I l e a d s t o t h e f o l l o w i n g e x p r e s s i o n s
g
1
TV V L HX HX, . 2 0 ,
2 , . 2 vl
=—— g TI +g,
I ( s i n B+cos Bsin a)\
V-HX
aa
V-HX I i
aa
l
aa
g
V-HX
bb
==
11
~V=HX
V-HX
T
bb
•'•KX
V ^ HX HX,
L VVTTV
hgii' bbkb ^ x * < c o s
2,
2»
B+sin ,3sin a)
L
2
+
V-„ X
g
cc
2,-
HX
V H X HX
— p n — y (cosacosB)
]
2M A H X
[
•»
2
_ _ J L _ • - » »"
7-HX
cc
V V __, H X H X ,
2 x ,
p
HX,
0v 1
g3 i i Tl cc +g
r
i I (*c o s a)' + — er ^ — uK z ( c o s a c o s B / I
X = C1,CN
.
(11-27)
By using the molecular g-values for cyclopropane-HCl in Table II-3, free
cyclopropane and HCl molecular parameters in Table II-2, along with the
rotational constants given in Table II-5 and Table 1-3, and the vibrational angles in Table II-7, the molecular g-values can be calculated
for cyclopropane using Eq. (11-27).
Since cyclopropane is an oblate
symmetric top, there are two independent g-values, g
are reported in Table II-8. g
independently from g
and g
and g n , and tnese
for cyclopropane can be calculated
of the complex.
Both values, which are in
excellent agreement, are reported and reflect the accuracy of the projection equations. If we take their average value as the true one, the
standard deviation is a = .0014 putting the uncertainty at 6%.
culated gi I and g
value for g, . + g
The cal-
values of cyclopropane can now be used to predict a
for the cyclopropane-HC
15
N complex.
This will determine
64
Table I I - 8
M o l e c u l a r P r o p e r t i e s of Cyclopropane
Qi I ( e s u cm )
1.04(40)xlO
2
—25
Q x ( e s u cm )
- . 5 2 ( 3 0 ) xlO
gii
.067(1)
g
.026 ( l ) a
.024(l)b
-6C
2
X M - X (erg/G mole)
-9(l)xl0
-10(1) xlO
2
Xi I ( e r g / G mole)
2
-9(1)xl0~6
-6f
-45(l)xl0
-6f
X ( e r g / G mole)
-36(1) xlO
X?i(erg/G 2 mole)
101(1) x l o " 6
X9 (erg/G 2 mole)
75(l)xlO_6
'9
'5
•p
XM (erg/G 2 mole)
-147(1) x l o " 6
Xd (erg/G 2 mole)
-111(1)xlo"6
(a2>,<b2>(A2)
17.3(2)f'g
(c2>(i2)
Calculated using g
8.8(2)
for
cyclopropane-HCl.
C a l c u l a t e d u s i n g g:
for
cyclopropane-HCl.
C a l c u l a t e d u s i n g 2x
-XKv,~X
f
ft
'?
'9
clcl
f o r
cyclopropane-HCl.
~X
f o r
~XbD~X
f o r
cyclopropane-HCl.
15
cyclopropane-HC N.
clcl
JDD
C a l c u l a t e d u s i n g 2X..-X
e
C a l c u l a t e d u s i n g 2X
Calculated using x
g
CC
= -39.2xl0~ erg/G mole.
See Ref.
62.
Calculated using s t r u c t u r a l information o r r o t a t i o n a l constants
cyclopropane.
See Ref. 16 and Ref.
19.
for
65
the sign of the experimental value and also comparison of the relative
magnitudes of the calculated and observed values could serve as additional
confirmation of the accuracy of the projection equations.
cyclopropane and HC
Using free
15
N parameters given in Table II-2, structural mfor-
mation obtained from the rotational constants of cyclopropane-HC
along with gii and g
for g.
+ g
15
N
just obtained for cyclopropane, - o 014 is calculated
using Eq„ (11-27) as compared with our experimentally deter-
mined value of ±„013.
In summary then, both g>i and g
values for cyclo-
propane have been checked in some independent fashion and are expected
to be fairly accurate.
F.
Magnetic Susceptibility Amsotropy
29
The magnetic susceptibility tensor elements are given by
x=
Z_|i (o|J(r2l-r.r.) |o> - - s i - J> <°1^><^1°>
4c m
l
2m c
k>0
o
(II.28)
k
where the first term is the diamagnetic response of the molecule and the
second term involving excited electronic states is the paramagnetic response
of the molecule„
The individual tensor elements for cyclopropane-HCl are
given in Table II-3. These were obtained by using the susceptibility
anisotropies also reported in Table II-3 and the bulk susceptibility,
—V—HCl
X
, for cyclopropane-HCl where
—7—HCl
X
=1
/3(Xaa+Xbb+Xcc) .
(H-29)
—7—HCl
X
is obtained by taking the sum of the bulk susceptibilities for cyclo-
propane and HCl which are given in Table II-2„ This is justified by the
33
linear hydrogen-bond Zeeman studies
which show that the susceptibility
66
anisotropy of the substituent molecules project to give the value for
—V—HCl
the complex along with the mvariance of X
to vibrational motions
of the substituent molecules introduced upon complexation.
x
and X h h
are equal within experimental error as would be expected since the a and
b directions are equivalent in cyclopropane and the susceptibility
anisotropy of HCl is only -.19 x 10
erg/G mole.
The paramagnetic contributions to the susceptibility tensor elements
can be obtained from the molecular g-values, the structure, and the rotational constants of the complex.
From the paramagnetic contributions
and the total magnetic susceptibilities the diamagnetic contributions are
then derived as well as the second moments of the electronic charge distribution, (a ) , etc., where
(a2> = <0|5"ai2|0>
i
(11-30)
These constants are all reported in Table II-3.
It is now of interest to obtain the magnetic susceptibility anisotropy
of cyclopropane.
Various estimates of this quantity presently in the
literature vary by as much as 100% and will be discussed in more detail
later.
We will again use projection equations to subtract out the effects
of the two different binding partners and then check this assumption as
the susceptibility anisotropy will be determined from any of the three
susceptibility anisotropies obtained for the complexes.
The appropriate
equations for either complex will be
V—MY
7
9
HM
'^aa'Xbb'Xcc'
r | |'
+
<
6cos a-l> (X| |-XA>
("-3D
(2X
=
Xx"X| | ) V
+
(3sm 2 Bcos 2 a-l> (X | fXj"*
(H-32)
bb"Xaa"Xcc)V"HX
(
3cos
9
= (X X
X = C1,CN
67
Using the three measured anisotropies for the complexes in Table II-3
35
15
and Table II-5, X||~X for H Cl and HC N given in Table II-2 and values
for a and B given in Table II-7, three values for Xi | - X
are independently obtained.
for
cyclopropane
These are listed in Table II-7. The uniformity
of the values is striking especially when considering that the magnetic
susceptibility anisotropy of the binding partner has changed considerably
in going from HCl (-.19 x 10~ erg/G mole) to HCN (7.2 x 10~ 6 erg/G 2 mole).
This can be taken as strong evidence that the projection equations are
accurately subtracting out the effects of the binding partner and that
the average of the three values is good to better than 10%. This uncertainty would also be consistent with the findings of Read, et_ al. for
linear hydrogen-bound complexes regarding the accuracy of projection equations for susceptibility anisotropy.
-7
Using the bulk susceptibility of cyclopropane, X r given in Table II-2,
the individual tensor elements of the magnetic suscpetibility for cyclopropane can be obtained and these are reported in Table II-8 using the
7
average of the three (xii~X ) values in Table II-8. The use of
Eqs. (11-31) and (11-32) assumes that x
and X h h are equal for cyclo-
propane in the complex as they must be for free cyclopropane.
To prove
this is the case, this restraint can be lifted by using (2x ~ X K K ~ X J
33
7-HCl
DD
7—HCl
CC
7
V
t0
^bb-Xaa-Xcc'
° b t a i n ^ a a ^ - X ^ a n d (2 Xbb-X aa -X cc >
7
where these later two quantities replace (x _ X||) i-n Et3s» (H-31) and
and
(11-32), respectively. These two cyclopropane anisotropies can then be
-7
V
V
combined with X to obtain X
= 36.2(8) and AY,. = 35.7(8) which are
aa
bb
equal within error and serve to confirm the method.
68
The diamagnetic and paramagnetic contributions were obtained using
the g-values calculated earlier and the structure and rotational constants for cyclopropane
'
and are reported in Table II-8 along with the
second moments of the electronic charge distribution.
The diamagnetic
susceptibilities and second moments of the electronic charqe distribution
for cyclopropane are in excellent agreement with those calculated using
*
various methods.
59
Maksic, et al,,
showed how calculation of these proper-
ties is relatively insensitive to the quality of the wavefunction used
and utilizing STO wavefunctions with optimized exponents calculated
values remarkably close to the present values. This is illustrated in
Table II-9 alonq with the excellent agreement between the value obtained
9
fin
in this work for (c \ and that obtained using a semi-empirical method.
The value of (c ) obtained for cyclopropane (8.8A ) is smaller than that
for the complex (11.4& ) in accord with the extra contribution in the
complex due to the chlorine lone pairs.
G.
Molecular Quadrupole Moments
The molecular quadrupole moment is in general given by
= e/2£ Za(3g2-r2) - e/2(o|£ O g ^ - r 2 ) 10>
a
i
Q
2
where g
g = a,b,c
(11-33)
2
and r
have been averaged over molecular vibrations.
From the
definition of the molecular g-value tensor elements and the magnetic susceptibility tensor elements given in Eqs. (II-7) and (11-28) it is evident
that
Q
2mc
aa ' —
2
<
W X oc" 2 Xaa )
+
e
iM^bbWWcc^aaV
and cyclical permutations for Q . and Q .
CD
CC
(II
"34)
The values obtained for Q ,
cict
69
Table I I - 9
Comparison of Values O b t a i n e d f o r t h e Diamagnetic
Susceptibility
and Second Moment 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
for
Cyclopropane i n This Work w i t h P r e v i o u s C a l c u l a t e d Values
j
P r e s e n t Work
Calculated
•147x10
-145x10
Calculated
5
X i I ( e r g / G mole)
-111x10
-6
-111.6x10
X± (erg/G mole)
<a2>(X2)
17.3
17.2
(b2> a2)
17.3
17.2
(c2) a2)
8.8
9.1
See Ref.
59.
See Ref.
60.
-6
70
Q,, , and Q
in the cyclopropane-HCl complex are given in Table II-3
along with their uncertainties.
The positive value for Q
indicates
CC
that most of the electron density is located near the plane containing
the heavy atoms.
The molecular quadrupole moments for cyclopropane are
similarly obtained using average values for Xl |~X
determined for gii.
and
9", a n ^
tne
value
Though the uncertainties of the cyclopropane mole-
cular quadrupole moments reported in Table II-3 are high, they are in
qualitative agreement with intuition.
Q
The positive value obtained for
is expected as only hydrogen atoms project out of plane and is in
agreement with the sign of Q
predicted by a semi-empirical method
cc
for calculating quadrupole moments though quantitative agreement is poor.
H.
Discussion
The magnetic susceptibility tensor elements obtained for cyclopro-
pane become especially significant in light of the body of literature
concerning the supposed high susceptibility anisotropy of cyclopropane
and various ring current theories utilized to account for it.
Early measurements
'
34-39
of the bulk susceptibility of cyclopropane showed
values enhanced over predictions from semi-empirical methods
speculation about delocalized p
prompting
electrons giving rise to an enhanced
z
susceptibility normal to the ring.
The NMR proton shift in cyclopropane
has been noted to occur at unusually high field (9.78 ppm with reference
to tetramethylsilane) relative to normal methylene protons and has been
,_ 34-36,38
,
,
36,37,66
taken to be evidence of ring current.
Also various studies
of shieldings of other protons by cyclopropyl groups have obtained
values of Ax = Xl|~X
consistent with ring current effects by relating
Ax of the cyclopropyl group to long range shielding effects.
&X can be
71
obtained in t h i s way by observing the r-hange in the s h i e l d i n g e x p e r i enced by a proton with the i n t r o d u c t i o n of a cyclopropyl group using the
67
McConnell equation
0 = M.
(i-3cos 2 Y> .
(11-35)
3R
Here 0 is the shielding at a given proton due to the magnetic susceptibility anisotropy of the cyclopropyl group, R is the distance between
the proton and the center of the ring, y is the angle between R a n d the
symmetry axis of cyclopropane, and averaging is over all internal motion.
This equation assumes a point magnetic dipole for the cyclopropyl group
fifl
and is most accurate
when the cyclopropyl group is 3A or more from the
proton.
Table 11-10 compares the value
obtained in this work for Ax for
cyclopropane with those obtained by other means.
In three cases the
values are obtained by a best fit of Eq. (11-35) to many cyclopropyl
—
fi
9
compounds.
The variability is large, ranging over 11-21 x 10
erg/G mole
29 69 70
and is an indication of the crudeness of this method. ' '
The value
obtained from magnetic birefringence measurements is contingent on
assumptions regarding certain higher polarizability terms which give
this value a certain amount of uncertainty.
29 70 71
' '
The value obtained
by Flygare was obtained by reasoning that Ax for cyclopropane must lie
between X
~V2(X
—6
9
+X„„) for ethylenimme (-10.9 x 10
erg/G mole) and
ethylene oxide (-9.5 x 10~
erg/G mole).
As the error in Ax presented
in this work is estimated to be less than 10% the large error to be
expected with the other methods can be seen from Table 11-10.
That the present results could be indicative of ring current can
best be seen by considering semi-empirical methods for predicting the
72
T a b l e 11-10
Values O b t a i n e d f o r X|I~X
f°r
Cyclopropane
Using V a r i o u s Methods
X| '—X
Method
-a.
X
io"6
-10.0
X
io-6a
Comparison t o c h e m i c a l l y
s i m i l a r systems
-13.6
X
io-*b
ab i n i t i o
-19.2
X
io"6C
Magnetic B i r e f r i n g e n c e
-21.0
X
io-6d
NMR S h i e l d i n g s
-15.0
X
io"6e
NMR S h i e l d i n g s
-11.0
X
io-6
NMR S h i e l d i n g s
-
a
2
( e r g / G mole)
9.7
P r e s e n t Work
R. C. Benson and w. H. F l y g a r e , J . Chem. P h y s . 5_1, 3087 ( 1 9 6 9 ) .
See Ref.
72.
A. D. Buckingham, W. H. P r i t c h a r d , and D. H. W h i f f i n ,
Soc. 6_3, 1057 (1967) .
See Ref.
76.
See Ref. 6 6 .
See Ref.
37.
T r a n s . Faraday
73
i n d i v i d u a l magnetic s u s c e p t i b i l i t y t e n s o r e l e m e n t s .
In t h e a b s e n c e of
r i n g c u r r e n t s t h e l o c a l i z e d m a g n e t i c s u s c e p t i b i l i t y method of F l y g a r e
is quite accurate.
By assuming s p
3
h y b r i d i z a t i o n on t h e carbon atoms
and
for t h e moment, Xaa , XT,K'
X cc a r e c a l c u l a t e d f o r c y c l o p r o p a n e by t h i s
DD
method and p r e s e n t e d in T a b l e 1 1 - 1 1 .
t h i s work.
A l s o given a r e v a l u e s o b t a i n e d in
The agreement between c a l c u l a t e d and o b s e r v e d i n - p l a n e compo-
n e n t s i s s t r i k i n g , however, t h e measured X
v a l u e i s c l e a r l y enhanced
over p r e d i c t i o n a s would be e x p e c t e d by r i n g c u r r e n t s i n t h e p l a n e of t h e
carbon a t o m s .
Also i n c l u d e d i n Table 1 1 - 1 1 a r e a b i n i t i o r e s u l t s by
Bley f o r c y c l o p r o p a n e
72
where n o n l o c a l c o n t r i b u t i o n s a r e c a l c u l a t e d by
i n c l u d i n g s e l e c t e d two c e n t e r i n t e g r a l s .
With t h e e x c l u s i o n of
n o n l o c a l c o n t r i b u t i o n s t h e v a l u e s for t h e s e c a l c u l a t e d magnetic
these
suscepti-
b i l i t y t e n s o r e l e m e n t s a r e i n r e l a t i v e agreement w i t h t h e v a l u e s u s i n g
F l y g a r e ' s method and w i t h X and \ , , d e t e r m i n e d i n t h i s work. However
A
aa
bb
with t h e i n c l u s i o n of n o n l o c a l e f f e c t s B l e y ' s c a l c u l a t e d X v a l u e becomes
cc
almost i d e n t i c a l t o t h e measured value w i t h l i t t l e change in X
o r X,_,_.
aa
bb
Though t h e above c o m p a r i s o n s may seem i n d i c a t i v e of r i n g c u r r e n t ,
3
l e g i t i m a t e q u e s t i o n s may be r a i s e d r e g a r d i n g t h e u s e of s p h y b r i d i z a t i o n
in t h e s e m i - e m p i r i c a l c a l c u l a t i o n .
From t h e f a c t t h a t t h e J
spin-spin
CH
coupling constant i s , within c e r t a i n l i m i t s , p r o p o r t i o n a l to the s character
13
of t h e carbon atom
73 74
'
t h e h y b r i d i z a t i o n of t h e carbon atom in c y c l o p r o -
2
2 5 38 73 75
pane h a s been found t o b e sp - s p
'
'
Coulson and Moffit
s i m i l a r c o n c l u s i o n s r e g a r d i n g carbon h y b r i d i z a t i o n in t h e
reached
carbon-hydrogen
bond by p a r a m e t e r i z i n g t h e e n e r g y of t h e c a r b o n - c a r b o n v a l e n c e b o n d s i n
c y c l o p r o p a n e i n terms of t h e h y b r i d i z a t i o n of t h e carbon atoms.
Mini-
2 28
m i z a t i o n l e d t o sp "
h y b r i d i z a t i o n for o r b i t a l s a s s o c i a t e d w i t h
carbon-
4.12
hydrogen bonds and sp '
hybridization for o r b i t a l s associated
with
74
Table 11-11
S u s c e p t i b i l i t y Tensor Elements f o r C y c l o p r o p a n e '
ab i n i t i o
(local
con t r i b u t i o n )
Localized
Model b
ab i n i t i o
( i n c l u d e s nonloc:al
contribution)
Presen
Work
-34xl0"6
-31xl0-6
-30xl0~6
-36x10
-34xl0_6
-31xl0~6
-30xl0~6
-36x10'
-32xlo"6
-33xlO~6
-44xl0~6
-45x10'
o f ergs/G m o l e .
30.
72.
Assume sp
3
h y b r i d i z a t i o n f o r the carbon a t o m s .
75
carbon-carbon b o n d s .
It has been suggested by T o r i and Kitahonoki
7fi
that the change in hybridization of the orbitals in cyclopropane changes
the susceptibility anisotropy associated with the carbon-carbon bond so
that shieldings by cyclopropyl groups can be explained without resorting
to ring currents.
In this study a modified IlcConnell equation was used
to predict the additional proton shift observed in a number of molecules
with the introduction of a cyclopropyl qroup.
By ignoring the carbon-
hydrogen bond anisotropy the additional shift is then given by
*
2
3 3cos 6.-1
Aa = ^f I
^i—
l
(11-36)
R.
l
where Ax is now the anisotropy of the carbon-carbon bond and this bond is
treated as a point dipole. A more recent study
37
however has shown the
failure of Eq. (11-36) in predicting certain proton shifts due to cyclopropyl groups.
This study considered 18 proton shifts with a wide variety
of orientations of the cyclopropyl group with respect to the protons including 6 shifts where the group anisotropy theory described by Eq. (11-35)
predicts opposite signs for the additional shift as bond anisotropy theory
utilizing Eq. (11-36).
The study concluded that group anisotropy was
strongly superior in its predictions and in the six cases mentioned predicted the correct sign while bond anisotropy theory did not. While this
is not proof of ring current in cyclopropane it does seem to indicate the
importance of nonlocal effects in explaining the susceptibility anisotropy
of cyclopropane as do results for other 3 member rings.
'
The magnetic susceptibility due to ring current is given in a simple
picture by
40
Ne
x zz - " — 7
4mc
2
p
(II 37)
~
76
where p is the assumed radius of the ring, N is the number of circulating
electrons and the z direction is normal to the ring.
If in the present
case we attribute most of our determined magnetic susceptibility anisotropy to ring current as would be suggested by the semi-empirical calculations as well as Bley's ab initio results, we obtain ~3 electrons for
a radius of . 88A* (the centroid to carbon distance) . Burke and Lauterbur
observed that in order to account for the ratio and magnitude of carbon
and hydrogen shieldings in cyclopropane relative to those in central
methylene groups in long alkanes it was necessary to have 3.5 electrons
o
36
flow in a 1.10A radius. A more recent study
of 52 proton shieldings
influenced by cyclopropyl groups utilized the more sophisticated Johnson
78
and Bovey technique
°
to show that 4.5 electrons circulating in a .88A
radius optimized agreement between experiment and calculation.
Other
ring current models for cyclopropane utilize 3-6 electrons.
I.
Matrix Elements in the Uncoupled Basis
The Hamiltonian for the first order Zeeman effect given in Eq. (II-l)
for an external magnetic field in the z direction is equal to
\
" -HZ 3f (g » J x + ^ B J y +g »« J » )
where all coordinates are in a space-fixed coordinate system.
(II 38)
"
We will
now redefine the tensor elements and angular momentum operators in
spherical notation with the following phase conventions
g
g
= g 2 + l/3Trg
zz
o
~
xz
=
^
(g
-l~ g +l }
(11-39)
(II
"40)
77
g y z = i/378 (g+^g_*>
(n-41)
J = /2/2 (J i'-J.h
(11-42)
X
^ 1
"r* J.
J
1 1
= i/2/^ (J+x+J.i)
J
-jj
0
z
(11-43)
The superscripts, j, refer to the fact that the spherical operators span
an irreducible representation,JS-
, of the infinite rotation group
with the subscripts indicating which of the 2j+l components is given.
Substitution leads to
K
i = \ v*[/5/2 g - 2 i j +i + ^ / 2 g +i j -i - g o jl 0 ]
z
-
\i /Xl H 1/3 Tr g J*
o
z
a 0
(11-45)
It is now convenient to express the first three terms as a zeroth rank
tensor product. This can be done utilizing
k
k
n
o v
{T(l) ®T(2) 2 T =
1
q
£
(-1)
-k +k -q
. 1 1 2
^ (2k+l) V ^
qnq,
\ k
k
T 1 (l)T/(2)
U, q, -q/ %
12
\1
2
/
q
2 ,
(11-46)
where the right hand side represents the qth component of the kth rank
irreducible tensor formed from the direct product of two tensor operators
where 3-j symbolism
80
has been used.
The following Hamiltoman is then
obtained
K
zl
=
^
H
{g2
z
®
jl}
0 ' V11
H
z
1/3Tr
In the uncoupled b a s i s , |jKMIM), t h i s leads to
g J
0
"
(H-47)
78
(JKMIM |K
|j'K'M'I'Mp=S
6
M,
I I
<JK||{g2®J1}J||J'K')-U0^
, M / J 1 J'
y 41/572 H ( - 1 ) J ' " [
\ - M 0 M'
1/3 Tr g H ^ ^ ^ . i ^ . S ^ ,
Q1
where the Wigner-Eckart theorem
9
(II-48)
1
has been used and (JK||{g © j } ||j'K')
is the well known reduced matrix element.
