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MICROWAVE-FREQUENCY CONDUCTIVITY OF ALPHA SILVER-IODIDE, MICROWAVE SPECTROSCOPY OF HYDROGEN-BONDED SPECIES, AND DESIGN OF A HIGH-TEMPERATURE NOZZLE SOURCE

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SOPER, PAUL DONALD
MICROWAVE-FREQUENCY CONDUCTIVITY OF ALPHA SILVER-IODIDE,
MICROWAVE SPECTROSCOPY OF HYDROGEN-BONDED SPECIES, AND
DESIGN OF A HIGH-TEMPERATURE NOZZLE SOURCE
University ofIllinois at Urbana-Champaign
University
Microfilms
I n t e r n a t i o n a l 300N ZeebRoad,AnnArbor,MI48106
PH.D. 1981
J
MICROWAVE-FREQUENCY CONDUCTIVITY OF ALPHA SILVER IODIDE,
MICROWAVE SPECTROSCOPY OF HYDROGEN-BONDED SPECIES,
AND DESIGN OF A HIGH-TEMPERATURE NOZZLE SOURCE
BY
PAUL DONALD SOPER
B.S., Rensselaer Polytechnic Institute, 1973
B.S., Rensselaer Polytechnic Institute, 1973
M.S., University of Illinois, 1978
THESIS
Submitted in partial fulfillment of the requirements
for the degree of Doctor of Philosophy in Chemistry
i n the Graduate College of the
University of I l l i n o i s at Urbana-Champaign, 1981
Urbana,
Illinois
UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN
THE GRADUATE COLLEGE
JUNE 1981
W E H E R E B Y RECOMMEND T H A T T H E T H E S I S BY
PAUL DONALD SOPER
F.MTTTT.F.n
MICROWAVE-FREQUENCY CONDUCTIVITY OF ALPHA SILVER IODIDE,
MICROWAVE SPECTROSCOPY OF HYDROGEN-BONDED SPECIES, AND DESIGN OF A
HIGH-TEMPERATURE NOZZl.F SOIIRCF
BE ACCEPTLD IN PARTIAL F U L F I L L M E N T O F T H E REQUIREMENTS FOR
T H E DEGREE OF.
DOCTOR OF PHILOSOPHY
£t^J£j^O=.
Director of Thesis Research
Head of Department
Committee on Final Examination!
t Required for doctor's degree but not for master's
iii
MICROWAVE-FREQUENCY CONDUCTIVITY OF ALPHA SILVER IODIDE,
MICROWAVE SPECTROSCOPY OF HYDROGEN-BONDED SPECIES,
AND DESIGN OF A HIGH-TEMPERATURE NOZZLE SOURCE
Paul Donald Soper, Ph.D.
Department of Chemistry
University of I l l i n o i s a t Urbana-Champaign,
Chapter I r e p o r t s the measurement of s i l v e r
in
the
40 GHz.
and
alpha
phase
of
silver
iodide
1981
ion
conductivities
over the frequency range 4 to
The conductivity i s independent of frequency
has a value of 1.2 (ohm-cm)™1 a t 429 K.
over
this
range
These r e s u l t s are combined
with o t h e r recent measurements t o i n t e r p r e t t h e ionic t r a n s p o r t i n terms
of motion between t h e t e t r a h e d r a l s i t e s of the Agl l a t t i c e .
The remainder of the t h e s i s r e p o r t s r e s u l t s based on the use
of
a microwave-frequency spectrometer i n c o r p o r a t i n g a Fabry-Perot c a v i t y , a
pulsed
supersonic
Chapter
II
nozzle
reports
beam,
the
and
microwave
geometries, and m t e r m o l e c u l a r
Fourier
transform
rotational
interaction
techniques.
spectra,
potentials
for
molecular
dimers
of
carbon monoxide with hydrogen c h l o r i d e and hydrogen f l u o r i d e (0C-HC1 and
OC-HF).
37ci
Nuclear quadrupole coupling c o n s t a n t s are r e p o r t e d for 35^1
in
OC-HC1 and
for
deuterium in OC-DF.
Values of the H, 1 9 F and
D,19F n u c l e a r spin - nuclear s p i n coupling c o n s t a n t s
OC-HF and
OC-DF.
Both
the
OC-HC1 and
and
are
reported
for
OC-HF dimers are l i n e a r a t
e q u i l i b r i u m with binding o c c u r r i n g through a hydrogen bond to the carbon
atom
of
carbon
monoxide.
This i s the f i r s t observation of a hydrogen
bond t o a carbon atom in the g a s phase.
iv
Chapter
nuclear
III
quadrupole
reports
the
microwave
rotational
coupling constants and H,19F nuclear spin - nuclear
spin coupling constants of the dimers formed by hydrogen
cyanogen and nitrogen (NCCN-HF and Ng-HF).
at equilibrium.
coupling
The differences
constants
cyanogen
in
the
with
These dimers are both linear
two
1^N
nuclear
It is found that polarization
and nitrogen components of the dimers.
corresponds to a negative charge of ca 0.02e on
and also of ca 0.02 e on N(2) in N(1)N(2)-HF.
N(2)
quadrupole
occurs
within
This polarization
in
N(1)CCN(2)-HF
Separation of vibrational
and electrical effects on the magnitudes of the 1*N
coupling
fluoride
within each dimer have been interpreted in terms of
the Townes-Dailey theory.
the
spectra, 14N
nuclear
quadrupole
constants was made possible by the symmetry of the NCCN and N 2
components of the two dimers.
This represents the first
separation
of
these effects, without which estimation of polarization is impossible.
Chapter IV reports the
nuclear
spin
-
nuclear
l4
spin
N nuclear quadrupole coupling and H,19p
coupling constants of the dimer between
acetonitrile and hydrogen fluoride
(CH3CN-HF).
A vibrational
normal
mode analysis using force constants from earlier infrared and relatively
high-temperature
vibrational
microwave
measurements
allowed
separation
of
electrical effects in the magnitude of the 1l*N nuclear
and
quadrupole coupling constant and led to
an
charge
It is ca 0.03e more negative in
on
the
nitrogen in the dimer.
the dimer than it is in free acetonitrile.
separation
temperatures
of
estimation
This
of
represents
the
the
excess
first
these effects by the use of results from spectroscopy at
high
relative
expansion (10 K or lower).
to
those
resulting
from
a
supersonic
V
The final chapter describes additions made to
in
the
spectrometer
order to extend the range of possible components of dimers to solids
and liquids of low vapor pressure at room temperature.
transitions
observed.
from
dimers
involving
such
components
Speoifio modifications of the oven design are
future experiments are proposed.
No
have
rotational
yet
suggested
been
and
vi
DEDICATION
This thesis is dedicated to the memory of my father,
Donald Soper
whose constant dream was for the educational
fulfillment of his children.
vii
ACKNOWLEDGEMENTS
I would like to express my deep appreciation for
inspiration,
support,
ceaseless
and guidance of Professor Willis H. Flygare from
the beginning of my graduate career until his
1981.
the
untimely
death
in
May,
I feel fortunate to have been part of his research group.
Virtually everyone who has been a member of Dr. Flygare's
group
in the last five years has contributed to my efforts here by providing a
stimulating atmosphere in which to work, as well as by practical
and assistance.
the
silver
Special thanks go to Dr. Karl Gebhardt, the mainstay of
iodide
discussions;
to
work;
to Dr. Leonard Duda
for
many
helpful
Dr. Antony Legon, who provided many interesting ideas
and was an ideal partner in the laboratory;
and
advice
Edward Campbell,
and
to
L. William Buxton
whose intimate understanding of the peculiarities
of the spectrometer used in the studies described in chapters
II
to
V
proved the salvation of many a day's effort.
Thanks too are due to the excellent
Chemistry
support
of
the
Department who machined the vacuum chambers, designed, built,
or repaired the electronics, prepared the drawings,
located
personnel
the
obscure
books
typed
the
papers,
and journals, and chased down the purchase
orders during my time here.
I am grateful to the
fellowship
for
one
Eli
Lilly
Corporation,
which
a
year, and for financial assistance provided by the
University of Illinois, the Materials Research Laboratory, the
Science Foundation,
funded
and
the
donors
of
the
Petroleum
National
Reseach
Fund
viii
administered by the American Chemical Society.
Thanks are most certainly due to my wife Kathleen who
endured
the
sacrifices,
patiently
exhilarations and disappointments of the last
five years. Finally, a special thanks to my two sons, Christopher
and
Timothy, who helped me to keep things in perspective throughout it all.
ix
TABLE OF CONTENTS
CHAPTER
I.
CONDUCTIVITY OF ALPHA SILVER IODIDE IN THE MICROWAVE RANGE....
A.
B.
C.
D.
II.
III.
IV.
V.
Page
Introduction
Experimental
Analysis and Results
Discussion
1
1
7
10
15
HYDROGEN BONDING TO CARBON IN THE GAS PHASE: THE CARBON
MONOXIDE - HYDROGEN CHLORIDE AND CARBON MONOXIDE - HYDROGEN
FLUORIDE COMPLEXES
17
A.
B.
C.
D.
17
18
25
32
Introduction
Spectroscopic Constants
Molecular Geometries
Intermolecular Interaction Potentials
SEPARATION OF POLARIZATION EFFECTS BY USE OF MOLECULAR
SYMMETRY: THE CYANOGEN - HYDROGEN FLUORIDE AND NITROGEN HYDROGEN FLUORIDE COMPLEXES
36
A.
B.
C.
D.
E.
36
38
42
57
59
Introduction
Experimental
Spectroscopic Constants
Molecular Geometry
Interpretation of Quadrupole Coupling Constants
SEPARATION OF POLARIZATION EFFECTS BY VIBRATIONAL ANALYSIS:
THE ACETONITRILE - HYDROGEN FLUORIDE COMPLEX
65
A.
B.
C.
D.
E.
65
68
71
74
79
Introduction...
Experimental
Results
Discussion
Conclusions
DESIGN OF A HIGH-TEMPERATURE NOZZLE SOURCE
81
A.
B.
C.
D.
81
82
87
89
Introduction
Vacuum Chamber and Oven Assembly.
Experimental
Conclusions and Recommendations
LIST OF WORKS CITED
91
1
CHAPTER I.
CONDUCTIVITY OF
ALPHA SILVER IODIDE IN THE MICROWAVE RANGE
A.
INTRODUCTION
Electrical conductivity of solid salts has excited interest ever
since
the
1834.
Research in this century was inspired by the discovery by Tubandt
and
first
Lorenz
silver
observation
(1914)
iodide
electrolytes.
has
that
of this phenomenon by Michael Faraday in
between
420 K and its melting point at 828 K
conductivities
Indeed,
solid
electrical conductivity than
comparable
silver
molten
iodide
to
at
silver
those
810
iodide
of
K
at
molten
has a higher
840
K
(Funke
(1976)).
Below 420 K silver iodide exists as an
structure
with
both
small-amplitude
the
silver
vibrations
and
about
the
their
iodide
is
characterized
as
iodide
(1934
and
1936),
This
hopping
which
The
'alpha
phase'
of
silver
having the iodide ions in a body-centered
Hoshino
(1957)),
tetrahedral sites of the iodide-ion lattice.
silver-ion
positions.
Above 420 K a significantly
cubic lattice (see Figure 1-1) while the silver ions
(Strock
wurtzite-type
ions restricted to
equilibrium
conductivity is low, typical of such salts.
different crystal structure is found.
hexagonal
is
reflected
ie,
appear
they
to
'melt'
hop among the
It is this low barrier
in
the
high
to
electrical
conductivity of this phase of silver iodide.
The simplest possible hopping model would have to include
parameters;
the
three
jump length 1, the flight time between sites l ^ , and
the dwell time at the sites T'o*
Evaluation of these
parameters
would
2
Figure 1-1. The silver iodide lattice. The large circles are iodide
ions and the small circles are possible silver ion sites.
3
Table 1-1:
The conductivity and relative dielectric
constant of alpha silver iodide at 429 K as reported by
Funke and Jost (1971).
conductivity
(ohm-cm)"1
frequency
(GHz)
9.8
dielectric
constant
59
72
60
49
36
27
25
21
1.11
0.69
0.60
0.69
0.80
0.86
0.81
0.64
18.5
21
24
28
32
36
40
provide some understanding of the transport mechanism.
One of the earliest studies of the silver ion transport dynamics
in silver iodide was that of Funke and Jost (1971).
In their experiment
they replaced the side walls of a waveguide section with
and
terminated
this
section
with
a movable short.
voltage standing wave ratio in front of this section as
the
position
of
the
short
they
(1971),
Funke
(1973)).
By measuring the
a
function
silver
iodide
between 8
structure
and
in
40 GHz.
copper(I)bromide
(Clemen
of
(Funke
and
Their results for silver iodide at 429 K
are listed in Table 1-1 and shown graphically in Figure 1-2.
significant
iodide
were able to calculate the relative
dielectric constant and conductivity of the
Jost
silver
They found
the frequency dependence of the conductivity
Similar
and
results
Funke
were
also
found
for
beta
(1975)) and alpha copper(I)iodide
(Funke and Hackenberg (1972)).
Their results give a value of 1.11 (ohm-cm)"'1 at 9.8 GHz,
is
comparable
to
the
which
dc value of 1.35 (ohm-cm)"1 (Tubandt and Lorenz
(1914), Kvist and Josefson (1968)).
As
the
frequency
increases
the
m
(VI
O
I
o
tn
en
ui
> •
>-
at
cS.
CO
to
ID
+
Figure 1-2.
10
15
420
+25
4—
30
35
^
40
FREQUENCY <GHZ>
The microwave-frequency conductivity of Agl according to Funke and J o s t (1971)
5
conductivity decreases until reaching a minimum of 0.6
21 GHz.
(ohm-em)"1
at
From this point the conductivity increases until it peaks at
32 GHz with a vaJue of 0.86 (ohm-cm)"1. Above 32 GHz the conductivity
(ohm-cm)"1
decreases until finally falling to 0.64
at 40 GHz, the
highest-frequency measurement.
These data are
(Drude
(1900)).
inconsistent with a simple Drude-type
model
Such a model predicts the frequency dependence of the
conductivity to be
CT(V)
<*Po<l2
2TrV 0 m(1+(M' 0 ) 2 )
(1-1)
where c* is the fraction of silver ions in the mobile state, /°Q is the
number density of all silver ions, q is the charge on each ion, m is the
ion mass, and
V Q ia
C ( V Q ) = (7(0)/2.
characteristic
a
The
conductivity
frequency. As the frequency
frequency
defined
decreases monotonieally
is increased
by
with
from dc the conductivity
decreases very slowly, having dropped only 10 per cent from the dc value
by V= V Q / 3 . In this region the drop
C^OJ/IO
by
V- 3 V o *
As
the
is precipitous, falling to
frequency
increases further the
conductivity tends asymptotically to zero.
If one knows the do value of the conductivity, VQ may be
found
by rearrangement of equation (1-1):
y0 =
*Poq2
2irmcr(0)
The only unknown parameter
(1-2)
in this equation
conducting ions in the mobile state.
is O,,
the number of
Estimates of oC based on the
6
temperature dependence of
probably
the
dc
much greater than 0.05.
least 130 GHz.
conductivity
indicate
that
it
is
This value then predicts V Q to be at
The data of Funke and Jost reach <7"(0)/2 at 20 GHz.
The two features in these data which had to
be
explained
were
the occurance of the Drude-like fall-off at such a low frequency and the
presence of a peak.
Clemen and Funke (1975) addressed this problem in a
paper which applied the following model to all three of the systems then
studied.
The decrease in the fall-off frequency
'start
effect,'
in
was
attributed
to
the
which the electrical field influences the rates of
ion jumping with and against the field.
The peak
in
the
conductivity
was said to be caused by the 'acceleration effect." This arises from the
dynamics of a weakly bound ion experiencing
presence
of
the
external
harmonic
oscillator.
time-of-flight, f f ,
driving
The
field,
main
Together with a
neutron
scattering
dwell
data
time
is
flight
actually
of
(Eckold
time
of
of T n= 7 pa
et
al
the
this
model
is
to
15 ps
from
quasielastic
(1975) and (1976)) this time
one
is
lattice
roughly
expected if the ions moved this distance with
and
in
ie, it behaves as a damped
parameter
predicts a jump length of 5 A, equal
The
forces
which was calculated to be 15 ps for alpha silver
iodide.
(1976)).
frictional
longer than the dwell time.
their
constant
(Funke
ten times the time
thermal
velocity,
Other theories have also
arisen to explain these data (Hinkelmann and Huberman (1976), Pietronero
et al (1970), and Funke (1979)).
The data of Funke and Jost —
in
<y(l>)
with
increasing
frequency
and specifically the fast fall-off
—
thus give f 1 > ^ 0
being quite long times, and a correspondingly long
jump
witn
length,
bofcn
about
7
5 A.
Because of the profound impact of these data on the understanding
of the transport mechanism in alpha silver iodide, we
the
frequency
dependence
the dc value.
a
We find no structure in the conductivity
range, with all values of CT(V) within experimental error of
this
for
remeasured
of the conductivity from 4 to 40 GHz using a
cavity perturbation technique.
over
have
These results, along with other recent experiments, allow
more orthodox interpretation of the dynamics of ionic conduction
in alpha silver iodide.
B.
EXPERIMENTAL
In this work the differences
resonant
(^Q)
frequency
°^
an
in
the
ODen
quality
factor
resonator (Fabry-Perot cavity)
before and after introduction of the sample were used to
conductivity
and
relative
a
temperature-controlled
100 MHz and fed into an harmonic
portion
of
determine
the
dielectric constant of alpha silver iodide.
