JOURNAL OF CHEMICAL PHYSICS
VOLUME 110, NUMBER 10
8 MARCH 1999
Gas phase spectroscopy of alkali carbides: The pure rotational spectrum
of KC „ X 4 S 2 …
J. Xin and L. M. Ziurys
Department of Chemistry, Department of Astronomy and Steward Observatory, 933 North Cherry Avenue,
University of Arizona, Tucson, Arizona 85721-0065
~Received 2 September 1998; accepted 1 December 1998!
The pure rotational spectrum of the KC radical in its X 4 S 2 ground state has been recorded using
millimeter/submillimeter direct absorption spectroscopy. This study is the first gas phase
observation of potassium carbide, and of any alkali metal carbide species. The molecule was
produced under d.c. discharge conditions by the reaction of potassium vapor and CH4; the vapor
was generated in a Broida-type oven. Eleven rotational transitions were measured for KC in the
frequency range 344–515 GHz; fine structure was resolved in every transition, which consisted of
a quartet pattern. The data were analyzed using nonlinear least-squares methods in a Hund’s case ~b!
basis, and rotational and fine structure parameters were accurately determined. The third-order
contribution to the spin–rotation term was not found necessary for the data fit, although it has been
suggested for states of quartet multiplicity and higher. The spin–spin interactions in KC appear to
have a significant direct dipolar component. The bond length and electron configuration in KC have
also been established, which suggest some covalent character to its bonding. © 1999 American
Institute of Physics. @S0021-9606~99!01909-1#
ence of M–C triple bonds,7 unusual perturbations from
close-by electronic states,4,6 and unexpected electron
configurations.14
Because of the obvious chemical significance of metal
carbide species, and the fact that they may be abundant in
circumstellar envelopes of late-type stars,15 we have been
interested in measuring the pure rotational spectra of such
species at millimeter and sub-mm wavelengths. Following
the LIF study by Balfour et al.,7 we succeeded in obtaining
the pure rotational spectrum of FeC16 in its 3 D i ground state.
Unlike the previous measurements, we produced this carbide
using a Broida-type oven17 as a source of metal vapor, which
was then reacted with CH4, the same carbide precursor used
in the laser ablation experiments ~e.g., Refs. 6–8!. We were
uncertain, however, whether we could produce carbides of
lower melting point metals, such as the alkali or alkaline
earth groups, using this same technique.
Here we report on some of the results of these experiments, namely, the measurement of the pure rotational spectrum of potassium carbide, KC. To our knowledge, this study
is the first spectroscopic detection of gas phase KC by any
technique, as well as the first alkali monocarbide to be observed. Eleven transitions of this free radical were recorded
in the submillimeter wave region for the main potassium
isotope, 39K. The ground state of this species was readily
identified as 4 S because of the regular spaced quartet features present in the spectra. The data have been analyzed in a
case ~b! basis and rotational, spin–rotation, and spin–spin
parameters have been determined for this radical, as well as
its bond length. Such an analysis is of particular interest
because few molecules with 4 S ground electronic states have
been investigated at high resolution ~,1 MHz!. The parameters of KC are also compared with other carbides and
I. INTRODUCTION
Metal monocarbide molecules are of general chemical
interest. First of all, they are the simplest of organometallic
compounds, as they involve one bond between carbon and a
metal in the smallest possible unit. Evaluating the characteristics of this bond should yield fundamental information on
how carbon interacts with metal atoms, and possible ways to
better activate C–C and C–H bonds.1 Investigating metal
carbide species also can lead to further developments in organic synthesis, where simple organometallic compounds
such as methyl lithium and Grignard reagents are routinely
used.2 Moreover, it is important for understanding homogeneous and heterogeneous catalysis,3 especially in examining
interactions between carbon-containing gases and metal surfaces. Finally, it has recently been suggested that adding
metal carbides to H2 may provide high energy density
fuels.4,5 Knowledge of how to create such species and their
properties is essential for such fuel research.
Metal carbides pose a great challenge to experimentalists, not only because these species are mostly short-lived
free radicals, and difficult to create in detectable concentrations in the gas phase, but also in the interpretation of their
complex spectra arising from states with high multiplicity.
Recently, development of laser ablation and supersonic beam
techniques, coupled with laser induced fluorescence ~LIF!,
have allowed detailed studies of electronic spectra of transition metal carbides, including CoC,6 FeC,7 IrC,8 and YC.9
Also, optical transitions of AlC have been recorded using
hollow cathode methods.4 Previous to these works, the only
structural data on metal carbides was from optical spectroscopy of Scullman and co-workers, who examined PtC, RhC,
IrC, and RuC.10–13 These recent studies have yielded interesting information on the metal carbides, including the pres0021-9606/99/110(10)/4797/6/$15.00
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© 1999 American Institute of Physics
4798
J. Chem. Phys., Vol. 110, No. 10, 8 March 1999
potassium-containing molecules to establish the nature of an
alkali–carbon bond.