The reduced matrix element can
however be separated into products of two reduced matrix elements so that
< J K||f<,W|| J .K.>-3 1/2 l/ 2
U
J"
^V"1'1™'
J ' J J"j
(jK||g2||j,K'><J"||j||vJ,>
.
(11-49)
S u b s t i t u t i o n of
(j"||j||j'>
= [ ( 2 J ' + 1) ( J ' + 1 ) J ' ] 1 / 2 5 J l t J I
(11-50)
into Eq„ (11-49) and use of Eq. (11-48) leads to
(JKMIM IK , Ij'K'M'IMj = /1572 ]1 /tl H (-1)1+J " M
I' zl '
I
o
z
[(2J'+1)(J'+1)J']1/2 [
)(
U J K | |g2||j'K')
\-M o My Jj' J J'j
- yo/Tl 1/3 Tr 9 »»,«„• 6MH'6XK-
(II
"51)
Evaluation of (JK||g ||JK) entails relating the space fixed tensor
g to the molecular fixed tensor g1 which is normally dealt with in
z
«
molecular considerations.
If the Euler angles a, 3, and y locate the
body-fixed axes in the space fixed axis system then
<3Q = l 9 ^ 0 ( a , 3 , Y )
H
q
79
(n-52)
82
79
c*k
where Jj
qq
,(cc,8,Y) i s the Wigner r o t a t i o n matrix element and g
2'
u
the molecular fixed axis system.
i s in
From the properties of these matrices
83
we have that
^K^O^'- 6 '^ *
Since g
2
(II 53>
"
q
i s r e a l we can take the complex conjugate of t h e r i g h t hand
side t o y i e l d
% = I (-Dq 9 ^ o a ( a ' e ' Y )
q
T oq
*
(H-54)
2
The matrix element of g can now be calculated i n the symmetric top
basis making use of the f a c t t h a t
,1/2
l^-^-.a.B.Y)
M
(11-55)
L87T J
This y i e l d s
<JKM|g?|j'K'M'> = r ( 2 J + l > ( 2 J ' + l ) ] 1 / 2 ,J g 2
8TT
I
I
q
^q+M'-K',
~
q
J^^^-MLK'^dSdyda
(11-56)
which upon evaluation of t h e i n t e g r a l and use of the Wigner-Eckart
Theorem gives the d e s i r e d r e s u l t
/ J
(JK||g2||j»K'} = [(2J+1)(2J'+l)]1/2(-l)K"J I
2 J'\
] g 2 q'
VrK-qK7 "
(11-57)
where q is determined by the triangle relationship for 3-j symbols.
Substitution of this into Eq. (11-51) gives
80
(JKMIM |K J j ' K ' M ' I M > = / l 5 / 2
1
J
Z
Zl
J2 1 1
(-1) K + J + J ' - M + 1 y / t l H
2 J'\
/J
|
Z
^ M O M',
•
U / t l H [J 1 ( J ' + l ) ( 2 J ' i - l ) (2J+1) ( 2 J ' + 1 ) ]
}
Z
J' J J'f V-K - q K'7 °
g2g-U0/^
'
1/3 T r g M H z 6 ^ , 6 ^ , 6 ^ ,
(11-58)
The H a m i l t o n i a n f o r t h e second o r d e r Zeeman e f f e c t i s simply
H
= -1/2 H
2
z2
z
(X2 + 1/3 Tr X)
0
~
.
(11-59)
The second term is clearly not dependent on rotational quantum numbers
and thus is unnecessary for rotational transitions.
Matrix elements of
the first term are obtained by use of the Wigner-Eckart theorem followed
by use of Eq. (11-57) and leads to
(JKMIMJJC
I
Jj'K'M'IM,.)
z2
I
2 ,>K-M
= - 1 / 2 H (-1)
z
2 J
1/2 r
w J 2 J,\
2l/
[(2J+l)(2J'+l)]- ^
) X
q
\-K q K ' / \-M 0 M'/
(11-60)
2*
where the prime indicates again that X
is defined in the molecular fixed
coordinate system.
The nuclear Zeeman term can be shown using Eq. (II-l) and Eqs. (11-39)
to (11-44) to be equal to
jc = u /fog [~/3/2 i \a2 ~Ji/2
NZ
o
-11
i J-02 + i V + i\ a
+1-10 0
0
]H
avg
z
- y /h g I* H
o
0 z
where g represents the g-value of the nucleus.
(11-61)
Matrix elements of this
interaction can best be evaluated by applying the closure property
81
I
|JKMIM >(JKMIMJ
J,K,M,I,MI
so
(11-62)
= 1
that
(JKMIM |3C
V q/h
o
|J'K'M'I'M'>
I
H [
z
-/3/2(JKMIM
« M""IT"»M
M '"I >)
| l _1J jI "TK» "V M
J",K",M",I",Mj.
x
(j"K"M"I"M"|a21|j,K,M,I,Mp-/3/2(jKMIM:].|l+^|j"K,,M"I"M^>
x
*• I T, ,»K"M
V " M ", lTI"M">
<lMlO
( j " K " M " I " M ^ | a _ 1 | j ' K , M , I l M : J . > + (JKMIM : i : |lQ|j
x
(j''K»M"I''M»|a0|j'K'M'I'M')]
V
+ —
Use o f t h e W i g n e r - E c k a r t t h e o r e m ,
MxHz ( 0 - 1 ) 6 ^ , 6 ^ , 6 ^ ,
Eq.
(11-50),
I
(JKMIM IK
|j'K'M'IM'>
1 I \ / J
)a
1 M/
rKqr'i
q
(-1)
leads
to
I I
- 1 M'
2 J '
[(21+1)(I+1)I(2J+1)(2J'+1)]
J 2 J'\
x i
(11-57)
= - / J / 2 U q/b. n^
V-M
'J 2 J'\
f I
x /
I +
l-M 1 M1
-M
and Eq.
(11-63)
VTM
1/2
- 1 MV
I-M +K-M
x
+y g/fo H MT ( - 1 ) * "
o
zl
'J 2 J'\ / J 2 J"
-MOM'/ 1-K q K'
x [(2J+1)(2J'+1)]1/2 o J V l J ^ - U - a ^ M ^ g / h «jcr, «„,«,„,
(11-64)
The nuclear quadrupole interaction is given by the definition of a
contraction of two tensors by
KU = I (-DqQ2V2
Q
„
q -q
(11-65)
82
Use of Eq. (11-62) leads to
(JKMIM |K |J'K'M'I'M'.>^(-I)q
I
(JKMIM |Q2|J"K"M"I"M">
q
I Q
I
J"K"M"I"M"
/
(J«K"M"I"MJV2
Ij'K'M'I'M')
I1 -q'
I
,
(11-66)
84
Using the Wigner-Eckart theorem, Eq. (11-57) , and
<I||QIII>
("-67>
=jfrK
V^I 0 l)
gives the desired matrix element
q+I-M -M+K
( J K M I M J | KJj'K'M'I'Mp
= £(-1)
q
2 i y j 2J\
V"Mr q Mj\^M -q M'7
/ J
[(2J+1)(2JI+1)]i/2
2J\
W
/
W
^k
(II_68)
M
V-i
o 1/
The m a t r i x e l e m e n t s f o r n u c l e a r s p m - s p m and n u c l e a r
spin-rotation
were n o t n e c e s s a r y f o r t h i s work however a r e p r e s e n t e d h e r e as they do n o t
appear i n the l i t e r a t u r e in t h i s b a s i s .
For s p i n - r o t a t i o n we have t h e
i n t e r a c t i o n g i v e n by
K_„ = - I • M • J
SR
~
~
~
where M is the spin-rotation constant.
(11-69)
Using similar techniques as
before we have
J+J'+K+I-M -M
( J K M I M J K JjKMIM_>
X SR
X
= (-1)
2
[1(1+1)(21+1)(2J+1)
X
1/2
(2J'+1)(J+1)J) '
1/
(15/2) '
t
!l
2
ll
r J
2
J,>
J 1 J jj V-K q K.'J
v.
83
+ l/3Tr M {l(I+D(2I+1)J(J+1)(2J+1)}1/2 6
6
& ,
~
J J ' KK' MM'
I
l l W J l J M
-M - 1 M ' / U M 1 M ' /
I I I
j
I
I I
J
1 J'
V-M 1 M'7 \ - M - 1 M*.
J 1 J'
(11-70)
-M O M / \-M O M*
I
1/
2'
where M i s d e f i n e d i n t h e m o l e c u l a r f i x e d a x i s s y s t e m .
The n u c l e a r
s p i n - s p i n i n t e r a c t i o n i s g i v e n by
K
= I, • r • I„
ss
~1
~
~2
(11-71)
where T is the tensor describing the spin-spin interaction of nuclear
spin I
and I„.
Expanding the basis set to include I„ is trivial in
the uncoupled basis.
All interaction not involving I„ need only extra
Kronecker deltas 6„ ., and the basis set becomes |jKMI,M, I„M_ )„
M_ Ml
'
1 I, 2 I '
12 I2
1 2
The matrix element is
I.+I--M,. -MT +K-M
1 2
I2MX I^JJ'K'M'^M' I2M' > = (-1)
(JKMIJMJ
X
<*
X
<&
h
T
2
84
/ J 2 J' \
1/2
[(21 1+1) (11 + 1 )11 (21
+1)
(
1
+
1
)
1
(2J+1)
(
2
J
'
+
1
)
]
(
J Tq2 '
2
2
2
UqKl/
X
h
'J 2 J»>
1/2
l-M
-M O M'
X
^ V ^ 1 X2
-1 Ml /\-M
I
l / \X2
l
X
2
+
1
X
1 Ml
^
I
2
l
1
*1
2
2
1/2
,-M
1 M' M-M
X
J 2 J1
X
l
l
+ I
] /6/2
,-M
\-M 2 M'
l
1
I
X
\
*1
l
l
2/ V
2
0 M'
1
I
I
-M
2
0 Ml
2'
2
-1 Ml IV-M -1 Ml
1/ V 2
2/
1
I
-1 M' / l-M
V \ 2
l
*2
(11-72)
\-MT
X
l
1 Ml / V -M,
X
V
V
2
1 Ml
X
2j
The intensity of the transitions is obtained by calculating the
transition dipole matrix in the uncoupled basis. This matrix can then
be transformed to the basis under which the Hamiltonian matrix is diagonal
and the resulting matrix elements squared to give the relative intensities
of the transitions between-states.
The matrix element for the transition
dipole operator is equal to
(JKMI M
1 X
l
...|y |j'K*M'rM' ...)
X X
r
l
(11-73)
where r r e f e r s t o t h e s p h e r i c a l component of t h e d i p o l e o p e r a t o r and any
number of n u c l e a r s p i n s can be includedo
derived to be
The m a t r i x e l e m e n t i s q u i c k l y
85
/ J 1 J'\ /J 1 J \
(JKMI M , . . | y |J'K'M'I'M1 . . . > =
(
] (-1)
1 X
r
l
1
V-M r M'y UK q K'V
[(2J+1) ( 2 J ' + 1 ) ] 1 / 2 y ' 5
q
,
I
1
I
Oo.
1
where Kronecker deltas e x i s t for a l l s p i n s .
(11-74)
86
CHAPTER III
THE ACETYLENE-HCN COMPLEX
A.
Introduction
It has been a major emphasis in the studies that comprise this
thesis to consider complexes of major chemical importance.
In the first
two chapters rotational studies of complexes containing cyclopropane,
1
both at zero-field
2
and with an external magnetic field,
elucidated
details of the well studied but poorly understood cyclopropane molecule.
25
The ethylene-HCl complex,
discussed in later chapters, could be a precursor to carbomum ion formation. In this chapter rotational spectra
of various isotopic species of a complex between acetylene and HCN are
9fi on
examined in great detail at zero-field
'
to demonstrate the structure and
also to study perturbing forces and vibrational motions introduced upon
complexation.
Hydrogen cyanide is a weak acid and is quite capable of
hydrogen bond formation as both a proton donor and proton acceptor.
It is thus interesting to see if HCN will readily form a complex analogous
89
24
to the acetylene-HF,
acetylene-HCl
complexes, with acetylene as a
proton acceptor, and have similar properties.
In acetylene-HCl, the Cl
nuclear quadrupole coupling constant gives possible evidence for the
hydrogen atom of HCl experiencing an anisotropic potential.
The nitrogen
quadrupole coupling constant can also help establish this in the acetyleneHCN dimer as well as whether or not the electronic environment at the
nitrogen atom is perturbed by complex formation.
Two sites for deuterium
isotopic substitution exist to also measure these effects elsewhere in
the complex.
87
B.
Experimental
The zero-field experimental method referenced and described briefly
in the two previous chapters was used. Four a-dipole, R branches between
12 12
12 14
12 12
12 14
3 and 17 GHz were obtained for the H C CH-H C N and H C CH-D C N
isotopic species in their ground vibrational states. The 1
->• 2
and
12 13
12 14
2
•*• 3
transitions were obtained for H C CH-H C N in natural abundance. The o^„ •*• 1„, , 1„, •*• 2„„, and 1, „ •+ 2,, transitions were observed for
00
01
01
02
10
11
12 12
12 14
D C CD-H C N. The HCN used was supplied by Fumico and the acetylene
was supplied by Matheson.
DCN was prepared by dripping concentrated
deuterated orthophosphoric acid on KCN and condensing the gas evolved
in vacuo.
Acetylene-d
was prepared by dripping D O on calcium carbide
and condensing the gas m
vacuo.
Determination of Molecular Constants
The hyperfme components for the J = 0 ->- 1, J = 1 + 2, J = 2 -»• 3 and
J = 3 -*• 4 rotational transitions are listed in Table III-l for the
12 12
12 14
H C CH-H C N isotopic species.
This data was reduced in a two step
procedure in which the hyperfine structure is first fit to give the
N
nitroqen nuclear quadrupole constants X
rotational transitions.
and
N
Xbh
and tne
unperturbed
This fit ignores the small 2nd and higher order
effects of the nitrogen quadrupole interaction which are small and
utilizes the equation
v v, = c x N + c. x!L + V
ob
where \)
aAaa
bAbb
is the unperturbed rotational frequency and C
by Eqs. (1-2) and (1-3).
(III-l)
o
and C
are given
Because of the limited number of rotational
88
Table
III-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 H C CH-H
K
_!K+1
K
liK+l
°00 * L oi
\ l
-
2
12
V * 202
2
2
12 *
0 2 "*
3
3
13
03
C N
F + F'
Observed
(MHz)
Calculated
(MHz)
Difference
(kHz)
1 + 1
3984.230
3984.229
+1
1 + 2
3985.544
3985.544
0
1 + 0
3987.515
3987.516
-1
1 + 2
7846.684
7846.684
0
2 + 2
7847.341
7847.342
-1
1 + 1
7847.778
7847.778
0
2 + 3
7848.047
7848.046
+1
0 + 1
7849.424
7849.424
0
2 + 2
7968.892
7968.893
-1
o + 1
7969.116
7969.112
+4
1 + 2
7970.208
7970.208
0
2 -v 3
7970.302
7970.302
0
1 -v 1
7972.397
7972.399
-2
2 + 3
11770 .914
11770.914
0
3 + 4
11771.305
11771.306
-1
2 + 2
11772.39 3
11772.392
+1
1 + 2
11953.990
11953.988
+2
2 -y 3
11954.209
11954.207
+2
3 + 4
11954.258
11954.259
-1
2 + 2
11956.179
11956.179
0
3 + 3
11952.795
11952.798
-3
89
Table I I I - l
jK K
-i +r
2
11 *
3
13 +
3
03
3
J
^IK+I
3
4
12
14
+4
12 *
4
(Continued)
04
13
F'
Observed
(MHz)
2 -> 3
12132.851
12132.848
+3
F
->•
Calculated
(MHz)
Difference
(kHz)
3
-y
4
12133.244
12133.239
+5
3
-y
3
12132.138
12132.143
-5
2
-y
2
12134.326
12134.328
-2
3 + 4
1569 3 . 9 1 9
15693.918
+1
2
->•
3
15694.037
1 5 6 9 4 . 0 36
+1
4
-y
5
15694.090
15694.092
-2
2
•y
3
159 3 6 . 7 8 9
159 3 6 . 7 8 9
0
3
-y
4
15936.881
15936.883
-2
4
•y
5
159 3 6 . 9 1 8
159 3 6 . 9 1 5
+3
3
•y
4
16176.408
16176.408
0
2 + 3
16176.526
16176.525
+1
5
16176.582
16176.582
0
4
-y
90
transitions observed the unperturbed rotational line centers were then
fit to a rotational Hamiltonian that included a symmetric top centrifugal
distortion analysis.
This two step procedure prevents the errors result-
ing from the limited centrifugal distortion treatment, which amount to as
much as 27 kHz for a given rotational transition, from entering into the
N
determination of X
aa
and
X
N
•
bb
Tne
differences given in Table III-l reflect
the accuracy of the first step of this procedure and average about 2 kHz.
A similar procedure was used for the J = 2 + 3 and J = 3 + 4 hyperfme
12 12
12 14
transitions of H C CH-D C N given in Table III-2. For these transitions the effects of a deuterium quadrupole could be ignored with only a
small loss of accuracy and thus 1 = 1 for all of these transitions in
Table III-2.
The H
13 12
12 14
C CH-H C N hyperfme components in Table III-3
were also reduced using Eq. (III-l).
For the 0 Q 0 + 1 Q 1 , l
transitions in H
rot
+ 2 1 2 , l Q 1 + 2Q2 and 1 ^ + 2^rotational
12 12
12 14
C CH-D C N the deuterium quadrupole effects were
clearly resolved.
K =K
n
The Hamiltonian
+ Q(N):V(N) +Q(D):V(D) = K
+ K,
ro
2 2
z
z
*2
(III-2)
was used where Q and V are the nuclear quadrupole and electric field
gradient tensors for either nitrogen or deuterium.
Matrix elements are
computed in the basis
!« + ~D
1 = 1
~N
I + J = F .
Briefly we have
(III-3)
Table I I I - 2
Observed and C a l c u l a t e d T r a n s i t i o n
12 12
12 14
F r e q u e n c i e s f o r H C CH-D C N
I,F + I ' ,F'
Observed
(MHz)
Calculated
(MHz)
2,2 + 0 , 1
3981.846(4
3981.850
2,2 + 2 , 2
3981.881(2
3981.879
1.1 + 1,0
3981.914(3
3981.920
0,0 +
1,1
3983.162(3
3983.168
2.2 + 2 , 3
3983.197(2
3983.190
1.1 + 1,2
3983.228(2
3983.231
2.2 + 2 , 1
3985.186(1
3985.185
0,1 + 2,2
7842.452(2
7842.450
2.3 + 2,3
7843.107(2
7843.107
1,2 + 2 , 2
7843.140(4
7843.142
2.2 + 0 , 2
7843.556(2
7843.556
1.1 + 1,2
7843.792(3
7843.793
2.3 + 2,4
7843.815(2
7843.813
1.2 +
1,3
7843.858(3
7843.859
1.2 + 2 , 2
7964.186(4
7964.187
2.3 + 2,3
7964.200(3
7964.199
2,1 + 0,2
7964.411(3
7964.413
2.1 + 2,1
7964.444(3
7964.440
2.2 + 2 , 3
7965.511(3
7965.510
2 . 3 + 2,4
7965.611(3
7965.612
1,2 + 1,3
7965.619(4
7965.622
Table I I I - 2
(Continued)
I , F + I ' ,F'
Observed
(MHz)
i , o •»• 2 , 1
7967.703(5)
7967.705
2,2 + 0 , 2
796 7.719(3)
7967.719
0,1 + 0,2
7967.752(9)
7967.748
2,2 + 2 , 2
8083.049(2)
8083.049
0,1 + 2,2
8083.064(2)
8083.063
1,1 + 1,2
8084.387(2)
80 84.390
2,3 + 2,4
80 84.411(3)
8084.410
1,2 + 1 , 3
8084.460(3)
8084.457
2,1 + 0,2
8085.805(2)
8085.806
2,1 + 2 , 1
8085.822(3)
8085.820
+1
J
K
-1 K +1
^o*
2
12-
2
+
02
2
+
J
^IK;I
2
3
3
3
13^
03 +
13a
3
3
11
3
11
03a
12a
4
a
14
a
4
Calculated
(MHz)
1,2 + 1 , 3
11764.578
11764.578
1,3 + 1 , 4
11764.978
11764.978
1,1 + 1 , 2
11946.960
11946.962
1,3 + 1 , 4
11947.241
11947.239
1,2 + 1 , 3
12125.426
12125.425
1,3 + 1 , 4
12125.823
12125.824
1,3 + 1 , 4
15685.482
15685.483
1,2 + 1 , 3
15685.608
15685.60 3
1,4 + 1 , 5
15685.657
15685.660
1,3 + 1 , 4
15927.531
15927.534
1,4 + 1 , 5
15927.571
15927.568
1,3 + 1 , 4
16166.536
16166.5 36
04
a
12 + 4 13
93
Table I I I - 2
J
(Continued)
K . K . " ^ ' K',
-1+1
-1+1
„ __ _, „ ,
I,F+I',F'
T
Observed
(MHz)
Calculated
(MHz)
Difference
(kHz)
1,2 + 1 , 3
16166.658
16166,.655
+3
1,4 + 1,5
16166.710
16166,.714
-4
Deuterium n u c l e a r q u a d r u p o l e i n t e r a c t i o n n o t c o n s i d e r e d .
94
Table
III-3
Observed and C a l c u l a t e d T r a n s i t i o n
12 13
12 14
F r e q u e n c i e s f o r H C CH-H C N
JK
-IK+I"^:IK+I
^ l
2
^
02 *
2
3
02
03
Observed
(MHz)
Calculated
Difference
2+2
7824.990
7824.993
-3
0 + 1
7825.211
7825.208
+3
1 + 2
7826.314
7826.309
+5
2 + 3
7826.395
7826.400
-5
1+2
11738.146
11738.144
+2
2 + 3
11738.368
11738.368
0
3 + 4
11738.415
11738.416
-1
p
->• p '
(MHz)
(kHz)
95
((I D I N )IJKFM|K Q |(I D I N )I-J'K'F'M'>
I
1
J
J
F|
[((iDiN)i|
|Q(D)
11
= S ^ . ^ l - D I'+J+F
(IDIN)I')(JK| |V(D) I
|J'K'>
I' 21
+
<( I D I N )I ll2 (N> I I
(I^JI'XJKUVCN)
I
|J'K'>]
(in-4)
Evaluation of the reduced matrix elements containing the electric field
gradient operator has been done in Eq. (11-57) except the right hand side
is divided by 2 from the definition of the electric field gradient operator.
