Download Carbon-13 hyperfine structure of the CCCCH radical

Carbon-13 hyperfine structure of the CCCCH radical
Wei Chen and Stewart E. Novick
Department of Chemistry, Wesleyan University, Middletown, Connecticut 06459
M. C. McCarthy
Harvard–Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138
and Division of Applied Sciences, Harvard University, Cambridge, Massachusetts 02138
C. A. Gottlieb
Division of Applied Sciences, Harvard University, Cambridge, Massachusetts 02138
P. Thaddeus
Harvard–Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138
and Division of Applied Sciences, Harvard University, Cambridge, Massachusetts 02138
~Received 26 April 1995; accepted 18 July 1995!
The fundamental ~N 5 1 – 0! rotational transitions of the ground 2 S 1 electronic state of the four
singly substituted 13C isotopomers of CCCCH have been measured by pulsed-jet Fourier transform
microwave spectroscopy. In each isotopomer this transition is split into many well-resolved
hyperfine components owing to interaction between the electron spin and the molecular rotation, the
proton spin, and the 13C nuclear spin. Here, the hyperfine transition frequencies are analyzed with
the higher rotational millimeter-wave frequencies described in the previous paper of McCarthy et al.
to produce a precise set of rotational, centrifugal distortion, spin-rotation, and hyperfine coupling
constants. In particular, the Fermi-contact interaction of the 13C nucleus has been measured at each
substituted position, yielding information on the distribution of the unpaired electron spin density
along the carbon chain. The Fermi-contact constants, b F ~13C!, of 396.8~6!, 57.49~5!, 29.54~2!, and
18.56~4! MHz, for successive 13C substitutions starting furthest from hydrogen indicate that the
electronic structure is essentially acetylenic with alternating triple and single bonds. © 1995
American Institute of Physics.
I. INTRODUCTION
Magnetic hyperfine structure is a sensitive probe of the
bonding and electronic structure of open shell molecules.
The CCCCH radical is a particularly interesting case because
a 2 P electronic state is calculated to lie extremely close to
the 2 S ground state and the millimeter-wave spectra of the
vibrationally excited states are anomalously strong, possibly
for this reason. To better understand the electronic structure
we have undertaken a detailed study of the rare isotopic species of CCCCH with the goal of determining the hyperfine
coupling constants at each carbon position along the chain. A
summary of the CCCCH spectroscopic results obtained to
date is given in the accompanying paper1 ~hereafter paper I!.
There, millimeter-wave rotational transitions from N
5 10 to 32 in the range of 100–300 GHz were measured for
the four singly substituted 13C isotopomers. The resolution in
the millimeter-wave experiments is limited to a fraction of
the ;1 MHz pressure-broadened linewidths, allowing spindoubling to be observed, but generally little or no hyperfine
structure ~hfs!. An exception, however, is 13CCCCH where
the Fermi-contact hfs was large enough to be observed rather
far up the rotational ladder, an indication that the unpaired
electron is mainly localized on the terminal carbon. To measure the hfs at each of the other three carbon positions and
determine the unpaired electron spin density along the entire
carbon chain, the lowest N transitions of all four singly substituted 13C isotopic species of CCCCH were observed by
pulsed-discharge pulsed-jet Fabry-Perot Fourier transform
microwave ~FTM! spectroscopy — a high resolution tech-
nique recently applied to the study of rotational spectra of a
number of reactive species.
II. EXPERIMENTAL TECHNIQUES
Our pulsed-jet FTM spectrometer2 is similar to an instrument at the National Institute of Standards and Technology,3
derived in turn from the original design of Balle and
Flygare.4 Briefly, an intense pulsed jet of gas produced with
a very low rotational temperature (< 1 K! by standard
pulsed supersonic expansion passes through a high-Q FabryPerot microwave cavity. The cavity ~Q '23104 near 10
GHz! is tunable between 6 and 26.5 GHz. A pulse of microwave radiation at frequency n 0 and width D n , timed to coincide with the arrival of the gas pulse, is coupled to the
cavity by a small L-shaped antenna. If a molecular absorption line lies within the '500 kHz bandwidth of the microwave pulse, a macroscopic polarization is induced; following
decay of the pulse in ;5 m s, the molecules coherently absorb and emit at the resonant frequency. Signals are detected
by monitoring the free induction decay, the Fourier transform
of which is the absorption profile ~Fig. 1!. In the configuration used here, where the supersonic molecular beam is perpendicular to the Fabry-Perot axis, the linewidths are typically 30 kHz ~full width at half maximum!.