Figure 1-3 shows a block diagram of the apparatus used.
from
(Q) and
crystal
mixer
oscillator
where
it
A 20 MHz signal
is
is
multiplied
beat
to
against
a
the signal from an intermediate oscillator operating in the
4-8 GHz range.
A phase-lock frequency stabilizer controls the frequency
of this oscillator so that the beat signal is maintained at 30 MHz.
intermediate
oscillator
is
thus
stabilized
at
a
The
frequency
Vio = «100 +/- 30 MHz where n is the appropriate harmonic of 100 MHz to
achieve the desired frequency.
power
is
fed
into
Most
is
the
intermediate
oscillator
a second harmonic mixer along with the output of a
variable frequency oscillator (VF0).
this
of
One of
the
beat
frequencies
of
combination with the main microwave backward wave oscillator (BW0)
used
to
phase-lock
stabilize
the
BWO
at
Multiplier
x5 = 100MHz
20 MHz
Frequency Stabilizer
MW Oscillator
4 - 8 GHz
Frequency
Stabilizer
MW Oscillator
Di e C
C o upfG n r a,
Analog-toDigital
Converter
and
Memory
Interface
Figure 1-3.
Punch
Varlab,e
Iso,ator
Attenuator
Paper
Tope
The apparatus used in this study.
Computer
It is described in the text.
05
9
)^BWO = n V j o +/- P V V F O +/- 30 MHz. When the
this
stabilization
system
causes
the
BWO
VFO
frequency
frequency
changes,
to change in a
parallel fashion.
Frequency measurement is accomplished through direct counting of
the VFO frequency followed by calculation of the BWO frequency according
to the equation above.
Fabry-Perot
cavity
The BWO provides the radiation for
formed
by
This
is
used
to
measure
the
A
signal
signal is amplified and digitized in a Fabri-Tek 1070
series instrument computer.
generate
tunable
two equally curved aluminum mirrors.
broad-band square-law diode detector
intensity.
the
electronic
The
markers
VFO
which
frequency
advance
counter
is
used
to
the memory address in the
Fabri-Tek every 10 or 100 kHz. The final result
is
that
each
memory
location holds a digitized value of the diode signal, and the address of
that location serves as a point on a frequency axis.
the
Fabri-Tek
When the memory of
is full, its contents are transfered to paper tape which
is later read into a DEC-20 computer for curve fitting and analysis.
The Fabry-Perot cavity is operated in a
spherical
samples
placed
at
the
center
TEMQQQ
of the cavity.
obtain the maximum sensitivity of the Q change and
changes
in
the
conductivity
and
mode
with
In order to
frequency
shift
Under
these
to
dielectric constant given the known
dielectric properties and the sizes of our samples, q was chosen
odd.
the
to
be
conditions the electric field is zero at the sample
location.
The samples are supported in the cavity on
with
a
wall
thickness of 0.01 mm.
the whole cavity.
a
quartz
capillary
Heating is accomplished by heating
In order to account for any possible effects
due
to
the presence of the capillary, frequency shifts and Q changes due to the
10
capillary alone are subtracted from those with the sample in place.
The analysis desoribed
below requires the use of
spherical
samples, the preparation of whioh presented some difficulties. Various
grinding techniques were unsuccessful. The method finally chosen was to
melt silver iodide powder on a mica plate, shake the plate so as to form
drops, and then allow the drops to fall through the air.
spheres as
they hardened
during
the fall.
They
formed
The samples were then
annealed at 670 K in the presence of iodine while in a tumbling device.
Any adsorbed
iodine was removed by a stream of nitrogen. The final
color of the samples was a pale yellow. Effective radii of the
were calculated
samples
from their masses and the average density in the alpha
phase of 5.5 +/- 0.2 g cm"3, a n d ranged from 0.7 to 3.5 mm.
This technique
examining
several
conductivities
for measuring
conductivities was checked
by
samples of silicon of known dielectric constants and
(ranging
from 0.4
to 4.5
(ohm-cm)"1).
The values
obtained with this apparatus were within five per cent of the known
values.
C. ANALYSIS AND RESULTS
The appropriate
frequency
perturbation
formula for analysis
of
the
shifts and Q changes in a resonant cavity is (Muller (1939),
Waldron (1960)):
SQJ
Co
=
( £ ? * -fi-|)jEEf/dVg + (A2*-/^l)/HH 0 *dV fl
2£ 2 j r E 0 E 0 dV c
where co is the complex frequency defined by
(I"3)
11
CO = Cd 0 /l - (1/2Q) 2 - iW 0 /2Q
£•) and £ 2 a r e
tne
(1-4)
complex dielectric constants of the sample and of
the oavity medium respectively and are defined by
£j = 61, + i £
JJL-\ and M-2.a r e
tne
1
"sfi
1
'+
icr/OJ 0
(1-5)
complex permeabilities, V 3 is the sample volume, V 0
is the cavity volume, E and E 0 are the electric fields in the cavity
with and without the sample in place respectively, and H and H Q are the
corresponding magnetic fields. This equation is only valid as given for
small changes in the resonant
frequency
and bandwidth upon sample
insertion, ie, for C T O J ^ W .
Evaluation of the numerator of equation (1-3) requires knowledge
of the fields within the sample. The standing-wave pattern near the
center of a Fabry-Perot cavity operating
approximated
in a TEMgoq mode
is well
by the superposition of two traveling waves propagating in
opposite directions along the cavity axis. This reduces the problem of
finding
the fields
in the sample to that of the scattering of a plane
wave by a sphere, a problem solved by G. Mie (1908). The results of the
application
of this theory to a cavity are given by Brodwin and Parsons
(1965). They find the relative frequency shift to be
<fc
21TTS9
u>
Ak23
2 (2n+1)an + £ (2n+1)bn
n=1
n=2
n odd
n even
(1-6)
with
A = €pTTdyd(2R Q -d)
2k 2
(1-7)
12
an =
(1.8)
/^ 2 J n (k 2 a)(k ia j n (k ia ))'-/g j n (k ia )(k 2 aj n (k 2 a))'
/I1jn(k1a)(k2ahn(1)(k2a)),-/^2hn(1)(k2a)(k1ajn(k1a))'
and
bn =
£iJ n ^ 1 a)(k 2 aJ n (k 2 a))'-g 2 J n (k 2 a)(k 1 aj n (k 1 a))'
1
,
1
fT .q)
e 2 h n ( )(k 2 a)(k 1 aj ^ (k 1 a)) -£ 1 j n (k 1 a)(k 2 ah n ( )(k 2 a))
In these equations a is the sample radius, d is the
,
separation
of
the
mirrors in the cavity, RQ is the radius of curvature of the mirrors, and
k is the complex propagation constant:
k 1 j 2 = +/-^o///<1,2 6l,2
(1-10)
where the sign is chosen .so as to make the imaginary part of k positive.
jn(x)
and
h n (D(x)
respectively.
are
(xjn(x))f
the
spherical
Bessel
and
denotes differentiation with
Hankel functions
respect
to
the
argument, x.
Equation
equation
(1-3),
(1-6)
ie,
is
valid
over
for oco4< to.
those
conditions
imposed
This presents no problem since the
parameter A is just four times the energy stored in the cavity
be
varied
volume.
one
over
a
wide
by
and
can
range of values simply by changing the cavity
The value of A calculated according to equation (1-7) is within
per cent of the exact value found by numerical integration over the
field configuration in the Fabry-Perot cavity for values
of
d
and
R0
used in this experiment.
Since alpha silver iodide is nonmagnetic, ily has been set equal
to M. 2•
The procedure used is to measure <fco /co in the experiment and
then numerically solve equation
each
frequency
two
to
(1-6)
for
£•) = £•)' +
ICT/COQ.
For
five different samples were measured at 429 K.
13
Table 1-2.
Values of the conductivity and
dielectric constant of alpha silver iodide
obtained in this work.
frequency
(GHz)
conductivity
(ohm-cm)~1
4.08
6.00
8.86
9.45
11.73
14.59
17.45
20.32
23.42
26.33
29.23
30.37
33.35
36.36
39.38
1.094
1.180
1.182
1.161
1.132
1.122
1.084
1.154
1.188
1.094
1.129
1.215
1.189
1.170
1.219
relativeat 429 K
dielectric
constant
30.7
37.9
10.3
21.0
22.0
18.0
30.7
36.4
22.0
39.9
24.0
13.2
7.8
13.1
10.4
The results are given In Table 1-2 and shown graphically in Figure 1-4.
Nonsystematie errors arise primarily from uncertainties
sample
radii
and
variations
severe uncertainties in
the
in
sample density.
values
of
the
in
the
Along with the less
frequency
shifts
and
Q
changes, these combine to give an estimated error of fifteen per cent in
each conductivity value.
is
much greater.
The estimated error in the dielectric constant
A possible systematic error may arise from the use of
the capillary to support
the
sample,
rigorously included in the analysis.
since
its
presence
cannot
be
CONDUCTIVITY (INVERSE OHM-CM)
0.5
01
tn
8'
8"
S'
o
M
0.6
0.7
0.6
0.9
1.0
1.1
1.2
1.3
15
D.
DISCUSSION
The data
dependence
presented
above
show
that
there
is
the
density
of
our
corrected
conductivity
over
this
This is comparable to the dc value of 1.35 (ohm-cm)"1.
These data
experiments
of the
When
samples relative to crystalline alpha silver
iodide, these data give 1.22 (ohm-cm)"1 as the
range.
frequency
in the conductivity of alpha silver iodide from 4 to 40 GHz.
The mean value of our measurements is 1.154 (ohm-cm)"1.
for
no
with
the
results
of
a
variety
of
other
may be combined to give a reasonable and consistent picture
behavior
contribution
along
of
of
the
silver
ion
in
alpha
silver
iodide.
The
this work to such a picture is to render it consistent
with the Drude model at low frequencies, eliminating
the
necessity
of
positing large flight times or long jump lengths.
Recent studies using extended X-ray
(EXAFS)
(Boyce
absorption
fine
structure
et al (1977)), neutron diffraction (Cava et al (1979)),
and X-ray diffraction (Hoshino et al (1977)) have demonstrated that
silver
ion
the
hops between adjacent tetrahedral sites (see Figure 1-1), a
conclusion also reached in a recent molecular dynamics 3tudy (Vashihstra
and
Rahman
(1978)).
iodide is 1.784 A.
of
the
silver
The
The EXAFS study also indicated that the
A
low-frequency
et al (1978)) gives the sum of T
0
value of f 1 of 0.6 or 0.35 ps would predict X§
In
neither
ease
from 4 to 40 GHz.
dwell
time
ion " C Q i s about three times the flight time ~C<\, which
was calculated to be 0.6 ps.
(Winterling
distance between such sites in alpha 3ilver
would
light
scattering
study
and "^ to be 1.4 ps. A
to be 840 or
1410 GHz.
the Drude model predict any variation in
C(V)
16
These studies thus combine to give
rather
than
5 A,
a
flight
a
jump
length
of
1.784 A
time which is shorter than the dwell time
rather than the reverse, and a flight time of less than 1 ps rather than
15 ps.
The
model
described
above
is
consistent
with
an
early
theoretical study on alpha silver iodide (Flygare and Huggins (1973)) in
which point charge and higher-order attractive terms were
overlap
repulsive
terms
The
choice
of
path
by the relative sizes of the silver and iodide ions.
iodine ion radius of 1.75 A any silver ion radius
predicts
the
with
to determine the minimum energy positions and
likely transport channels of the silver ion.
determined
summed
greater
is
For an
than
0.83 A
motion to be along the path indicated above, ie, from one
tetrahedral site to another.
More recent theories (Pietronero et al (1979), Dieterich
(1977),
Kimball
and
Adams
(1978),
Richards
(1979))
Our
al
predict a weak
increase in the conductivity throughout the microwave and
(FIR) regions.
et
far
infrared
data are not inconsistent with such theories, but
neither are they a demonstration of their validity.
The results of thi3 investigation are published in
of
Chemical
'Conductivity
Physics,
of
volume
oC-silver
72, pp
iodide
in
272
the
-
276
under
microwave
the
Journal
the
range*
title
by
K. F. Gebhardt, P. D. Soper, J. Merski, T. J. Balle and W. H. Flygare.
17
CHAPTER II. HYDROGEN BONDING TO CARBON IN THE GAS PHASE:•
THE CARBON MONOXIDE - HYDROGEN CHLORIDE AND
CARBON MONOXIDE - HYDROGEN FLUORIDE COMPLEXES
A.
INTRODUCTION
Complexes in which the components interact
bond
have
through
a
been of special interest both because of their prevalence in
nature and because they are frequently more amenable to study
more
weakly-bound
complexes.
stable enough to be
mixtures
found
in
than
The hydrogen-bonded complexes are often
significant
population
in
equilibrium
Such has been the case for CHgCN-HF (Bevan et
(1980A)), H20-HF (Bevan et al (1980B)), (CH3)3CCN-HF (Georgiou et al
(1980)) and HCN-HF (Legon et al (1980A)),
successfully
in
a
standard
all
of
Stark-modulated
which
were
waveguide
studied
cell.
relatively strong binding is also attractive for study by nozzle
and
are
of the component gases, allowing for their observation without
recourse to nozzle beams.
al
hydrogen
this
This
beams,
technique has been applied to HCN-HCN (Buxton et al (1981B)),
HF-HF (Dyke et al (1972)) and H20-H20 (Dyke et al (1977)).
In this study the range
formation
of
complexes
interesting base.
intuition
bases
containing
It is far
alone, which
of
end
from
of
carbon
clear,
the
has
been
extended
monoxide,
on
the
a
basis
and
hydrogen
with hydrogen bromide
the
particularly
of
chemical
CO molecule is the better proton
acceptor. This study of the complexes of carbon monoxide with
chloride
by
hydrogen
fluoride, as well as a concurrent study of that
(Keenan
et
al
(1980B)),
establish
that
each
complex is linear at equilibrium with a hydrogen bond to the carbon atom
of carbon monoxide.
18
B.
SPECTROSCOPIC CONSTANTS
The apparatus is described in
detail
elsewhere
(Balle
et
al
The gas mixtures were typically four
(1980), Balle and Flygare (1981)).
percent HC1, four percent CO and ninty-two percent argon for C0-HC1
and
one percent HF, four percent CO and ninety-five percent argon for CO-HF.
The
total
pressure
atmospheres.
The
varied
from
about
one
to
A F = 1 transitions
of
OC-HCl
time
one-half
domain
or
better
for
the
and the transitions of OC-HF where the
splitting of the hyperfine components is much
A
and
signal-to-noise ratios ranged from about 2:1 for the
weakest (A. F = 0) transitions of OC-HCl up to 20:1
OC-HCl.
two
lower
than
it
is
for
signal of the J = 1<-0 transition of OC-HF is
given in Figure II-1. Its Fourier
transform,
shown
in
Figure II-2,
clearly exhibits the Doppler doubling phenomenon related to the dynamics
of the
gas
expansion
(Campbell
et
al
(1981A
and
B)).
The
true
frequencies of the four components of this transition lie midway between
the Doppler pairs and are marked in the figure.
The spectra observed were characteristic of those
molecule
or
states of K > 0
hyperfine
the
a
linear
very slightly asymmetric rotor in which no transitions for
are
observed.
structure
in
the
The
only
measurable
electric
field
contribution
gradient
it
the
experiences.
chlorine
nucleus
The form of the
Hamiltonian is (Townes and Schawlow (1955)):
H Q = -Xa
to
OC-HCl complex is that resulting from the
interaction of the electric quadrupole moment of
with
of
3(I-3*)2+(3/2)q-J)--I232
21(21-1)(2J-1)(2J+3)
(II-1)
32
64
Time (/i.s)
Figure II-l. The J = l<-0 transition of OC-HF m
96
128
the time domain.
20
27,7028
27.7582 27.7733
27.8728
Frequency (MHz)
Figure I I - 2 .
The J = l-<S-0 t r a n s i t i o n of OOHF in the frequency domain.
21
where I is
the
chlorine
nuclear
spin
angular
momentum,
rotational
angular momentum, and p£a is the component of the quadrupole
coupling constant along the a inertial axis of the complex.
J
is
The
the
energy
levels resulting from both rotation and the quadrupole Interaction for a
linear molecule are given by (Townes and Schawlow (1955)):
E(J,I,F)/h = B0J(J+1)+DjJ2(J+1)2-XaY(J,I,F)+;£a10-3g/B0
where I = 3/2 for both 35ci and 37ci, p is the total
Bg
is
the
distortion
effective
constant,
second-order
rotational
Y(J,I,F)
correction
to
constant, Dj
is
the
used to fit the observed transition
Casimir's
angular
is
the
function
quadrupole energy.
frequencies
to
(II-2)
momentum,
centrifugal
and
g
is
a
This equation was
B Q , D J and ,%a*
Table II-1 lists the observed frequencies and those calculated by use of
the constants of Table II-2
comparing
the
in
equation
II-2.
As
may
be
seen
by
two sets of frequencies, the quality of the fit is quite
good.
Analysis of the OC-HF spectra was complicated by the presence of
nuclear
spin
-
nuclear
spin
coupling
arising
from the interaction
between the magnetic dipole moment of the fluorine nucleus and
the
hydrogen
(or
deuterium)
nucleus.
that
of
The form of the Hamiltonian is
(Ramsey (1953)):
HSS
= SHF
3(IH-J)(IF-J)+3(IF , J)(IH-J)-2(TP'I'H)J 2
(H-3)
(2J+3K2J-1)
where S^p i s the HF (or
Ipj = 1/2
and
Ip = 1.