Taking out the I
dependence from the quadrupole reduced matrix element
in the first term and the I dependence in the second gives
S^,6m,(-1)
((IDIN)UKFM|KQ|(IDIN)I'J'K'F'M-> =
I
J
F
I +I„+I'+K+F
D N
/ J 2 J'
[(2J+1)(2J'+1)(21+1)(2I'+1)]
J' I' 21 l-K q K1
(-1)1' ^
>X2(D)/4I
v
x
(-D
X
D
2
q
Kxt> ° V
/
/ /\
II 2 IM
Ua(N)/4
<
\
X
D
M
q
/
2
V
(III-5)
^- ° x -
.2,.,
where X (i) (* = N,D) is the spherical component of the nuclear quadrupole
q
coupling constant tensor in the molecular fixed axis system. The matrix
elements for the rotational part of the Hamiltonian are 40
<(IDIH)IJKPM|K^|(IDIM)I'J-IC'P'M->
[^P-[J (J+D-K ]
2
•J
+ hK2A
= ^.Sjj.VV
96
+
6
MM'Sn.6JJ.5K+2,K' V4(B-C)[J(J+1) - K(K+1)] 1/2
x [J(J+1) - (K+l)(K+2)]1/2
-[DJJ2(J+1)2 + V J ( J + 1 ) K 2 ] 6 I I . 5 J J . 6 K K ' 6 M M '
(III 6)
"
A value for A was assumed from a fit of the J = 2 + 3 and J = 3 + 4 unperN
N
turbed line centers and B, C, D , and D
were fit along with X , Xi_i»
J
JK
aa
bb
D
D
X , and x. , • A weighted non-linear least squares program was used in
aa
bb
2
which a weight of 1/a.
was assigned to each transition where a
is the
standard deviation of the measurement given in parentheses after each
measurement in Table III-2.
Because four rotational parameters are fit
to four rotational transitions, the values obtained for B, C, D , and D
J
JK
are useful only for calculating line centers from the analytical expressions for the 0 Q 0 + 1 ^ , l
n
+ 2 ^ , 1 Q 1 + 2 ^ , and 1 ^ + 2
n
transitions
given elsewhere.
12 12
12 14
The 1„, + 2„„ and 1 + 2,. transitions of D C CD-H C N were
01
02
10
11
fit according to Eq. (III-l) ignoring the deuterium hyperfme components.
12 12
12 14
The 0
+ 1
transition of D C CD-H C N was resolved into its
deuterium quadrupole hyperfme components which are listed in Table
III-4
along with the standard deviation, a , of the measurements. These components were fit using Eq. (III-2) where a third term is added for the
second deuterium nuclear quadrupole interaction in the basis
J + I
~D1
= F.
~1
F. + I
= F„
~1
~D 2
~2
F, + I M = F
-.2.
~N
~
.
(III-7)
97
Table I I I - 4
Observed and Calculated T r a n s i t i o n
12 12
12 14
Frequencies for D C CD-H C N
J
+J' .
1
o
00
L
a
+ l
01 +
Observed
(MHz)
Calculated
(MHz)
Difference
(kHz)
-y
F[,F^,F'
1,2,2
-y
2,1,1
3813.2006(52)
3813.2074
-6.8
1,2,3
-y
2,3,3
3813.2330(17)
3813.2360
-3.0
1,2,3
-y
1,2,2
3813.26 34(20)
3813.2589
4.5
1,0,1
-y
1,1,2
3814.5246(10)
3814.5252
- .6
1,2,2 + 1,2,3
3814.5458(14)
3814.5 365
9.3
P
1'F2'F
01
2
02b
1,2,3
-y
2,3,4
3814.5627(7)
3814.5675
-4.8
1,0,1
-y
2,1,2
3814.5874(10)
3814.5815
5.9
1,2,3
•y
2,3,2
3816.5 306(12)
3816 .5308
- .2
2,2,2
-y
2,2,2
7626.5389
7626.5476
-8.7
0,0,0
•y
1,1,1
7626.7736
7626.7675
6.1
1,1,1
-y
2,2,2
7627.8789
7627.8673
11.6
2,2,2
-y
3,3,3
7627.9519
7627.9615
-9.5
1,1,1 + 1,1,1
7630.0672
7630.0667
5.2
1,1,1
-V
2,2,2
7777.1674
7777.1640
3.4
2,2,2
-y
3,3,3
7778.5278
7778.530 9
-3.1
0,0,0
•y
1,1,1
7779.9124
7779.9127
-
F i t with deuterium quadrupole i n t e r a c t i o n s i n c l u d e d .
Deuterium quadrupole i n t e r a c t i o n s
ignored.
.3
98
A weight of 1/a
2
was assigned to each transition and matrix elements
off-diagonal in J were ignored.
The advantage to this coupling scheme
lies in the fact that for J = 0, the F„ quantum number is actually the
I
quantum number where
r
+ i = i
~Dn
~D
~D
1
2
(III-8)
thus identifying the symmetry of the spin states. The importance of this
will be discussed later.
Because the deuterium nuclei lie in identical
molecular environments, the two deuterium quadrupole coupling constants
were constrained to be equal.
All unperturbed line centers for the four isotopic species of
acetylene-HCN are given in Table III-5.
Nuclear quadrupole coupling
constants obtained from the hyperfine data in Tables III-l through III-4
along with rotational constants and centrifugal distortion constants obtained from the line centers in Table III-5 are presented in Table III-6
where the numbers in parentheses represent one standard deviation in the
fit.
For H
13 12
12 14
C CH-H C N only two line centers were obtained and thus
A, B, and C given in Table III-6 were obtained by setting D and D
to
u
JK
12 12
12 14
their values in H C CH-H C N and constraining A, B and C to the
12 12
12 14
H C CH-H C N mertial defect which is defined later. For
12 12
12 14
D c CD-H C N only three line centers were obtained and A, B, and C
were fit by constraining D and D
J
JK
D.
to their values in H
12 12
12 14
C CH-H C N.
Structure
The average and equilibrium structure of the acetylene-HCN complex
is planar, T-shaped, and has C
symmetry (see Fig. III-l).
The HCN
99
Figure III-l. The molecular geometry and identification of
the principal axes of the acetylene-HCN complex.
100
(B>
<§>
<£>
<*>
<§>
®
<B)
101
Table I I I - 5
Observed and Calculated Unperturbed Rotational Line
Centers for Four I s o t o p i c Species of Acetylene-HCN
Complex
H12C12CH-H12C14N
Rotational
T r a n s i 1t i o n
°00
hi
hi
H12C12CH-D12C14N
•
2
12
2
02
2
11
3
13
3
03
3
12
°00
*
X
01
-y
2
12
+
2
02
+
3
13
+
3
0 3
-y
3
12
-y
4
14
-y
4
04
+
4
13
+
hi
-y
2
12
V
+
2
0 2
ho
+
2
11
3
13
->•
3
0 3
+
3
12
+
4
14
+
4
04
+
4
13
X
ll
hi
2
02
2
11
3
13
3
03
3
12
- > •
Observed
(MHz)
Calculated
(MHz)
Difference
(kHz)
3985.324
3985.324
0
7847.780
7847.794
-14
7970.208
7970.20 7
+ 1
11771.188
11771.199
-11
11954.207
11954.20 7
0
12133.122
12133.095
+27
15694.028
15694.012
+16
15936.883
15936.883
0
16176.518
1 6 1 7 6 . 5 38
-20
3982.978
3982.980
- 2
7843.555
7843.578
-23
7965.521
7965.5 21
0
8084.153
8084.126
+27
11764.858
11764.872
-14
11947.186
11947.185
+ 1
12125.704
12125.694
+10
15685.595
15685.573
+22
15927.534
15927.534
0
16166.647
16166.667
-20
102
Table I I I - 5
(Continued)
Complex
»"•*<«»«*.
Rotational
Transition
1Q1
•
2
02
12 12
12 14
D C CD-H C N
202
+ 3
0QO
+
hi
+
^0
*
03
1Q1
2
02
2
ii
Observed
(MHz)
7826.30 2
11738.365
3814.338
7627.867
7778.264
Calculated
(MHz)
Difference
(kHz)
103
Table
III-6
S p e c t r a l C o n s t a n t s f o r Four
Isotopic
S p e c i e s o f Acetylene-HCN
H 1 2 C 1 2 CH-H 1 2 C 1 4 N
H 1 2 C 1 2 CH-D 1 2 C 1 4 N
H 1 3 C 1 2 CH-H l 2 C 1 4 N
D 12 C 12 CD-H 12 D 14 N
A(MHz)
35517(809)
35844(817)
31518 a
26896 b
B(MHz)
2052.988(5)
2051.637(6)
2012.839a
1983.084b
C(MHz)
1932.356(5)
19 31.362(6)
1900.549a
1831.272b
D T (kHz)
4.8(2)
4.9(2)
-4.385(17)
-4.385(11)°
-4.399(14)°
J
D j K (kHz)
527(6)
497(7)
Xaa(MHz) - 4 . 3 8 2 ( 2 )
-4.413(2)
Xbb ( M H z )
2.194(3)
2.206(7)
2.202(54)d
XcC(MHz)
2.188(4)
2.207(7)
2.197(55)d
182(5)
Xaa ( k H Z »
Xbb(kHz)
-
94(12)
X° c (kHz)
-
88(13)
I n e r t i a l d e f e c t c o n s t r a i n e d t o 1.2 amu A* .
-105(12)°
D„ and D „ , c o n s t r a i n e d t o
J
JK
H 12 C 12 CH-H :L2 C :L4 N v a l u e s .
D, and D„„ c o n s t r a i n e d t o H C CH-H C N v a l u e s .
J
JK
Q
Obtained i n f i t o f 0 . . + 1 , t r a n s i t i o n s .
00
01
Obtained i n f i t of 1
2 ^ transitions.
2
0 2 md ^0
01
104
subunit lies along the C„ symmetry axis with the hydrogen atom pointing
midway between the triple bond of acetylene.
Support of these conclusions
is given by considering the rotational constants.
Planarity is established
by considering the inertial defect, A, defined as
A = i° - i°
cc
0
0
0
where I , I . , and I
cc
ob
aa
i°
bb
(in-9)
aa
are the effective moments of inertia obtained from
the ground vibrational state rotational constants.
In the absence of
vibrational motion
A = -2 y m c
7
l
where c
(111-10)
1 1
is the c coordinate of the I
1
2
atom and thus A would necessarily
J
-
be 0 for a planar molecule.
In weakly bound molecules with low frequency,
large amplitude bending modes the inertial defect may however differ
considerably from zero.
In the necessarily planar
was found to be 2.75 amu A ,
complex Ar-CNCl,A
and a similar value was found for Ar-CO .
In the present complex the inertial defect of ~1.1 amu & given in Table
III-7 for acetylene-HCN and acetylene-DCN conclusively establishes the
complex as planar.
The C
model for the structure requires that HCN lie on the C
symmetry axis which coincides with the a principal axis of the dimer.
The
contribution of HCN to the moment of inertia about the a-axis and consequently to the observed A rotational constant is only through its zeropoint vibrational motion.
As can be shown from the vibrationally averaged
angles obtained later from the nuclear quadrupole coupling constants,
the two heavy atoms of HCN have vibrationally averaged displacements of
~.09A from their equilibrium position on the a_-axis with regard to
their contribution to the moment of inertia I . This compares
aa
105
T a b l e 111-7
S t r u c t u r a l P a r a m e t e r s for Four I s o t o p i c
S p e c i e s o f Acetylene-HCN
12 12
12 14
12 12
12 14
13 12
12 14
12 12
12 14
H C CH-H C N H C CH-D C N H C CH-H C N D C CD-H C N
R
CM (A)
Ac-C
°2
A(amu A )
y(N) ( d e g ) a
Y (D)
4.216(5)
4.157(5)
3.656(5)
3.656(5)
1.1(3)
1.2(3)
12.43(4)
11.69(4)
(deg)b
11.9(23)
QA&eq)C
8.78(6)
8.34(14)
9 (deg)°
8.93(10)
8.32(14)
b
C a l c u l a t e d u s i n g Eq. ( I I I - l 3 )
f o r X (N) .
aa
^ C a l c u l a t e d u s i n g Eq. (111-13) f o r X ( n ) •
SL3L
'See t e x t f o r means o f c a l c u l a t i o n .
12.37(34)
12.23(25)
106
with the acetylenic carbon and hydrogen atoms which are displaced about
.6& and 1.2A, respectively.
Since this moment of inertia varies with
the squares of these displacements then the value of A is almost solely
determined by the acetylenic atoms. Comparison of the values for A for
19 1?
1914
1219
1214
H C CH-H C N and Hx C CH-DX CX*N in Table III-6 with the free
acetylene value in Table III-8 shows that the a-axis of the complex
coincide with the b_-axis of free acetylene and establishes the C
struc-
ture.
A direct consequence of the C
symmetry is that the overall wave-
12 12
12 14
function, lb, for H C CH-H(D) C N must be antisymmetric with respect
to the exchange of the two acetylenic protons.
If ty is written as a pro-
duct of electronic (e), vibrational (v) , rotational (r_), and nuclear (n)
wavefunctions,
\l> = IJJ ty ty \\)
e v rn
(III-ll)
then i t i s evident that i n the vibronic ground s t a t e degeneracy of the
nuclear wavefunction i s determined by t h e p a r i t y of the r o t a t i o n a l wavefunction.
Arguments concerned with t h e p a r i t y of asymmetric r o t o r wave-
function 14-15 lead to the conclusion t h a t r o t a t i o n a l t r a n s i t i o n s o r i g i n a t i n g
in l e v e l s of t h e type J
and J
(where s u b s c r i p t s refer t o p a r i t y of K .
ee
eo
-l
and K , respectively) will have a nuclear spin statistical weight of I
while those originating in levels of the type J
and J will have a weight
oo
oe
of I + 1. Thus, if C in acetylene-HCN exchanges equivalent acetylenic
protons, the ground state transitions originating in states of odd K
will
have a weight of 3 compared with that of 1 for those originating in states
of even K . Though the spectrometer does not give quantitative intensity
107
information these effects were seen qualitatively with the effect that
all K
= 1 lines were stronger than K
1
= 0 lines though the normal
line strength factor predicts otherwise.
The deuterium quadrupole
split J = 1 "*" 2 transitions were measured approximately during the same
time period for both acetylene-DCN and a similar complex ethylene-DCN
which has opposite overall parity and thus K
5:3.
27
= 0 lines are enhanced
Measurement of 20-30 hyperfine components in each complex clearly
showed the K
= 1 lines to be stronger than the K
= 0 lines in the
acetylene-DCN complex with opposite results in the ethylene-DCN complex.
This observation is unexplamable without consideration of nuclear spin
statistics as the normal line strength factor is the same in both complexes.
Further evidence for the observation of the effects of nuclear spin
statistics is the absence of all transitions originating in the J = 0,
F
= 1 state from the observed 0
12 12
12 14
+ 1 . spectrum of D C CD-H C N
where the basis is described in Eq. (III-7).
species two bosons are exchangeable by a C
since in this isotopic
symmetry operation about the
a_-axis, the overall wavefunction given in Eq. (III-ll) must be symmetric
with respect to this operation.
This will eliminate all antisymmetric
nuclear spin states from existing in the symmetric 0
rotational state
where the nuclear spin state is defined in terms of the total spin of
the deuterium nuclei.
It is easily shown for two identical 1 = 1 nuclei
that the nuclear spin state is symmetric for I . , = 0,2 and antisymtotal
metric for I. . , = 1 . For the J = 0 rotational state and the basis
total
given in Eq. (III-7) the F
deuterium nuclear spin.
quantum number will be equivalent to the total
Therefore all states with J = 0, F„ = 1 will
108
be nonexistent for this isotopic species under the assumption of C
symmetry.
The difference between spectra predicted with and without
consideration of nuclear spin statistics is shown in Fig. III-2.
The rotational constants obtained for H
D
13 12
12 14
C CH-H C N and
12 12
12 14
C CD-H C N also reinforce the proposed structure. The B and C
values for these isotopic species are within a few MHz of those calculated
using a rigid structure.
This level of error has been found to be common
in fitting a rigid structure to rotational constants in these loosely
bound asymmetric rotors where large amplitude bending modes are produced upon complexation.
Though no standard deviation is available
for the A rotational constant in D
12 12
12 14
C CD-H c N it is slightly larger
than the rotational constant of free D
12 12
C CD given in Table III-8.
This is most likely due to the in-plane bending motion of acetylene
with respect to HCN.
This will effectively decrease I
and thus in-
del
crease the observed value of A slightly.
The distance, R„„, between the centers of mass of the subunits can
CM
be calculated from the B and C rotational constants.
Since (
) (g = b,c)
1°
is determined from the rotational constants, where 1° is the moment of
gg
inertia in the ground vibrational state, we first make the approximation
Secondly, since (i
(-~>
= —J—
1°
gg
<X° >
gg
g = b, c
(XXI-12)
) (g = b, c) depends upon (g. )(g = a,b,c) where g.
i
gg
i
A.T-
is a principle axis coordinate for the i
atom, we have to assume
2 =
2
=
(g. ) (g ) (g a,b,c) when no vibrational information is present.
We have no vibrational information about the acetylene subunit and will
109
Figure III-2„
The difference in predicted spectra for the
J = 0 + 1 transition considering and not
considering nuclear spin statistics in AC-d -HCN.
The first multiplet has been shifted up one MHz
in frequency to get both multiplets on one scale.
no
not consJ uoi'in;.;
nuclear svdn cLaLis Lies
3814.10 3814.16 3814.25 3814.33 3814.40 3814.47 3814.55 3814.83 3814.70
FREOUEMCY
considering nuclear
siDin GLatisticc
L
L
3814.10 3814.18 3 8 1 4 . 2 5 3 6 1 4 . 3 3 3814.40 3814.47 3814.55 3814.83 3814.70
ncoucHcr
i
i
Ill
Table I I I - 8
Molecular Constants for I s o t o p i c Species
of free HCN and Acetylene
b(MHz)
44,315.975(4)a
r (H-C) (A)
s
1 . 0 6 317°
r
1.15538°
r
s
e
r
(C-N) (&)
12 12
H C CH
12 12
D C CD
35,455.53b
25,419.0*
D12C14N
H12C14N
36,207.4627(a)3
(H-C) (A)
1.06250(I0)b
(C-C)(A)
1.20241(9)b
e
a
il
CN(&3)
3.1*
- 4 . 70 91 (13)
XQ(MHZ)
°SCcm)
0(lO-26SCcm2)
$(10
-42
- 4 . 7 0 30 ( 1 2 ) a
194.4(22)a
X^(kHz)
u(10
a
2.985e
3.1(6)f
4
SCcm )
8.39f
2.18g
F. C. deLucia a n d W. Gorcfy, P h y s . Rev. A187, 58 ( 1 9 6 9 ) .
E. Kostyk and H. L. Welsh, Can. J . P h y s . 58_, 912 ( 1 9 8 0 ) .
°C. C. C o s t a m , J . Chem. P h y s . _29_, 864 ( 1 9 5 8 ) .
<
T C . G. Denbigh, T r a n s . Faraday S o c . 36_, 936 ( 1 9 4 0 ) .
e
A . G. Maki, J . Chem. P h y s . Ref. Data ,3/ 221 ( 1 9 7 4 ) .
S . L. H a r t f o r d , W. C. A l l e n , C. L. N o r r i s , E . F . P e a r s o n , and W. H.
F l y g a r e , Chem. P h y s . L e t t . 18_, 153 (1973).
g
R . D. Amos a n d J . H. W i l l i a m s , Chem. P h y s . L e t t . 6 6 , 471 ( 1 9 7 9 ) .
112
have to neglect these effects in fitting R
to B and C. We do however
have some information about the large amplitude vibrational motion of
H(D)CN off the a-axis.
If for the moment we neglect changes in the
environment of N and D upon complexation in acetylene-HCN and acetyleneN
D
DCN we can represent X and X a s
clcl
X
aa
=
clcl
2X0 ^ c o s ^ - l ) i =
N
'D
(111-13)
where C, is the instantaneous angle between C=N and the a-axis of the dimer
if i = N and between D-C and the a-axis if i = D. X n is the free coupling
constant of nitrogen in HCN or DCN if i = N or of deuterium in DCN if
i = D and is given in Table III-8, and the brackets indicate averaging
over the ground state vibrational wavefunction.
From Eq. (111-13) we may
N
obtain an operationally defined angle, y , for X
clcl
an<
D
5 X ^ o r t n e various
clcl
isotopic species of acetylene-HCN where
Y = arccos(cos 2 £)
0
(111-14)
The acute values for Y are taken for reasons to be discussed shortly.
These angles are listed in Table (III-7) with their uncertainties, C ,
given analytically by
2
.180. | „2
•rr
[a
, A a a 2 |l/2
+
f^]
ay = -rr-xr.
, °°, ,-,r^.. " — = ;
ll-f—5S+l/3n
I r-SS + 1/3 l~'" 3Y Q
(111-15)
N
The agreement within experimental uncertainty of Y obtained from X= and
aa
from X i-n acetylene-DCN indicates we can probably treat H(D)CN as a
clcl
rigid subunit for the present calculation.
The six instantaneous moment
113
of inertia tensor elements can then be derived in terms of the moments
of inertia of HCN and acetylene and the parameters R
Eq. (111-14), and B shown in Fig. III-3.
, Y (given in
Since X,, = X
within experiA
bb
cc
mental error then under the present assumption of unchanged electronic
environment at N we can average isotropically over the $ dependence
1
2^1
I(R
0
CM'Y'6)ijd8
= I(R
CM' Y) ij
X D = X,y,Z
'
•
(HI-16)
This results in all off-diagonal elements equaling zero and gives for I
bb
and I
cc
I^v,
4. +
bb = Iacet
I
2
^PD+ *„,,„
Y)
HCNr(l+cos
2
(111-17)
^ c - XPD+
I
I
HCM
I ( 1 + c o s 2 Y) •
is the pseudodiatomic moment of inertia given by
X
^HCCH^HCN
PD
We then fit R
M
HCCH +M HCN
2
CM
in both isotopes using values for Y from Table III-7.
resultant values of R
carbon distances, R
The
are given in Table III-7 along with the acetylene
, which are shown to be constant in both isotopes.
This reflects the fact that the change m
R
from acetylene-HCN to
CM
*
acetylene-DCN corresponds almost exactly to the change in the center of
mass of HCN in going to DCN.
In taking the acute values for the angles, Y, obtained from Eq. (111-13)
it has been assumed that the complex is hydrogen-bonded like the analogous
89
complexes acetylene-HF
and acetylene-HCl (to be discussed in the next chapqo
94
ter) rather than antihydrogen-bonded like HF-Cl?
and HF-C1F.
This is
114
Figure I I I - 3 .
The structure of the acetylene-HCN complex.
The
angles y and 3 are vibrational coordinates.
The
average values of these coordinates are zero.
115
116
easily shown by considering R
for both isotopes which could have been
calculated within the uncertainty of the values in Table III-7 without
knowledge of the orientation of HCN. By ignoring HCN zero-point vibrations out of plane and using the equation for a planar molecule
I
= I„„„ + I„„„„ + I„„
cc
HCN
HCCH
PD
°
R
(111-19)
o
is calculated to be 4.219A and 4.160A for acetylene-HCN and acetylene-
DCN respectively.
Since R
calculated here is .059A shorter for acetyO
lene-DCN and since the c m . in DCN is .059A farther from nitrogen than in
o
HCN the antihydrogen-bonded model requires that N in H(D)CN be .118A
closer to acetylene in the acetylene-DCN complex than in the acetylene-HCN
complex.
This is unreasonable and discounts the antihydrogen-bonded pos-
sibility.
E.
Interpretation of the Nuclear Quadrupole Coupling Constants
The previous assumption of unchanged nuclear environments upon
complexation will now be examined.
97
CH_CN-HF
95
96
Previous work on N -HF,
NCCN-HF,
98
and HCN-HCN
has shown that effects other than second rank
tensor projection as described by Eq. (111-13) contribute to the measured
nuclear quadrupole coupling constants in many of these loosely bound
complexes.