The CCCCH radical and its isotopic species were produced in a pulsed dc discharge of isotopically enriched
acetylene in argon immediately following the supersonic expansion from a 1 mm diameter commercial pulsed nozzle.
This source is similar to a design first described by Tsay
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J. Chem. Phys. 103 (18), 8 November 1995
0021-9606/95/103(18)/7828/6/$6.00
© 1995 American Institute of Physics
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Chen et al.: Hyperfine structure of CCCCH
7829
FIG. 2. The pulsed nozzle and discharge electrodes.
FIG. 1. The strongest hyperfine component in the N5120 transition of
CC13CCH: ~a! the free induction decay ~FID! and ~b! the Fourier transform
spectrum. The frequency difference is displayed in ~b! because the FID is
mixed with the microwave pump frequency ~9463.610 MHz!. The spectrum,
an average of 2000 gas and microwave pulses ~10 Hz repetition rate!, is the
result of about 3 minutes collection time. The linewidth, calculated at a
resolution of 5 kHz/pt, is about 25 kHz ~full width at half maximum!.
electrodes that gave optimum yield is shown in Fig. 2. We
found that the quality of the discharge ~as monitored by the
current and radical production! degraded after a few hours of
running with stainless steel electrodes because of the buildup
of a small amount of dark polymer; cleaning the plates restored the discharge and significantly increased the yield of
CCCCH. It was subsequently found that with OFHC copper
electrodes the discharge was stable for weeks of operation.
Finally, Helmholtz coils were used to cancel the earth’s magnetic field within the Fabry-Perot cavity.
The relative intensities of the lines of different isotopomers have only been determined to within a factor of two
or three owing to day-to-day variations in the discharge conditions and other factors, but to that accuracy the 13C was
found to be uniformly distributed along the carbon chain.
Because of the isotopic and hyperfine dilution, the strongest
transitions of the 13C isotopic species were about 50 times
weaker than the analogous transition in normal CCCCH. One
transition of a doubly substituted 13C isotopomer, roughly
1/4 as strong as the strongest components of the singly substituted isotopomers, was also observed and assigned.
III. ANALYSIS OF THE SPECTRUM
et al.5 and subsequently employed by Endo and
co-workers.6,7 The argon/acetylene ratio was 200:1, and was
partitioned between the isotopomers with zero, one, and two
carbon-13 in the ratio 5:2:1. Enriched acetylene was prepared by hydrolyzing a sample of Li2 C2 containing a 1:1
mixture of 12C and 13C to produce a statistical mixture of
acetylene isotopomers. The final gas mixture was chosen to
maximize single 13C substitution if carbon inserts randomly
along the CCCCH chain. A discharge voltage of 21000 V
was applied 130 m s after the 260 m s duration gas pulse,
resulting in a 20 mA current lasting 100 m s. The electrode
spacings and hole size were varied to optimize production of
CCCCH. A schematic diagram of the nozzle and discharge
A. The Hamiltonian
The hyperfine structure was analyzed with a standard
Hamiltonian for a linear molecule in a 2 S electronic state
with two spin 1/2 nuclei:8
H5BN2 2DN4 1 g N•S1 g D ~ N•S! N2
1bF~ H! I~ H! •S1c~ H!@ Iz ~ H! Sz2 31 I~ H! •S#
1bF~ 13C! I~ 13C! •S1c~ 13C!@ Iz~ 13C! Sz2 31 I ~ 13C! •S# ,
~1!
where N is the rotational angular momentum of the molecule, S is the electron spin angular momentum, and I (H)
and I( 13C) are the nuclear spins of the respective nuclei. The
J. Chem. Phys., Vol. 103, No. 18, 8 November 1995
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Chen et al.: Hyperfine structure of CCCCH
7830
z axis is taken to lie along the linear carbon chain. The first
line of Eq. ~1! gives the contributions of pure rotation, centrifugal distortion, and the magnetic interaction between the
electronic spin and the molecular rotation ( g ), including centrifugal distortion ( g D ). The second line represents the hyperfine interactions between the hydrogen nucleus and the
electron spin, and the third line is the same interaction between the 13C nucleus and the electron spin. The first and
second terms in lines two and three in Eq. ~1!, respectively,
are the Fermi contact and electron2nuclear dipole2dipole
interactions.