DF)
spin-spin
coupling
constant,
Ip = 1/2,
The OC-DF spectra are further complicated by the
deuterium quadrupole coupling, the Hamiltonian for
which
is
given
in
22
Table II-1: Observed and calculated frequencies in MHz
for rotational transitions of several isotopie species of
OC-HCl.
isotopie
species
J« pi
16
0 1 2 C-H 3 5 C1
4
4
4
4
4
4
4
5
5
5
5
5
5
5
4.5
2.5
3.5
4.5
5.5
3.5
2.5
5.5
3.5
4.5
6.5
5.5
4.5
3.5
6O12C-H37CI
4
4
4
4
5
5
5
5
013C-H35C1
16Q12C-D35CI
1
16
<j-• J
F
observed
frequency
calculated
frequency
3
3
3
3
3
3
3
4
4
4
4
4
4
4
4.5
1.5
2.5
3.5
4.5
3.5
2.5
5.5
2.5
3.5
5.5
4.5
4.5
3.5
13359.930
13371.441
13371.441
13372.955
13372.955
13377.529
13384.456
16702.087
16714.212
16714.212
16715.109
16715.109
16718.783
16727.231
13359.933
13371.440
13371.440
13372.953
13372.953
13377.529
13384.457
16702.087
16714.212
16714.212
16715.107
16715.107
16718.787
16727.231
2.5
3.5
5.5
4.5
4.5
3.5
6.5
5.5
3
3
3
3
4
4
4
4
1.5
2.5
4.5
3.5
3.5
2.5
5.5
4.5
13065.138
13065.138
13066.331
13066.331
16331.212
16331.212
16331.916
16331.916
13065.138
13065.138
13066.331
13066.331
16331.211
16331.211
16331.916
16331.916
4
4
4
4
5
5
5
5
3.5
2.5
5.5
4.5
4.5
3.5
6.5
5.5
3
3
3
3
4
4
4
4
2.5
1.5
4.5
3.5
3.5
2.5
5.5
4.5
13232.137
13232.137
13233.654
13233.654
16540.106
16540.106
16541.003
16541.003
13232.137
13232.137
13233.654
13233.654
16540.106
16540.106
16541.003
16541.003
4
4
4
4
4
4
5
5
5
5
5
5
5
4.5
3.5
2.5
5.5
4.5
3.5
5.5
4.5
3.5
6.5
5.5
4.5
3.5
3
3
3
3
3
3
4
4
4
4
4
4
4
4.5
2.5
1.5
4.5
3.5
3.5
5.5
3.5
2.5
5.5
4.5
4.5
3.5
13391.876
13404.085
13404.085
13405.686
13405.686
13410.537
16742.249
16755.115
16755.115
16756.064
16756.064
16759.967
16768.925
13391.875
13404.082
13404.082
13405.687
13405.687
13410.541
16742.252
16755.114
16755.114
16756.064
16756.064
16759.968
16768.925
23
Table II-2: Spectroscopic constants for several isotopie•
species of OC-HCl. The values in brackets represent one
standard error of the fitting.
isotopie
species
]jjo]fc-H35ci
16O12C-H3JCI
JDO13C-H35CI
16
0 12 C-D 35 C1
a.
B 0 (MHz)
Dj (kHz)
^
1671.7234(4)
1633.3988(2)
1654.3070(2)
1675.8027(3)
4.802(9)
4.574(5)
4.682(5)
4.507(6)
-52.086 (9)
-4l.070(38)a
-52.219(29)a
-55.254 (7)
a
(MHz)
The standard errors for these two isotopie species
are high because no A F = 0 transitions were measured
for them. See Table II-1.
equation (II-1).
Only hyperfine structure in
the
J = 1<-0
transition
was used to determine the spin-spin and quadrupole coupling constants of
OC-HF and OC-DF.
The appropriate hyperfine Hamiltonian was evaluated in
the coupled basis set:
" j + % ( D ) = "F"I J
T-i + I p s T
(11-4)
and the resulting matrix diagonalized to give the energies and hence the
frequencies of the hyperfine components relative to the center frequency
of the transition, Vn»
OC-HF
and
to
This procedure was used to fit V Q and S^p
fit VQ, SDp and ^ D for OC-DF.
were then used to determine the line
centers
J = 2«-1
the
transitions,
and
finally
The hyperfine constants
of
the
partly
resolved
J = 1<H) and J = 2<-1 center
frequencies were used to calculate B Q and Dj
according
to
the
linear
molecule equation
V0
=
2B0(J+1) - 4Dj(J+1)3
for
(II-5)
24
Table II-3: Observed and calculated frequencies in MHz
for rotational transitions of several isotopie species of
OC-HF.
isotopie
species
J»
V
pt <r-J
16
1
1
1
1
2
0.5
1.5
1.5
0.5
2.5
1
1
2
0
2
16013C_HF
1 0.5
1 1.5
1 1.5
1 0.5
2 2.5
18
0 12 C-HF
0 12 C-HF
1
6o 1 2 c-DF
1
8n 1 2 c-DF
1
F
observed c a l c u l a t e d
frequency frequency
0
0
0
0
1
0.5
0.5
0.5
0.5
1.5
1
0
1
1
1
6127.703
6127.758
6127.773
6127.873
12255.285
6127.703
6127.760
6127.771
6127.873
12255.285
1
1
2
0
2
0
0
0
0
1
0.5
0.5
0.5
0.5
1.5
1
0
1
1
1
6099.526
6099.581
6099.597
6099.698
12198.934
6099.526
6099.583
6099.595
6099.698
12198.933
1 0.5
1 1.5
1 1.5
1 0.5
2 2.5
1
1
2
0
2
0
0
0
0
1
0.5
0.5
0.5
0.5
1.5
1
0
1
1
1
5855.734
5855.789
5855.803
5855.904
11711.372
5855.733
5855.790
5855.802
5855.904
11711.372
1
1
1
1
1
1
1
2
2
2
0
0
2
1
1
1
1
3
3
2
0.5
0.5
2.5
1.5
1.5
0.5
0.5
2.5
3.5
2.5
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
2
2
1
1.5
0.5
0.5
1.5
1.5
0.5
1.5
1.5
2.5
1.5
6095.618
6095.618
6095.750
6095.819
6095.819
6095.848
6095.848
12191.285
12191.285
12191.296
6095.619
6095.619
6095.749
6095.818
6095.818
6095.846
6095.846
12191.284
12191.287
12191.295
2
2
0
0
2
2
1
1
1
1
1
3
0.5
0.5
1.5
2.5
1.5
1.5
0.5
0.5
1.5
3.5
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
2
1.5
0.5
0.5
1.5
1.5
0.5
0.5
1.5
1.5
2.5
5820.355
5820.355
5820.471
5820.486
5820.556
5820.556
5820.585
5820.585
11640.650
11640.791
5820.355
5820.355
5820.473
5820.484
5820.555
5820.555
5820.586
5820.586
11640.653
11640.789
F
25
Table II-4: Spectroscopic constants for several isotopie
species of OC-HF. The values in brackets represent one
standard error of the fitting.
isotopie
species
4
°012C-HF
6o13c_HF
°0 2C-HF
1
18
0 12 C-DF
a.
B0(MHz)
Dj(kHz)
3063.89943
3049.8111
2927.9125
3047.8981
2910.2637
9.77a
9.72
8.69
9.40
8.17
XD(kHz)
SHF(kHz)
278.6(3.5)
278.5(3.5)
113.4(1.8)
114.9(1.8)
114.1(1.4)
19.3(1.7)
20.9(1.7)
Bg and Dj are determined from the center frequencies
of only two transitions.
If all of the estimated
error in these center frequencies is assigned to B 0 ,
its estimated error is 1 kHz. If all of the error is
attributed to Dj, its estimated error is 0.05 kHz.
where J is the rotational angular momentum quantum number of
state
in
the
R-branch transition.
of
them in Table II-3.
lower
The agreement between the observed
and calculated transition frequencies is very good, as may
comparison
the
be
seen
by
The derived constants are listed in
Table II-4.
C.
MOLECULAR GEOMETRIES
The following discussion assumes that the geometries of CO,
and
HF
survive
dimer
formation
unchanged,
an
assumption
HC1
which is
justified by the strong binding in CO, the weak binding of the dimer and
the
relative
of the hydrogen
insensitivity of the rotational constants to the position
atom
because
of
its
low
mass.
Spectroscopic
and
molecular constants for CO, HC1 and HF are given in Table II-5.
The coordinates used in this analysis are shown in Figure
The
three
heavy atoms in both complexes are collinear.
II-3.
This assertion
is supported by the absence of any transition attributable to states
of
Center
of mass of CO
Center of mass of HF
-—tf-axis
CM
Figure I I - 3 .
The coordinates used in the t e x t to describe the geometries of OC-HF and OC-HCl.
en
Table II-5: Spectroscopic and molecular constants for
various isotopie species of free CO, HCl, and HF.
B0(MHz)
r 0 (A) X D or CI(MHz) S HF (kHz)
12c160
13c160
12 18
C 0
57635.971a
55099.748°
54890.138°
1.13090b
1.13084°
1.13084°
H35ci
H37ci
D35ci
312989.297d
312519.121d
I6l656.238 d
1.28387e
1.28386e
1.28l24e
H 1 9F
D 1 9F
616365.5h
325584.98k
0.92560"
0.92324k
a.
b.
c.
d.
e.
f.
g.
h.
j.
k.
-67.6l893 f
-53.2949S
-67.39338 f
0.354238i
143.375J
22.170J
Helminger et al (1979)
Watson (1973)
calculated from b.
DeLucia et al (1971)
calculated from d.
for the chlorine nucleus. Kaiser (1970)
calculated from f. and ^oC 3 7 Cl) = %o( 35 Cl)/1.2688
Guelachvili (1976)
Muenter (1972)
Lovas and Tiemann (1974)
28
K>0
as
well
as
rg(C-Cl) and
II-6).
by
rg(C-F)
the
evidence
consistency
in
the
values
of
calculated assuming a linear geometry (see Table
It is impossible to
without
excellent
from
establish
rotational
states, but the angle ^
this collinearity
transitions
that the C-0 bond makes
conclusively
in excited vibrational
with
the
a
inertial
axis of the complex is certainly small.
The order of the heavy atoms is readily ascertained from the
values.
This
Is most clearly seen for isotopie changes in OC-HF where
substitution of 13c for
while
that
Bg
of
1
12
C produces a small
change
in
the
for 1 ^0 produces a much larger change.
&o
Bg value
The oxygen
atom must be further away from the center of mass of the complex than is
the
carbon
atom.
Only the heavy atom orders 0-C-C1 and 0-C-F produce
the consistency in rg values apparent in Table II-6. This study
in
way
exist.
precludes
the
possibility
that
Preliminary ab initio studies indicate
the
C-O-F
that
the
isomer
two
may
no
isomers
may
be
atom
rely
on
comparable in their stabilities.
Arguments as to the
interpretation
of
the
vibrational averaging.
the
quadrupole
position
hyperfine
of
the
structure
interaction
constant
in
light
of
Consider first the case of OC-HCl.
lies
along
the
measured in this experiment is the projection
coupling
hydrogen
along
the
a
diatomic
of
the
zero-point
In free
bond.
free
HCl
What is
quadrupole
inertial axis of the complex as it is
averaged over the zero-point motions:
yCa
= / 0 ( 1 / 2 ) <(3cos2 V - l)
The mode which produces the greatest excursion of the hydrogen
(II-6)
atom
is
29
VB
(see Figure 2 of Legon et al (1980A)), in which the heavy atoms are
displaced very little. Under these circumstances the angle of the
bond
H-Cl
with the a inertial axis is essentially equal to the angle of that
bond with the
assumption
assumed
that
the
molecular
value
axis.
This
result
relies
of ~/-§ for HCl in the complex is unchanged
pC = -eQqz/h
(II-7)
where e is the electronic charge, Q is the nuclear
and
qz =
at
the
electric
saying
that
the
distance,
electric
field
chlorine nucleus is unchanged upon complex formation.
Considering the weak nature of the binding of the dimer
C-Cl
quadrupole
/ c > 2 V / 5 z 2 ) is the electric field gradient along the
diatomic bond, this is tantamount to
gradient
the
Since JC is given by
from that for free HCl.
moment
on
this
is
and
not an unreasonable assumption.
the
large
Values of $
calculated by use of equation (II-6) are listed in Table II-6.
That the hydrogen atom lies
atoms
y,
between
the
carbon
and
chlorine
rather than outside the latter is indicated by the small value of
about
23
corresponding
degrees.
obtuse
Because
the
average
is
over
cos2o , the
angle, 157 degrees, is mathematically acceptable.
However, it is not physically acceptable since if the hydrogen were
involved
in
the
weak
bond
one
vibrationally-averaged angle. The angle o
would
is small
expect
because
a
not
larger
the
weak
bond restrains the motion of the hydrogen atom.
Examination of Table II-6 will show that the consistency
and
0
of
rg
values among the various isoptopic species of OC-HCl breaks down
for 0C-DC1.
This is due to the changes in zero-point
averaging,
which
30
Table II-6:
Vibrationally-averaged parameters of themolecular geometries of several isotopie species of
OC-HCl and OC-HF.
isotopie
species
23.0 a
23. oaa
22.9 a
20.3
16 12
0 C-H35ci
16O 1 2 C-H3JCI
16O13C-H35CI
1
6O12C-D35C1
1
6o12C-HF
2 1 < 9
O13C-HF
18O12C-HF
16o12C-DF
1
8o12C-DF
CI or F)(A)
3.6939
3.6937
3.6944
3.6845
3.0468
3.0470
3.0460
3.0364
3.0355
K
21.3°
21.6°
22.17°
22.18°
16
a.
ro(C-
CUdeg)
calculated from the chlorine quadrupole coupling
constant.
calculated from the HF spin-spin coupling constant.
calculated from the deuterium quadrupole coupling
constant.
b.
c.
are more severe for
deuterium
substitution
than
for
other
isotopie
substitutions.
Similar arguments also establish that the hydrogen atom in OC-HF
lies
between
the
carbon and fluorine atoms.
The deuterium quadrupole
coupling constant, given by equation (II-7), also projects according
equation
II-6.
(II-6).
The
values of O thus calculated are given in Table
The assumption that the field gradient asymmetry at the deuterium
nucleus
is
unchanged
from that in free DF is not as good as that made
for the chlorine nucleus in HCl, but the argument about the small
of
0
to
dictating
atoms is
that the hydrogen lie between the carbon and fluorine
unchanged.
electrical
upper limit.
value
properties
This
in
is
DF
because
the
assumption
of
unchanged
leads to a calculation of 0 which is an
31
In free DF, the electron density lies
atoms,
leading
to
a
high
field
In OC-DF the deuterium will encounter
electron
density
the
between
carbon
some
small
y
two
amount
of
atom, thereby decreasing the field
If
gradient asymmetry and the appropriate value of 7^0*
complex
the
gradient asymmetry at the deuterium
nucleus.
from
mainly
%Q
in
the
is indeed lower than it was assumed to be, the correct value of
The values of a for
will be lower as well.
OC-DF
given
in
Table
II-6 are upper limits.
The HF spin-spin coupling constant projects in the same
way
as
the quadrupole coupling constants:
SHF = SapOd/2) <(3eos2 ^ - l )
(II-8)
giving the values of o for OC-HF shown in Table II-6.
In free
HF
the
spin-spin coupling constant is given by
=/V g H g F < 1 / r 3 >
SHF0
/n
(II 9)
"
The assumption that Sflp0 is unchanged from the free HF value amounts
assuming
that the H-F bond length is unchanged.
is changed, it will be longer in the complex than
thereby
decreasing
the
value
again making the values of
limits.
Note
o
of
for
it
is
in
free
HF,
Syp0 appropriate to the complex and
OC-HF
given
OC-HCl does not appear for OC-HF.
This is because
these
electric
length in OC-HF.
If the H-F bond length
in
Table
II-6
upper
the substantial decrease in 0 upon deuteration of
that
assumptions
to
of
unchanged
of
the
failure
of
field gradient and H-F bond
32
The Bg, /^ci> A D and Syp values thus combine to indicate that
both OC-HCl and OC-HF have linear equilibrium geometries where binding
in the dimer occurs through a hydrogen bond to the carbon atom.
D.
INTERMOLECULAR INTERACTION POTENTIALS
It is possible to estimate the
hydrogen-bond
stretching
parameters and the dissociation energies of the complexes through a set
of relationships which parallel those for a diatomic molecule
(Townes
and Schawlow (1955)). These values are useful for comparative purposes,
although their approximate nature should be realized.
The hydrogen-bond stretching frequency
l^
is related
to the
centrifugal distortion constant Dj through
Vj= ^/Dj
'cr
(11-10)
where Bn is the pseudodiatomic rotational constant defined by
B„ a h/8ir2 / «e,r a m 2
(H-H>
in which r c m is the separation of the CO and HCl or HF centers of mass
and
Ug. is the reduced mass defined by
Atr - m C0 m HX / ( m C0 +m Hx)
where X = CI or F. This approximation relies on the fact
(H-12)
that in a
linear molecule only stretching force constants contribute to Dj and
that in OC-HCl and OC-HF the frequency of the hydrogen-bond
stretch is
33
much
lower
than
those
for
the
C-0,
H-Cl
or H-F stretches.1 It is
possible to calculate an effective force constant kg. , which
true
force
constant
is
not
unlike
a
isotopically independent, from the usual
relationship
A
Values of k^
and
(2TTVfl.)2
(11-13)
Vg- for each isotopie species
of
OC-HCl
and
OC-HF
investigated are listed in Table II-7.