The long range effects of the presence of acetylene on the
electric field gradient (EFG) experienced at the nitrogen nucleus can be
obtained by considering the potential V(r,8), at a given point due to
acetylene
0P (cos6)
$p (cos6)
V(r,0) = — ^ - 3
+ —4~5
•••
r
r
(111-20)
117
where 0 and $ are the molecular electrostatic quadrupole and hexadecapole
moments of acetylene, P (cos6) and P.(cos9) are Legendre polynomials,
and all odd moments are 0 due to symmetry.
Since the nitrogen atom
lies on average on the a-axis, the EFG experienced by the nitrogen
nucleus directly as a result of the multipole moments of acetylene,
99 .
with a correction for the Sternheimer shielding phenomenon,
is given
by
»
N
3 2„
..
120P„(cos6)
N
q = (1-Y )<H> " ^ > <
3a
30$P.(cose)
+
5
r
S
'••> '
(III 21)
"
r
We will calculate expressions for P (6) in Eq. (111-21) algebraically
N
using 8 = 90°. Using the values of 0 and $ from Table III-8,y = +3
for N in HCN, 100 r = 4.812, and
= l e lqg
*
h
v
(111-22)
where e i s the fundamental charge and QN i s the nuclear quadrupole moment
of nitrogen taken to be 1.93 x 10
cm ,
we obtain a contribution of
N
12 12
12 14
+5 kHz to t h e observed value of X for this e f f e c t i n H C CH-H C N
aa
12 12
12 14
and H C CH-D C N.
first.
The second term of Eq. (IH-21) i s 2% of the
N
A greater contribution to the observed value of x
i-s likely to
act
come about as a r e s u l t of p o l a r i z a t i o n of C = N by the e l e c t r i c
field
generated by the acetylene subunit whereby N becomes s l i g h t l y more negasol
i s cconcrioution,
This
o n t r i b u t i o n , %•
x^ , to the observed coupling constant
c
aa
can be expressed as
tive i n charge.
„„i
C
9
xL
30p„(cos6)
" <-#»!—-*3
r
5<SP.(cos9)
+
~^
r
-1
<IIJ-23)
118
N
N
where Oxaa /3E) is the f i r s t order change in Xaa r e s u l t i n g from charge
rearrangement within H(D)CN o c c u r r i n g in an axial f i e l d and the s e r i e s
in parentheses represents the e l e c t r i c field a t the C = N c e n t e r of
mass r e s u l t i n g from a c e t y l e n e . Calculations for HCN give .87 MHz/(D/A )
N
for O x / 3 E ) however a value can a l s o be c a l c u l a t e d within the l i m i t a t i o n s
aa
10 2
of simple Townes-Dailey arguments
in the following manner. We f i r s t
i n t e r p r e t t h e dipole induced i n C = N as a r e s u l t of f r a c t i o n a l
transfer
of an electron from t h e 2p or 2p tranverse atomic o r b i t a l s of C i n t o
r
x
y
the corresponding o r b i t a l s a t N. )f sol i s then given by
v
aa
(I11 24
C • ^ k ><*
r
CN' '
- '
x
N
where x, i s t h e change i n x
experienced with the addition of one e l e c t r o n
2p
aa
to t h e nitrogen 2p o r b i t a l . X3 n a s been c a l c u l a t e d as 4 . 9 MHz for the
,
x
HCN molecule
but can be c a l c u l a t e d for the n i t r o g e n atom by using
(I11 25
X2p = 4 ^ f <^>2p
x
3
Using (1/r ) __
r
- ^
^x
24
- 3-^4
cm
gives 6.0 MHz which serves only to
X
ol
confirm the v a l i d i t y of the f i r s t v a l u e . By noting t h a t x^
is the only
of 22.5 x 10
clcl
N
f i e l d dependent contribution t o X , we d i f f e r e n t i a t e Eq. (111-24) w i t h
aa
r e s p e c t to E and obtain
,
X
aa,
4.9 MHz ,
y
m d , _ 4.9 MHz
<1ir> " i ^ I e T '-XT'
~ i J I T ^N
where arM i s the p a r a l l e l p o l a r i z a b i l i t y of CN.
,___
(III 26)
-
Using values in Table I I I - 8
119
for a.,
CN
and R„„ we o b t a i n 2.7 MHz/CD/A1 ) f o r
CN
3 times the previous value given.
upper l i m i t s , s u b s t i t u t i o n i n t o Eq.
acetylene-H(D)CN where now r =
OxA
aa
/ 3 E ) which i s
about
Using t h e two v a l u e s as l o w e r and
(111-23) gives 32-100 kHz for
4.278A.
I n summary t h e n , t h e major c o n t r i b u t i o n t o the o b s e r v e d v a l u e of
N
X
m a c e t y l e n e - H ( D ) CN i s given by t e n s o r p r o j e c t i o n
d e s c r i b e d by
clcl
Eq. (111-13) w i t h p o l a r i z a t i o n a c c o u n t i n g f o r 1-2% o f t h e o b s e r v e d v a l u e .
N
The a n g l e s thus d e r i v e d from X t o d e s c r i b e the z e r o - p o i n t
vibrational
clcl
motion of C E N away from the a_-axis i n a c e t y l e n e - H ( D ) CN a r e no more
t h a n 2° t o o high .
We now examine t h e d e u t e r i u m n u c l e a r q u a d r u p o l e c o u p l i n g i n
12 12
12 14
H
C
CH-D
C N.
The l o n g range e f f e c t s
d e s c r i b e d b y Eq. (111-21)
a p p l i e d t o d e u t e r i u m can be c a l c u l a t e d u s i n g y
10
cm ,
= .33,
Q
as
= 2.86 x
and r = 2.59 3$ t o g i v e - 6 kHz.
P o l a r i z a t i o n of the D-C
106
bond i s e s t i m a t e d t o be 4 times s m a l l e r t h a n for C = N
and thus
p o l a r i z a t i o n e f f e c t s on x
might a t f i r s t b e e x p e c t e d n o t t o be s e v e r e .
clcl
However any a t t e m p t t o v e r i f y t h i s by s i m p l e c a l c u l a t i o n i s
by t h e i n a p p l i c a b i l i t y of Tow n e s - D a i l e y t h e o r y h e r e .
frustrated
The s i t u a t i o n
is
f u r t h e r c o m p l i c a t e d s i n c e the a f o r e m e n t i o n e d p o l a r i z a t i o n of C = N by
a c e t y l e n e w i l l be n o n - n e g l i g i b l e i n terms o f i t s e f f e c t on t h e EFG a t
t h e d e u t e r o n and a l s o s i n c e some bond e l o n g a t i o n of t h e D-C bond may o c c u r .
D
12 12
12 14
For t h e s e r e a s o n s f u r t h e r a n a l y s i s o f X
f o r H C CH-D C N w i l l n o t
cla
be a t t e m p t e d .
The v a l u e o b t a i n e d f o r X ,
i n d i c a t e s i s o t r o p y m the EFG
e x p e r i e n c e d a t d e u t e r i u m , however, t h e u n c e r t a i n t y o f 12 kHz p r e c l u d e s
any d e f i n i t i v e s t a t e m e n t s .
120
In considering x
D
12 12
12 14
obtained for D C CD-H C N i t i s unlikely
aa
there i s s i g n i f i c a n t p o l a r i z a t i o n near the s i t e s of the deuterium n u c l e i .
Furthermore, the long range effects of HCN on X by an equation s i m i l a r
aa
to Eq. (111-21) with the addition of a dipole term and u t i l i z i n g information i n Table I I I - 8 are n e g l i g i b l e .
Therefore any changes i n X
i n the
clcl
D
12 12
complex from X.. m f r e e D C CD a r e l i k e l y a r e s u l t of Eq. (111-13) o r
quantum mechanical changes i n t h e s u b u n i t s upon c o m p l e x a t i o n .
Values
D
D
f o r x b b m D-C=C-R a r e i n f a c t very c o n s i s t e n t w i t h Xuh e q u a l l i n g
10 7
- 1 0 6 ( 4 ) k H z , - l 0 5 ( l ) k H z , - l 0 0 ( 5 ) k H z , and - l 0 4 ( 5 ) k H z for R = F,
R = Cl,
R = D,
and R = CH ,
respectively.
The a g r e e m e n t b e -
D
12 12
12 14
tween t h e o b s e r v e d v a l u e of V
i n D C CD-H C N and t h e s e v a l u e s
A
aa
i n d i c a t e s t h a t the n e t c o n t r i b u t i o n of v i b r a t i o n a l e f f e c t s
m e c h a n i c a l changes t o X
and quantum
a r e no g r e a t e r than t h e u n c e r t a i n t y i n the
3,3,
value.
F.
Discussion
The binding of acetylene-HCN w i l l now be considered i n terms of
both binding s t r e n g t h and bending motion of HCN.
I t has been shown
t h a t to a good l e v e l of approximation the r e l a t i o n s h i p between D and
J
the hydrogen bond s t r e t c h i n g force c o n s t a n t , k , m t h i s and other
asymmetric r o t o r complexes i s given by
"3
2
2 2 2
4 4
8TT(u n R r [ ( l T + c V + 2(B +C*)]
ks 2DO
u
i s the pseudodiatomic reduced mass defined as
(III_27)
121
Upp - y \ ^ C C a
PD
M..„.+M,.„„„
HCN HCCH
From k
•
(HI-28)
a w e l l d e p t h , e , for t h e hydrogen bond i n t e r a c t i o n can be
o b t a i n e d u s i n g Eq. ( 1 - 2 2 ) .
k , e , and V , the hydrogen bond s t r e t c h i n g
a
S
12 12
12 14
frequency a r e g i v e n i n Table I I I - 9 for t h e H C CH-H C N i s o t o p i c
24
s p e c i e s a n d i s compared t o a c e t y l e n e - H C l
which has a s i m i l a r w e l l
depth.
Also given i s R
which i s t h e d i s t a n c e between a c e t y l e n e
acet—HA
and the f i r s t heavy atom of i t s b i n d i n g p a r t n e r .
t h e s e two C_
I t i s apparent t h a t
complexes a r e s i m i l a r i n b o t h £ and R
«. „«•
Though the a n g l e s d e r i v e d from t h 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 s h a v e
a c e r t a i n amount of e r r o r as d i s c u s s e d p r e v i o u s l y owing t o e l e c t r o n i c
r e a r r a n g e m e n t and e l e c t r o s t a t i c i n t e r a c t i o n s , they do u n d e n i a b l y p r o v i d e
some i n s i g h t i n t o t h e z e r o - p o i n t v i b r a t i o n a l m o t i o n . F o r i n s t a n c e the
N
s m a l l e r a n g l e d e r i v e d from X i n acetylene-DCN as compared t o t h a t
33
o b t a i n e d i n acetylene-HCN c l e a r l y shows t h a t t h e h e a v i e r d e u t e r o n i s
a t t e n u a t i n g t h e z e r o - p o i n t v i b r a t i o n a l b e n d i n g motion o f C = N as a l l
c h a r g e r e a r r a n g e m e n t and e l e c t r o s t a t i c c o n t r i b u t i o n s t o x
in both i s o t o p i c s p e c i e s .
N
aa
are
t n e same
The much s m a l l e r v a l u e of y o b t a i n e d from
N
Cl
X
i n acetylene-HCN a s compared to y o b t a i n e d from X
m the analogous
aa
aa
acetylene-HCl
complex, a s shown i n T a b l e I I I - 9 , can be e x p l a i n e d
similarly.
The b e n d i n g motion of t h e b i n d i n g p a r t n e r of a c e t y l e n e a b o u t i t s
of mass i s
center
a t t e n u a t e d more i n acetylene-HCN by t h e c a r b o n and n i t r o g e n
atoms t h a n i n a c e t y l e n e - H C l where t h i s motion i n v o l v e s a n e a r s t a t i o n a r y
Cl atom.
N
I t i s i n t e r e s t i n g t o compare the v a l u e of y o b t a i n e d from X
clcl
acetylene-HCN w i t h v a l u e s o b t a i n e d for o t h e r hydrogen-bound systems
for
122
Table I I I - 9
Comparison of B i n d i n g P a r a m e t e r s for the
Acetylene-HCN and Acetylene-HCl Dimers
Acetylene-HCN
Acetylene-HCl
k (mdyne/A)
s
.053
.067
V (cm )
s
,
- ! v)
e(cm
82
87
642
614
acet-HA
3.656
3.699
y(degrees)
12.43(4)
21.21(1)
9 (degrees)
8.1(2)
15.69(1)
0 (degrees)
8.2(2)
15.00(2)
123
i n v o l v i n g HCN as a p r o t o n donor o r p r o t o n a c c e p t o r as i l l u s t r a t e d i n
87
Table I I I - 1 0 .
I n HCN-HC1
ceptor, Y i s 17-18°.
88
and HCN-HBr
A s i m i l a r v a l u e o f y of 17° i s o b t a i n e d f o r the
p r o t o n a c c e p t o r HCN i n (HCN) .
However when HCN s e r v e s as a p r o t o n
27 85
26,85
donor i n (HCN) , ethylene-HCN,
11-13°.
where HCN i s a p r o t o n a c -
'
and acetylene-HCN,
y is
The c o n s i s t e n c y i n these v a l u e s i n d i c a t e s t h a t HCN p r o b a b l y
e x p e r i e n c e s a n a r r o w e r b e n d i n g p o t e n t i a l when s e r v i n g as a p r o t o n donor
than as a p r o t o n a c c e p t o r .
Another comparison of i n t e r e s t i n c o n s i d e r i n g t h e a n a l o g o u s C
p l e x e s a c e t y l e n e - H C l and acetylene-HCN, i s the a n g u l a r i n f o r m a t i o n
comobtained
from t h e Cl and N 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 when b r o k e n down t o i n - p l a n e
and o u t - o f - p l a n e b e n d i n g a n g l e s where t h e s e r e f l e c t y p r o j e c t e d i n t o
the ab and ac p l a n e s , r e s p e c t i v e l y .
t e r IV,
This i s e x p l a i n e d i n d e t a i l i n Chap-
however we w i l l u s e the r e s u l t s t o c a l c u l a t e 8, and 8 where
b
c
t h e s e r e p r e s e n t the m - p l a n e and o u t - o f - p l a n e b e n d i n g a n g l e s
For a c e t y l e n e - H C l , v
and X
d i f f e r i n t h e t h r e e i s o t o p e s s t u d i e d by
.5 MHz o r more t r a n s l a t i n g i n t o 9. b e i n g g r e a t e r t h a n 9
degree w i t h u n c e r t a i n t y of
=
X
by a l m o s t one
.01° a s shown i n Table I I I - 1 0 .
HCN no such a n i s o t r o p y i s p r e s e n t as shown by 8, and 8
as Xu.h
respectively.
within experimental
error.
In acetylene-
i n Table I I I - 1 0
124
Table 111-10
N
Comparison of Values f o r y Obtained from X
in
clcl
Hydrogen-Bonded Complexes I n v o l v i n g HCN
4
HCN a s a P r o t o n
Acceptor
Complex
HCN-HC1
HCN-HBr
HCN-HCN
y (deg)
87
17
88
18
86
17
HCN a s a P r o t o n
Acetylene-HCN
26
Ethylene-HCN27'85
HCN-HCN
86
Donor
12
13
11
125
CHAPTER IV
THE ACETYLEUE-HC1 COMPLEX-
A CASE OF
NUCLEAR OUADRUPOLE COUPLING ANISOTROPY
A.
Introduction
In this chapter another complex formed as a result of a hydrogen
bond between an electrophilic hydrogen atom and a region of IT electron
density is studied through its rotational spectra.
analysis of acetylene-HCl
of acetylene-HCN.
24
In many cases the
is totally analogous to the preceding analysis
The present complex is shown to have C
symmetry like
acetylene-HCN with the binding partner of acetylene on average on the
C
symmetry axis.
Also, the present binding partner of acetylene contains
a nuclear quadrupole moment allowing an analysis of bending motions.
How-
ever with acetylene-HCl, it is shown that the Cl nuclear quadrupole coupling tensor shows anisotropy in all three isotopic forms studied unlike
the nitrogen nuclear quadrupole tensor in acetylene-HCN.
Two possible
arguments exist to explain the experimental fact that the electric field
gradient at the Cl nucleus is different for the b and c_ directions. One
explanation relies on HCl having anisotropic bending motion with less
constrained motion along the axis of acetylene as compared to the out-ofplane direction.
The other explanation depends upon the Cl nuclear site
experiencing an anisotropic perturbation as a result of complexation.
Both possibilities will be discussed in detail and then considered in
light of the acetylene-HCN findings.
126
B.
Experimental Method and Determination of Molecular Constants
Zero-field spectra were obtained for the acetylene-H
37
H
35
Cl, acetylene-
35
Cl and acetylene-D
Cl isotopic species using the pulsed Fourier
transform method described briefly in earlier chapters. Six nuclear
quadrupole-split, ground vibrational state J = 1 ->• 2 and J = 2 •> 3
transitions were observed for each isotopic form and are listed in
Tables IV-1, IV-2, and IV-3. We note that transitions having K_ =2
are absent from Tables IV-1, IV-2 and IV-3. A careful search in the
predicted region failed to reveal any components of the 2
2
->• 3
->• 3
and
transitions. We attribute their absence to the low effective
temperature (~4K) of the gas.
Rotational levels having K
higher in wavenumber than those having K
ficiently populated in this experiment.
=2 are 4 cm
=0 and are presumably insufThe hyperfine structure attrib-
utable to the Cl nuclear quadrupole coupling was reduced by the two step
process described in Chapter I where the nuclear quadrupole interaction is
treated as a perturbation to the effective rotational Hamiltonian. First,
the unperturbed rotational line centers, reported in Table IV-4, and the
Cl nuclear quadrupole coupling constants, given in Table IV-5, were obtained for all three isotopic forms using a linear least squares fit of
35
all transitions to Eq. (I-l) . For the acetylene-D Cl species, the deuterium
nuclear quadrupole interaction is neglected as it is only resolvable
in the J = 0 -> 1 transition which is discussed in Chapter VI.
As the
interaction is greater in splitting produced for lower J transitions,
the error in neglecting the deuterium interaction can be seen to be greater
for the J = 1 •*• 2 transitions than the J = 2 •* 3 transition as reflected
in the residues in Table IV-3.
127
Table IV-1
Observed and Calculated Transition Frequencies
of C 2 H 2 - H 3 5 C 1
J
K
-1 K +1
-*- J'
K
-1 K +1
1
-+2
01
02
F •*• 1
Observed
(MHz)
9578.416
9578.417
-1
1/2 + 3/2
9564.843
9564.844
-1
3/2 •> 3/2
9589.298
9589.301
-3
3/2 -»• 1/2
9602.868
9602.873
-5
9579.581
5
9579.584
2
{
9479.586
.5/2 + 7/2
5/2 •>• 5/2
9565.999
9566.000
-1
5/2 + 3/2
9575.714
9575.720
-6
1/2 -*• 1/2
9418.227
9418.227
0
1/2 •»• 3/2
9411.347
9411.349
-2
3/2 ->• 3/2
9399.262
9399.261
1
3/2 •*• 1/2
9406.134
9406.138
-4
5/2
9394.351
9394.352
1
5/2 -»• 5/2
9401.062
9401.064
-2
5/2 -»- 3/2
9405.974
9405.974
0
5/2 -»• 7/2
9407.926
9407.924
2
1/2 -»• 1/2
9763.187
9763.186
1
3/2
9756.459
9756.462
-3
3/2 •* 3/2
9744.097
9744.095
2
1/2
9750.823
9750.820
+3
3/2 -*•
1
10 +2*H
Difference
(kHz)
1/2 -• 1/2
'3/2 •> 5/2
hi * hi
Calculated
(MHz)
1/2 •*•
3/2 •*•
128
Table IV-1
J
•*
K
-1K+1
2
02 +
(Continued)
J
K< K'
K
-1K+1
3
03
F -»• I?'
Observed
(MHz)
Calculated
(MHz)
Difference
(kHz)
3 / 2 -»• 5/2
9739.295
9739.295
0
5/2
-y
5/5
9746.161
9746.163
-2
5/2
-y
3/2
9750.965
9750.963
2
5/2
-y
7/2
9752.871
9752.868
3
ri/2
•y
3/2
14362.775
-5
14362.766
4
14376.348
-1
14366.137
2
14366.138
1
14362.770
V3/2
-y
5/2
3/2
-y
3/2
^5/2
•y
7/2
14376.347
14366.139
2
2
12*
11*
3
3
13
12
V.7/2
-y
9/2
7/2
-y
7/2
14352.558
14352.559
-1
1/2
-y
3/2
14107.398
14107.400
-2
3/2
-y
5/2
14104.008
14104.009
-1
5/2
•y
7/2
14104.126
14104.125
1
7/2
•y
9/2
14107.529
14107.527
2
1/2
-y
3/2
14624.795
14624.796
-1
3/2
•y
5/2
14621.409
14621.406
3
5/2
•y
7/2
14621.4B1
14621.483
-2
7/2
•y
9/2
14624.885
14624.885
0
129
Table IV-2
Observed and Calculated Transition Frequencies
for C
-»• J '
J
K
-iK+i
i
X
01
K
-y 2
:IK+I
02
F -* ]pi
2V
H 37,
cl
Observed
(MHz)
Calculated
(MHz)
Difference
(kHz)
1/2 •+• 1/2
9366.936
9366.935
1
1/2 -> 3 / 2
9356.239
9356.243
4
3/2
•y
3/2
9375.510
9375.512
-2
r3/2
•y
5/2
9367.853
1
9367.855
-1
9367.854
X
1
ll *
10
2
12
-*• 2
11
2 „ •+ 3„„
02
03
V5/2
•y
7/2
5/2
-y
5/2
9357.145
9357.148
-3
1/2
•y
1/2
9211.396
9211.397
1
1/2
-y
3/2
9205.975
9205.975
0
3/2
•y
3/2
9196.448
9196.448
0
3/2
-y
5/2
9192.577
9192.577
0
5/2
•y
5/2
9197.868
9197.870
-2
5/2
•y
7/2
9203.280
9203.279
1
1/2
•y
1/2
9541.333
9541.332
1
1/2
-y
3/2
9536.033
9536.034
-1
3/2
•y
3/2
9526.287
9526.287
0
3/2
-y
5/2
9522.504
9522.504
0
5/2
-y
5/2
9527.916
9527.918
-2
5/2
-y
7/2
9533.207
9533.205
2
-y
3/2
14046.289
-4
14046.284
1
ri/2
14046.285
\.3/2
•y
5/2
130
Table IV-2
JK
-IK+I *
(Continued)
J
^IK;I
F •> F 1
5/2 -»• 5/2
fS/2
-V
Observed
(MHz)
14053.942
7/2
Calculated
(MHz)
Difference
(kHz)
14053.942
0
14048.939
2
14048.940
1
14048.941
\l/2
2
2
11 ^ 312
12 * 313
-y
9/2
3/2
-y
5/2
14293.451
14293.444
7
5/2
•y
5/2
14297.229
14297.224
4
5/2
•y
7/2
14293.504
14293.504
0
3/2
•y
5/2
13798.580
13798.582
-2
5/2
•y
5/2
13802.454
13802.452
2
5/2
•y
7/2
13798.676
13798.678
-2
Table IV-3
Observed and Calculated Transition Frequencies
Eor C, H
2
J
2
K
-1 +1
12
Observed
(MHz)
Calculated
(MHz)
3/2 -y 3/2
9416.471
9416.468
5/2
5/2
9418.572
9418.588
7/2
9425.762
9425.749
1/2 ->• 1/2
9436.476
9436.478
1/2 ->- 3/2
9582.174
9582.173
5/2
•y
5/2
9483.379
9483.376
1/2
•y
1/2
9596.306
9596.309
3/2
•y
5/2
9597.521
9497.522
3/2
•y
5/2
9757.178
9757.177
3/2
•y
3/2
9762.175
9762.165
5/2
•y
5/2
9764.332
9764.346
5/2
•y
7/2
9771.311
9771.314
1/2
-y
1/2
9782.066
9782.060
5/2
•y
5/2
14399.604
14399.607
F
5/2
2
2
3
02
11
03
C1
->• ]
K ' K'
K
35.