B. Spectral assignment
We used the spectral prediction and least-squares fitting
programs written by H. M. Pickett9 to analyze our spectra.
These programs are general, well-tested codes for highresolution microwave and infrared spectra for molecules
with up to five spins10 and in our experience are the best
available for hyperfine analysis. All angular momentum are
treated in the same way and the user is free to choose the
coupling scheme appropriate to the problem at hand. If the
molecular Hamiltonian can be expressed as a function of
angular momentum operators and spectroscopic parameters,
then these programs can be used to predict ~SPCAT! or fit
~SPFIT! spectra. The generality is at first somewhat daunting
to a new user, but becomes advantageous with a little experience ~and help from Pickett!. The results were identical to
those from a less general program written at Harvard11 that is
capable of handling two nuclear spins and uses a different
coupling scheme.12
The coupling scheme
J5N1S,
F1 5J1I~ H! ,
F5F1 1I~ 13C!
~2!
13
was used to analyze the hyperfine structure of the four C
isotopic species of CCCCH, with N, S, I(H), and I( 13C) as
previously defined. Owing to the magnitude of the 13C hyperfine interaction at the terminal carbon relative to the spinrotation and H hyperfine interactions, a more natural choice
for the coupling scheme in 13CCCCH would be F1 5 N 1 I
( 13C), F2 5 F1 1 S, F 5 F2 1 I (H). The fitting program,
however, is able to handle large off-diagonal terms in the
Hamiltonian matrix which occur when the coupling scheme
of Eq. ~2! is used, so for uniformity it was adopted for
13
CCCCH as well.
tude of the 13C hyperfine splitting, the lines that were observed possess the strongest theoretical line strengths; a
number of weaker hyperfine transitions were below the
present detection sensitivity.
In initial fits to the microwave data in Table I, the rotational constant B, the centrifugal distortion constant D, and
the spin-rotation distortion constant g D were constrained to
the millimeter-wave-derived values, and the proton hyperfine
constants constrained to the values for normal CCCCH. The
three remaining constants g , b F ~13C!, and c~13C! were varied
in fits to the seven or eight strongest hyperfine components
of the 1 – 0 transition for each isotopomer, resulting in a rms
of typically <20 kHz; subsequently, b F ~H! and c~H! were
varied as well, giving a rms comparable to the 5 kHz uncertainty in line measurements.
After the microwave transitions were assigned, global
fits including the millimeter-wave data of paper I were performed. For these, the microwave lines were assigned a frequency uncertainty of 5 kHz, and the millimeter-wave lines
uncertainties of between 35 kHz and 165 kHz, with most an
uncertainty of 50 kHz. Thus, in a typical global fit, say that
for 13CCCCH, each of the seven N 5 1 – 0 transitions were
given a weight of 100 relative to each of the eighteen
millimeter-wave transitions in the range of N 5 10 to 32.
The final hyperfine parameters derived from the global fits
were nearly identical to those calculated from the initial fits
and the global rms are comparable to those obtained from the
millimeter-wave data alone. Table II lists the spectroscopic
parameters determined from the global fit for each singly
substituted 13C isotopic species of CCCCH — the best summary of all the data at hand. For comparison, the spectroscopic constants of normal CCCCH from Ref. 13 are also
given. The predicted N 5 1 – 0 transitions of CCCCH are all
within a few kHz of the observed lines ~which for completeness are included in Table I!.