Table II-7:
Effective hydrogen-bond stretching
and
radial potential parameters for several isotopie species
of OC-HCl and OC-HF.
isotopie
species
kcr(mdyne/A)
i^.(cm"1)
16 12
0 C-H35ci
0.0446
69
16O12C-H37CI
0.0445
69
569
1
6o13c-H35ci
16o12C-D35ci
0.0453
0.0491
69
72
573
616
16
0 12 C-HF
16o13c-HF
lSo12C-HF
0.108
0.108
0.109
125
125
124
987
988
1014
16O12C-DF
18Q12C-DF
0.115
0.118
127
127
1024
1074
The exact form of the intermoleoular
not
£(em~ 1 )
ascertainable
interaction
569
potential
without data from excited vibrational states.
is
It is
nonetheless possible to estimate the dissociation energy from the values
of
kg-
derived
above.
Lennard-Jones 6-12 form:
Assume
that the radial interaction is of the
34
V(r) = e[(
re/r)12
Expansion of V(r) in a Taylor
(11-14)
- 2(ra/r)6
series
about
r = re
and
equating
the
quadratic term to k^/2 gives
k^
= 72£/r£
(11-15)
It still remains to determine r e , the 'equilibrium'
centers
of
mass.
This
is
done
through
separation
the
of
the
vibration-rotation
interaction constant, o< e :
B e = B D + (1/2) °<e
o(e
where B e = h/8-rr2/^ r e 2 .
The
(11-16)
= 368^/^
value
of
re
(H-17)
obtained
from
equations
(11-16) and (11-17) allows calculation of the dissociation energy £ by
equation (11-15).
The values of £ obtained are listed in Table II-7.
This work represented the first measurements of a hydrogen
to
carbon
in
the
gas phase.
The study of OC-HCl is published in the
Journal of Chemical Physics, volume 74, pp 2138 - 2142, under the
'Microwave
rotational
interaction
potential
P. D. Soper,
spectrum,
of
the
hydrogen-bonded
A. C. Legon and W. H. Flygare.
spectrum,
H,1°F
title
molecular geometry and intermolecular
nuclear
spin
dimer
OC-HCl'
by
That of OC-HF is published
in the same journal, volume 74, pp 4944 - 4950,
rotational
bond
under
the
title
'The
- nuclear spin coupling, D
nuclear quadrupole coupling and molecular geometry
of
a
weakly
bound
35
dimer
of
carbon
monoxide
and
P. D. Soper and W. H. Flygare.
A
hydrogen
fluoride'
preliminary
by
A. C.Legon,
communication
on
these
dimers along with that of carbon monoxide with hydrogen bromide was also
published in the Journal of Chemical Physics, volume 73, PP 583
- 584,
under the title 'The rotational spectra of weakly bound dimers of carbon
monoxide and the hydrogen halides HX
(X=F,
CI,
Br)' by
A. C. Legon,
P. D. Soper, M. R. Keenan, T. K. Minton, T. J. Balle and W. H. Flygare.
36
CHAPTER III.
SEPARATION OF POLARIZATION EFFECTS BY USE OF-
MOLECULAR SYMMETRY:
THE CYANOGEN - HYDROGEN FLUORIDE
AND NITROGEN - HYDROGEN FLUORIDE COMPLEXES
A.
INTRODUCTION
Rotational spectroscopy can provide experimental information not
only
about
the
geometries
and interaction potentials of weakly bound
complexes, but also about the electrical changes which
formation.
For
example,
the
electrical
dipole
accompany
dimer
moment of HCN-HF is
greater than the sum of the dipole moments of the two components, giving
clear
evidence
(1980A)).
nuclear
of
electronic
rearrangement
(Legon
et al (1976) and
Another potential source of such information is the change in
quadrupole
coupling
constants
upon
complex
formation.
particularly simple case is that where the quadrupolar nucleus
A
lies
on
the symmetry axis of an axially symmetric molecule which forms a complex
which is also axially symmetric.
The quadrupole coupling constant "JC is
related to the field gradient, qz, along the symmetry axis by:
96= -eQqz/h
(III-1)
where e is the electronic charge, Q is the nuclear
moment
and
q2 = ^d 2 V/c>z 2 ^ .
relate
the
observed
corresponding
change
change
observed
quadrupole
It is therefore possible, in theory, to
in ~)C upon
complex
formation
with
in the electronic structure of the complex.
procedure is rendered considerably more difficult
the
electric
in
practice
a
Thi3
because
value of /£ is averaged over the zero-point vibrations of
the complex, which can be
considerably
different
from
those
in
the
37
isolated molecule. What is in faot observed is a combination of both of
these effects.
fluoride
It is easy to imagine that the presence
molecule
near
a
cyanide
of
a
hydrogen
group will considerably modify the
electrical environment of the quadrupolar nitrogen nucleus and that this
could
responsible for any observed decrease in the magnitude of J^.
be
Unfortunately, Jt would be lower than O^g even in the
effects
because
of zero-point averaging.
absence
of
such
In such cases, "JC is related
to y^o by
; £ = (1/2)^o <3cos 2 y- l)
(III-2)
where the average is taken over the bending of the weak hydrogen bond if
one
assumes
that
the
vibrational
modes
of
the nitrogen-containing
component of the complex remain unchanged on dimer formation
y
and
where
is the angle between the instantaneous a axis of the complex and the
C-N bond axis.
assumed
to
be
In complexes where electrical changes may reasonably
insignificant,
vlbrationally averaged angle.
be
this analysis yields an estimate of the
This approach was applied
to
OC-HF
and
OC-HCl in the previous chapter.
The complexes of cyanogen (NCCN) and nitrogen (NN) with hydrogen
fluoride
were
chosen for study because their symmetry and the presence
of a quadrupolar nucleus at both ends of these molecules made it
that
these
effects
could
be separated to a certain extent.
indeed possible and allowed an estimation of
the
polarization
cyanogen and nitrogen components of these two complexes.
likely
This was
in
the
38
B.
EXPERIMENTAL
The spectrometer used in this study is described
Balle
et al (1980) and Balle and Flygare (1981).
in
detail
The gas mixtures used
consisted of roughly one percent each of hydrogen fluoride and
or
nitrogen
in
argon
with
Llnde.
The
cyanogen
a total pressure of 2.5 atmospheres.
cyanogen was supplied by Matheson, Inc.
in
and the
hydrogen
fluoride
The
by
isotopically-substituted cyanogen was prepared as follows:
equimolar amounts of KC1i*N and
KC15N
were dissolved in water.
Addition
of silver nitrate solution led to precipitation of silver cyanide, AgCN,
with fifty mole percent of each of the nitrogen isotopes.
the
After drying,
AgCN was heated in vacuo at 340 - 380 °C (Cook and Robinson (1935))
and the evolved cyanogen collected at liquid nitrogen temperature.
resulting
mixture contained fifty mole percent
mole percent each of
1l
isotopie
was
abundance
*NCC1l*N and
1
5NCC1^N.
supplied
The
1l
The
*NCC15N and twenty-five
nitrogen
of
ordinary
by Linde while the 1 ^N 1 ^N and
1
5N1^N
enriched samples were supplied by Prochem Isotopes.
For the J = 2^-1 transitions
complicated
spectra
of
NCCN-HF,
measurement
where
the
Doppler
phenomenon (Campbell (1981A and B)) is essentially eliminated.
This doubling made determination of
other
the
arising from the multiple nuclear interactions was
greatly simplified by operation at low frequencies,
doubling
of
transitions
the
hyperfine
structures
of
the
in NCCN-HF and of all the transitions of N2-HF quite
difficult.
Fortunately,
accessible,
and
its
the
greatly
accurate determination of the
J = 1<r-0
simplified
appropriate
transition
of
hyperfine
patterns
constants.
III-2, and III-3 show the J = 1«-0 transition of
1l, 1l<
N
Ng-HF
Figures
was
allowed
III-1,
N-HP, the J = 2«-1
JL
4.00
-3.00
-2.00
-1.00
V^
0.00
I
T
1.00
2.00
T
3.00
4.00
FREQUENCY
Figure III-l.
Hyperfine components in the J = 1^-0 transition of
14
N -HF.
10
J
JU
f M Jy
-3.00
-2.00
-1.00
0.00
AIflA
JUL
1.00
2.00
3.00
T
4.00
1
5.00
FREQUENCY
Figure I I I - 2 -
Hyperfine components i n the J = 2^-1 t r a n s i t i o n of 14N -HF.
o
r
-4.00
T
-3.00
-A- «-2.00
A
i
-1.00
r
0.00
Z—j
1.00
I i j
1A
2.00
FREQUENCY
Figure I I I - 3 .
Hyperfine components of the J = 3<—2 t r a n s i t i o n of 14 NCC14N-HF.
T
3.00
"l
4.00
42
transition of
11
*N14N-HF
and
These
spectra
respectively.
the
J = 3«-2
have
transition
been
constants in Tables III-9 and 111-10.
1
of
calculated
by
The components of
%CG1l*N-HF
use
the
of
the
hyperfine
structure typically had HWHM of 5 kHz.
C.
SPECTROSCOPIC CONSTANTS
The appropriate Hamiltonian for the cyanogen - hydrogen fluoride
and
nitrogen
-
hydrogen
H = HR + H s s + HQI + HQ2«
line
centers
formed
complexes
A S was the ease for
consists of four terms:
OC-HCl
and
OC-HF,
the
of the various R-branch transitions for the two complexes
patterns
asymmetric
fluoride
characteristic
rotors
population
molecules
states
with
slightly
rotational part of the Hamiltonian, HR, is therefore assumed to be
that
a linear molecule.
in
or
The
for
no
linear
K>0.
appropriate
with
of
It predicts the unperturbed center
frequencies of the rotational spectra to be at
V 0 = B0(J+1) + Dj(J+1)3
(IH-3)
where Bg is the rotational constant, Dj is
constant
the
centrifugal
distortion
and J is the rotational angular momentum quantum number of the
lower level of the R-branch transition.
The
other
three
terms
arise
from nuclear interactions and serve to complicate the spectra.
The direct interaction of the nuclear magnetic dipole moment
of
the hydrogen nucleus with that of the fluorine nucleus gives rise to the
spin-spin term of the Hamiltonian, H s s .
above
in
equation
(II-3),
Its
specific
form
where I H = 1/2 and Ip = 1/2.
terms arise from the interaction of the electric quadrupole
is given
The last two
moments
of
43
Table III-1: Observed and calculated frequencies in MHzfor the hyperfine components in rotational transitions of
14
NCC1UN-HF.
J' F-i' F2'F3' P* <~<J
Ft
F2 F3 F
observed calculated
frequency frequency
2 2.5
2 2.5
2 1 2
3 2 3
1 1.5 1 0 1
1 1.5 2 3 2
4778.7904 4778.7891
4778.7917
2 2.5
2 1.5
3 3 3
2 2 2
1 1.5 1 1 2
1 0.5 1 1 1
4779.6560 4779.6578
4779.6611
2 2.5
2 2 2
1 1.5 1 1 1
4779.6959 4779.6806
2 1.5
2 2.5
2 3 3
2 3 3
1 0.5
1 1.5
2 1.5
2 2.5
1 2 2
3 4 4
1 0.5 0 1 1
1 1.5 2 3 3
4780.1438 4780.1421
4780.1465
2 2.5
2
1 1.5 1 2
1
4780.2314 4780.2356
2 2.5
3 2 3
I 1.5 2
1 2
4780.2572 4780.2487
2
1.5
2 3 4
1 0.5
1 2 3
4780.4095 4780.4147
2 2.5
2 1.5
2 2.5
2 3 4
1 2 3
3 4 5
1 1.5 1 2 3
0.5 0 1 2
1.5 2 3 4
4780.4251
4780.4328 4780.4292
4780.4298
2 1.5
2 2 3
1.5 2 2 2
4780.4747 4780.4699
2 2.5
2 2 3
1
1.5
1 1 2
4780.5139 4780.5189
2 2.5
3 3 4
1
1.5 2 2 3
4780.5400 4780.5340
2 1.5
2 2.5
1 1 2
3 4 3
1
1
0.5 1 0 1
1.5 2 3 4
4780.5743 4780.5688
4781.2432
2 1.5
2 2.5
1 2 1
2 3 2
1
1
0.5 0 1 2
1.5 1 2 3
4781.2439 4781.2457
4781.2463
2
1.5
2 3 2
1
0.5
1 2 3
4781.2537 4781.2533
2 2.5
2 2 1
1
1.5
1 1 0
4781.3425 4781.3392
2 2.5
3 3 2
1
1.5 2 2 1
4781.3523 4781.3454
2 2.5
2 2.5
3 2 3
2 1 2
1
1
1.5 2 3 3
1.5 1 2 2
4781.5519 4781.5564
4781.5592
2
2
1
0.5
1 2 2
4781.5782 4781.5719
1.5
1 2
1 2
1 2 2
1 2 2
4780.1266
4780.1334
4780.1418
44
Table III-1 (continued)
p
l ' F 2 'F3' F' ^ - J
F-|
F 2 F3 F
observed calculated
frequency frequency
3
3
3
2.5
3.5
3.5
2 2 3
4 4 5
3 3 4
2 1.5
2 2.5
2 2.5
1 2 3
3 4 5
2 3 4
7168.5780
7168.5842
7168.5887
7168.5937
3
3
3
2.5
3-5
2.5
3 3 3
4 4 4
2 2 2
2 2.5
2 2.5
2 1.5
2 2 3
3 3 4
1 1 2
7169.5410
7169.5285
7169.5349
7169.5432
3
3
3.5
3.5
3 2 2
4 3 3
2 2.5
2 2.5
2 1 1
3 2 2
3
3
3
3.5
3.5
2.5
3 4 3
4 5 4
2 3 2
2 2.5
2 2.5
2 1.5
2 3 2
3 4 3
1 2 1
7170.1470
7170.1414
7170.1473
7170.1476
3 2.5
3 3.5
3 2.5
3 3 3
4 4 4
2 2 2
2 1.5
2 2.5
2 1.5
2 2 2
3 3 3
2 1 1
7170.1981
7170.1882
7170.1941
7170.1968
3 2.5
3 2.5
3 3.5
3 3.5
3
2
3
4
4 4
3 3
4 4
5 5
2 1.5
2 1.5
2 2.5
2 2.5
2
1
2
3
3 3.5
3 2.5
3 3.5
3 2 3
2 1 2
4 3 4
2 2.5
2 1.5
2 2.5
2 1 2
1 1 1
3 2 3
7170.3360
7170.3332
7170.3382
7170.3390
3 3.5
3 2.5
3 3.5
3 4 5
2 3 4
4 5 6
2 2.5
2 1.5
2 2.5
2 3 4
1 2 3
3 4 5
7170.4391
7170.4385
7170.4392
7170.4411
3
3
3
3.5
3.5
2.5
3 3 4
4 4 5
2 2 3
2 2.5
2 2.5
2 1.5
2 2 3
3 3 4
2 2 4
7170.4977
7170.4902
7170.4972
7170.5022
3
3
3.5
3.5
3 3 2
4 4 3
2 2.5
2 2.5
2 2
3 3
1
2
3
3
3
2.5
3.5
3.5
2 1 2
4 3 4
3 2 3
2 1.5
2 2.5
2 2.5
1 2
3 4
2 3
2
4
3
3
3
3
3
2.5
3.5
3.5
2.5
2 1 1
4 3 3
3 2 2
3 2 2
2 1.5
2 2.5
2 2.5
2 1.5
1
3
2
2
1
3
2
2
2
4
3
3
3
3
3.5
3.5
4 3 3
3 2 2
2 2.5
2 1.5
3 3
2 2
3
2
3 3
2 2
3 3
4 4
7169.6780
7170.2786
7170.5520
7171-7458
7172.0494
7172.7055
7169.6711
7169.6795
7170.2783
7170.2801
7170.2814
7170.2840
7170.5532
7170.5605
7171.7472
7171.7489
7171.7507
7172.0423
7172.0426
7172.0429
7172.0434
7172.7018
7172.7027
45
Table III-2: Observed and calculated frequencies in MHz'
for the hyperfine components in rotational transitions of
14
NCC 15 N-HF.
J'
V
F 2 ' F'
2
2
2.5
2.5
3
2
2
1.5
2
*-
J
*1
F2 F
observed c a l c u l a t e d
frequenoy frequency
3
2
1.5
1.5
2
1
3
2
4775.1995
4775.1966
4775.2003
2
2
0.5
1
2
4775.2199
4775.2102
1.5
1
1
0.5
0
1
4775.1786
4775.1855
2
2
2.5
2.5
2
3
1
2
1.5
1.5
1
2
0
1
4775.4350
4775.4327
4775.4378
2
1.5
1
0
1.5
2
1
4775.4851
4775.4900
2
1.5
2
2
1.5
1
1
4776.5377
4776.5381
2
2.5
2
2
0.5
1
1
4776.5876
4776.5947
2
2.5
3
3
1.5
2
2
4776.6118
4776.6093
2
1.5
2
3
0.5
1
2
4776.6818
4776.6848
2
2
2.5
2.5
2
3
3
4
1.5
1.5
1
2
2
3
4776.7011
4776.6943
4776.6993
3
3
3
3
2.5
3.5
3.5
2.5
2
4
3
3
2
4
3
3
2
2
2
2
1.5
2.5
2.5
1.5
1
3
2
2
2
4
3
3
3
3
3.5
3.5
3
4
2
3
2
2
2.5
2.5
2
3
1
2
7164.6491
7164.6383
7164.6456
3
2.5
3
3
2
1.5
2
2
7164.8609
7164.8566
3
3
3.5
2.5
4
2
4
2
2
2
2.5
1.5
3
1
3
1
7164.8785
7164.8771
7164.8772
3
3
3
3
2.5
2.5
3.5
3.5
3
2
3
4
4
3
4
5
2
2
2
2
1.5
1.5
2.5
2.5
2
1
2
3
3
2
3
4
7163.3717
7164.9164
7163.3704
7163.3744
7163.3767
7163.3820
7164.9224
7164.9239
7164.9260
7164.9288
46
Table I I I - 3 : Observed and calculated frequencies in MHz
for the hyperfine components in rotational transitions of
15
NCC%-HF.