21°
- > •
- > •
14392.994
r*5/2 •y 7/2
14392.996
3
12
V7/2
•y
9/2
7/2
-y
7/2
14378.851
14378.850
1/2
•y
3/2
14652.330
14652.328
3/2
-y
5/2
14648.790
14648.791
14392.996
132
Table IV-3
\s+1
2
(Continued)
* JK:!K+1
12 * 3 13
Observed
(MHz)
Calculated
(MHz)
Difference
(kHz)
5/2 -y 7/2
14648.868
14648.870
-2
7/2
7/2
14641.905
14641.905
0
7/2 ->- 9/2
14652.418
14652.417
1
1/2 ->- 3/2
14133.975
14133.972
3
p -v p 1
- > •
i
3/2 -»- 5/2
14130.441
14130.446
-5
5/2
•y
7/2
14130.564
14130.567
-3
7/2
•y
7/2
14123.407
14123.406
1
7/2
-y
9/2
14134.109
14134.105
4
Table IV-4
Observed and Calculated Unperturbed Center Frequencies
for Three Isotopic Species of Acetylene-HCl
Observed
Isotope
C 2 H 2 ,H 3 5 C1
C 2 H 2 ,H
37
Cl
C 2 H 2 ,D 3 5 C1
Trans:Ltion
x
oi +
2
02
L
io
-•
2
11
Hi
•y
2
12
2
02
•y
3
03
2
11
•y
3
12
2
12
•y
3
13
hi
•y
2
02
Ho
•y
2
11
hi
-y
2
12
2
02
•y
3
03
2
11
•y
3
12
2
12
•y
3
13
•y
2
02
2
11
^1
Ho
•y
hi
•y
2
12
2
02
•y
3
03
2
11
•y
3
12
2
12
•y
3
13
Calculated
(MHz)
(MHz)
9578.417
9578.417
9749.571
9749.555
9404.613
9404.629
14365.489
14365.489
14623.430
14623.441
14106.064
14106.054
9366.936
9366.936
9530.606
9530.591
9200.670
9200.685
14048.429
14048.429
14295.038
14295.048
13800.202
13800.192
4596.309
9596.309
9767.881
9767.868
9422.299
9422.312
14392.321
14392.321
14650.900
14650.909
14132.585
14132.577
134
T a b l e IV-5
M o l e c u l a r C o n s t a n t s f o r Three I s o t o p i c
of
Species
Acetylene-HCl
37
C2H2,H35C1
C2H2,H
A(MHz)
36084(838)
36065(857)
36075(670)
B(MHz)
2481.065(6)
2424.423(6)
2485.696(5)
C(MHz)
2308.602(6)
2259.470(6)
2312.913(5)
D,(kHz)
7.9(4)
7.6(4)
7.9(3)
DJk(kHz)
497(8)
Inertial
D e f e c t (amu & ) , A *
ks(mdyne A
1.2(3)
.069(4)
)
Cl
476(8)
1.2(3)
.068(4)
C„H„,DC1
2 2
471(6)
1.2(3)
.068
X (MHz)
aa
-54.342(4)
-42.832(3)
X b b (MHz)
26.862(5)
21.173(4)
27.91(1)
X c c (MHZ)
27.480(9)
21.659(7)
28.68(2)
8b(deg)
15.69(1)
15.68(1)
14.21(2)
8
15.00(1)
15.00(1)
13.26(2)
(deg)
3.699(6)
(A)
*A = I
cc
- I. , bb
I
aa
3.699(5)
-56.587(9)
3.700(5)
135
The unperturbed line centers were next fit to rotational and centrifugal distortion constants, reported in Table IV-5, using the Hamiltonian
given in Ea. (II-2) where again the symmetric top centrifugal distortion
is utilized being justified by the complex being so nearly prolate
(K = -.9898).
C.
Molecular Structure
The rotational constants for the three isotopic forms reported in
Table IV-5 can be interpreted readily to establish that the acetyleneHCl complex has a planar, T-shaped equilibrium geometry with C
and the HCl lying in the C
symmetry
axis, forming a hydrogen bond to the center
of the carbon-carbon triple bond (See Fig. IV-1).
The planarity of the
complex is demonstrated by the small inertial defects, A, listed in
Table IV-5 and defined by Eq. (III-9), for the three isotopic forms studied,
all of which have a value of 1.2 amu & . In planar monomers that have no
°2
low frequency vibrational modes, A is usually near to 0.1 amu A . The
presence of low frequency, large amplitude in-plane bending modes causes
A to increase while out-of-plane modes cause A to decrease.
For acety-
lene-HCl, the lowest frequency mode is likely to be the m-plane motion
of acetylene with respect to the HCl thus causing A to be greater than
0.1 amu A* . Values of A between 2 and 3 amu &
van der Waals complexes of argon with CO
have been observed for
and with C1CN.
91,92
The equality of the A value for all three isotopic forms to the
corresponding constant B for the ground state of free acetylene (35280)
suggests that the HCl subunit lies along the a_ principal axis.
A slightly
larger value of A in the complex arises because of the contribution to the
zero point motion of the low frequency m-plane bending mode of the
136
Figure IV-1.
Molecular geometry and identification
of the principal inertial axes of the
acetylene-HCl complex.
137
<e>
•©•
<£>
<H)
•*-b
(A)
<§)
138
acetylene subunit with respect to HCl which tends to increase A by
effectively decreasing the moment of inertia about the a-axis.
That the
complex is hydrogen-bonded, with the hydrogen atom facing towards the 7r
electron density of acetylene rather than away is shown by the small
(~4 MHz) shifts in B and C for the complex upon deuteration.
It can also
be demonstrated using Eqs. (111-18) and (111-19) to show that R
by . 038A in going from acetylene-HCl to acetylene-DCl.
shortens
This is close to
the center of mass shift in going from HCl to DC1 (.039) and shows the
hydrogen atom to be closest to acetylene.
D.
Nuclear Quadrupole Coupling
It is immediately evident from consideration of the Cl nuclear quadrupole coupling constants in Table IV-5 that there is anisotropy present
that was not present in cyclopropane-HCl.
As the nuclear quadrupole
coupling tensor element is given by
«C1
eO, q
^ - - I T
where q
2 1
9 = a'b'c
<IV-X>
32V
is the electric field gradient, —r-, in the g_ principal axis
59
9g
ci
direction and Q
is the nuclear quadrupole moment of Cl, then the aniso-
tropy indicates an inequality in the electric field gradient in the b and
c directions.
Initial analysis will proceed with the assumption of an
unchanged electric field gradient at the Cl nucleus from free HCl. This
is initially justified by the distance of 3.70A between the Cl nucleus
and the perturbing acetylene molecule.
Because of zero-point bending motions involving HCl in the complex,
the principal axes of the complex do not coincide with the original
principal axes of HCl at each instant and thus vibrational averaging
139
effects must be accounted for in expressing the measured coupling constants f o r the complex in terms of those of free HCl.
The instantaneous
position of the HCl molecule with respect to the p r i n c i p a l axis system of
the complex is shown in F i g . IV-2 where, in g e n e r a l , the HCl w i l l be
out of t h e ab p l a n e .
Under the present assumption of an unchanged
e l e c t r i c f i e l d gradient a t the Cl nucleus, the nuclear quadrupole coupling constant tensor elements for free HCl must be rotated from the
instantaneous a x i s system of HCl i n t o the p r i n c i p a l a x i s system of the
complex and averaged over z e r o - p o i n t bending motions t o arrive a t expressions for t h e coupling constants for acetylene-HCl.
This w i l l r e q u i r e
rotation through two Euler angles, a and 3 , defined in Fig. IV-2.
For
a clockwise r o t a t i o n of an axis system in two dimensions we have t h a t the
new coordinates ( „} in t h e new coordinate systems are related t o the
old coordinates
CD *
^ '
/cosa
-sina\
VeinfY
'ypina
nnnnl
cosa/
V.
/
For rotations through two Euler angles, a and (3, in three dimensions we
have
DJ = R2(B) R2(a) fb"j
(IV-3)
where
^ ( a ) =|
0
1
'cos|3
-sinB
R 2 (3) = | sinB
cos3
0
I
(IV-4)
0 )
(IV-5)
0^
140
Figure IV-2. Euler angles, a and P, for rotation of
HCl axis system from its instantaneous
position into the axis system of the
complex.
141
142
If we r e p r e s e n t the nuclear quadrupole coupling tensor in dyadic form
as
X
aa
X
ab
X
ba
X
bb
X
ca
X
cb
X
X
ac'
=X(a,b,c)
(IV-6)
X(a,b,c) = U(a,3) x ( a " , b " , c " ) U (a,3)
(IV-7)
X
bc j= [ b ] abg
cc'
then i t follows t h a t
where
u(a,3) = R 2 (3)
R (a)
(IV-8)
This can be seen from
U(a,3) I b") a"b"c" U (a,3) = b) U(a,3) l b " )
~
\c"' s
" ~
Vc'LT
\.c"{J
= [ b abc
\cJ
(IV-9)
The nuclear quadrupole coupling constant of free HCl is simply
0
X
o
=
j °
"X0/2
(IV-10)
°
-X0/2/
and U(a,3) i s given e x p l i c i t l y by
/cos3cosa
-sin3
-cos3sina >
U(a,3) = | sin3cosa
cosg
-smftsina
sina
0
(IV-11)
cosa
Using Eq. (IV-7) where X ' defined in Eq. (IV-10), is substituted for
X(a",b",c") leads to
143
2
2
1/2>X
(IV-12)
X b b = (3/2 cos 3cos a - l/2>x
(IV-13)
X c c = <3/2 sin2a - 1/2>X0
(IV-14)
Xaa = ( 3 / 2 cos (3cos a o
2
a and 3 can now be algebraically solved for from the measured values of
X
, X hb » X
and x • Because of the vibrational averaging the values
obtained are only operational however they are indicative of the bending
motion amplitudes.
8
and 8
, shown in Fig. IV-2, represent the pro-
clC
3D
jection of the angular displacement of HCl into the ab and ac planes
respectively and are more useful.
As shown, 8 , = 3 and 9
is related to
ab
ac
a and 3 by
8
ac
= arctan
[tanacosS]
(IV-15)
Algebra leads to
1/2
X
8
ag
= arccos
X
aa+Xo/2
, g = b,c
aa+Xgg%
(IV-16)
The uncertainty in these angles can be calculated from
88 \2
,
• , -sa) a2
ag
X
bb
1/2
(IV-17)
V 8 X o J Xc
g=b,c
where the O's
derived that
represent the various uncertainties.
From this it can be
144
°9
"
.180
IT '
.,
ag
1
2 , 1 / 2 1/2
U-y )
•t
tx
1
„.
y
A
^
.2
2(x aa +x gg +x 0 >
gg + x o / 2 ] 2 g x
^
,
+tx
aa+V2]2CTx
A
aa
gg
2 J2 "jl/2
+ I-Xaa/2 + X g g / 2 ] ' O x ]
(IV-18)
where
Y=
x
<IV 19)
aa*xo/2
*5£K '
aa gg
"
0
The values of 6 , and 9
and uncertainties for the three isotopic
ab
ac
forms are given in Table IV-5 under the assumption of an unchanged
electric field gradient at the Cl nucleus upon complexation.
These
angles indicate less constrained motion of the HCl subunit in the plane
of the complex as compared to the out-of-plane direction.
That the angles
are close in value might be expected by the remoteness of the Cl atom
from the acetylene.
This was the case also with the cyclopropane-HCl
complex except that there 8 , and 8
were found to be equal within experiab
ac
mental error.
The conclusion drawn with the cyclopropane-HCl dimer was
that this equality results from the b and c directions being mechanically
and electrically equivalent.
That the b and c principal axis directions
may not be equivalent for the electrophilic hydrogen atom in acetylene-HCl
can be understood by considering the potentials governing the motion of
the hydrogen atom in these directions.
Since the hydrogen atom is pre-
sumed to be engaged in hydrogen bonding with the IT electrons of acetylene,
the in-plane movement would be along what might be viewed as essentially
a cylinder of negative charge. Viewing the acetylene in this way allows
145
one to see whv the m-plane excursions of the hydroqen atom might be
governed by a relatively broad potential whereas the out-of-plane motion
in the c principal axis direction could be governed by a sharper potential,
thus giving a larger average angle of displacement in the b direction as
compared with the c direction.
The above analysis is not supported, however, by the nitrogen nuclear
quadrupole coupling constants in the acetylene-HCN complex where the hydrogen atom of HCN is expected to experience a similar potential.
Under the
assumption of unchanged electric field gradient at the nitrogen nucleus
upon complexation, then the anisotropy in X. i_ and X
might be expected
bb
cc
to be scaled down from acetylene-HCl at least by the ratio of the coupling
N
Cl
constants in the two complexes, X /X • This would predict 50 kHz anisoaa aa
tropy where in fact none is observed outside of experimental error.
An
alternative explanation for the nuclear quadrupole coupling anisotropy
in cycloprppane-HCl requires that it comes at least in part from a perturbation to the electric field gradient of the Cl nucleus with the onset of
complexation.
If we consider the effects of the molecular electrostatic
moments of acetylene on the potential at Cl as described by Eq. 111-20
where r is the distance from acetylene to the Cl nucleus then we can reexpress the potential in cartesian coordinates (a,b, and c) to give
„, u v 0[2b2-a2-c2]
V(a,b,c) =
, 2 5/2
2
2(aW+c )3/
, <j>[8b4-24a2b2-24b2c2+6a2c2+3a4+3c4]
2 2 2 9/2
.„ „.
(IV-20)
8(aW+c )y/
where for convenience we treat the acetylene molecule as fixed and convergence at the hexadecapole term appears complete. We find that at the
position of the Cl nucleus where b = 0, c = 0 that (rr-) and (-r—) are both
—
—
db
dc
zero precluding the chance of anisotropy as a result of induced moments.
146
We can next solve for the electric field gradients in the b and c directions due to the electrostatic moments of acetylene under the condition
of b = 0, c = 0.
This leads to
&> - A» - H - Jf
3b
dc
a
a
where the series is clearly converged for the displacement of the Cl
nucleus from acetylene and the values of 0 and $ in Table III-8.
accounting for Sternheimer shielding
bb
cc
99
we obtain the result
h
~, 2
db
2
3c
Cl
where 0
By
—24
is the nuclear quadrupole moment of Cl (-.085 x 10
14
).
It is clear from Eqs. (IV-21) and (IV-22) that this effect has the right
sign to account for the experimental evidence.
Whether it is of reason-
able magnitude depends upon the Sternheimer shielding constant for Cl in
Cl
HCl. We can solve Eq. (IV-22) for y
using the experimentally determined
value of X,, X
and using Eq. (IV-21) to see if a reasonable value of
bb cc
Y
is obtained.
Substitution of 0 and $ from Table III-8 and 3.69A for
Cl
a leads to y
112
= -26. -39 has been calculated
be off by as much as a factor of 2 or more.
for Cl in HCl but could
The fact that a reasonable
number is obtained is very convincing for this explanation of the value
of X, ,-X
obtained for acetylene-HCl. The evidence for acetylene-HCN
bb cc
is also consistent with this alternative.
In acetylene-HCN the nitrogen
nucleus is 1.10A further from perturbing effects decreasing the perturbation by about a factor of 4.
Furthermore, the Sternheimer shielding
112
constant is at least an order of magnitude lower for N than for Cl
reducing Xhh~X
for N in
acetylene-HCN compared to Cl in acetylene-HCl by
147
by a factor of 40 or more.
This would make the anisotropy perhaps
less than 10 kHz in acetylene-HCN and is consistent with experiment.
148
CHAPTER V
THE ETHYLENE-HCL COMPLEX
A.
Introduction
The ethylene-HCl complex
25
completes a series of complexes involving
HCl and nucleophilic binding partners.
In acetylene-HCl and acetylene-HCN
the hydrogen atom of the electrophilic binding partner bonds to the IT electron density of acetylene.
If this were to be true also with a complex be-
tween ethylene and HCl then the structure would be predicted to be nonplanar
with HCl perpendicular to the plane of ethylene bonding to the Tr orbitals of the carbon-carbon double bond (see Fig. V-l).
This is found
to be the case and confirms our understanding of the nature of the bonding
in these weakly bound complexes.
The cyclopropane-HCl, acetylene-HCl,
and ethylene-HCl complexes all show remarkable similarity in terms of
structure, dissociation energy and dynamics and are all consistent with
the notion of hydrogen-bound complexes between a hydrogen atom and a
region of high electron density.
In acetylene-HCl, anisotropy was found in the Cl nuclear quadrupole
coupling with X
offered.
greater than y , and two possible explanations were
With ethylene-HCl, x h h is greater than X
indicating either
an anisotropic perturbation of the Cl electric field gradient or anisotropic bending motion.
Both of these possibilities are discussed.
Finally, outside of the perspective of the study of weakly bound
complexes, the importance of the present complex is apparent in terms
of synthetic organic chemistry.
The existence of weakly bound ir-complexes
has been postulated before as occurring as reactive intermediates in the
VO
Figure V-1.
The e t h y l e n e - H C l complex.
150
X
o.
E
o
o
I
O
X
I
UJ
151
addition reactions of unsaturated hydrocarbons.
Intuition leads
one to envision an intermediate which includes a nucleophilic unsaturated
hydrocarbon, and in the case of addition reactions with hydrogen halides,
an electrophilic hydrogen atom on the hydrogen halide.
The present com-
plex could then be a precursor to carbonium ion formation and similar
T-shaped complexes could be intermediates for Markovnikov addition of
hydrogen halides to unsaturated systems.
B.
Experimental Method and Determination of Molecular Constants
The zero-field, pulsed, Fourier-transform technique, carried out
in a Fabry-Perot cavity and described in Chapter I was used to obtain
ground vibrational state rotational spectra for the ethylene-H
ethylene-H
37
35
Cl, and ethylene-D Cl isotopic species.
35
Cl,
The J = 0 ->• 1,
J = 1 -*- 2, and J = 2 -> 3 nuclear quadrupole-split R-branches were ob35
37
Cl and ethylene-H Cl and the J = 1 -*• 2 and
35
J = 2 -*• 3 R-branches were obtained for ethylene-D Cl with the deuterium
tamed for ethylene-H
nuclear quadrupole interactions ignored.
The transitions were observed
between 4 and 14 GHz. The determination of rotational constants, centrifugal distortion constants, and nuclear quadrupole coupling constants
was performed in a manner analogous to that presented in Chapters I and IV.
The hyperfine transitions for the three isotopic species studied are given
in Tables V-1, V-2, and V-3. The unperturbed rotational transitions are
given in Table V-4 and derived constants are in Table V-5.
C.
Molecular Structure
The spectral constants point to the equilibrium and average structure of the complex as having C„
symmetry with the HCl molecule
152
Table V-1
Observed and Calculated Transition Frequencies
for C 2 H 4 -H35C1
J
-»•
K
-1K+1
K
- 1 K +1
°oo" Hi
•*• 2
1
01
Ho"
Hi-
2
2
02
11
12
F -> i
Observed
(MHz)
Calculated
(MHz)
V
-V
obs calc
3/2 + 5/2
4478.7961
4478.7950
1.1
3/2
•y
3/2
4465.2816
4465.2811
.5
3/2
•y
1/2
4489.6166
4489.6181
-1.5
1/2
•y
1/2
8951.3608
8951.3658
-5.0
1/2
•y
3/2
8937.8544
8937.8501
4.3
3/2
•y
3/2
8962.1960
8962.1983
-2.3
5/2
•y
5/2
8939.0123
8939.0135
1.2
5/2
-y
7/2
8952.5272
8952.5274
-.2
1/2
-y
1/2
9104.6107
9104.6085
2.2
1/2
-y
3/2
9097.8258
9097.8271
-1.3
3/2
•y
3/2
9085.6819
9005.6825
-.6
3/2
•y
5/2
9080.8378
9080.8412
-3.4
5/2
-y
5/2
9087.5846
9087.5857
-1.1
5/2 •> 7/2
9094.3516
9094.3473
4.3
1/2
•y
1/2
8824.2393
8824.2392
.1
1/2
-y
3/2
8817.4834
8817.4814
-.7
3/2
•y
3/2
8805.2923
8805.2922
.1
3/2
•y
5/2
8800.4692
8800.4697
-.5
153
Table v-1
J
K
K
K
-1K+1
(Continued)
"* JK<
K
K«
-1K+1
2
•> 3
^02
03
•p -y
p'
Observed
(MHz)
Calculated
(MHz)
V
-V
obs
calc
5 / 2 -*• 5 / 2
8807.2384
8807.2404
-2.0
5 / 2 -" 7 / 2
8813.9787
8813.9757
3.0
13422.3305
13422.3297
.8
13425.6856
13425.6840
1.6
7/2 •* 7/2
13412.1650
13412.1674
•2.4
< " l / 2 ->• 3 / 2
\ , 3 / 2 •+ 5 / 2
c
/2 -»• 7/2
7/2 -y 9/2
V.7
2
Hi
2
12
->- 3
^-3
12
13
1/2
-y
3/2
13637.0844
13637.0867
-2.3
3/2
•y
5/2
13633.7073
13633.7128
-5.5
5/2
•y
7/2
13633.8169
13633.8119
5.0
7/2
-y
9/2
13637.1998
13637.1970
2.8
1/2
-y
3/2
13216.5827
13216.5871
-4.4
3/2
•y
5/2
13213.2141
13213.2132
.9
5/2
•y
7/2
13213.3073
13213.3058
1.5
7/2
•y
9/2
13216.6928
13216.6908
2.0
154
T a b l e V-2
Observed and C a l c u l a t e d T r a n s i t i o n
Frequencies
for C 2 H 4 - H 3 7 C 1
J
K
K
"
-1 +1
K
-l +1
° O o " Hi
Hi"
2
02
F -> ?'