Table I also lists an assigned transition from the doubly
substituted CC13C13CH isotopomer. The coupling scheme for
doubly substituted isotopomers is similar to that for
the singly substituted species except that F2 5F1 1I
( 13C at position i) and F5F2 1I( 13C at position j!. This
transition was assigned to CC13C13CH on the basis of the
expected rotational constant ~see the r 0 structure in paper I!
and the hyperfine constants b F ~13C! and c~13C! of
CC13CCH and CCC13CH and b F ~H! and c~H! of normal
CCCCH. Two additional lines at 9266.130 and 9278.790
MHz were also observed but not assigned.
IV. RESULTS
Seven or eight hyperfine components of the N 5 1 – 0
transition were observed for each isotopomer. Table I gives
the measured frequencies of the observed transitions and
their assignments; a typical spectrum is shown in Fig. 1 together with the free induction decay from which it is derived.
In the Fourier transform spectrometer, the transition strength
is proportional to the product of the lower state population
~here all equal! and the first power — not the square — of
the absolute value of the transition dipole moment, assuming
the microwave power is adequate to achieve the p /2 pulse
condition. Although the assignment of the hyperfine components is different for each isotopomer owing to the magni-
V. DISCUSSION
Magnetic hyperfine coupling constants are sensitive
probes of the electronic structure and chemical bonding in
open-shell radicals like CCCCH, because they are proportional to expectation values of the valence electron, and thus
provide direct information of the molecular wave function.
Carbon-13 is particularly valuable because its hyperfine
structure provides additional probes of the wave function in
the neighborhood of each substituted position along the carbon chain.
J. Chem. Phys., Vol. 103, No. 18, 8 November 1995
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Chen et al.: Hyperfine structure of CCCCH
7831
TABLE I. Observed microwave transition frequencies and assignments for the carbon-13 isotopic species of CCCCH.
Frequencya
~MHz!
Species
CCCCH
13
CCCCH
C13CCCH
CC13CCH
CCC13CH
CC13C13CH c
9493.060
9497.615
9508.005
9547.960
9551.720
9562.905
9166.245
9167.370
9187.120
9188.325
9198.330
9218.700
9227.440
9448.165
9449.910
9458.940
9464.915
9495.830
9502.090
9502.270
9462.615
9463.810
9464.295
9474.860
9515.015
9519.530
9522.870
9533.800
9208.770
9211.425
9213.470
9221.490
9222.440
9253.940
9266.650
9183.205
O-C
~kHz!
21
21
0
21
3
1
3
4
3
4
1
2
3
24
1
0
24
22
21
21
0
5
2
24
22
21
2
2
25
5
27
25
11
4
25
Sb
N8
J8
F 18
F8
N
J
F1
F
0.17
0.42
0.08
0.08
0.08
0.17
0.129
0.249
0.166
0.083
0.071
0.071
0.130
0.119
0.249
0.152
0.075
0.056
0.057
0.109
0.063
0.249
0.154
0.085
0.095
0.065
0.075
0.071
0.111
0.249
0.138
0.052
0.056
0.054
0.089
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1.5
1.5
1.5
0.5
0.5
0.5
1.5
1.5
1.5
1.5
0.5
0.5
0.5
1.5
1.5
1.5
1.5
0.5
0.5
0.5
1.5
1.5
1.5
1.5
0.5
0.5
0.5
0.5
1.5
1.5
1.5
1.5
1.5
0.5
0.5
1.5
—
—
—
—
—
—
1
2
2
1
1
0
1
1
2
2
1
0
1
1
1
2
2
1
1
0
1
1
1
2
2
1
1
1
1
[email protected]#
1
2
1
1
0
1
1.5
2.5
1.5
0.5
0.5
0.5
1.5
1.5
2.5
1.5
0.5
0.5
1.5
0.5
0.5
2.5
1.5
1.5
1.5
0.5
0.5
1.5
1.5
2.5
1.5
1.5
0.5
1.5
1.5
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
—
—
—
—
—
—
0
1
1
1
1
0
1
0
1
1
1
1
1
0
0
1
1
1
0
1
1
1
0
1
1
1
1
0
1
[email protected]#
0
1
1
0
1
1
0.5
1.5
0.5
0.5
1.5
0.5
1.5
0.5
1.5
0.5
0.5
1.5
1.5
0.5
0.5
1.5
0.5
1.5
0.5
1.5
0.5
1.5
0.5
1.5
0.5
1.5
0.5
0.5
1.5
2
a
Measurement uncertainty is 5 kHz.