*1
F2 F
observed calculated
frequency frequency
3 3
2 2
1.5
1.5
2 3
1 1
4671.6012
4671.6025
4671.6059
2
3
1
2
1.5
1.5
1 0
2 1
4671.8227
4671.8166
4671.8211
1.5
2
2
1.5
1
1
4672.8180
4672.8187
2
2.5
2
2
0.5
1
1
4672.8634
4672.8698
2
1.5
2
3
0.5
1 2
4672.9557
4672.9515
2 2.5
2 2.5
2 3
3 4
1.5
1.5
1 2
2 3
4672.9629
4672.9601
4672.9646
3 2.5
3 3.5
3 3.5
3 2.5
2 2
4 4
3 3
3 3
2
2
2
2
1.5
2.5
2.5
1.5
1
3
2
2
2
4
3
3
7007.9239
7007.9205
7007.9241
7007.9262
7007.9309
3
3
3
3
3 4
2 3
3 4
4 5
2
2
2
2
1.5
1.5
2.5
2.5
2
1
2
3
3
2
3
4
7009.3312
7009.3272
7009.3285
7009.3305
7009.3330
J'
"V f y
2
2
2.5
1.5
2
2
2.5
2.5
2
2.5
2.5
3.5
3.5
F'
*- J
Table I I I - 4 : Observed and calculated frequencies in MHz
for
the hyperfine components in rotational transitions of
15
NCC15N-HF.
J' F-|» F'
<-
J FT
F
observed calculated
frequency frequency
2
2
2
1.5
2.5
2.5
2
3
2
1 0.5
1 1.5
1 1.5
1
2
1
4668.8675
4668.8637
4668.8688
4668.8637
2
1.5
1
1 0.5
1
4668.9813
4668.9817
2
1.5
2
1
1.5
2
4668.7883
4668.7929
2
1.5
1
1 0.5
0
4668.8034
4668.8047
3
2.5
3
2
2.5
3
7003.2034
7003.1990
3
2.5
2
2
1.5
1
7003.2614
7003.2631
3
3
3
3.5
2.5
3.5
3
3
4
2
2
2
2.5
1.5
2.5
2
2
3
7003.2750
7003.2749
7003.2749
7003.2777
3 2.5
2
2
1.5
2
7003.3809
7003.3811
48
the two nitrogen nuclei ( 1 = 1 ) with the different field gradients about
each.
Its
form
may
be
found
Since 1 5 N has no
in equation (II-1).
nuclear quadrupole moment, substitution of this isotope
one of the quadrupole terms for
1l
*NCC15N-HF, 1 5NCC%-HF,
15 1l|
N
for
N-HF while the doubly-substituted
15
NCC15N-HF and
1
1,
1^N
drops
*N 1 5N-HF,
5N15N-HF
and
require
only H S s to analyze their hyperfine structures.
For each of the molecular and isotopie species
form
of
the
Hamiltonian
wa3
the
appropriate
used to evaluate matrix elements in the
coupled basis set:
J + I H = F^,
Ip + "F-i = F*2, T N 1 + "F2 =13, T N 2 + F3 s T
(III-4)
The resulting matrices were diagonalized to give
the
energies
of
the
different
corresponding
to
the
hyperfine
states.
The
frequencies
various hyperfine transitions were then added
equation (III-3) to give the spectra.
to
those
calculated
The various constants were fitted
by a non-linear least squares analysis which relied on the
diagonalization.
The
observed
calculated from the derived
11|
NCC15N-HF,
and
III-4
15
respectively.
frequencies
for
transition
constants
NCC 14 N-HF, and
15
*N1I,N-HF,
are
full
frequencies
compared
which
the
observed
14N15N-HF,
and
*NCC1^N-HF,
calculated
^N^N-HF,
and
1
transition
5N15N_HF
derived
are
For cases
separation of calculated frequencies approaches or falls
below the experimental resolution all assigned frequencies
The
those
1i
for
listed in Tables III-5, III-6, III-7, and III-8 respectively.
in
and
matrix
NCC15N-HF in Tables III-1, III-2, III-3,
The
1l
by
values
of
the
rotational
constant
are
listed.
B 0 , the centrifugal
distortion constant Dj, the two quadrupole coupling constants ^£(1) and
Table III-5: Observed and calculated frequencies in MHzfor hyperfine components in rotational transitions of
1 4
V N-HF.
3 ' F« < - J
3 F
J»
V V
1
1
1
1
1
1
1.5
1.5
1.5
1.5
1.5
1.5
2
2
2
2
2
2
2
2
2
2
2
2
1
1
1
1
1
1
0
0
0
0
0
0
0.5
0.5
0.5
0.5
0.5
0.5
1 2
1 2
1 1
1 1
1 1
1 0
2
1
2
1
0
1
1
1.5
1
1
0
0
0.5
0
1
1 0.5
1 0.5
1 0.5
1 0.5
1 0.5
1
1
1
1
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0.5
0.5
0.5
0.5
0.5
1
1
1
1.5
1.5
1.5
2
2
2
2
2
2
3
3
3
0
0
0
1
1.5
1
1
2
1
1
1
1
1
1.5
1.5
1.5
1.5
1.5
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
1
1
1
1
1
1.5
1.5
1.5
1.5
1.5
1
1
1
1
1
1
1
0.5
0.5
1
1
1
1
1
1
1
1
1
1
1
F
p
1
F2
F
observed c a l c u l a t e d
frequency frequency
6388.2256
6388.2231
1
6388.2256
6388.2241
1 2
1 2
1 1
1 1
1 0
2
1
2
1
1
6388.9200
6388.9094
0.5
0.5
0.5
1 2
1 2
1 1
3
2
2
6388.9332
6388.9369
0
0.5
0
1
2
6388.9477
6388.9480
0
0
0
0
0
0.5
0.5
0.5
0.5
0.5
1 2
1 2
1 1
1 1
1 0
3
2
2
1
1
6388.9801
6388.9841
1
1
1
1
1
0
0
0
0
0
0.5
0.5
0.5
0.5
0.5
1 2
1 2
1 1
1 1
1 0
2
1
2
1
1
6389.1259
6389.1270
1
1
1
1
0
0
0.5
0.5
0
0
1
1
2
0
6389.1589
6389.1642
0.5
0.5
0.5
0.5
0.5
0.5
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
0
0
0
0
0
0
0.5
0.5
0.5
0.5
0.5
0.5
1 2
1 2
1 2
1 1
1 1
1 0
3
2
1
2
1
1
6389.1658
6389.1715
0.5
0.5
0.5
0.5
0.5
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
0
0
0
0
0
0.5
0.5
0.5
0.5
0.5
1 2
1 2
1 1
1 1
1 0
2
1
2
1
1
6390.3601
6390.3591
50
Table I I I - 5 (cent
J ' F / F 2 ' F 3 ' F' < - J
Fi
F2 F3 F
observed calculated
frequency frequency
1
1.5
1 2
2
0
0.5
0
1
1
6390.3968
6390.3971
1
1
1.5
1.5
2
2
3
3
3
3
0
0
0.5
0.5
1
1
2 2
1 2
6390.4100
6390.4078
1 0.5
1 0.5
1 0.5
0
0
0
1
1
1
1
1
1
0
0
0
0.5
0.5
0.5
1
1
1
? 3
2 2
1 2
6391.0881
6391.0893
1
1.5
1 2
3
0
0.5
0
1
2
6391.1213
6391.1210
1
1.5
2
3
4
0
0.5
1
2
3
6391.1340
6391.1317
1 0.5
1 0.5
1 0.5
1 0.5
1 0.5
1 0.5
0
0
0
0
0
0
1
1
1
1
1
1
2
2
2
2
2
2
0
0
0
0
0
0
0.5
0.5
0.5
0.5
0.5
0.5
1 2 3
1 2 2
1 2 1
1 1 2
1 1 1
1 0 1
6391.1486
6391.1476
1
1
1
1
1
1.5
1.5
1.5
1.5
1.5
2
2
2
2
2
1
1
1
1
1
2
2
2
2
2
0
0
0
0
0
0.5
0.5
0.5
0.5
0.5
1 2 2
1 2 1
1 1 2
1 1 1
1 0 1
6391.8397
6391.8400
1
1.5
1 2
1
0
0.5
0
6391.8391
6391.8448
1
1
1
1
1
1
0.5
0.5
0.5
0.5
0.5
0.5
1
1
1
1
1
1
2
2
2
2
2
2
1
1
1
1
1
1
0
0
0
0
0
0
0.5
0.5
0.5
0.5
0.5
0.5
1 2 2
1 2 1
1 1 2
1 1 1
1 1 0
1 0 1
6391.8821
6391.8742
1
1
1
1
1.5
1.5
1.5
1.5
2
2
2
2
1
1
1
1
1
1
1
1
0
0
0
0
0.5
0.5
0.5
0.5
1
1
1
1
2 2
2 1
1 2
0 1
6393.7728
6393.7821
1
1
1.5
1.5
1 0
1 0
1
1
0
0
0.5
0.5
0
0
1 2
1 0
6393.8086
6393-8025
1
1
1
1
1
1.5
1.5
1.5
1.5
1.5
2 3
2 3
2 3
2 3
2 3
2
2
2
2
2
0
0
0
0
0
0.5
0.5
0.5
0.5
0.5
1 2 3
1 2 2
1 2 1
1 1 2
1 0 1
6393.8086
6393.8076
1
1
51
Table I I I -5 (continued)
J'
V V
2
2.5
2
2
1
1
1.5
1 2
1
12778.4469 12778.4509
2
2
2.5
2.5
3
2
3
2
4
3
1
1
1.5
1.5
2 3
1 2
4
3
12778.9955 12778.9950
12779.0022
2
2
2
1.5
2.5
2.5
2
2
3
3
1
2
2
2
3
1
1
1
1.5
1.5
1.5
2 1
1 0
2 3
1
1
2
12779.2813
12779.2883 12779.2857
12779.2883
2
2
2.5
1.5
3
2
3
2
3
2
1
1
0.5
0.5
1
1
1
1
2
1
12780.2321 12780.2340
12780.2371
2
2
2
2
1.5
2.5
1.5
2.5
2
2
1
3
3
3
2
4
3
3
2
4
1
1
1
1
0.5
1.5
0.5
1.5
1 2
1 2
0 1
2 3
2
2
1
3
13680.7536
12780.7617 12780.7618
12780.7621
12780.7664
2
1.5
2
3
4
1
0.5
1 2
3
12781.0602 12781.0619
2
2
2
2.5
1.5
2.5
2
1
3
3
2
4
4
3
5
1
J
1
1.5
0.5
1.5
1 2
0 1
2 3
3
2
4
12781.0720
12781.0777 12781.0760
12781.0766
2
2
1.5
2.5
2
2
2
2
3
3
1.5
1.5
2
1
2
1
3
2
12781.1726 12781.1745
12781.1752
2
2.5
3
3
4
1.5
2
2
3
12781.1947 12781.1898
2
1.5
2
3
2
1
0.5
1 2
3
12781.9806 12781.9741
2
1.5
2
2
1
1
1.5
2
2
1
12782.0394 12782.0450
2
2
2.5
2.5
2
3
2
3
1
2
1
1
1.5
1.5
1 1
2 2
0
1
12782.0764 12782.0716
12782.0776
2
2
2
1.5
2.5
2.5
1
3
2
0
4
3
1
3
2
1
1
1
0.5
1.5
1.5
0 1
2 3
1 2
1
3
2
12782.3038
12782.3073 12782.3100
12782.3128
2
1.5
2
1
2
1
0.5
1
2
2
12782.3261 12782.3250
2
1.5
2
1
0
1
1.5
1
1
1
12783.5226 12783.5302
2
2.5
2
1
2
1
1.5
1
1
2
12784.1391 12784.1402
2
2.5
3
2
3
1
1.5
2
2
3
12784.1676 12784.1590
2
2
2.5
2.5
3
2
2
1
1
0
1
1
0.5
0.5
1
1
1
1
2
1
12784.7484 12784.7469
12784.7531
F
3 ' F' « - J
FT
F2
F
3 F
observed c a l c u l a t e d
frequency frequency
52
Table III-6: Observed and calculated frequencies in MHz
for hyperfine components in rotational transitions of
%15N-HF.
J'
F
r
F2' p i
<-
J
F
1
P2 F
observed c a l c u l a t e d
frequency frequency
1.5
1.5
2
2
2
2
0
0
0.5
0.5
1
1
2
1
6354.1480
6354.1522
0.5
1
1
0
0.5
0
1
6354.1586
6354.1586
1.5
1.5
1.5
1
1
1
1
1
1
0
0
0
0.5
0.5
0.5
1
1
1
2
1
0
6354.1877
6354.1844
0.5
0.5
1
1
2
2
0
0
0.5
0.5
1
1
2
1
6355.6153
6355.6122
1.5
1
2
0
0.5
0
1
6355.6495
6355.6519
1.5
2
3
0
0.5
1
2
6355.6640
6355.6634
0.5
0.5
0.5
0
0
0
1
1
1
0
0
0
0.5
0.5
0.5
1
1
1
2
1
0
6355.6943
6355.6940
1.5
1
0
0
0.5
0
1
6357.8922
6357.8919
1.5
1.5
1.5
2
2
2
1
1
1
0
0
0
0.5
0.5
0.5
1
1
1
2
1
0
6357.8922
6357.8931
2
2
2.5
2.5
3
2
3
2
1
1
1.5
1.5
2
1
3
2
12708.8987 12708.8996
12708.9034
2
2
2
1.5
2.5
2.5
1
2
3
2
3
4
1
1
1
0.5
1.5
1.5
0 1
1 2
2 3
12710.5006
12710.5055 12710.5077
12710.5026
53
Table I I I - 7 : Observed and calculated frequencies in MHz
for
hyperfine components in rotational transitions of
15 1I|
N N-HF.
j» FT' F 2 ' F»
«- J
FT
F2 F
observed c a l c u l a t e d
frequenoy frequenoy
6231.7072
6231.7099
1.5
2
2
0
0.5
1
2
1.5
2
2
0
0.5
1
1
0.5
1
1
0
0.5
0
1
6231.7165
6231.7160
1.5
1.5
1.5
0.5
1 1
1 1
1 1
1 2
0
0
0
0
0.5
0.5
0.5
0.5
1 2
1 1
1 0
1 2
6231.7414
6231.7405
6233.0885
6233.0873
0,5
1
2
0
0.5
1 1
1.5
1
2
0
0.5
0
1
6233.1241
6233.1250
1.5
2
3
0
0.5
1 2
6233.1382
6233.1360
0.5
0.5
0
0
1
1
0
0
0.5
0.5
1 2
1 1
6233.1647
6233.1651
0.5
0
1
0
0.5
1 0
1.5
1
0
0
0.5
0
1
6235.2388
6235.2386
2
2
2
3
1
1
1
3
0
0
0
1
0.5
0.5
0.5
1.5
1 2
1 1
1 0
2 3
6235.2388
6235.2398
2
1.5
1.5
1.5
2.5
12463.9816 12463.9841
2
2.5
2
2
1
1.5
1 2
12463.9876
2
1.5
2
3
1
0.5
1 2
12465.4916 12465.4884
2
2
2
1.5
2.5
2.5
1 2
2 3
3 4
1
1
1
0.5
1.5
1.5
0 1
1 2
2 3
12465.4954
12465.5000 12465.4973
12465.5020
Table III-8: Observed and calculated frequencies in MHz
for hyperfine components in rotational transitions of
15 15
N N-HF.
J' FT' F»
*-
J
F
observed calculated
frequency frequency
1
6202.0990
6202.0999
1 1.5 1
0 0.5 0
6202.1524
6202.1522
1 1.5 2
0 0.5
1
6202.1641
6202.1627
1 0.5 0
0 0.5
1
6202.2562
6202.2568
2 1.5 2
1 1.5 2
12403.8523 12403.8583
2 1.5 1
1 0.5 0
12403.8738 12403.8688
2
2
2
1 0.5
1 1.5
1 1.5
12403.9211
12403.9229 12403.9211
12403.9256
1 0.5
1.5
2.5
2.5
1
2
2
3
F
1
0 0.5
1
1
2
55
X ( 2 ) , and the spin-spin constant S ^ for NCCN-HF appear in Table III-9.
The
constants
for
N2-HF
are listed in Table 111-10.
chapter the index *1' refers to
fluorine
while
the
index
the
nitrogen
^NCC1^N-HF
was
away
NCCN-HF,
only
in
the
transitions.
In
be
applied
to
both
the
the
of
transitions
as
of
explaining
may
be
and
the other three isotopie species of NCCN-HF
J = 2<r~ 1 transition.
adequate job
the
case
J = 3^2
the least-squares analysis of the hyperfine structure was
to
from
the hyperfine structure well enough resolved to enable
the least-squares analysis to
J = 2<-1
further
'2' refers to the nitrogen which is closer.