1
11
Hi " 212
2
02 "
3
03
V
obs
-\)
calc
4385.0300
4385.0329
-2.9
3/2
- » •
3/2
4365.8447
4365.8450
-.3
3/2
- > •
5/2
4376.5016
4376.4983
3.3
1/2
- > •
1/2
8747.9889
8747.9891
-.2
3/2 ->• 3/2
8756.5305
8756.5331
-2.6
8748.9083
8748.9055
2.8
-y
5/2
-y
7/2
1/2
•y
3/2
8886.7284
8886.7264
2.0
3/2
-y
5/2
8873.3402
8873.3448
-4.6
5/2
-y
7/2
8883.9927
8883.9902
2.5
1/2 -y 3/2
8618.9431
8618.9420
1.1
5/2 •*• 7/2
8616.1801
8616.1822
-1.1
13118.0068
13118.0046
2.2
13120.6485
13120.6507
-2.2
V.5/2
2
Calculated
(MHz)
3/2 -»•1/2
p/2
Ho"
Observed
(MHz)
1/2 -»• 3/2
C
3/2 -• 5/2
5/2 •*• 7/2
{
7 / 2 ->• 9 / 2
155
Table V-2
J
K
(Continued)
•*• J '
-ix+i
2
11
K
-i K H
-y 3
12
F -y F '
3/2 •*• 5/2
5/2 -> 7/2
7/2 •*• 9/2
2
12 " 3 13
3/2 -v 5/2
5/2 •*• 7/2
7/2 •> 9/2
Observed
(MHz)
13319.7041
13319.7880
13322.4537
12918.0501
12918.1172
12920.7883
Calculated
(MHz)
13319.7050
13319.7855
13322.4552
12918.0482
12918.1180
12920.7904
obs
calc
-.9
2.5
-1.6
2.9
-.8
-2.1
i
I
156
Table V-3
Observed and Calculated Transition Frequencies
Jfor C2H -D
K
-1K+1
1
01
K
-y 2
-l
02
+1
F "»• F '
2
->• 2
02 "
3
11
03
Calculated
(MHz)
obs
calc
8968.0492
-.9
1/2
-•
3/2
8953.9774
8953.9700
7.4
3/2
•y
3/2
8979.3296
8979.3266
3.0
•y
5/2
8969.2556
8969.2522
3.4
•y
7/2
5 / 2 -> 5 / 2
8955.1791
8955.1807
-1.6
3/2
•y
3/2
9102.4707
9102.4764
-5.7
3/2
•y
5/2
9097.4381
9097.4338
4.3
5/2
•y
7/2
9111.5049
9111.5034
1.5
13447.2278
13447.2388
-11.0
13450.7417
13450.7327
9.0
7/2
13436.6545
13436.6525
2.0
3/2
13662.6811
13662.6769
4.2
3/2 + 5 / 2
13659.1621
13659.1639
-1.8
a/2
3/2
V3/2
5/2
J-5/1
•y
7/2
\l/2
•y
9/2
7/2
H i " 312
Observed
(MHz)
8968.0483
V5/2
10
C1
1 / 2 •+ 1 / 2
p/2
1
35
1/2
•y
5/2
•y
7/2
13659.2623
13659.2671
-4.8
7/2
•y
9/2
13662.7972
13662.79 30
4.2
157
Table V-3
J„
K
„
-1 K +1
2
(Continued)
~* J '
K
-»• 3
„.
HKH
Observed
F - F-
(MHz)
Calculated
(MHZ)
V
°bS
-V
°alC
3/2 -»• 5/2
13237.8036
13237.8096
-6.0
5/2 -> 7/2
13237.9065
13237.9062
.3
7/2 -*• 9/2
13241.4378
13241.4321
5.7
158
Table V-4
Observed and Calculated Unperturbed (Zero-Quadrupole)
Rotational
Frequencies for Three Isotopes of the Ethylene-HCl Complex
->•
Is o t o p e
C2H4-H35C1
V+l
°00
Hi
C2H4-H37C1
C2H4-D35C1
-•
->-
J
K
^l ll
Hi
2
02
Ho
-•
Hi
Hi
•y
2
12
2
02
•y
3
0 3
2
11
3
12
2
12
3
13
°00
•y
•y
-y
Hi
•y
Ho
-y
Hi
•y
2
•y
02
Hi
•y
2
•y
12
Hi
2
02
2
11
2
12
3
03
3
12
3
13
02
Hi
•y
2
Ho
•y
Hi
Hi
•y
2
02
•y
2
11
2
12
-y
•y
2
12
3
0 3
3
12
3
13
Observed
(MHz)
Calculated
(MHz)
V
-V
obs
calc
(kHz)
4476.0854
4476.0852
8951.3661
8951.366 3
9091.0579
9091.0470
10.9
8810.6886
8810.6995
-10.9
13425.0391
1 3 4 2 5 . 0 391
0.0
136 3 5 . 7 4 5 5
13635.7532
13215.2407
13215.2334
4374.3609
4374.3622
8747.9894
8747.9883
1.1
8881.3948
8881.3854
9.3
8613.5894
8613.5987
-
9.3
13120.1420
13120.1423
-
.3
13321.3101
13321.3163
-
6.2
12919.6441
12919.6379
6.2
8968.0494
8968.0489
.5
9108.0772
9108.0640
13.2
8827.1314
8827.1446
-13.2
13450.0610
13450.0611
-
.1
13661.2812
13661.2900
-
8.8
13239.9216
13239.9128
.2
-
-
.2
7.2
7.3
-
1.4
8.8
159
Table V-5
R o t a t i o n a l Constants, Centrifugal D i s t o r t i o n Constants,
and Nuclear Quadrupole Coupling Constants for Three
Isotopes of the Ethylene-HCl Complex
C 2 H 4 -H 3 5 C1
C 2 H 4 -H
37
Cl
C 2 H 4 -D 3 5 C1
A(MHz)
25457(349)
25618(335)
25 312(415)
B(MHz)
2308.143(3)
2254.141(3)
2312.457(4)
C(MHZ)
2167.970(3)
2120.248(3)
2171.997(4)
7.2(2)
6.7(2)
6.7(3)
D(kHz)
J
DjK(kHz)
282(5)
268(4)
272(6)
Xaa(MHz)
-54.076(4)
-42.633(7)
-56.331(14)
xgvMHz)
27.091(6)
21.399(13)
28.218(17)
X^(MHZ)
26.985(10)
21.235(19)
28.113(31)
160
perpendicular to the ethylene molecule.
The hydrogen atom of HCl is
nearest to the ethylene molecule pointing to the center of the TT electron
density, presumably engaged in hydrogen bonding (See Fig. V-2).
principal axes of the complex correspond to the three local C
The
symmetry
axes of ethylene.
This structure is supported by consideration of the planar moments
P (g=a,b,c), reported and defined in Table V-6. In going from free ethylene
to the complex, the proposed structure results in a rotation of principal
axes as illustrated in Fig. v-3. Thus since HCl is presumed to lie on the
a-axis for reasons to be discussed shortly, P
and P
in the complex
should be almost unchanged from the corresponding quantities m
ethylene.
116
free
Consideration of Fig. V-3 and Table V-6 shows this to be the
case with differences accountable to vibrational effects.
Further evi-
dence for HCl lying on the local c axis of free ethylene is comparison
of the rotational constants of free ethylene with those of the complex.
The A, B, and C rotational constants of ethylene have been determined
to be 145987(120) MHz, 30022.0(39) MHz and 24837.2(48) MHz, respectively.11'
The C value corresponds very closely to the A values obtained for all
three isotopic forms of the complex with the small differences again
easily attributed to the vibrational modes introduced upon complexation.
It is also clear that the complex cannot be the planar C
possibility
as then the A rotational constant for the complex would be close to the
B value for free ethylene.
Two further conclusions can be drawn from the rotational constants
for the complex.
The equality within error of the A values for the
three isotopic species indicates that HCl lies on the a-axis of the
161
Figure V-2. Molecular geometry and identification of
the principal axes m
complex.
the ethylene-HCl
The principal axes of the complex
correspond to the local C
ethylene.
symmetry axes of
162
Table V-6
P l a n a r Moments f o r Three I s o t o p i c S p e c i e s of t h e
E t h y l e n e - H C l Complex and f o r E t h y l e n e
Ethylene-H35Cl
^ ,
°2.a
P (amu A )
cl
216
Ethylene-H3?Cl
221
Ethylene-D35Cl
216
P, (amu A )
17.0(3)
16.9(3)
17.1(3)
P (amu & )
c
2.9(3)
2.8(3)
2.9(3)
Sp
a " i<-Iaa«bb+Iee)
W
1
P.b = -=-(-I.
2
bb, + 1 a a +1 cc)
C
P c = -2( - I cc +1 a a +1.bb
.)
Ref.
116.
164
Figure V-3. Orientation of the principal axes
with respect to ethylene in free
ethylene and the ethylene-HCl complex.
165
Dimer (nonplanar)
*
-
r
Free Ethylene
166
complex which, from arguments given above, must correspond to the local
C
axis of ethylene perpendicular to the ethylene molecule.
Also, it is
clear that the hydrogen atom of HCl is between the chlorine atom and
ethylene.
This is evident from the small effect deuteration has on the
moments of inertia about the b and c axes as compared to the dramatic
change on
37
Cl substitution.
proximity to the center
This follows from the hydrogen atom's
of mass.
Lastly regarding structure it will be mentioned that the effects of
C
symmetry on line intensities were observed in a qualitative way in
that the intensities of K
line strength factor.
= 0 lines seemed enhanced over the normal
This is consistent with the nuclear spin statistics
appropriate for a complex with two sets of fermions (hydrogen nuclei) that
exchange through a C
symmetry operation.
nuclei obey Fermi-Dirac statistics, a C
overall wavefunction unchanged.
Since both pairs of hydrogen
symmetry operation leaves the
Therefore the overall wavefunction, \\>,
is symmetric where fy is given in Eq. (III-ll).
For the near prolate
asymmetric top, all K_1 even levels will have symmetric rotational wavefunctions and all K
odd levels will have antisymmetric rotational wave-
functions with respect to a C
axis.
symmetry operation about the a principal
As the degeneracies of corresponding nuclear wavefunction are given
by
n
n
1
TI
= •=• [ TT (2i.+l)][ TT (2I.+D+1]
sym
2 . ,
I
,
i
1
i=l
i=l
(v-1)
n
n
2l +1
-nM«nn
1 * < , > H TT (21 +1)-1] ,
(V-2)
antisym
2 . ..
i
1
J
i=l
i=l
there will be a 5/3 ratio over the normal line strength factor favoring
1
n
=
[
167
J
eo
and J
levels as in the vibronic ground state the parity of the
ee
rotational wavefunction will govern the parity of the nuclear wavefunction.
D.
Vibrational Effects
Upon complexation, 5 vibrational modes are introduced into the complex.
One is a stretch mode involving the stretching of the centers of mass
of the subunits about their ground vibrational state, average separation.
Two bending modes involve essentially the motion of the hydrogen atom of
HCl along the carbon-carbon internuclear axis and also perpendicular to
it.
The final two bending modes involve the ethylene molecule.
One is
the rotation of ethylene about an axis running through the carbon-carbon
internuclear axis and the other involves the rotation of ethylene about
its other local C„ axis perpendicular to the heavy atom plane of the complex.
The frequency and force constant for the stretching mode have been
calculated using Eqs. (1-16) through (1-19) applied to the present situation and are given in Table V-7.
The force constant is compared to
force constants for other hydrogen bonds and van der Waals bonds in
Table V-8.
It is seen from inspection that the present value is similar
to those obtained for other hydrogen-bound complexes in the gas phase but
larger than those found in complexes involving rare gases and hydrogen
halides.
Examination of Table V-6 shows that P, for ethylene and P
b
*
three i s o t o p i c forms of ethylene-HCl d i f f e r s i g n i f i c a n t l y .
for the
c
This can be
explained i n terms of the v i b r a t i o n a l modes involving the motion of
ethylene i n the complex.
The moments of i n e r t i a for the complex can
168
T a b l e V-7
Some Molecular C o n s t a n t s of T h r e e
Isotopes
of t h e Ethylene-HCl Complex
C 2 H 4 -H 3 5 C1
k (mdyne A )
V (cm
s
)
C 2 H 4 -H 3 7 C1
.066
C 2 H 4 -D 3 5 C1
.066
.070
84.3
83.3
86.3
Y(degrees)
21.43
21.42
19.49
8 .(degrees)
15.46(1)
15.39(1)
13.99(2)
8
15.57(1)
15.61(1)
14.11(2)
3.724
3.724
3.719
ac
(degrees)
r(&)
e(cm_1)
627
627
663
I
169
Table V-8
Comparison of k
and e f o r Various Hydrogen-Bound
and Nonhydrogen-Bound Complexes
k
0"
s (mdyne A
Hydrogen-bound
•H
£ (cm
C2H4-HC1
.066
627
C2H2-HCia
.06 9
643
0C-HC1
.045
569
HCN-HCN°
.110
1540
HF-HC1
.057
451
0C-HBrS
.0113
469
KrHBr
.0192
247
ArHBr-
.0166
206
KrHCl
.0156
180
)
J3
Nonhy drogen-bound
Ref.
24.
P. D , S o p e r , A. C. Legon, and W. H. F l y g a r e , J . Chem. P h y s . 7 4 , 2138 (1981)
C
L. W . Buxton, E . J . Campbell, W. H. F l y g a r e , Chem. Phys . 56, 3 9 9 ( 1 9 8 1 ) .
K. C . J a n d a , J . M. S t e e d , S . E. Novick, and W. K l e m p e r e r , J . Chem.
Phys . 6 7 , 5162 ( 1 9 7 7 ) .
S
M. R , Keenan, T. K. Minton, A. C. Legon, T. J . B a l l e , and W. H. F l y g a r e ,
P r o c . N a t l . Acad. S c i . USA, 77, 5583 ( 1 9 8 0 ) .
f
M. R , Keenan, E. J . Campbell, T. J . B a l l e , L. W. B u x t o n , T. K. Minton,
P . D. S o p e r , and W. H. F l y g a r e , J . Chem. P h y s . 72_, 3070
g
(1980).
T . J , B a l l e , E . J . Campbell, M. R. Keenan, and W. H. F l y g a r e , J . Chem.
Phys . 72, 922 ( 1 9 8 0 ) .
170
be e x p r e s s e d in terms of the moments of i n e r t i a of t h e s u b u n i t s and
f i v e i n t e r n a l c o o r d i n a t e s c o r r e s p o n d i n g t o t h e f i v e modes i n t r o d u c e d
w i t h c o m p l e x a t i o n . I t was shown
117
t h a t motion of e t h y l e n e a b o u t i t s
l o c a l C„ a x i s p e r p e n d i c u l a r t o the c o m p l e x ' s heavy atom p l a n e i s s m a l l .
The motion of e t h y l e n e a b o u t i t s l o c a l C
a x i s which runs t h r o u g h the
c a r b o n - c a r b o n i n t e r n u c l e a r a x i s can be c a l c u l a t e d from P
for
the
c
complex as
P
c
=
^cc^bb^200329-^
+
X
aa
+
1 / 2
*HCl<sin2Y>
(v"3>
•
Here 8 r e p r e s e n t s t h e a n g u l a r d i s p l a c e m e n t o f e t h y l e n e from i t s
average
p o s i t i o n i n t h i s motion and y r e p r e s e n t s t h e a n g u l a r d i s p l a c e m e n t of
HCl from i t s a v e r a g e p o s i t i o n on t h e a - a x i s and i s c a l c u l a t e d from the
n u c l e a r q u a d r u p o l e i n f o r m a t i o n u s i n g Eq.
(1-15) and X = - 6 7 . 6 1 8 MHz.
20
Using moments of i n e r t i a for e t h y l e n e o b t a i n e d from i t s r o t a t i o n a l constants,
116
a v i b r a t i o n a l l y a v e r a g e d v a l u e f o r 8 of 26° i s o b t a i n e d
i n d i c a t i n g c o n s i d e r a b l e motion a b o u t t h i s l o c a l C
axis.
This v i b r a -
2 1/2
t i o n a l l y a v e r a g e d v a l u e f o r 8, o b t a i n e d from a r c c o s ( c o s 8)
, is
117
confirmed from t h e Zeeman s t u d i e s of e t h y l e n e - H C l .
also
In these studies
an a p p r o a c h , s i m i l a r t o t h a t i n C h a p t e r I I , i s t a k e n t o gain m o l e c u l a r
c o n s t a n t s f o r e t h y l e n e from t h e Zeeman p a r a m e t e r s of t h e complex.
It
is
found t h a t t h e b e s t agreement between v a l u e s c a l c u l a t e d for t h e m o l e c u l a r
q u a d r u p o l e moment and d i a m a g n e t i c s u s c e p t i b i l i t y f o r e t h y l e n e i n t h i s s t u d y
and between ab i n i t i o v a l u e s i s o b t a i n e d w i t h s i m i l a r
averaged values for
I t was n o t e d m
vibrationally
8.
the i n t r o d u c t i o n t h a t t h e n u c l e a r q u a d r u p o l e
c o n s t a n t , & , , i s g r e a t e r than x
f ° r a l l t h r e e i s o t o p i c forms
coupling
studied.
171
Attempts t o c a l c u l a t e any p e r t u r b a t i o n i n t h e e l e c t r i c f i e l d
gradient
a t t h e C l n u c l e a r s i t e as a r e s u l t of t h e e l e c t r o s t a t i c moments of
ethylene are unsuccessful.
This a n a l y s i s would depend upon c a l c u l a t i n g
the second d e r i v a t i v e s of the p o t e n t i a l a t Cl as a r e s u l t of e t h y l e n e
and given by
Y (8,cp)
m
t
*«
*
0
T
x.,m
ri
V(r,8,cp) = 4 * 1
where q„
^ - ^ g
i s the s p h e r i c a l t e n s o r form of t h e m o l e c u l a r
m u l t i p o l e moment of e t h y l e n e .
(V-4)
a
electrostatic
This s e r i e s when d i f f e r e n t i a t e d
i s d i v e r g e n t a f t e r t h e hexadecapole t e r m .
twice
I f we assume the Cl n u c l e a r
s i t e i s f o r t h e most p a r t u n p e r t u r b e d w i t h complex formation t h e n t h e
v i b r a t i o n a l l y a v e r a g e d angles 9 , and 8
oiJ
can be o b t a i n e d u s i n g Eq. (IV-16) .
discussed i n the l a s t
chapter
clO
These a r e given i n Table V-7 and
i n d i c a t e s l i g h t l y l e s s c o n s t r a i n e d motion for the b e n d i n g of HCl o u t of
t h e heavy atom p l a n e as compared t o i n t h e heavy atom p l a n e .
Though
t h e d i f f e r e n c e i s s l i g h t , p r e l i m i n a r y n o t i o n s might s u s p e c t a c o n t r a r y
t r e n d a s t h e IT o r b i t a l s t o which t h e hydrogen atom bonds e x t e n d along t h e
a x i s of e t h y l e n e .
However, due t o the l a r g e angle g i v e n p r e v i o u s l y
the motion of e t h y l e n e about t h e l o c a l C
a x i s through the c a r b o n -
carbon i n t e r n u c l e a r a x i s , i t i s e x p e c t e d t h a t t h e r e w i l l be an
s p r e a d i n g of the e l e c t r o n d e n s i t y p e r p e n d i c u l a r t o t h e
axis.
for
effective
carbon-carbon
This argument, however q u a l i t a t i v e , would a c c o u n t f o r t h e p r e s e n t
s i t u a t i o n as compared t o the c o n t r a r y s i t u a t i o n i n a c e t y l e n e - H C l where
X
cc
>
\b'
172
E.
Discussion
Outside of the differences discussed in Chapters I , IV, and V,
the three complexes of HCl with cyclopropane, a c e t y l e n e , and ethylene
are a l l very s i m i l a r i n terms of s t r u c t u r e and binding strength and
dynamics.
They a l l e x h i b i t C
tances (See Fig. V-4).
symmetry with s i m i l a r edge to Cl d i s -
In a l l these complexes the binding has been
a t t r i b u t e d to hydrogen bonding between the hydrogen atom of HCl and
the region of high electron density i n the binding p a r t n e r .
The strength
of the binding i n terms of force constant and w e l l depth i s shown i n
Table V-9 where the force constant has been c a l c u l a t e d with the more
accurate method given by Eq. (111-27).
Also given are the angles
obtained from the Cl nuclear quadrupole coupling constants using
Eq. (1-15) .
Though these angles are obtained ignoring perturbing e f f e c t s
a t the Cl nuclear s i t e from complex formation, there i s a remarkable
s i m i l a r i t y in values which seems to i n d i c a t e s i m i l a r bending p o t e n t i a l s .
Also noticeable from examination of the distances in Fig. V-4 and the
well depths in Table V-9 i s a c o r r e l a t i o n between the edge to Cl d i s tance and well depths.
173
Figure V-4.
Geometry and edge to Cl distances
in cyclopropane-HCl, acetylene-HCl,
and ethylene-HCl.
174
Edge to Cl Distance (A)
3.57
3.69
3,72
175
Table V-9
F o r c e C o n s t a n t s , Well Depths and Bending Angles
f o r Cyclopropane-HCl,
Acetylene-HCl,
and Ethylene-HCl
k (mdyne A
)
e (cm
)
Y(deg)
cyclopropane-HCl
.079
855
21, .2
acetylene-HCl
.067
614
21, .2
ethylene-HCl
.061
575
2 1 , .4
176
CHAPTER VI
PERTURBATION IN THE ELECTRIC FIELD GRADIENTS
IN ACETYLENE-DCL AND ETHYLENE-DCL
A.
Introduction
In this chapter the influence of complex formation on the electric
field gradients at the deuterium nuclear sites in acetylene-DCl and
ethylene-DCl will be examined.
The J = 0 •> 1 zero-field transition in
these complexes has enough splitting due to the deuterium nuclear quadrupole interaction to allow measurement of this effect.
Because two quadru-
polar nuclei will be present on the DCl subunit in each complex, this will
allow a unique determination of whether the electric field gradients at
either quadrupolar site is perturbed as vibrational effects will be the
same at both nuclei.
Thus if both observed nuclear quadrupole coupling
constants in the complex are related to their free DCl values by an
2
euqation similar to Eq. (TII-13) then similar values of (3cos Y"1) should
be obtained from the Cl and D quadrupole coupling constants.
B.
Results
The measured transition frequencies and corresponding assignments for
35
six hyperfine components of the 0
•*• 1
transition in acetylene-D Cl
35
and seven components for ethylene-D Cl are listed in Table VI-1. Each of
these reported frequencies is the average of 20 to 40 individual measurements performed in a variety of carrier gases.
Numbers in parentheses
177
Table
Observed F r e q u e n c i e s
for
VT-1
the 0
00
1Q,
35
Ethylene-D
Transition
I
F
•*• I '
F'
Transition
in
35
Cl a n d A c e t y l e n e - D
Cl
Observed (MHz)
Observed(MHz)
35 ,
H2C=CH^C1
Difference
(kHz)
HC=CH,D35C1
Difference
(kHz)
3/2 3/2 -y 3/2
3/2
4473.1424(31)
0.6
4787.2490(27)
0.9
5/2 5/2 -»• 5/2
5/2
4473.1747(19)
-1.3
4787.2783(17)
-0.5
1/2 1/2 -y 1/2
1/2
4473.2084(44)
4.8
1/2 1/2 -> 1/2
3/2
4487.2223(23)
-0.1
4801.3869(24)
-0.4
5 / 2 5/2 -y 5/2
7/2
4487.2450(17)
0.6
4801.4122(20)
0.1
3/2 3/2 -y 3/2 5/2
4487.2735(33)
-1.3
4801.4368(25)
0.7
5/2 5/2 ->• 5/2
4498.5272(17)
-0.1
4812.7393(11)
0.0
3/2
Numbers 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 i n t h e measured
value.
Observed f r e q u e n c y - f r e q u e n c y
c a l c u l a t e d from the
fit.
178
after the measured values represent one standard deviation, o\, in the
The I, F = 1/2 -*• I', F' = 1/2 line, which has the least
measurement.
intensity of any of the lines reported, could not be accurately measured
for acetylene-D 35Cl.
The Hamiltonian for acetylene-DCl and ethylene-DCl is the sum of
rotational, nuclear quadrupole, DCl spin-spin, and deuterium spin-rotation
termsH = H . + p(Cl):V(Cl) + 0(D) :V(D) + H „ + H„„ ,
rot
~
~
~
~
SS
SR
(VI-1)
where Q and V a r e the nuclear quadrupole and e l e c t r i c f i e l d g r a d i e n t
t e n s o r s for e i t h e r the deuterium or chlorine nucleus.