Relative intensities, normalized to unity.
c
The F 2 quantum number is shown in square brackets.
b
2
There are only two non-zero hyperfine parameters for a
S state, the Fermi-contact term, b F ~Ref. 14!,
b F5
8p
g b g b u ^ c ~ 0 ! & u 2 1 spin polarization
3 e n N
~3!
and the dipole–dipole term, c,
c5 32 g e b g N b N ^ ~ 3cos2 u 21 ! /r 3 & .
~4!
In Eqs. ~3! and ~4!, g e and g N are the electron and nuclear g
factors, b and b N are the Bohr and nuclear magnetons, r and
u are the spherical polar coordinates of the unpaired electron
with respect to the nucleus, and the brackets ^ & denote an
TABLE II. Spectroscopic constants of CCCCH isotopic species ~in MHz!.
Constanta
CCCCH b
B
D3103
g
g D 3103
b F ~13C!
c~13C!
b F ~H!
c~H!
4758.6557~7!
0.8627~10!
238.555~2!
0.127~9!
214.943~7!
12.44~1!
13
CCCCH
4594.5409~3!
0.8127~1!
236.670~4!
0.121~12!
396.8~6!
89.12~1!
214.91~1!
12.42~3!
C13CCCH
CC13CCH
CCC13CH
4734.6329~6!
0.8521~4!
238.001~5!
0.176~7!
57.49~5!
21.91~3!
214.99~2!
12.51~2!
4741.8672~7!
0.8561~4!
238.363~2!
0.113~6!
29.54~2!
9.84~8!
214.93~1!
12.50~6!
4614.9705~8!
0.8055~6!
237.491~11!
0.107~15!
18.56~4!
219.23~7!
214.935~5!
12.43~4!
The 1s uncertainties ~in parentheses! are in the units of the last significant digit.
Constants from Ref. 13.
a
b
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7832
Chen et al.: Hyperfine structure of CCCCH
FIG. 3. Resonance structures of CCCCH.
expectation value. The Fermi-contact constant b F can shed
light on the location of the unpaired electron along the carbon chain in s bonded radicals like CCH, CCCCH, and
CCCN because only s electrons have non-zero amplitude at
r50 and the unpaired electron is expected to have significant s character. In such cases, the contribution from the first
term in Eq. ~3! should be much larger than that from spin
polarization, which is typically &50 MHz in absolute magnitude. The magnetic dipole coupling constant c also provides useful information on the orbital occupation of the unpaired electron, because it is a function of both an angular
average and the radial expectation value of 1/r 3 . We will first
present a qualitative model for the Fermi contact interaction
along the carbon chain, followed by a more quantitative
analysis of the hyperfine constants.
A description of the bonding in CCCCH requires a superposition of several different electronic structures. Figure 3
shows the plausible resonance structures for CCCCH. Structure 1, with the unpaired electron localized on the terminal
carbon has the highest stability of all the resonance structures
because it has four p bonds: two between C(1) and C(2) , and
two between C(3) and C(4) , the carbon next to the H. Resonance structure 2, with the unpaired electron on C(2) , and
structure 4, with the electron on C(4) , each have three p
bonds and are less stable. Structure 3, with the unpaired electron on C(3) , is the least stable structure with only two p
bonds. The spin density should therefore be greatest at
C(1) , less at C(2) and C(4) , and least at C(3) . Assuming that
the electron configuration is identical in all four isotopomers,
then b F ~13C! for each isotopomer is a measure of the spin
density at carbon C(i) . From Table II we see that b F is 397,
57, 210, and 19 MHz, for C(1) through C(4) , which qualitatively is the predicted decrement. The negative value for
b F ~13C! at C(3) is an obvious manifestation of spin polarization, an effect which arises when the paired electrons in the
s orbital are slightly polarized by the electrons in the nearby
p orbitals.15
It is also useful to compare the hyperfine constants of
CCCCH with those of CCH since the bonding in both radicals should be somewhat similar. In 13CCH and C13CH ~Ref.