Among the various isotopie species of
1
Throughout this
only
Nonetheless, the derived constants do an
the
seen
applied
hyperfine
through
comparison
III-1,
the
higher
of the observed and
J = 3<-2
Similarly,
J = 1<-0 transition was used to fit the hyperfine
the
Tables
of
calculated values for
only
in
structure
constants of the various isotopie species of
constant
and
only
transitions.
the
line
centers
This complex also showed
III-2,
N2-HF.
were
fitted
satisfactory
and
These
for
III-3.
were
held
the J = 2<-1
agreement
between
the observed and calculated frequencies as may be seen by examination of
Tables III-5, III-6, III-7, and III-8.
transitions
for
each
The
line
centers
the
two
molecular and isotopie species were then used to
give Bg and Dj values according to equation (III-3).
in
of
The
values
shown
brackets in Tables III-9 and 111-10 are the standard errors from the
least-squares analysis.
complexes
the
three
Note that within the isotopie
hyperfine
essentially isotopically
ranges
constants, /£(1), j£(2),
invariant, although the R v a l u e s
of
both
and Stjp, are
are
better
determined in the slngle-quadrupole spectra and Sjjp is better determined
in the spectra where it is the sole hyperfine interaction.
56
Table III-9: Spectroscopic constants for
species of N(1)CCN(2)-HF.
Bga
(MHz)
isotopie
species
1
jNCC%-HF
™NCC15N-HF
15
1
NCC11|N-HF
5NCC15N-HF
a.
D.
four
isotopie•
X(D
(MHz)
X(2)
(MHz)
S^
(kHz)
-4.56(5)
-4.65(1)
-
-4.28(5)
-4.21(1)
-
110(10)
117 (8)
106(11)
118 (2)
Dja
(kHz)
1195.0616
1194.1515
1168.2207
1167.2187
0.34
0.36
0.41
0.34
The estimated error in the center frequencies of the
two transitions is 2 kHz. If all of this error is
assigned to B 0 , then its error is 1.2 kHz.
If the
error is assigned to Dj, its error is 0.08 kHz.
MOLECULAR GEOMETRIES
As was remarked above, the observed spectra of
hydrogen
fluoride
K>0
are
cyanogen
-
and nitrogen - hydrogen fluoride complexes are those
of linear molecules or slightly asymmetric rotors for
with
the
observed.
which
no
states
The geometries of NCCN-HF and N2-HF will be
considered in turn.
A linear geometry for NCCN-HF is reasonable in light of the fact
that collinearity has been unambiguously established for other cyanide hydrogen fluoride
complexes, namely
CH3CN-HF
(Bevan
(1980)).
It is possible to calculate
using
this
et
al
(1980A)),
upon
complex
particularly good
calculated,
a
(CH3)3CCN-HF
series
is
assumption,
relatively
111-11.
The
fluoride
formation.
atom because of its low mass.
in Table
and
(Legon
of
et
al
(1980A)),
(Georgiou
et al
r0(N-F) distances
linear geometry by assuming that the structures of cyanogen
(Morino et al (1968)) and hydrogen
unchanged
HCN-HF
the
(Guelachvili
Although
value
of
the
B0,
(1976)) are
latter
from
is
which
not
r0
a
is
insensitive to the position of the hydrogen
Values of r0(N-F) for NCCN-HF
are
given
excellent consistency in the values of r0(N-F)
57
Table 111-10: Spectroscopic constants for four
species of N(1)N(2)-HF.
Isotopie
species
1
fN l4 N-HF
1
%15N-HF
15 14
N N-HF
N N-HF
15 15
BQa
(MHz)
3195.3534
3177.7361
3116.4771
3101.1081
Dja
(kHz)
%(l)
(MHz)
%{Z)
(MHz)
isotopie
Sm
(kHz)
17.2 -4.91(14) -4.75(14) 107(6)
17.1 -4.978(3)
115(5)
16.0
-4.697(2) 110(3)
16.0
105(1)
a. The estimated error in the center frequencies of the
two transitions is 2 kHz. If all of this error is
assigned to Bg, then its error is 1.5 kHz. If the
error is assigned to D j , its error is 0.25 kHz.
within the isotopie range of NCCN-HF also
lends credence
to the
assertion that the equilibrium geometry is linear.
Further evidence in favor of this linear geometry comes from the
hyperfine
constants. The 1^N quadrupole coupling constants are similar
to those in other molecules where the nitrogen atom lies on the symmetry
axis of an axially symmetric molecule, eg CH3CN (Kukolich et al (1978))
and HCN (Bhattacharya and Gordy
(1960)).
Recall that the
spin-spin
coupling constant projects in the same manner as the quadrupole coupling
constant, ie
SHP = (1/2) SHpO ^3cos 2 cV- 1^
(IH-5)
where 0 is the instantaneous angle between the H-F bond and the a
Inertial
axis of the complex. If one assumes that the value of Sipr0 is
unchanged from that in free HF ~ an assumption
which gives an upper
limit on Y — the value of a is found to be 20.1 degrees in NCCN-HF.
This value is comparable to those in HCN-HF (Buxton et al (1980)), OC-HF
(see above), and
Ar-HF (Keenan et al (1981)). As in those cases, the
58
Table 111-11: Values of
species of NCCN-HF.
rg(N-F)
for
several
isotopie species
isotopie
rg(N-F)(A)
%CC14N-HF
NCC15N-HF
1
5NCC%-HF
1
5NCC15N-HF
2.8615
2.8616
2.8613
2.8615
14
small value of a indicates that the
fluorine
and
nitrogen
atoms
and
hydrogen
is
atom
lies
between
the
restricted in its motion by the
relatively tight nature of the hydrogen bond.
The
conclusion
is
then
that NCCN-HF is linear with the atom order as shown.
Although no states of
impossible
K>0
were
observed
for
N2-HF,
it
is
to reproduce the observed rotational constants of all of the
isotopie species by assuming a linear geometry.
equilibrium
geometry
is
linear
but
that
It is likely
bending
of
that
the
the
nitrogen
component in the complex is more significant than is that of cyanogen in
NCCN-HF.
The coordinates used in the following analysis are the same as
those shown in Figure II-3, where nitrogen takes
monoxide.
Although
0 ,
the
line connecting the centers of
the
place
of
carbon
angle of the nitrogen component with the
mass
of
N2
and
HF,
depends
on
the
isotopie species, it is possible to fit this angle and r c m , the distance
between the centers of mass, while holding the N-N and H-F bond
fixed
at
their
values
in
the
free
molecules
lengths
(Bendtsen (1974) and
Guelachvili (1976)).
The result is ^ = 1 2 degrees and
This
be used in the quadrupole coupling analysis below.
geometry
will
r c m = 3.5747 A.
It is also possible to estimate fi by use of equation (III-2).
value
of
the
-4.838 MHz.
two
nitrogen
The mean
quadrupole coupling constants in N2-HF is
Using the free nitrogen value of /^N = ~5«5 MHz
estimated
59
from
nuclear
librations
quadrupole
resonance
(Brookeman
* = 16 degrees.
et
The
studies of the solid corrected for
al
(1971)),
of a
value
this
equation
gives
found from the spin - spin coupling
constant in N2-HF according to equation (III-5)
is
25.1 degrees.
The
value of a indicates that the hydrogen lies between the nitrogen
small
and fluorine atoms, as it does in NCCN-HF.
NN-HF
is
linear
The conclusion is then
that
at equilibrium with the atom order as shown, but that
significant bending of the complex
occurs
in
the
ground
vibrational
state.
E.
INTERPRETATION OF QUADRUPOLE COUPLING CONSTANTS
The values of
the
two
nitrogen
nuclear
quadrupole
coupling
constants in free cyanogen must be equal to each other on the grounds of
symmetry.
Suoh is also true for the constants in free nitrogen.
complexes
values yC{-\)
the
= -4.65 MHz
N(1)CCN(2)-HF are clearly not equal.
%{£)
= -4.697 MHz
be
shown
for
below
In the
and /£(2) = -4.21 MHz
The values pC(1)
= -4.978 MHz
N(1)N(2)-HF also differ significantly.
that
the
observed
for
and
It will
difference
of
/£(1) - /£(2) = -0.281 MHz for N2-HF is exact and that the difference of
-0.44 MHz for NCCN-HF is a lower limit.
and
Polarization
of
the
cyanogen
nitrogen components of the two complexes must be invoked to explain
these differences.
It was remarked at the beginning of
analysis
of
electrical
changes
in
this
chapter
zero-point
the
absolute
averaging.
magnitude
of
proper
complex formation from quadrupole
coupling constants is made difficult because of the
in
that
concurrent
changes
The effect of such averaging is to decrease
the
observed
constant
through
what
is
60
essentially a projection effect.
In N2-HF the projection angles must be
identioal for both of the nitrogen atoms.
/L(1)
is
greater
than
that
of
In NCCN-HF the
"X-iZ).
If
magnitude
one assumes the electrical
properties of cyanogen to be unchanged and attributes these
to
vibrational
averaging,
then
the
nitrogen
hydrogen bond must be bending over a smaller
which
is
participating
in the bond.
further
angle
differences
away from the
than
the
nitrogen
This is quite unreasonable since
the effect of the bond should be in exactly the opposite direction:
extra
mass
the
associated with N(2) should serve to decrease the amplitude
of its bending relative to the free N(1). This means not only that
observed
difference
must
observed
difference
for
equilibrium
of
value
have
electrical
cyanogen
must
the
origins, but also that the
be
a
lower
limit
for
the
since bending should decrease the magnitude of /£(1)
relative to that of %{2)
within the complex.
There are a number of possible origins of the electrical effects
responsible
for
the
differences in the quadrupole coupling constants.
Recent measurements of rare-gas quadrupole coupling in
Kr-HF
(Campbell
et al (1980) and Buxton et al (1981A)) and Xe-HCl (Keenan et al (1980C))
suggest that charge transfer amounts to less than 1/1000 of an
in
these
cases.
A
comparable
electron
transfer in NCCN-HF or N2-HF would be
unmeasurable in these experiments.
A much more
gradients
at
the
significant
two
nearby HF molecule.
effect
is
the
difference
in
field
nitrogen nuclei of either complex caused by the
This
arises
in
two
ways;
the
first
is
the
difference in field gradients caused by the electrical properties of the
HF alone, and the second is induced polarization along the
nitrogen
molecule.
The
difference
of
-0.44 MHz
in
cyanogen
the
or
coupling
61
constants
in
difference
of
the
cyanogen
component
3.2 x 10™ SC cm"3
equation (III-1).
nitrogen component
in
of
NCCN-HF
a
the field gradients according to
The corresponding field gradient
of
corresponds' to
difference
in
the
is 2.0 x 101^ SC cm~3. Using a multipole
N2-HF
Table 111-12: Multipole moments of HF.
value
moment
source
1.826526 x 10- 18 SC cm
2.36 x 10-26 SC c m 2
1.699 x 10-34 s c c m 3
1.804 x 10-42 s c o m 4
Qm
XL
5
expta
exptb
ab initio0
ab initio0
a. Muenter and Klemperer (1970)
b. deLeeuw and Dymanus (1973)
c. Maillard and Silvi (1980)
expansion to describe the field gradient of the cylindrically
symmetric
HF molecule gives
q2°(n) = -
6^PT(COS©)
/y>4
where yO., Qm,il , ...
- 12Qm_P 2 (cos©) -_20JL P3(cos © ) - ... (III-6)
w5
are
the
permanent
moments
molecular
quadrupole,
octupole,
polynomial.
The argument of the oosine, 9, is the
assumed
make
to
...
WO
electric
dipole,
of HF and Pi(cos ©) is a Legendre
with the molecular axis.
angle
that
HF
is
For NCCN-HF it has been set
equal to the angle of 20.1 degrees calculated from Syp.
For
N2-HF
the
angles have been calculated from the geometry described above and differ
slightly for the two nitrogen atoms.
gradients
at
the
The main difference in
the
field
two nitrogen nuclei within each complex is caused by
62
the two different values of r, the distance from the HF center
to
N(n).
with the
known
multipole
moments
of
HF
the
nuclei
in
cyanogen
(see
for
0.18 x 1014 SC cm"3 for nitrogen in N2-HF.
this,
causes
Table
cyanogen
The
actual
111-12)
in
gives
NCCN-HF
effect
on
and
the
or nitrogen is considerably greater than
however, because of Sternheimer shielding.
HF
mass
Using the geometries described in the previous section along
Qz°(1) - qz°(2) = 0.34 x lO 14 SC cm"3
nitrogen
of
The field gradient of
a field gradient to be induced in the electronic clouds
about the nuclei.
The nitrogen nuclei actually experience
the
sum
of
the external and the induced field gradients:
qz<n) = q z °(nX 1 - S >
(IH-7)
Applying the Sternheimer shielding constant
al
(1977))
to
the
present
cases
gives
1.0 x 1011* SC cm""3 for cyanogen in NCCN-HF
for
nitrogen
in N2-HF.
% = -2 of HCN (Engstrom
and
a
total
of
difference
et
of
0.55 x 101i* SC cm~3
Both of these values correspond to only thirty
percent of the observed difference in their respective complexes.
The remaining differences in the
nitrogen
nuclei
within
either
field
gradients
(1955)).
may
theory
(Townes
the
two
complex can be related to the internal
polarization of the cyanogen and nitrogen components
Townes-Dailey
at
and
Dailey
by
means
of
the
(1949), Townes and Schawlow
It is assumed that the two nitrogen atoms
in
either
complex
be considered to be in a state of sp hybridization in which the spz
hybrid orbitals lie along the molecular axes and that electron transfer,
if
any,
occurs between p x orbitals.
electron about
the
The contributions of each kind of
nitrogen (px, p y , bonding spz, and non-bonding spz)
63
Table 111-13:
Contributions to the field gradients'
experienced by nitrogen nuclei in atoms of different
charges as used in
the
Townes-Dailey
theory
of
polarization.
orbital
contribution
px
py
-1/2
-1/2
bonding
s
Pz
1/2
1
1
occupancies
N+
N°
N~
1
1
1
2
1
1
to the field gradient are shown in Table 111-13.
in
units
orbital.
of
of
The contributions
in
each
type of orbital, multiplying by the appropriate
The
value
of
The occupancies used are also given in Table
-eQq210/h
negatively charged, neutral,
or
depends
on whether the nitrogen is
positively
-8.0 MHz, -10.0 MHz, and -12.5 MHz
charged,
being
The result is
theory,
N+
7^=
(1) (-eQq+210/h) = -12.5 MHz
N°
- ^ = (1/2)(-eQq°210/h) =
N"
% =
(0) (-eQq"2i0/h) =
result
in a difference of
quadrupole coupling constants.
0.31 MHz
typically
respectively (Townes and Schawlow
-5.0 MHz
0.0 MHz
The transfer of a full electron from N(1) to N(2) would,
this
are
q2T0» that due to a single electron in an unhybridized p 2
contribution, and summing.
(1955)).
2
2
The total contribution is found by simply counting the numbers
electrons
111-13.
non-bonding
s
Pz
1/2
in
the coupling
/£JJ+
The as yet
according
to
- /^N~ = -12.5 MHz in the
unexplained
difference
of
constants of the nitrogen nuclei in NCCN-HF
thus corresponds to a transfer of 0.02 of an electronic charge from N(1)
64
to
N(2)
for this complex.
of N2-HF corresponds
to
a
The difference of 0.20 MHz in the constants
transfer
of
0.0l6e
within
the
nitrogen
component of this complex.
The results of the study of NCCN-HF are published in the Journal
of
Chemical
Physics,
rotational spectrum,
volume
74, pp 4936 - 4943, under the title "The
1l
*N nuclear quadrupole coupling constants and H, 1°-F
nuclear spin - nuclear spin coupling constant of the cyanogen - hydrogen
fluoride dimer" by
A. C. Legon,
P. D. Soper
and
W. H. Flygare.
results of the N2-HF study are being prepared for publication.
The
65
CHAPTER IV.
SEPARATION OF POLARIZATION EFFECTS BY VIBRATIONAL
ANALYSIS:
A.
THE ACETONITRILE - HYDROGEN FLUORIDE COMPLEX
INTRODUCTION
A key question in the study of weakly bound complexes is whether
the
binding
can
be
understood
in terms of electrostatics or whether
molecular orbital arguments must be invoked.
the
resolution
complexes.
of
Of crucial
this question are the electronic properties of such
Almost all of the weakly bound complexes whose rotational
spectra have been reported to date have included isotopie
least one quadrupolar nucleus.
isotopes, the two bromine isotopes,
most
common
to
Nuclear quadrupole coupling constants are one source of this
information.
at
importance
geometry
species
with
Such nuclei include the two chlorine
nitrogen-14,
and
deuterium.
The
is that in which a quadrupolar nucleus along the
symmetry axis of one of the component molecules lies on the a
inertial axis of the complex.
principal
An example would be HBr in Ar-HBr (Keenan
et al (1980A)), which is linear at equilibrium.
The nuclear quadrupole coupling constant of the
free
component
molecule, p£g, is given by
X-Q = -eQqz/h
(IV-1)
where e is the electronic charge, Q is the appropriate nuclear
quadrupole moment, and qz =
<^2v/o)z2^>
electric
is the electric field gradient
at that nucleus along the symmetry (z) axis.
The value of the
coupling
constant measured for the complex, p d a a , is the projection of X o ° n
a inertial axis of the complex and is given by
tne
66
X a a = X o ( 1 ' 2 ) <3oos 2 )l -1>
(IV-2)
where the average is taken over the ground vibrational state and
the
angle
between
^
is
the a inertial axis and the z axis of the component
molecule (essentially angle HBrAr in Ar-HBr).
Quite apart from vibrational effects, %
complex
for
the
may differ from that for the free component molecule because of
a change in qz.
of
as measured
a a
these
If it is possible to estimate the
factors
in
determining
the
value
relative
of ?^ aa ,
importance
one oan
elicit
information about the molecule which is not otherwise accessible.