The s p i n - s p i n
Hamiltonian i s given by Eq. (11-71), with spin-spin coupling tensor with
elements given by
~
D
13
where g
=
g n1 g n U 2 (R 2 6 -3R.R )
Cl D N
IT
1 1J
r—'
5
R
.
1,3 = x , y , z ,
is t h e g-value of the i ' t h nucleus, y
,„„ „.
(VI-2)
i s the nuclear magneton,
and R i s the vector joining the c h l o r i n e and deuterium n u c l e i .
deuterium s p i n - r o t a t i o n c o n t r i b u t i o n i s given by Eq. (11-69).
The
The 0
-*• 1
t r a n s i t i o n i s independent of M , M,, -M , X. , - X , n , , -D , and a l l of faa
bb cc A bb cc bb cc
diagonal elements of the coupling tensors. The 0 -*• 1 data was fit
to a line center, chlorine and deuterium quadrupole coupling constants,
X
Cl
D
and x , and a deuterium spin-rotation constant, 1/2(ML. + M ) ,
aa
aa
DD
CC
using an exact diagonalization procedure combined with a least squares
-2
f i t t i n g program, assigning a weight C.
to each measured component.
Matrix elements for the nuclear quadrupole i n t e r a c t i o n s have already been
179
presented in Eq. ( I I I - 5 ) in the 1 + 1 = 1 ,
I + J = F basis.
Matrix
~D
~C1
~ -- ~
~
elements for the nuclear spin-rotation and nuclear spin-spin interactions
are given elsewhere.
89
Values of the rotational constants A, B, and C
needed to construct the rigid rotor portion of the Hamiltonian matrix
were taken from Table V-5 for ethylene-D
35
D Cl.
35
Cl and Table IV-5 for acetylene-
35
The D Cl nuclear spin-spin constant, D
, was held fixed in the
clcl
fit at
D
= 1/2D <3cos2?-l) ,
aa
o
where D
is the spin-spin constant for free D
(VI-3)
35
Cl, £ is the instantaneous
angle between the DCl axis and the a-axis of the complex, and the brackets
represent the expectation value in the ground vibrational state.
Because
the effect of D
was very small, producing changes in the fit to X
°f
aa
aa
less than one kHz for values of D
ranging from zero to the value in
aa
35
2
free D Cl, (3cos ?-l) in Eq. (VI-3) was adjusted to the value obtained
Cl
Cl
35
by comparing x t o X , the chlorine coupling constant m free D Cl,
aa
o
which are related by an expression similar to Eq. (VI-3) if small electronic effects are ignored.
Differences between the measured frequencies
and those calculated from the fit are listed in Table VI-1. The spectroscopic constants obtained from the fit, along with their uncertainties,
35
are listed in Table VI-2. The spectroscopic properties of free D Cl and
acetylene are listed in Table VI-3.
The inclusion of a deuterium spin-rotation constant is justified as
follows.
With the deuterium spin-rotation constant set to zero for both
Cl
D
molecules, a weighted fit to a line center, X , a n d X < left residuals
aa
aa
in the strongest intensity multiplet (AF = 1) of -4.9, 5.3, and -2.3 kHz
180
Table VI-2
Values of t h e S p e c t r o s c o p i c C o n s t a n t s Derived
from t h e Data i n Table VI-1
H C=CH ,D 3 C l a
HCHCH,D35Clb
V (MHz)C
o
4484.4267(6)
4798.5792(3)d
X° (kHz)
'a a
171.1(71)
146.3(35)
XC1(MHz)
aa
-56.3450(39)
-56.5896(16)
l/2(M b b +M c c )
a
D
aa
,D
(kHz)
-2.25(85)
-4.49(48)
h e l d f i x e d a t - 1 . 4 3 7 7 kHz.
D h e l d f i x e d a t - 1 . 4 4 3 9 kHz.
aa
B+C-4D, where C and D„ are f i x e d a t v a l u e s i n Ref. 24 f o r Ac-DCl and
J
J
t o v a l u e s i n Ref. 26 f o r Et-DCl.
l u m b e r s 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 o f
uncertainty.
181
Table VI-3
M o l e c u l a r P a r a m e t e r s for Free DCl and Acetylene
2 2
DCl
R(i)
1.28124 a
a(A 3 )
3.l3b
161,656.238a
b DCl (MHz)
M°(kHz)
o
M C1 (kHz)
o
D (kHz)
o
-3.295°
27.426C
-1.720C,d
X^HMHZ)
-67.39338(9)°
Xg(kHz)
187.36 ( 30)
0
(10~
zz
d>T
a
zzzz
(10
C
e s u cm )
-42
8.39
4
e s u cm )
2.18
F . C. DeLucia, P . H e l m i n g e r , and W. Gordy, P h y s . Rev. A3, 1849
f
(1971).
Lan d o l t - B o m s t e i n ( S p r i n g e r - V e r l a g , B e r l i n , 1 9 5 1 ) , V o l . I , P a r t 3 .
°E. W. K a i s e r , J . Chem. P h y s . 5 3 , 1686 (1970) .
I n o r d e r t o r e t a i n t h e form of E q . ( V I - 5 ) , D
-2g
f o r f r e e DF i s t a k e n t o be
2 3
g u^/R , which d i f f e r s by a f a c t o r of - 2 from t h a t n o r m a l l y u s e d .
f a c t o r of - 2 f o l l o w s from Eq.
(VI-3).
S . L. H a r t f o r d , W. C. A l l e n , C. L. N o r r i s , E. F . P e a r s o n , and W. H.
F l y g a r e , Chem. P h y s . L e t t .
1§_, 153 (1973).
R. D. Amos and J . H. W i l l i a m s , Chem. P h y s . L e t t . 66_, 471 ( 1 9 7 9 ) .
This
182
for acetylene-DCl, and -2.8, 3.1, and -2.5 kHz for ethylene-DCl.
The
center transition is apparently systematically shifted to higher frequency relative to the outer lines and, at least in the case of acetyleneDCl, unacceptably large residuals are obtained.
This observation seems
to indicate that an additional interaction is present involving the
deuterium nucleus.
Inclusion of a deuterium spin-rotation interaction
leads to a dramatic reduction of the residuals in both complexes and to
(Vcc)
well determined values for
-
. Attempts to fit a chlorine spin-
rotation constant led to very poorly determined and negligibly small
values for this constant, with no noticeable improvement in residuals.
C.
Nuclear Quadrupole Coupling
An initial approach to the nuclear quadrupole coupling constants
m
both complexes is to assume that no dramatic electronic rearrangement
occurs upon complexation.
Then the observed coupling constants X
D
and X
are given by Eq. (1-15) .
aa
Cl
aa
Cl
The measured values of x
can be
aa
used in Eq. (1-15) to obtain values for (3cos y-l) for both complexes.
X
aa
is then given by X
= <X /X )X ' giving 157.3(3) kHz for acetyleneaa
aa o
o
DCl and 156.6(3) kHz for ethylene-DCl.
Comparison of these numbers with
the values of X
listed in Table VI-2 shows that these predictions differ
aa
by two standard deviations from the experimental results for either complex.
If the deuterium spin-rotation interaction is neglected, x
determined for acetylene-DCl (155(18)kHz), however, X
aa
in
^ s poorly
aa
ethylene-DCl
changes little (173(9)kHz vs. 171(7)kHz), still differing from the simple
projection prediction to within a 90% confidence level.
At least in the
case of ethylene-DCl, then, one or both of the DCl nuclear sites experiences
183
an e l e c t r i c f i e l d g r a d i e n t d i f f e r e n t from the p r o j e c t e d monomer v a l u e ,
and t h i s c o n c l u s i o n i s i n d e p e n d e n t of w h e t h e r t h e d e u t e r i u m s p i n rotation effect is
considered.
P o s s i b l e e l e c t r o n i c changes a t t h e c h l o r i n e s i t e w i l l f i r s t be
95
gg
considered.
S t u d i e s of the h y d r o g e n - b o u n d s y s t e m s N - H F ,
NCCN-HF,
and o t h e r s , have shown measurable changes i n n u c l e a r q u a d r u p o l e
coupling
c o n s t a n t s upon complexation t h a t c a n n o t be a t t r i b u t e d t o v i b r a t i o n a l
Cl
a v e r a g i n g . However, changes i n x
m i g h t be e x p e c t e d t o be l e s s i m p o r t a n t
D
than t h o s e i n x
o
b e c a u s e of t h e g r e a t e r ,
3.7 A s e p a r a t i o n between t h e
c h l o r i n e atom and t h e p e r t u r b i n g p a r t n e r m o l e c u l e .
v a l u e s of x
Cl
I n Table VT-4
have been t a b u l a t e d for f i v e hydrogen-bonded complexes
clcl
i n v o l v i n g DCl as t h e proton d o n o r .
2.5%.
These v a l u e s vary by no more than
F o r e t h y l e n e - D C l and a c e t y l e n e - D C l t h e v a l u e s o f x
only .4%.
Cl
d i f f e r by
aa
The u n i f o r m i t y of t h e s e v a l u e s , d e s p i t e a v a r i e t y of b i n d i n g
p a r t n e r s , s t r o n g l y suggests t h a t t h e r e a r e no major changes o c c u r r i n g i n
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 t h e c h l o r i n e n u c l e a r s i t e i n t h e s e complexes .
E l e c t r o n i c changes a t t h e d e u t e r i u m n u c l e a r s i t e w i l l
therefore
be c o n c e n t r a t e d o n .
The e f f e c t o f bond e l o n g a t i o n on x
upon c o m p l e x a t i o n w i l l be c o n clcl
s i d e r e d f o r b o t h complexes.
The p r i m a r y s o u r c e of 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 d e u t e r o n in complexes o r o t h e r w i s e i s t h e atom c o v a l e n t l y
bonded t o t h e d e u t e r i u m atom, a s t h e c h a r g e d i s t r i b u t i o n a t t h e
nucleus i s nearly spherically symmetric.
mental r e s u l t s of d e c r e a s e d v a l u e s of y
'
deuterium
This e x p l a i n s t h e e x p e r i -
i n hydrogen-bound complexes o f the
type - 0 - D . . . 0 - , - N - D . . . N - , and o t h e r t y p e s as w e l l as where bond e l o n g a t i o n
120-127
occurs upon c o m p l e x a t i o n .
S t u d i e s of - 0 . . .H-0 t y p e complexes h a s
shown good c o r r e l a t i o n between t h e i n c r e a s e i n O-H bond l e n g t h upon
184
Table VI-4
Measured Values of xA
Cl
in Different
aa
Complexes I n v o l v i n g DCl
Complex
X^(MHZ)
Ethylene-DCl
•56,. 3 3 1
Ace t y lene-DCl
•56,. 5 8 7
Cyclopropane-DCl
•56..650
HCN-DCld
•55.. 2 2 9 2
OC-DCl 6
•55., 2 5 4
Ref.
1.
Ref.
24.
'Ref.
25.
Ref.
87
'Ref.
18
185
complexation with decreasing O. . .0 distance. At short 0...0 distances
o
the 0...H bond elongates as much as
2A, however elongation seems to
asymptotically decrease to z e r o at -3.0A separation.
'
Pimentel
suggests t h a t a similar c o r r e l a t i o n e x i s t s for other hydrogen-bound s y s tems if one accounts for the change i n van der Waals r a d i i in going from
oxygen to other heavy atoms.
If 0Q = 1.40 A,
a c l = 1.70 A,
and
131
a
. = 1.70 A,
i s used, then the predicted acetylene . . .Cl threshold d i s ace t
tance would be 3.60 K. This contrasts with the actual separation of ~3.70 A
for both complexes and suggests that bond elongation i n DCl would be s m a l l .
132
An ab i n i t i o study of (HCl)
a t the SCF level
~.005 & in the proton donor HCl molecule.
finds bond elongation t o be
This would change X
by
aa
133
-5 kHz
in the acetylene-DCl and ethylene-DCl complexes, however, this
would probably be an upper limit as the predicted well depth for (HC1)2
is 1259 cm
compared to 600 cm
for the present complexes.
The direct effect of the electronic multipole moments of acetylene
or ethylene at the electric field gradient at the deuterium site may
significantly affect X
• For the case of acetylene-DCl we write x
aa
aa
as a sum of a v i b r a t i o n a l l y averaged c o n t r i b u t i o n of the free monomer
constant and an additional c o n t r i b u t i o n X
r e s u l t i n g from t h e presence
acl
of the acetylene molecule:
- XDQ <3cos 2 vM>/2 + x ^ 8 C t ,
X°
del
u
(VI-4)
ad
where
^ e li e c t
cici
=
12ep (cosCp)
2^
|lelo(l-Y)
e | B U y) ^,
n
30<t
+
cosc
V
P> + . . . )
1
a
(vi-5)
i
-J
a
—on
2 xrm
and e is the fundamental charge, Q = 2.86 • 10
cm ,
the nuclear
quadrupole moment of deuterium, y is the Sternheimer shielding parameter
186
for D i n DCl, which i s
l i k e l y t o be s m a l l i n comparison t o u n i t y
104
and w i l l be n e g l e c t e d h e r e , P (coscp) i s a Legendre p o l y n o m i a l , cp i s
the a n g l e between the a c e t y l e n e axis and t h e a - a x i s of t h e complex, t a k e n
t o be 9 0 ° , and a i s t h e a c e t y l e n e c e n t e r of mass t o d e u t e r i u m d i s t a n c e of
2.41 A.
Cl
X •
aa
The v a l u e of <3cos y - 1 )
ls
o b t a i n e d from Eq. (1-15) a p p l i e d t o
The second term of the s e r i e s i n Eq.
of t h e f i r s t t e r m .
(VT-5) c o n t r i b u t e s only 10%
U s i n g E q s . (VI-4) a n d (VI-5) x
= (157.3-12) kHz =
aa
145 kHz i s o b t a i n e d which i s a s i g n i f i c a n t change from t h e f r e e monomer
p r o j e c t i o n term a l o n e .
The a p p r o p r i a t e e x p a n s i o n c o r r e s p o n d i n g t o
Eq. (VI-8) f o r e t h y l e n e - D C l , g i v e n i n E q .
however t h e s e e f f e c t s
(V-4), does n o t converge;
could be as l a r g e i n ethylene-DCl as i n a c e t y l e n e -
DCl.
I t i s e x p e c t e d t h a t some charge r e d i s t r i b u t i o n w i l l o c c u r w i t h i n
DCl upon complexation w i t h e t h y l e n e or a c e t y l e n e and t h i s w i l l
likely
a f f e c t t h e observed v a l u e of x
• Ab i n i t i o c a l c u l a t i o n s f o r HCl complex
aa
——
•
133
a t the STO-4/31 G l e v e l
show a b u i l d u p of charge i n t h e bond of t h e
p r o t o n d o n a t i n g HCl molecule w i t h d e p l e t i o n of charge a t t h e hydrogen.
An e s t i m a t e of t h e s e e f f e c t s w i l l n o t b e a t t e m p t e d h e r e .
D.
Nuclear Spin-Rotation
Upon complexation t h e s p i n - r o t a t i o n c o n s t a n t , M , i n f r e e DCl i s
p r o j e c t e d i n t o the p r i n c i p a l a x i s s y s t e m of t h e complex as
+M
\
/ * b b + M c---*
o\
v.
2
h-pro
3
M
o ,_
2-
B+C
" T ^ 1+COS S> 2 5 ^
35
where b „ „ , i s t h e r o t a t i o n a l c o n s t a n t f o r f r e e D C l .
DCl
,f_
,.
(VI 6)
"
S u b s t i t u t i o n of
187
values from Table VI-3 and using (1+cos £) ~ 2 gives a negligible cont r i b u t i o n in both complexes .
The nuclear contribution a r i s i n g i n both complexes from the binding
p a r t n e r i s c a l c u l a t e d d i r e c t l y to be =2.2 kHz, meaning that an e l e c t r o n i c
contribution of -4.5(5) kHz and -2.4(9) kHz occurs as a r e s u l t of the
binding partner of DCl i n acetylene-DCl and ethylene-DCl r e s p e c t i v e l y .
Enhancement of the s p i n - r o t a t i o n constant upon complexation was observed i n the case of NO dimer
l y i n g e l e c t r o n i c s t a t e s . 134
where i t was explained in terms of low
188
CHAPTER VTI
THE USE OF THE FOURIER-TRANSFORM, FABRY-PEROT MICROWAVE METHOD
FOR THE EXAMINATION OF PARAMAGNETIC TRANSIENT SPECIES
A.
Introduction
I n t h i s c h a p t e r an e x t e n s i o n of t h e s u c c e s s f u l e x p e r i m e n t a l t e c h n i q u e ,
whose r e s u l t s have b e e n p r e s e n t e d i n p r e v i o u s c h a p t e r s , w i l l be d i s c u s s e d .
This i n v o l v e s u s i n g t h e p u l s e d , F o u r i e r - t r a n s form microwave t e c h n i q u e ,
c a r r i e d o u t i n a F a b r y - P e r o t c a v i t y , t o examine t r a n s i e n t s p e c i e s w i t h
unpaired e l e c t r o n s .
The f i r s t p o s s i b i l i t y c o n s i s t s of s t u d y i n g complexes
containing a paramagnetic binding p a r t n e r .
This w i l l r e q u i r e a m a g n e t i c
s h i e l d for t h e e x p e r i m e n t t o p r e v e n t l i n e b r o a d e n i n g due t o t h e i n t e r a c t i o n of t h e u n p a i r e d e l e c t r o n s w i t h t h e e a r t h ' s magnetic f i e l d
( .6G) .
w i l l a l s o r e q u i r e a g r e a t e r t h e o r e t i c a l background as new i n t e r a c t i o n s
be p r e s e n t i n t h e s p e c t r u m as a r e s u l t of c o u p l i n g between t h e
s p i n and o t h e r s o u r c e s of a n g u l a r momenta.
be t h e ma^or focus of t h i s c h a p t e r , i s
will
electronic
The second p o s s i b i l i t y which w i l l
t h e microwave e x c i t a t i o n of m o l e c u l e s
i n i t i a l l y p r e p a r e d i n t h e ground v i b r a t i o n a l s t a t e of t h e f i r s t
t r i p l e t manifold.
It
excited
The p u l s e d , F o u r i e r - t r a n s form, F a b r y - P e r o t microwave
t e c h n i q u e i s i d e a l l y s u i t e d for t h i s s o r t o f e x p e r i m e n t .
The p u l s i n g of
the
gas t h r o u g h a s u p e r s o n i c n o z z l e g i v e s a g r e a t e r p o p u l a t i o n i n t h e ground v i b r a t i o n a l s t a t e r o t a t i o n a l energy l e v e l s and the c o l l i s i o n l e s s ,
adiabatic
e x p a n s i o n minimizes d e s t r u c t i o n of t h e s p e c i e s through c o l l i s i o n s .
Further-
more, the s e n s i t i v i t y g a i n e d i n u s i n g a p u l s e d gas s o u r c e and i n w o r k i n g i n
the time domain a l l o w s d e t e c t i o n of s p e c i e s t h a t e x i s t i n very low number
density.
189
Many molecules have t r i p l e t s t a t e lifetimes i n the gas phase of
10 - 1 sec
allowing observation through pulsed microwave techniques
where the duration of the microwave pulse i s 1-2 usee.
Many of the same
molecules, especially small azmes and molecules with carbonyl groups,
pass d i r e c t l y from the S (n,lT*) e l e c t r o n i c s t a t e to the T, (n,7T*) s t a t e
with nearly unit efficiency via m t e r s y s t e m crossing 141-145 upon e x c i t a tion from the ground e l e c t r o n i c s t a t e and within a time scale of
•i„-8 , r t -12
10
-10
146-148
sec.
„
,
_
.
,
. , . - , ,
^
-
Examples of molecules which f a l l i n t o t h i s
category and in addition w i l l have microwave l i n e s i n the appropriate
bands and w i l l not undergo extensive photochemistry under the conditions
of the experiment w i l l be discussed in t h i s c h a p t e r .
Similar experiments have succeeded i n a few i s o l a t e d cases for some
diatomic molecules using various techniques.
However, t h i s ex-
periment w i l l represent the f i r s t time radio frequency t r a n s i t i o n s have
been recorded for non-diatomic molecules i n e x c i t e d t r i p l e t s t a t e s
and as a r e s u l t much unique and previously unavailable information w i l l
be obtained i n some cases a t the very high level of accuracy i n t r i n s i c
to the pulsed, F o u r i e r - t r a n s form spectrometer with a Fabry-Perot c a v i t y .
Of much i n t e r e s t w i l l be the geometry of the e x c i t e d t r i p l e t s t a t e s as
obtained through t h e r o t a t i o n a l constants as many molecules are known or
postulated to undergo changes in geometry in the f i r s t excited e l e c t r o n i c
states.
Also available w i l l be z e r o - f i e l d s p l i t t i n g parameters
describing the i n t e r a c t i o n between the unpaired e l e c t r o n s as w e l l as
parameters describing the couplings between the angular momenta of the
unpaired electrons and other sources of angular momenta. In molecules
2
14
containing quadrupolar nuclei ( D,
N, e t c . ) e l e c t r i c field gradients
190
a t those nuclei can be obtained giving information regarding e l e c t r o n i c
d i s t r i b u t i o n i n the e x c i t e d e l e c t r o n i c t r i p l e t s t a t e .
B.
Experimental
Microwave e x c i t a t i o n w i l l be achieved by the techniques b r i e f l y
described in Chapter I and described in d e t a i l elsewhere.
In a d d i t i o n ,
however, the experimental region must experience magnetic f i e l d s of no
more than .OlG t o give l i n e s unbroadened by magnetic f i e l d mhomogeneities.
This w i l l require i n s t a l l a t i o n of a magnetic s h i e l d made
of m a t e r i a l of high permeability and annealed a f t e r being shaped to
the c o r r e c t form.
Frequent degaussing w i l l also be required t o
prevent buildup of permanent magnetism i n the s h i e l d .
I n i t i a l preparation of the molecules i n the t r i p l e t s t a t e experiment can occur via flashlamp e x c i t a t i o n in the v i s i b l e region
for the n -»• IT* e l e c t r o n i c t r a n s i t i o n in carbonyl molecules and w i l l
occur a t the s i t e of t h e supersonic nozzle.
The zenon flashlamp
can be provided with c u r r e n t from an overdamped LCR discharge c i r c u i t .
Four Sprague 3100 lifarad
450 V capacitors in s e r i e s w i l l , for example,
give a 1800 V, 800 ufarad
capacitor bank which w i l l provide over 1,000
Joules of energy.
Including a 300 LiH inductor i n s e r i e s with the flash-
lamp and the capacitor bank spreads the pulse width of c u r r e n t over a
couple of milliseconds.
Having t h i s s o r t of pulse width allows the
pulsing of the flashlamp to correspond to the approximate time during
which there are molecules flowing through the supersonic n o z z l e .
optimum shape of the flashlamp i s withan 11 1/2 cm.
flashlamp in a 8 cm. (inner diameter) l o o p .
The
(outer diameter)
A s t a i n l e s s s t e e l encasement
191
with a pyrex window w i l l serve as an a i r cooling mechanism with forced
a i r cooling being s u f f i c i e n t for the r e p e t i t i o n rate of ~1 Hz.