16!, respectively, b F ~13C! is 900.7~6! and 161.63~10! MHz,
and c~13C! is 142.87~3! and 64.07~5! MHz. Using simple
atomic orbitals, like those applied to CH ~Ref. 17!, it is possible to estimate crudely the fractional 2s and 2p character in
the 2 s molecular orbital,18 assuming the electron is localized
on either of the carbon atoms in CCH or on either of the two
carbon atoms furthest from hydrogen in CCCCH. For CCH
this calculation gives an unpaired electron spin density on
the terminal carbon of almost 75%, with the remaining 25%
on the adjacent carbon atom — there is little contribution
from the p p electronic configuration. This result is in good
agreement with the detailed ab initio calculations of Peyerimhoff and co-workers19 who conclude that the molecular
orbital is a s orbital, localized predominately on the terminal
carbon; they also calculate a slight ~7%! admixture of A 2 P
in the ground state even though this state lies 3600 cm21
higher in energy.
Although the hyperfine coupling constants of CCCCH
are smaller than those of CCH, a similar calculation gives
similar results except for the relative amount of p p character
~about 28%!, implying that the A 2 P electronic state may be
strongly mixed with the X 2 S 1 ground state. This result is
consistent with the ab initio calculations in paper I which
predict that the excitation energy of the A 2 P state is only
100650 cm21 . For even longer members of the ~CC!n H
homologous series, such as C6 H, the 2 P2 2 S energy separation is larger,20–22 with the 2 P ground state lying below the
2 1
S state.
A large zero-order mixing between the low-lying 2 P
state and the X 2 S 1 ground state might explain why ~i! b F
~13C! is a factor of two smaller for 13CCCCH than for
13
CCH; ~ii! c~13C! is 1.6 times smaller for 13CCCCH compared to 13CCH; and ~iii! c~13C! for C13CCCH is nearly zero,
whereas in C13CH it is 64 MHz. In isoelectronic CCCN,
where the 2 P state lies 2400650 cm21 above ground,1 the
effective b F ~13C! values at the terminal and the adjacent
carbon1 are comparable to CCH, suggesting that the admixture of 2 P character in the CCCN ground state will probably
be small. In fairly well-understood CCH it has been shown
that several other interactions,19 including the geometric dependence of the electronic matrix elements and vibronic effects, contribute to the hfs. Ultimately, high-level theoretical
calculations, similar to those on CCH,19 are needed for a
more detailed interpretation of the hyperfine interactions.
Further laboratory experiments to measure the Stark and
Zeeman properties of CCCCH are planned to better characterize the electronic ground state and in particular to determine the admixture of A 2 P.
ACKNOWLEDGMENTS
We are indebted to H. M. Pickett for providing us with
his computer programs and for assistance in using them and
J. M. Brown for helpful comments. We also wish to thank A.
R. Hight Walker who participated in our first attempts to
study radicals in the FT apparatus, M. J. Travers who assisted in the early FT experiments on CCCCH, E. W. Gottlieb for computer and programming assistance, and Y. Endo
for kindly providing us with a copy of the pulsed discharge
circuit diagram. In the preparation of the 13C enriched acetylene we also gratefully acknowledge the help and advice
from L. A. Silks III at the NIH Stable Isotope Resource at
Los Alamos, a facility supported by U.S.P.H.S. Grant No.
RR02231 and the Department of Energy. M.C.M. thanks the
Harvard-Smithsonian Center for Astrophysics for a post-
J. Chem. Phys., Vol. 103, No. 18, 8 November 1995
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Chen et al.: Hyperfine structure of CCCCH
doctoral fellowship and S.E.N. thanks the National Science
Foundation, Grant No. CHE-9423355, for partial support of
this research.
1
M. C. McCarthy, C. A. Gottlieb, P. Thaddeus, M. Horn, and P.
Botschwina, preceding paper, J. Chem. Phys. 103, 7820 ~1995!.
2
A. R. Hight Walker, W. Chen, S. E. Novick, B. D. Bean, and M. D.
Marshall, J. Chem. Phys. 102, 7298 ~1995!.
3
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4
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7833
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J. Chem. Phys., Vol. 103, No. 18, 8 November 1995
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