In many of the
bonding
interaction
weakly
is
bound
complexes
studied
to
date
the
weak enough or the distance of the quadrupolar
nucleus from the bond far enough so that it is reasonable to assume that
9Z
is
unchanged
molecule.
If this
vlbrationally
in
is
averaged
the
complex from its value in the free component
correct,
angle,
equation
$ .
(IV-2) directly
This
has
gives
the
been applied to Ar-HCl
(Novicket al, (1973)), Ar-HBr (Keenan et al, (1980A)), Kr-HCl (Balle et
al
(1980)
and
Barton
et
al
Xe-HCl (Keenan et al (1980C)),
OC-HBr
(Keenan
et
OC-HCl
valid.
rotor
chapter
II, above),
and
In Ar-DF ((Keenan et al
calculated from ^ n was found to agree with that
from the D , 1 9 F nuclear spin - nuclear spin coupling constant
S D F , which also projects according to
Waals
(see
al (1980B)), among others.
(1981)) the value of #
calculated
(1980)), Kr-HBr (Keenan et al (1980A)),
bond
in
Ar-DF
is
equation
(IV-2).
The
der
weak enough so that equation (IV-2) is still
A complete analysis of centrifugal distortion in the
formed
van
asymmetric
between argon and cyanogen chloride (Ar-CICN) (Keenan and
Flygare (1981)) allowed calculation of the
intramolecular
force
field
67
and
normal
modes of vibration.
In this complex the field gradients at
the nitrogen and chlorine nuclei were only slightly changed
in
free
C1CN
and
the
equation (IV-2) were
average
very
angles
close
to
calculated
those
found
from
those
by an analogue of
from
an
inertial
analysis.
In OC-DF (see chapter II, above),
calculated
the
value
of
)f
from ?£g by equation (IV-2) is greater than that calculated
for OC-HF from S^p.
electric
however,
field
It is clear that the
assumption
of
an
unchanged
gradient in the complex is inadequate for the deuterium
participating in the hydrogen bond.
This assumption has also been shown
to be incorrect for a number of other hydrogen-bonded species.
Under these circumstances, only a vibrational analysis
to separate electronic from vibrational effects.
is able
Arguments based on the
grounds of symmetry allowed an estimation of electrical effects
complexes
formed
by
for
the
significantly.
difference
was
the
cyanogen and nitrogen with hydrogen fluoride (see
chapter ill, above).
values
in
In these complexes (NCCN-HF
two
nitrogen-14
In free NCCN and NN they
nuclei
are
and
were
NN-HF)
found
necessarily
the ^-u
to
differ
equal.
The
explained to be due in part to polarization of cyanogen
and nitrogen by hydrogen fluoride.
Analysis of the
rotational
spectra
of four isotopie species of the hydrogen cyanide dimer (HCN) 2 (Buxton et
al (1981B)) showed that the two 1^N
differed
both
from
each
changes were estimated to
electrical
effects.
earlier study from the
(Bevan
et
al
other
be
due
coupling
constants
in
the
dimer
and from the value for free HCN.
half
to
vibrational
and
half
The
to
In this chapter, force constants calculated in an
excited
(1980A))
and
vibrational
infrared
state
spectrum
microwave
(Thomas
spectrum
(1971)) of
68
acetonitrile - hydrogen fluoride are used to
which
the
difference
in
acetonitrile and ^ a a
effects.
between X o
for
*ne
is
complex
determine
the
1i
*N
the
extent
nucleus
in
attributable
to
free
electrical
This is the first study to combine relatively high-temperature
low-resolution microwave, infrared, and low-temperature
microwave
to
data
to perform such an analysis.
high-resolution
It is determined that the
nitrogen atom in CH3CN-HF has a negative charge ca 0.03e
in
excess
of
that on it in free acetonitrile.
B.
EXPERIMENTAL
The spectrometer used in
elsewhere
(Balle
et
al
this
(1980),
study
Balle
is
described
and Flygare (1981)).
mixtures used consisted of the full vapor pressure
room
in
of
detail
The gas
acetonitrile
at
temperature (ca 100 Torr), 50 - 100 Torr of hydrogen fluoride, and
argon to achieve a total
molecular
signal
was
pressure
of
significantly
some
2
1/2
atmospheres.
The
enhanced by diluting this mixture
with argon until it was finally less than 0.1%
in
CH3CN
and
HF,
the
The Doppler doubling phenomenon (Campbell et al (1981A
and
B))
and J = 1*-0 transitions.
The
remaining percentage being argon.
was
observable
in
both
the
J = 3-*-2
spectral lines typically had half-widths at half-maximum of
the
uncertainty
in
the
4 kHz, and
frequencies is estimated to be 2 kHz. Figure
IV-1 shows the J = 1«-0 transition of CH3CN-HF as
calculated
constants
The technique used to
used
to
fit the hyperfine structure.
find these constants is described in the next section.
from
the
-2.00
-1.50
I
-1.00
-.50
J
0.00
0.50
1.00
1.50
2.00
FREQUENCY
en
Fxgure I V - 1 .
Hyperfine coznponents xn t h e J = 1<—0 t r a n s x t x o n of CH CN-HF.
70
Table IV-1: Observed and calculated frequencies in MHz
for hyperfine components in the J = 1«-0 rotational
transition of CH3CN-HF.
pi
F
1
F2
F
observed
frequency
calculated
frequency
2
2
2
2
0.5
0.5
1
1
2
1
3705.7195
3705.7210
0.5
1
1
0.5
0
1
3705.7284
3705.7291
1.5
1.5
1.5
1
1
1
1
1
1
0.5
0.5
0.5
1
1
1
2
1
0
3705.7586
3705.7579
0.5
0.5
1
1
2
2
0.5
0.5
1
1
2
1
3706.8019
3706.8001
1.5
1
2
0.5
0
1
3706.8478
3706.8472
1.5
2
3
0.5
1
2
3706.8599
3706.8611
0.5
0.5
0.5
0
0
0
1
1
1
0.5
0.5
0.5
1
1
1
2
1
0
3706.9002
3706.8989
1.5
1.5
1.5
2
2
2
1
1
1
0.5
0.5
0.5
1
1
1
2
1
0
3708.5259
3708.5269
FT'
F
1.5
1.5
2'
71
Table IV-2: Observed and calculated frequencies in MHz
for hyperfine components in the J = 3<-2 rotational
transition of CH^CN-HF.
No K = 2
components
were
observed.
C.
F' <- F
K
observed
frequency
calculated
frequency
3
2
4
2
3
1
3
2
0
0
0
11118.7004
11119.7086
11119.9368
11118.7001
11119.7081
11119.9380
0
11121.5652
11121.5649
3
2
4
2
2
1
3
2
1
1
1
1
11119.2624
11119.5817
11119.5949
11120.5041
11119.2628
11119.5847
11119.5913
11120.5043
RESULTS
The transition frequencies observed for CH3CN-HF are
Tables
IV-1
and
IV-2.
The
hyperfine
structure
arising
interaction of the nitrogen-14 nuclear electric quadrupole
the
electric
field
gradient
only in the J = 1<-0
components
of
the
in
from
the
moment
with
at that nucleus was clearly resolved not
transition,
J = 3«~2
listed
but
also
in
transition.
Ho
the
K = 0
K = 2
and
components
K =1
were
observed for this transition because of the low temperatures achieved in
the
expansion
of
the
corresponds to roughly
corresponds
to
30 K.
gas.
The
energy
7 K,
while
that
In
addition
of
of
to
the
the
J = 2, K = 1 state
J = 2,
K = 2
the quadrupole structure, the
J = 1<-0 transition also exhibited resolvable structure from
nuclear
state
the
H,19p
spin - nuclear spin interaction which is the direct interaction
of the magnetic dipole moments of the two nuclei.
Because
inclusion
of
the
three
analysis
nuclear
only one, different techniques
of
the
J = 1<-0
transition
required
spins while that of the J = 3<~2 required
were
used
to
evaluate
the
hyperfine
72
components
in the two eases. Consider first the J = 1«-0 transition.
The hyperfine Hamiltonian consists of two parts, one for the nitrogen-14
nuclear quadrupole coupling and one for the H,19p nuclear spin - nuclear
spin coupling. These two Hamiltonians are given in equations (II-1) and
(II-3), respectively.
Matrix
elements were calculated in the coupled
basis set:
J + % = %;
"?T + ?p = ? 2 ; ? 2 + "lN s ?
(IV-3)
and the resulting matrices diagonalized to give the energy levels and
transition
frequencies due
to the hyperfine interactions, which were
added to the center frequency of the transition
to give
the observed
frequencies.
The J s 3<-2 transition, where
structure
the only
resolvable hyperfine
is a result of nitrogen-14 nuclear quadrupole coupling, was
analyzed by using the quadrupole coupling energy levels for a
symmetric
rotor (Townes and Schawlow (1955)):
EQ(J,K,I,F) = -XNI 1 - 3K 2 1 (3/t)C(C+1)-I(I.f1)J(J+1) (17-4)
I
J(J+1)i
21(21-1)(2J-1)(2J+3)
where C = F(F+1)-I(I+1 )-J(J+1).
transition,
As in the case of the
J = 1«-0
the frequencies of the hyperfine transitions were added to
the center frequency to give the observed transition frequencies.
The observed frequencies for the J = 1-e- 0 transition were fitted
to give 9^N»
S
HF»
and
y
0«
Tne
K =
° and
K = 1
components of the
J = 3<—2 transitions were fitted independently to give Odfj and
both.
The
Vg
for
three transition center frequencies were used to calculate
73
the rotational constant Bg and the centrifugal distortion
constants
Dj
and D J K according to the equation (Townes and Schawlow (1955)):
= 2B0(J+1)-4DJ(J+1)3-2DJK(J+1)K2
Vo
The resulting constants along with those from
given
in
Table IV-3.
(IV-5)
the
previous
study
are
Note that all of the parameters measured by both
of the studies fall within the error bounds of the earlier one.
Table IV-3:
Spectroscopic constants of
measured in this and in an earlier study.
this work
B0(MHz)
Dj(kHz)
DJK(kHz)
CH3CN-HF
as
Bevani et al (198
1853.37(4)
0.82(20)
67(2)
1853.3323(5)
0.93(4)
66.8(5)
XN(MHZ)
J = 1-^-0
J = 3<-2, K =
K =
SnptkHz)
The difference in
components
of
the
-
-3.727(3)
-3.714(5)
-3.678(13)
138.1
0
1
the "^X-N values
J = 3*-2
transition
for
suggest
the
a
K = 0
decrease
centrifugal distortion, although they are too close to state
certainty.
This
and
K =1
due
this
to
with
is also true for the difference in ^ N values for the
J = 1<-0 transition and K = 0 components of the J = 3<-2 transition.
74
D.
DISCUSSION
The geometry of CH3CN-HF
(Bevan
et
al
(1980A)),
point group C3 V .
(Costain
calculated
and
(1976)),
to
discussed
in
the
earlier
study
and is found to be that of a symmetric top of
Using this geometry and the
(1958))
Guelaehvili
is
of
the
HF
structures
of
CH3CN
(calculated from Webb and Rao (1968) and
nitrogen
be 2.7403 A.
rs
-
fluorine
distance
r(N-F)
is
This bond length was used along with those
from the r s structures in the vibrational analysis below.
In order to separate the vibrational and electrical
T^N
ln
effects
on
CH3CN-HF, the GF method of Wilson (Wilson et al (1955)) was used
to calculate the L matrix which relates the normal
internal
displacement coordinates:
s* = LQ.
coordinates
to
the
The mean square amplitudes
of the normal coordinates are found by simple
integration
and
form
a
diagonal matrix, jo :
£ = (3x3)
which are
related
to
the
mean
(IV-6)
square
amplitudes
of
the
internal
displacement coordinates through
g =
L£LT
(IV-7)
The mean square amplitudes of the bending modes, when
factor
of
correct
for
their
projection angles of /K-N and
Sjjp
in
geometry.
two
As
to
in
the
original
multiplied
by
a
degeneracy, are related to the
equation
vibrational
(IV-2) through
analysis
(Bevan
simple
et
al
(1980A)), CH3CN-HF is treated as a five-mass linear molecule (see Figure
r
r
\
H3C
r
2
C^ ^
V„>
r
3
N
W
4
H
^
Figure IV-2. The internal displacement coordinates used in the vibrational analysis described in the
text.
76
Table IV-4:
Parameters of the vibrational analysis.
bond lengths (A)
r,
r2
r3
H,
1.4584
1.1571
1.8191
0.9212
stretching force constants (N m~')
fTT = 508
f 2 2 = 1813
f 33 =
23.27
fyH = 720.7
f 1 2 = f21 = 30
all others equal zero
bending force constants (10"20 J rad"2)
f«
= 27.3
fo
=
2.4
fy
=
8.0
all others equal zero
77
(IV-2)).
The parameters used in the analysis are listed in Table IV-4.
One internal check
comparison
of
the
on
values
the
validity
<r,
of
angle
of
HFN,
vibrational model and by equation (IV-2) using
SHF = 143.375(25) kHz
(Muenter
(1972)).
14.7 degrees while the latter gives
this
as
the
The
approach
a
calculated by the
free
first
9.0 degrees.
is
HF
value
analysis
This
is
of
gives
reasonably
close given the error in S^p measured for the complex.
Now consider the value
of jC^
= -3.727 MHz measured
for
the
as compared to pCu = -4.2244(15) MHz in free CH3CN (Kukolleh et
complex
al (1978)).
The normal mode analysis shows that the
average
angle
of
the cyanide group with the molecular axis is 8.0 degrees. Were this the
only effect,
one
would
predict
-4.102 MHz.
The
remaining
the
observed
difference
of
0.375 MHz
electrical effects. This difference is in faot a
magnitude
that
of
electrical
vibrational
effects
averaging
of pC^
value
must
lower
to
be
be due to
limit
on
the
since use of equation (IV-2) implies
of ^ N
in
free
acetonitrile
has
been
neglected.
One possible electrical effect,
insignificant.
that
of
charge
transfer,
is
Studies of rare gas nuclear quadrupole coupling in Kr-HP
(Buxton et al (1981A)) and Xe-HCl (Keenan et
al
(1980C))
demonstrated
that such transfer is negligible.
A more significant effect
component
presence
of
an
additional
and
higher-order
electical
moments.
These
are listed in Table IV-5. This effect may be calculated in the
same manner as was
nitrogen
the
to the field gradient at the nitrogen atom from the nearby HF
molecule with its dipole
moments
is
-
done
hydrogen
for
fluoride
the
cyanogen
complexes.
-
hydrogen
fluoride
and
The appropriate equation is
78
(III-5) where the argument of the Legendre polynomials is
the
cosine
of
14.7 degress and r is 2.6939 A.
q z ° = -4.83 x 1013
shielding
SC cm~3
is
considerably
(see chapter III, above).
taken -to be
The resulting value of
enhanced
by
Sternheimer
The electric field gradient at the
nitrogen nucleus corrected for this effect is q z = -1.45 x 101^ SC cm"3.
Recalling
equation
(IV-1)
and inserting Q^ = 1.93 x 10~26 C m 2 (Winter
and Andra (1980)), this corresponds to a frequency change of
The
value
of T^N predicted by invoking both vibrational averaging and
the HF field gradient still
value.
0.203 MHz.
This
differs
by
0.172 MHz
from
the
observed
difference, which is due to polarization of CH3CN, can be
explained by the Townes-Dailey theory (Townes and Dailey (1949),
Townes
and Schawlow (1955)).
Table IV-5: Multipole moments of HF.
moment
value
source
1.826526 x 10~ 18 SC cm
2.36 x 10- 26 SC cm 2
1.699 x 10-34 s c o m 3
1.804 x 10-42 s c c m 4
Qm
A
I
exptj*
exptb
ab initio0
ab initio0
a. Muenter and Klemperer (1970)
b. deLeeuw and Dymanus (1973)
c. Maillard and Silvi (1980)
This analysis is exactly analagous to
chapter
for
cyanogen
that
and nitrogen - hydrogen fluoride.
that the N in CH3CN is in a state of sp hybridization
transfer,
if
done
and
in
the
last
It is assumed
that
charge
any, occurs between the p x orbitals on the C and N atoms.
It is further assumed that the contribution of
one
electron
in
a
pz
79
orbital
-
z
being
"^e
the symmetry axis - is q2T0*
contributions of
electrons in p x , p y , and sp z orbitals will then be -1/2, -\/2r
respectively, in units of q2io*
and +1/2,
Using the empirically derived values of
-eQq21g/h for neutral, positively charged and negatively
charged
N of
-10.0 MHz, -12.5 MHz and -8.0 MHz (Townes and Schawlow (1955)) indicates
that, in CH3CN, one would expect to measure Xti
and
0.0 MHz, respectively.
nitrogen atom in
CH3CN-HF
CH3CN
somewhat
This agrees with one's intuition that the
should
more
= -5.0 MHz, -12.5 MHz,
so.
be
slightly
negative, with
that
in
Just how much more negative it is may be
calculated by noting that a difference of one electron corresponds to a
difference
of
5.0 MHz
in
the
coupling
constants.
The
observed
difference of 0.172 MHz represents an excess negative charge of ca 0.03e
on the N in the complex over that on it in free acetronitrile.
E.
CONCLUSIONS
An analysis of the normal modes of vibration in the acetonitrile
-
hydrogen
fluoride complex based on data from infrared and relatively
high-temperature
microwave
vibrational
electrical
upon
complex
fluoride
and
formation.
leads
to an
studies
effects
has allowed
the
separation
of
responsible for the change in pC^
Polarization
of
acetonitrile
by hydrogen
increase in the negative charge on the nitrogen
atom in the complex of ca 0.03e over that on it
in
free acetonitrile.