The
pyrex window is to be c y l i n d r i c a l so as to f i t through the center of
the loop and w i l l cut off undesirable s h o r t e r wavelengths .
Triggering of
the flashlamp can be provided by a series i n j e c t i o n t r i g g e r module commercially b u i l t and providing up to 25 kV.
C.
Examination of Electronic and Vibrational Processes Involved i n the
T r i p l e t State Experiment
Transitions w i l l be induced between energy levels which differ only
i n r o t a t i o n a l energy and other forms of energy of the same magnitude.
The t r a n s i t i o n s t o be observed w i l l be of molecules i n the ground v i b r a t i o n a l s t a t e of the T (n,Tf*) e l e c t r o n i c manifold.
For t h i s reason the
experiment must successfully produce an abundance of molecules in t h i s
energy l e v e l .
I t i s estimated t h a t ~10
13
molecules of i n t e r e s t must be
p r e s e n t for microwave emissions of s u f f i c i e n t i n t e n s i t y with the p r e s e n t
spectrometer assuming an e l e c t r i c dipole moment of ~1.0 Debeye.
Referring
to F i g . VII-1, t h i s requires t h a t s u f f i c i e n t molecules i n the ground
e l e c t r o n i c s t a t e be excited t o the S.. e l e c t r o n i c manifold and subsequently
pass over to the t r i p l e t manifold so as t o leave a t l e a s t the required
amount in the ground v i b r a t i o n a l s t a t e of the t r i p l e t manifold a t a time
T l a t e r taking i n t o consideration a l l of the processes t h a t deplete and
populate the s t a t e of i n t e r e s t during x s e c .
T w i l l be the time required
for the molecules to traverse t o the region of the mirrors where they w i l l
receive the microwave r a d i a t i o n .
The r e l e v a n t processes shown schemati-
cally i n Fig. VII-1 w i l l now be examined so as to arrive a t the population
of the ground v i b r a t i o n a l s t a t e of the t r i p l e t manifold.
192
Figure VII-1.
Electronic and vibrational processes
involved following excitation to the
f i r s t excited s i n g l e t s t a t e .
193
194
Fig. VII-2 shows absorption spectra for two candidates for the
experiment.
'
The extinction coefficient as a function of wave-
length is shown for benzaldehyde.
is 14 M
For propynal in the gas phase £
cm
If for simplicity we assume e
= 10 M
v
avg
50 nm, then we can w r i t e
-e
E . = E(A,8,cp) [1-e
obs
cm
max
over
Mx
a v g
]
(VII-1)
where E(X,8,cp) represents the energy irradiated into the proper volume
over the 50 nm wavelength range.
If i t is assumed that the molecules
spread 60° to each side of the vertical direction, then we will have a l l
the parameters needed for Eq. (VII-1) i f an energy input i s assumed and
i f i t is known how far from the nozzle molecules can be irradiated and
s t i l l have sufficient vibrational cooling.
With this distance the volume
of irradiation can be constructed and thus the molarity will be known and
Eq. (VII-1) can be used to give the number of molecules i n i t i a l l y excited.
I t is almost certain vibrational cooling continues for at least 10
nozzle diameters.
Though translational cooling may be completed after
only a few nozzle diameters, vibrational cooling is known to proceed
longer as lower energy collisions are necessary.
In fact, the vibrational
relaxation cross sections in a supersonic ;jet have lately been shown to
be quite large.
'
If a 3.0 mm diameter nozzle is used and the volume
of irradiation extends a conservative 1.5 cm vertically from the nozzle
then the irradiation volume is simply
1-5
V=J
x
0
2
2
3
Tftan TT/3 dx = 1 0 . 6 cm
.
(VII-2)
195
Figure V I I - 2 .
A b s o r p t i o n s p e c t r a f o r the n -> TT* t r a n s i t i o n
of benzaldehyde and p r o p y n a l .
The
s p e c t r u m i s t a k e n from M. B e r g e r , I .
first
Goldblatt,
and C. S t e e l , J . Am. Chem. S o c . 9 5 , 1717 ( 1 9 7 2 ) .
The second i s from D. Kumar and J . Huber, Chem.
P h y s . L e t t . 38, 537 (1976).
196
Fifiure 2. Sriution-pJ'ase absorption spectrum of benzsli.h.vde
, in then'-* s-* region
<-
J5K0
!£0^
27000
fc>MO
23033
30000
31009
3J0O0
3)055
34KO
3S0M
errf"
I ij. I Corrected phosphorescence cscitation spictra (-.otiil line) ofpjop> ruJ monlto.ed al 2-1J27 cm"' nnJ rccordej ov
first I'jMjrpuoi Turn! JI jonm icn'pi'uturc j-d ( J ) 0 0 O iurr, (b) 0 60 torr + lOOto.r He Superimposed on tint spent in
.il'vu.p ion spectrum (dotted lir.e) neisu-ed.it 10 torr
197
The number of m o l e c u l e s of i n t e r e s t i n t h i s volume i s g i v e n by
N = p a A t (.31)
K
o o n v
Here t
v
.
i s the time i t t a k e s f o r t h e n o z z l e t o f i l l
(VII-3)
up t h i s volume w i t h
m o l e c u l e s t r a v e l l i n g a t a v e l o c i t y given by
V. = a £%~l/2
t
O 2
(VII-4)
where y i s the r a t i o of h e a t c a p a c i t i e s of t h e c a r r i e r gas a t
constant
volume t o c o n s t a n t p r e s s u r e , a i s t h e speed of sound i n t h e c a r r i e r gas
4
(4.35 x 10 cm/sec i n n e o n ) , a n d p i s the number d e n s i t y of t h e m o l e c u l e
of i n t e r e s t b e h i n d t h e n o z z l e .
A i s the n o z z l e o r i f a c e a r e a .
Assuming
17
0 . 1 atm of the m o l e c u l e of i n t e r e s t g i v e s 3.75 x 10
molecules.
Further-
more s i n c e i t can r e a d i l y be shown t h a t e l e c t r o n i c e x c i t a t i o n i s f a r
short
of t h e s a t u r a t i o n l i m i t t h e n u n d e r t h e c o n d i t i o n s of t h e s u p e r s o n i c
jet
t h e number d e n s i t y of ground s t a t e m o l e c u l e s w i l l be n e a r l y c o n s t a n t and
very n e a r l y the number d e n s i t y of t h e sum o f ground s t a t e and e x c i t e d
state molecules.
I f i t i s now o b s e r v e d t h a t t h e e f f e c t i v e
f l a s h i n g time
i s t h e time i t t a k e s t o produce a volume of e x c i t e d m o l e c u l e s t h a t does
n o t e x c e e d t h e dimensions c o n t a i n e d by the m i r r o r s
(r = 15 cm) and i f
n e a r u n i t y m t e r s y s t e m c r o s s i n g i s assumed, t h e n t h e number of
triplet
s t a t e molecules p r o d u c e d i n one f l a s h w i l l be given by
T
N
o
=
hlc/A
) J" 'dt* d - e a p C - 1 0 " " cm" 1 2.6 cm 6 x l O _ 5 M ) ] d t .
avg
0
(VII-5)
dE
-5
Here — i s t h e power p u t o u t by t h e f l a s h l a m p , 6 x 10 M i s found by
using t h e volume a n d number of molecules o b t a i n e d f o r t h e
irradiation
198
volume and T I S the time required to f i l l up the mirror region and i s
given by
T -f
t
to 6)
^"f
"
3.76x10 cm/sec
Though the flashlamp w i l l probably produce more than 10 joules of
energy a t the wavelength desired i f needed, 1 joule w i l l be used for
calculations to follow.
Under these conditions the power can be w r i t t e n
as
dE ~ 1 joule
, , ..
1
•rr
dt = T-"
1 msec = 1 kwatt
, . „ , . _.
(VII-7)
.
Using Eqs. ( V I I - 5 ) , (VII-6), and (VII-7) gives 2 x 10
t r i p l e t molecules
produced m a l l v i b r a t i o n a l levels of the T manifold p r i o r to considerat i o n of processes which deplete t h i s l e v e l .
I t is now to be determined
what portion of t h i s can r e l a x t o the ground v i b r a t i o n a l s t a t e of T..
within the time c o n s t r a i n t s of the experiment and s t i l l survive e l e c t r o n i c
r e l a x a t i o n processes.
As mentioned, v i b r a t i o n a l r e l a x a t i o n i s estimated to proceed over a
distance of a t l e a s t 10 nozzle diameters.
However s i n c e i r r a d i a t i o n i s
t o occur during the f i r s t five nozzle diameters , the molecules have on
average 7.5 nozzle diameters or ~2.0 cm for v i b r a t i o n a l r e l a x a t i o n .
The velocity of gas away from the nozzle i s very c o n s i s t e n t due t o an
4
extremely narrow velocity d i s t r i b u t i o n and w i l l be around 4 x 10 cm/sec
with neon c a r r i e r gas
167
giving the v i b r a t i o n a l l y e x c i t e d t r i p l e t s t a t e
-5
molecules 5 x 10
seconds for r e l a x a t i o n .
t i o n a l relaxation can be assumed giving
A k i n e t i c model for v i b r a -
199
d[T*l
-^-L
= -k p[T*]
(VII-8)
where [T*] r e p r e s e n t s the concentration of v i b r a t i o n a l l y e x c i t e d t r i p l e t
7
molecules and p i s the pressure of a l l gases p r e s e n t .
10
-1
sec
-1
torr
i s commonly used for k with molecules such as benzaldehyde and a c e t o phenone.
'
'
Assuming p r e s s u r e s of - . 1 t o r r , i n t e g r a t i o n of
Eq. (VII-8) shows the majority of the t r i p l e t s t a t e molecules t o be p r e —6
dominantly thermalized by 1 x 10
s e c . well before the l i m i t of
5 x 10
sec.
Electronic r e l a x a t i o n processes leading t o depletion of the population
of the ground v i b r a t i o n a l s t a t e T during the time p r i o r to completion of
the microwave s p e c t r a must now be considered.
The major processes to be
considered are r a d i a t i v e phosphorescence and nonradiative r e l a x a t i o n
processes.
Radiative phosphorescence i s not a major concern i n the time
s c a l e of the proposed experiment as the r a d i a t i v e lifetime of themolecules
u
J
!„-3 -i^2
138,166,169,171,172 .
.. .
being considered are 10
-10
sec.
'
'
whereas the time
r e q u i r e d for the t r i p l e t molecules t o e x i s t i s ~.4 msec.
Thus m the
worse case, r a d i a t i v e phosphorescence w i l l deplete the t r i p l e t population
by l e s s than a f a c t o r of two.
Nonradiative processes t h a t w i l l deplete the t r i p l e t population
c o n s i s t of c o l l i s i o n induced and c o l l i s i o n free intersystem c r o s s i n g
from the T. manifold to the S manifold. These processes have a strong
v i b r a t i o n a l energy dependence 141 ' 146 ' 169 and as a r e s u l t w i l l play a
much reduced r o l e under conditions of free j e t expansion where vibrat i o n a l cooling o c c u r s .
Phosphorescence s t u d i e s a t room temperatures in
the gas phase have revealed the r a t e constants governing c o l l i s i o n induced
200
ISC from T to S
for many molecules by monitoring the decay of phos-
phorescence with time for various p r e s s u r e s .
3
4-1
-l
r a t e constant t o be 1 0 - 1 0 s
ered.
'
'
torr
These studies reveal the
for molecules being consid-
The r a t e constant governing c o l l i s i o n free intersystem
corssmg has been found to be 2600 s
for propynal.
This r a t e
constant i s usually not obtained except without extensive k i n e t i c modeling
as i t has no p r e s s u r e dependence b u t i s usually combined with the r a t e
constant for phosphorescence to form the r e c i p r o c a l zero pressure l i f e time .
These are commonly reported in the l i t e r a t u r e and since the non-
r a d i a t i v e rate constant i s the dominanting one and since these zero
pressure lifetimes are usually . 2 - . 8 msec for molecules of i n t e r e s t ,
i s c l e a r that -2000 s
is a typical value.
it
The time during which both
nonradiative processes (as well as r a d i a t i v e phosphorescence) w i l l take
e f f e c t i s the time during which c o l l i s i o n s occur.
As mentioned previously
v i b r a t i o n a l cooling i s estimated to occur for a given d i f f e r e n t i a l segment
of the pulse for ~5 x 10
has recently
sec.
Since the v i b r a t i o n a l cross s e c t i o n , a ,
been estimated to be large (>100 &.) for I , under free
jet
expansion, t h i s time, t , i s most c e r t a i n l y an upper l i m i t for c o l l i s i o n
induced r e l a x a t i o n .
The time during which only c o l l i s i o n free processes
w i l l occur i s given by
=
Z
17 cm
V
= 4.5 x 10~ 4 s e c .
(VXI-9)
t
where V i s given by Eq. (VII-4) and 17 cm i s the average distance
t r a v e l l e d by molecules once they have l e f t the area of c o l l i s i o n s and
p r i o r to being pulsed by microwaves.
The f r a c t i o n of t r i p l e t ste»te
201
molecules i n t h e ground v i b r a t i o n a l a t the t i m e of the microwave p u l s e
w i l l then be given by
f = e35>(-(t1+t2)/Traa)e^>[-t1(l/TCI+VTCF)]exp[-t2/Tcp)
where T , T„^, and T
are t h e r a d i a t i v e l i f e t i m e and t h e
r a d , CI
CF
(VII-10)
nonradiative
l i f e t i m e s as a r e s u l t of c o l l i s i o n i n d u c e d a n d c o l l i s i o n f r e e
respectively.
processes
S u b s t i t u t i o n o f the numbers p r e s e n t e d l e a d s t o f = . 2 .
S i g n a l t o n o i s e c o n s i d e r a t i o n s then w i l l be met by more t h a n an o r d e r of
14
magnitude s i n c e -4 x 10
molecules i n the ground v i b r a t i o n a l s t a t e of
\
D.
s h o u l d be p r e s e n t a t the t i m e of t h e microwave p u l s e .
I n t e r a c t i o n s to be C o n s i d e r e d i n P a r a m a g n e t i c Systems
With e i t h e r a p a r a m a g n e t i c complex or a molecule i n an e x c i t e d
t r i p l e t s t a t e t h e r e a r e a number of new i n t e r a c t i o n s i n t h e microwave
range t h a t must be c o n s i d e r e d i n c o n s t r u c t i n g an a p p r o p r i a t e H a m i l t o n i a n .
I n t h e most g e n e r a l c a s e of two u n p a i r e d e l e c t r o n s these a r e :
1)
The i n t e r a c t i o n of t h e two e l e c t r o n i c s p i n s w i t h e a c h
other
2)
The i n t e r a c t i o n of t h e e l e c t r o n i c s p i n s with o r b i t a l
a n g u l a r momentum
3)
The i n t e r a c t i o n of t h e e l e c t r o n i c s p i n s with t h e
rotation
of the molecule
4)
The i n t e r a c t i o n of e l e c t r o n i c s p i n s with n u c l e a r s p i n s .
I n t e r a c t i o n s 1) and 2) can be a s s i m i l a t e d i n t o one t e r m i n t h e
f o l l o w i n g manner.
The i n t e r a c t i o n of two e l e c t r o n i c s p i n s w i t h each
174
o t h e r h a s the w e l l known form
202
= g2,i
^SS
B[r2(5l"S2) "
3(
5 ' ? 1 ) (5'?2)
]r
"5
-
(VII-11)
This can be expressed as
K
SS
=
I %a S lp S 2q
p . q *"*
(p
'* = *'y'Z)
(V1I
~12)
where
2
. 2 . 2 , - 5
)r
a
=g
a
= -3g 2 y (pq)r"
pp
V * ~3P
p f q
.
(VII-13)
Furthermore an approximate form for the s p i n - o r b i t i n t e r a c t i o n i s
3{L„ = J A % • S
T30
v
1~1
l = 1.2
'
(VII-14)
~i
i
where i t i s noted i n
Eqs. (VII-11) through (VII-13) t h a t only the two un-
paired electrons contribute.
The combined e f f e c t s of JC
expressed by the s e c u l a r equation
|K - W 6
1
xj
and J{Ln can be
1=0
(VII-15)
ijI
where
K
3. i ! „
13
j ,
ij = < \ l « k a l V >
(VII-16)
n
1
E( lpn)-B(\)
Here t h e upper l e f t s u p e r s c r i p t of the wavefunction refers t o the multip l i c i t y and the upper r i g h t s u p e r s c r i p t r e f e r s t o the M quantum number.
The s u b s c r i p t i s an o r b i t a l angular momentum quantum number.
I t i s noted
203
in Eq. (VII-16) that t r i p l e t states will be uncoupled to singlet states
144
by 3C while there is no first order spin orbit effect.
By expressing the wavefunction as
M
S =
\
*k(1'2)8SM
<1,2)
M
S=
±1
'°
S = 1
(VII-17)
where the many electron wavefunction is reduced to i t s relevant two electron part, changing coordinate systems to eliminate off diagonal tensor
elements and doing a b i t of algebra i t can be shown that
^S
+ H
SO - I W S 1 P S 2 P
P = X Y Z
' '
(VII 18)
-
This form lends itself easily to representation with standard irreducible
tensor methods.
In fact by redefining JCS + 3CQ as
^S+KSO
= l VlPS2p
=
5l '
fl
' 52
(VII 19)
"
p
where Q is diagonal but not traceless for reasons intrinsic to the coordinate
transformations required to obtain Eq. (VII-13), 3Cgs + 3C0 can be rewritten
in irreducible tensor form to obtain
[S«>S<« + S » » s | f
*S(<"s«]
(WI-20)
where the usual transformations from cartesian coordinates to spherical
coordinates have been made.
204
The t h i r d i n t e r a c t i o n i s the coupling of the e l e c t r o n i c spins with
the r o t a t i o n a l angular momentum of the nuclear framework.
described by the equation
+
'
Z
K 2j
*S,J = i ^
<y>
[
£JKX I1
+
YjK]
tjr
k f T * <"e) rjk[rjK * k V
In Eq. (VII-21), r .
and x,
~JK
This i s
* sj •
(VII 21)
"
are the vectors connecting the displacement
~JK.
of the j t h e l e c t r o n to the displacement of t h e Kth nucleus and Kth e l e c t r o n
respectively.
Likewise
V
= v ~jK
~j
V
v
~JJS.
V
-K
= V - V
~J
(VII-22)
~K
where lower case subscripts r e f e r to e l e c t r o n s and upper c a s e , underlined
s u b s c r i p t s r e f e r to n u c l e i .
Eq. (VII-21) can be shown through extensive
manipulation to have the following form
3<
s,j=
(
5i ' " i ' 2> + (!2 ' *2
m J
J
(VTI-23)
Here M, and M, are complicated functions of nuclear and e l e c t r o n i c v e l o c i t i e s and displacements.
The fourth i n t e r a c t i o n has two p a r t s .
The f i r s t is j u s t the normal
spin-spin i n t e r a c t i o n and has the same form as Eq. (VII-20).
The second
p a r t i s the i s o t r o p i c Fermi contact term t h a t depends upon the p r o b a b i l i t y
205
of a given electron being at a nuclear site and has the form
K=Z^j-
q^iy/^OjI'S
(VXI-24)
where ^(0) i s t h e magnitude of the e l e c t r o n a t t h e nucleus with n e t nuclear
spin.
The importance of t h i s term i s dependent upon the d e r e a l i z a t i o n of
the e l e c t r o n and the proximity of n e t nuclear s p i n s .
In nonconjugated
systems where a carbonyl e l e c t r o n i s e x c i t e d , i t i s expected t h a t t h i s
term w i l l be small however otherwise i t can be appreciable and must not
be ignored.
75 179—181
'
Regardless of the s i t u a t i o n t h e form of t h e i n t e r -
action makes i t q u i t e simple t o include i t i n t h e Hamiltonian.
206
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VITA
Peter Douglas Aldrich was born April 5, 1954 in St. Louis, Missouri.
He grew up in Winnetka, Illinois and attended New Trier East High School,
obtaining a diploma in June, 1972 and being named an Illinois State
Scholar.
He attended the University of Illinois at Urbana-Champaign on
a State Senate Scholarship and then the University of Illinois at Chicago
on a Tennis Athletic Scholarship, receiving a B.A. degree in 1979. In
August, 197 9, he entered the graduate school at the University of Illinois
at Urbana-Champaign on a fellowship.
and research assistant.
He served as both teaching assistant
He presented papers at the 1981 American Physical
Society Meeting at Phoenix, the 1981 Symposium of Molecular Spectroscopy
at the Ohio State University and the 1982 Symposium of Molecular Spectroscopy at the Ohio State University.
He is coauthor of the following
publications*
A. C. Legon, P. D. Aldrich, and W. H. Flygare, Cyclopropane-Hydrogen
Chloride Dimer: Identification and Geometry from Its Rotational Spectrum,
J. Am. Chem. Soc. 102, 7584 (1980), (communication).
A. C. Legon, P. D. Aldrich and W. H. Flygare, The Rotational Spectrum
and Molecular Structure of the Acetylene-HCl Dimer, J. Chem. Phys. 75.'
625 (1981).
P. D. Aldrich, A. C. Legon, and W. H. Flygare, The Rotational Spectrum,
Structure, and Molecular Properties of the Ethylene-HCl Dimer, J. Chem.
Phys. 75., 2126 (1981) .
L. w. Buxton, P. D. Aldrich, J. A. Shea, A. C. Legon, and W. H. Flygare,
The Rotational Spectrum and Molecular Geometry of the Cyclopropane-HF
Dimer, J. Chem. Phys. 75, 2681 (1981).
A. C. Legon, P. D. Aldrich, and W. H. Flygare, The Rotational Spectrum,
Chlorine Nuclear Quadrupole Coupling Constants, and Molecular Geometry
of a Hydrogen-Bonded Dimer of Cyclopropane and Hydrogen Chloride, J. Am.
Chem. Soc. 104, 1486 (1982) .
216
S. G. Kukolich, P. D. Aldrich, W. G. Read, and E. J. Campbell, Microwave
Structure Determination and Quadrupole Coupling Measurements on AcetyleneHCN and Ethylene-HCN Complexes, Chem. Phys. Lett. 90, 329 (1982).
P. D. Aldrich and E. J. Campbell, Deuterium Nuclear Quadrupole Coupling
in the Hydrogen-Bound Systems Ethylene-D35d and Acetylene-D35ci, Chem.
Phys. Lett. 93_, 355 (1982).
P. D. Aldrich, S. G. Kukolich, and E. J. Campbell, The Structure and Molecular Properties of the Acetylene-HCN Complex as Determined from the
Rotational Spectra, J. Chem. Phys. 78.' 3 5 2 1 (1982).
S. G. Kukolich, W. G. Read, and P. D. Aldrich, Microwave Spectrum, Structure, and Quadrupole Coupling in the Ethylene-Hydrogen Cyanide Complex,
J. Chem. Phys. 78, 3552 (1982).
P. D. Aldrich, S. G. Kykolich, E. J. Campbell, and W. G. Read, The Magnetic
Susceptibility Anisotropy, Molecular g-values, and Other Molecular Properties of Cyclopropane as Determined from Rotational Zeeman Studies of the
Cyclopropane-H3^Cl and Cyclopropane-HC35N Complexes, J. Am. Chem. Soc.
(submitted for publication).
S. G. Kukolich, P. D. Aldrich, W. G. Read, and E. J. Campbell, Molecular
Zeeman Effect Measurements on the Ethylene-HCl Complex, J. Chem. Phys.
(submitted for publication).'
V
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