This occurs through transfer of electron density within the acetonitrile
component of the complex.
This transfer of electron density increases the dipole moment of
the
complex
over that of the sum of the moments of its two components.
If one assumes that the carbon atom of the methyl
group
becomes
0.03e
80
more
positive, this enhancement of the dipole moment will be 0.4.Debye.
The dipole
moment
enhancement
may
of
in
this
with
has
It is also of
case
complex, where it is
consistent
complex
yet
to
be
measured.
This
be compared with that in HCN-HF, where it is 0.8 Debye
(Legon et al (1976)).
charge
the
with
ca
the
that
0.02e.
interest
to
compare
the
excess
for the cyanogen - hydrogen fluoride
The
higher
value
for
CH3CN-HF
is
shorter N-F distance in this complex (2.7043 A vs
2.8616 A for NCCN-HF) and with the greater ability of the
methyl
group
to donate electrons.
The results of this study have been submitted for publication to
the
Journal
of
Physical
Chemistry
under
the
title
quadrupole coupling and H , 1 9 F nuclear spin - nuclear
the
microwave
fluoride
rotational
dimer,'
W. H. Flygare.
by
spectrum
P. D. Soper,
of
the
spin
acetonitrile
A. C. Legon,
'1^N nuclear
coupling
-
in
hydrogen
W. G. Read
and
81
CHAPTER V.
A.
DESIGN OF A HIGH-TEMPERATURE NOZZLE SOURCE •
INTRODUCTION
The spectrometer used in the studies described in
III,
and
IV
has
proven
the
II,
itself to be very versatile in measuring the
microwave rotational spectra of weakly bound complexes.
in
chapters
The key feature
success of this instrument is the use of a supersonic expansion
through a nozzle
temperatures
to
(ca
cool
the
components
of
a
gaseous
mixture
10 K or lower) where the complexes are stable.
there was no capacity for heating the components of the
mixture
to
Since
before
expansion, studies have so far been restricted to complexes all of whose
components
are
temperature.
gases
The
or
liquids
additions
to
made with a view to extending
complexes
to
liquids
high
vapor
pressure
at
room
the spectrometer described below were
the
and
of
range
solids.
Of
of
potential
particular
components
interest
of
was the
possibility of studying complexes containing metal atoms or clusters.
The idea of using an oven to
solids
into
expansion to
resonance
the
form
(MBMR)
rare gas -
alkali
alkali-metal
vapor
the
metal
atoms
or
other
phase so that they may be used in a supersonic
complexes
is
not
new.
Molecular
beam
magnetio
has been used to measure a variety of interactions in
metal
nuclear
complex formation in
(1976A)),
introduce
dimers.
spin
-
potassium
electron
spin
These
electron
-
argon
include
the
shift
in
the
spin hyperfine constant due to
(Freeman
et
al
(1974) and
- rotation coupling in potassium - argon
(Mattison et al (1974) and Freeman et al (1976B)) and rubidium - krypton
(Cooke
and Freeman (1977)) and the shift in the g-factor of potassium -
argon relative to free potassium
(Freeman
and
Cooke
(1976)).
Laser
82
fluorescence
spectroscopy has been applied with success to the sodium -
argon complex (Smalley et al (1977) and Tellinghuisen et al (1979)) and
to sodium - neon (Ahmad-Bitar et al (1977) and Lapatovich et al (1980)).
Nonetheless, no observation of
a
pure
rotational
transition
in any
weakly bound metal-containing complex has been reported to date.
Besides the possibility of studying complexes
containing
metal
atoms, the ability to produce significant vapor pressures of liquids and
solids would greatly extend the range of possible complexes of interest.
To
cite
just
one
example,
the spectrometer would then be capable of
studying complexes containing water.
In the course of experiments to examine
apparatus
the
viability
of
the
described below it became apparant that certain modifications
are required before routine
operation
will
be
possible.
These
are
discussed in the final section of this chapter.
B.
THE VACUUM CHAMBER AND OVEN ASSEMBLY
The addition of the capability to use an
beam
required
oven-generated
the design and construction not only of the oven proper,
but also of a vacuum chamber to enclose it.
One of the
considerations
to
was
that
atmospheric pressure and
chamber
nozzle
containing
it
be
vacuum
possible
without
primary
cycle
disturbing
quickly
the
design
between
main
vacuum
the mirrors. For a description of the spectrometer
proper see Balle and Flygare (1981).
Figure V-1 3hows a diagram of the vacuum chamber added for these
experiments.
Isolation of this ohamber from the main mirror chamber is
accomplished by a six inch gate valve. This gate
the front
end
of
the
oven
vacuum
chamber
valve
which
is
is
to
bolted
the
to
left
Figure V-1. The vacuum chamber for the oven and heated nozzle. It contains the tie rod assembly of
Fxgure V-2.
CD
^VV'vVV'vVVlvVV^^e.UvrV
.V, Wv'e'e-eWvV'eVVW U V \ \ W \
Figure v - 2 . ahe t i e rod assembly used to support and move the oven,
chamber shown i n Figure V-1.
S3=>
I t s l i d e s i n t o the vacuum
09
85
in Figure V-1. When this valve is shut the oven chamber can
without
disturbing
the
main
chamber.
be .opened
When this valve is open it is
large enough so that the oven can pass through it.
The oven chamber has a pumping system separate from that for the
body
of
the spectrometer.
This system is attached through a Witt seal
to the bottom of the chamber and consists of one
pump
separated
from
diffusion pump
mechanical
is
used
100 microns pressure.
micron.
The
final
between 10" 2 an(j 5
second
x
oil-sealed
mechanical
the chamber by a bellows valve and a two inch oil
separated
pump
oil-sealed
from
the
chamber
by
a
gate
valve.
The
to take the chamber from atmosphere to below
The diffusion pump draws
operating
pressure
ig-2 m i c r o n a .
mechanical
of
the
pressure
below
the system typically lies
The diffusion pump i3 serviced by
pump.
1
a
Because the diffusion pump can be
isolated from the oven chamber by use of the
gate
valve,
it
is
left
running continuously.
Access to the oven is provided through two side port3.
All
of
the connections between components of the vacuum chamber are sealed with
O-rings.
box,
Both ports have the capability of being attached
making
to
a
glove
it possible to handle materials under an inert atmosphere.
Pressure in the chamber is monitored by a thermocouple
gauge
near
the
front end.
The
schematically
tie
in
rod
assembly
Figure
used
to
support
the
oven
is
shown
V-2. Four precision-machined stainless steel
tie rods are held in plaoe by two plates, one of which is bolted to
rear
cover of the oven chamber.
bushings move along the tie rods.
by
a
worm
screw.
the
Two traveling plates supported on ball
The rear plate position is controlled
These two plates are bolted together with threaded
86
stainless steel rods which also support the oven proper. When the worm
screw
is
rotated,
these
two plates and the oven move in unison. The
moving parts are those shaded in Figure V-2. All
thermocouple
connections
are
through
the
eleotrioal,
rear
cover,
so
unbolting this cover the entire oven support assembly can be
These
connections
screw,
five
a
that by
withdrawn.
include a rotory motion feedthrough to turn the worm
electrical
feedthroughs,
gas and
gas
feedthroughs,
four
pairs
of
thermocouple
line for the oven, and a vent to atmosphere. The
electrical feedthroughs were used to power two independent heaters and,
later,
the
pulsed
valve.
One
pulsed valve was through ground.
inside
the
chamber
was
of
the electrical connections of the
The
removed
insulation
and
chromel - alumel thermocouples were used
The
on
the
wires
used
replaced by teflon tubing. Two
to monitor
the
temperature.
side port covers for the chamber are transparent, so it is possible
to check visually the various connections as well as
the positions
of
the traveling plates.
The design of the oven
satisfactory
state.
changed
stainless
steel
thousandths of an inch.
inch
Swagelock
tubing.
of
the
by
reaching
a
The
nozzles
themselves
disks with apertures ranging from 0.003 to 0.020
These were held in place by a standard
quarter
nut against the corresponding Swagelock male connector.
When the assembly was modified for pulsed
replaced
time, never
At first the oven and nozzle were simply Swagelock
brand connectors and stainless steel
were
with
operation,
this
nozzle was
a solenoid valve of the type used in the routine operation
spectrometer.
This
valve
is
provided
by
General
Corporation and has a base roughly 1.2 inches in diameter.
Valve
The aperture
size on this valve is controlled by bolting stainless steel plates
with
87
holes of various diameters to the base.
—
the pressure behind the nozzle ~
with
a
pulsed
as
opposed
to
a much larger aperture can be
a
continuous beam.
unchanged throughout this modification.
independently
by
nichrome
For a given stagnation pressure
ribbon,
used
The oven was left
The oven and nozzle were heated
with
a thermocouple measuring the
temperature of each.
The change to pulsed operations imposed
the
operating
temperatures
available
pulsed valve is made of viton, a
decomposes
above
130°C.
severe
limitations
to the system.
commercial
The seal of the
synthetic
elastomer.
valves
generation
is
of
a
the
operating
vapor
It
A valve with a teflon poppet which is capable
of withstanding temperatures of up to 230°C is on order.
these
on
pressure
For neither of
temperature high enough to enable the
of
100 Torr
of
any
metal.
No
satisfactory pulsed valves which can be operated at significantly higher
temperatures are now on the market.
C.
EXPERIMENTAL
Once the oven vacuum chamber was made leaktight and was attached
to the main vacuum chamber, the viability of operation with a continuous
nozzle beam was tested by examining the J = 1*-0 transition of
sulfide
transition
was
examined
stagnation pressures of from 2.5 atmospheres down to
the
disappearance
line
(OCS)
for
each
at
12162.97 MHz.
aperture.
thousandths of an inch.
without
averaging.
These
This
carbonyl
spanned
the
range
0.003
The molecular signal was clearly
With
the
exceptions
noted
below,
for
to
0.02
visible
even
the
Fourier
transforms of the time domain signals showed only one broad peak instead
of
the
two narrower ones expected on the basis of the Doppler doubling
88
phenomenon (Campbell et al (1981A and B)).
The doubling is a result of the dynamics of the expansion of the
gas.
The
narrowness of the lines is a result of the narrowness of the
velocity distribution of the molecules in the
mean
velocity.
This
nature of the beam.
significant
narrow
The
cooling
velocity
linewidth
gas
about
their
(high)
distribution reflects the cold
observed
for
OCS
indicated
that
was not taking place. This did not auger well for
the observation of weakly bound complexes.
It was then attempted to see the known J = 2«-1
(Harris
et al (1974)) at 12260.57 MHz.
continuous beam.
This may simply
line
of
Ar-HF
It was never detected using the
reflect
the
limits
of
the
signal
operation
placed
averager used.
As was remarked above„ the change
immediate
and
severe limitations on the temperatures at which the oven
could operate because of possible
solenoid
to pulsed
valve.
Once
decomposition
of
materials
in
the
it was demonstrated that Ar-HF could be seen in
pulsed operation with the oven at a temperature of 100°C, it was decided
to
search
for
the
hydrogen fluoride.
100 Torr
at
complex
Chromium
of
chromium
hexacarbonyl
ceramic
has
a
vapor
pressure
of
108°C. The oven used to achieve this vapor pressure was a
piece of half inch stainless steel tubing.
a
hexacarbonyl (Cr(CO)g) with
crucible
during operation.
and
The Cr(C0)g was loaded
into
placed inside the tubing, which is horizontal
A gas mixture of 2 percent hydrogen fluoride in argon
at 2.5 atmospheres was fed into the rear end of the oven, and the pulsed
valve was attached to the front end.
Cr(C0)g-HF
were
ever
observed.
No
transitions
attributable
to
Breakdown and examination of the oven
after the search was concluded clearly showed that the
problem
lay
in
89
recrystallization
of the solid on the cooler parts of the oven assembly
near the gas feed line.
It is
doubtful
that
significant
amounts
of
Cr(C0)g actually made it through the nozzle.
D.
CONCLUSIONS AND RECOMMENDATIONS
The oven assembly has
yet
to
demonstrate
its
viability
and
specifically seems limited at best to temperatures below 230°C if pulsed
operation is required.
complexes
containing
This would preclude any possibility of
metal atoms.
studying
Nonetheless, a few relatively minor
modifications may yet succeed in making operation below this temperature
routine, and the possibility of operating with a continuous beam has not
been foreclosed.
One obvious requirement is that an oven be
designed
for
recrystallization or recondensation of the vapor is obviated.
a stainless steel filter before the oven
but
well
within
which
Inserting
the
heated
region may eliminate this problem.
Replacing the averaging system, which should be possible in
near
future, may allow operation with a continuous beam.
Doppler doubling —
was
present
under
although without any noticeable
certain
combinations
aperture size in the observations on OCS.
cooling
was
taking
of
stagnation
It
is
insofar
A very slight
narrowing
pressure and
possible
that
molecules
in
the
some
beam.
as they provide collision partners for the cold dimers,
background molecules for the complexes do not present a
problem,
the
walls
dimers
—
place, but that the background pressure of OCS was
high enough to swamp the signal from any cold
Except
line
the
would
not
survive
collisions
with
the
and
since
the
rotational transition frequencies of tho dimer and of its components are
90
almost
inevitably
well separated.
It would shed a great deal of light
on the possibility of operating with a continuous beam if
established
definitively
whether
enough
achieve reasonable signal-to-noise ratios
should
system.
be
one
of
the
first
dimers
with
are
long
it
could
be
being formed to
averaging.
This
experiments done with the new averaging
If continuous beam operation is possible, complexes
containing
metal atoms could be studied immediately.
In summary, the heated nozzle beam has yet
viability,
but
a
recondensation
These consist of redesigning the oven
its
to
and recrystallization of liquids and solids and
improvements in the signal averaging capabilities of
system.
demonstrate
few relatively simple design changes could well make
successful operation routine.
inhibit
to
the
data-handling
91
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and Lorenz, E.
(1955)
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Waldron, R. A.
(I960) Proc. IEEE .107, 272
Webb, D. U.
Microwave Spectroscopy
(1978) Phys. Rev. Lett.
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Vashihstra, P.
Watson, J. K. G.
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Wilson, E. B.,
Deeius, J. C.
and
Cross, P. C.
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and Andra, H. J.
(1955)
(1980) Phys. Rev. A 21, 581
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96
VITA
Paul Donald Soper was born in Syracuse, New
1951.
His
undergraduate
earned him two B.S.
both
being
study
at
Rensselaer
in
May
1973.
on
July
23,
Polytechnic Institute
degrees, one in Chemistry and
awarded
York
After
one
in
teaching
Psychology,
with
the
U.S. Peace Corps in Kenya for three years he attended graduate school at
the University of Illinois.
in August 1978 and a Ph.D.
his
He was awarded an M.S. degree In Chemistry
in the same field in October
1981.
graduate study he received a fellowship from Eli Lilly and was both
a teaching and a research assistant.
He is a member of Phi
Phi
Physical
Lambda
Upsilon,
Chemical Society.
and
During
Company
the
American
He is presently employed
by
Kappa
Phi,
Society and the American
E. I. duPont de Nemours
at the Savannah River Laboratory in Aiken, South Carolina.
He is a co-author of the following publications:
•Conductivity of o< -silver iodide in the microwave
range,1
K. F. Gebhardt,
P. D. Soper,
J. Merski,
T. J. Balle and W. H. Flygare, J. Chem. Phys.
72, 272
(1980)
'Rotational spectra and molecular structures of ArHBr
and KrHBr,1 M. R. Keenan, E. J. Campbell, T. J. Balle,
L. W. Buxton,
T. K. Minton,
P. D. Soper
and
W. H. Flygare, J. Chem. Phys. 72, 3070 (1980)
'°3Kr nuclear quadrupole coupling in KrHF: evidence for
charge
transfer,'
E. J. Campbell,
M. R. Keenan,
L. W. Buxton, T. J. Balle, P. D. Soper, A. C. Legon and
W. H. Flygare, Chem. Phys. Lett. 70, 420 (1980)
'The rotational spectra of weakly bound dimers of carbon
monoxide and the hydrogen halides HX (X=F, CI, Br),'
A. C. Legon, P. D. Soper, M. R. Keenan, T. K. Minton,
T. J. Balle and W. H. Flygare, J. Chem. Phys. 73, 583
(1980)
'Microwave rotational spectrum, molecular geometry and
intermolecular
interaction
potential
of
the
hydrogen-bonded dimer OC-HCl,' P. D. Soper, A. C. Legon,
and W. H. Flygare, J. Chem. Phys. 74, 2138 (1981)
'The rotational spectrum, H, 19p nuclear spin - nuclear
spin
coupling,
D nuolear quadrupole coupling and
molecular geometry of a weakly bound dimer of carbon
monoxide
and
hydrogen
fluoride,'
A. C, Legon,
P. D. Soper and W. H. Flygare, J. Chem. Phys. 74, 4944
(1981)
l!
1l
'The
rotational
spectrum,
*N-nuclear
quadrupole
1
coupling constants, and H, 9p nuclear spin - nuclear
spin coupling constant of the cyanogen - hydrogen
fluoride
dimer,'
A. C. Legon,
P. D. Soper
and
W. H. Flygare, J. Chem. Phys. 74, 4936 (1981)
' 1 ^N nuclear quadrupole coupling and H,1^F nuclear spin
- nuclear spin coupling in the acetonitrile - hydrogen
fluoride dimer,' P. D. Soper, A. C. Legon, W. G. Read
and W. H. Flygare, submitted to the Journal of Physical
Chemistry.
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