J. Xin and L. M. Ziurys
TABLE I. Observed rotational transition frequencies of KC (X 4 S 2 ; v
50). a
N 8 ←N 9
II. EXPERIMENT
The millimeter/submillimeter spectrometer used to carry
out these measurements is described in detail elsewhere.18 It
consists of a Gunn oscillator/varacter multiplier source, a gas
chamber with an adjoining Broida-type oven, and an InSb
hot electron bolometer as a detector. Submillimeter radiation
is propagated quasioptically through this system, and phasesensitive detection is achieved through FM modulation of the
Gunn oscillator and use of a lock-in amplifier.
To synthesize KC, potassium vapor was reacted with
CH4 under extreme d.c. discharge conditions. To create the
vapor, a Broida-type oven was used, as mentioned. The
metal vapor was mixed with 8 mtorr of CH4 and 20–25
mtorr of argon, which was added through the bottom of the
oven. The whole mixture was then discharged over the top of
the oven using 500–700 mA of current at 200 V. The d.c.
discharge often became unstable and sometimes was difficult
to maintain. When stabilized, the plasma glowed a pale
purple. These conditions also produced the KCH radical. Extreme care had to be taken when removing the oven and
cleaning the cell after use because of the explosive nature of
potassium on contact with air.
In order to locate transitions, the rotational constant of
KC was estimated using the K–C bond length of KCCH.19
Large frequency ranges were then searched to locate the KC
lines, using scans 100 MHz in coverage. Experimental conditions were varied during scanning to enhance the production of the radical. Once found, transition frequencies were
measured using 5 MHz scans centered on individual features.
Typically for this measurement, an average of two scans
were used, one in ascending and the other in descending
frequency, each about 5 s in duration. This procedure was
done to compensate for a small frequency shift resulting
from the time constant delay of the lock-in amplifier. Experimental accuracy is estimated to be 650 kHz.
20←19
21←20
22←21
23←22
24←23
25←24
26←25
27←26
28←27
III. RESULTS AND ANALYSIS
The transition frequencies recorded for potassium carbide are listed in Table I. Each of the 11 rotational transitions
observed consists of four fine structure components. This
structure arises from spin–spin and spin–rotation interactions, which split each rotational level into four sublevels, as
shown in Fig. 1. These sublevels are indicated by quantum
Y 1SY and N is the rotational quantum
number J, where JY 5N
number. For a 4 S state, S53/2; hence, J5N61/2, N63/2,
resulting in four separate levels. In the Hund’s case ~b! limit,
appropriate for S states, these four sublevels are relatively
closely spaced and are indicated by F 1 (J5N13/2), F 2 (J
5N11/2), F 3 (J5N21/2), and F 4 (J5N23/2). The most
strongly allowed electric dipole transitions occur when DJ
5DN511. Each rotational transition should therefore consist of four strong lines, as shown in Fig. 1, with any additional components ~i.e., for DJ50) being much weaker.
As found in Table I, the four fine structure components
are relatively closely spaced in frequency, as expected for a
29←28
30←29
a
J 8 ←J 9
v obs
v obs – v calc
18.5←17.5
19.5←18.5
20.5←19.5
21.5←20.5
344 092.254
344 097.420
344 100.844
344 105.918
20.006
20.002
0.023
20.005
19.5←18.5
20.5←19.5
21.5←20.5
22.5←21.5
361 222.102
361 227.325
361 230.857
361 235.943
20.053
20.014
20.008
0.014
20.5←19.5
21.5←20.5
22.5←21.5
23.5←22.5
378 341.095
378 346.323
378 349.961
378 354.930
20.001
0.025
0.029
20.030
21.5←20.5
22.5←21.5
23.5←22.5
24.5←23.5
395 448.578
395 453.802
395 457.532
395 462.491
0.018
0.028
0.032
20.004
22.5←21.5
23.5←22.5
24.5←23.5
25.5←24.5
412 544.021
412 549.258
412 553.026
412 558.034
20.002
0.011
20.026
0.020
23.5←22.5
24.5←23.5
25.5←24.5
26.5←25.5
429 626.981
429 632.150
429 636.045
429 640.997
0.018
20.044
20.020
0.001
24.5←23.5
25.5←24.5
26.5←25.5
27.5←26.5
446 696.854
446 702.081
446 705.998
446 710.907
20.003
20.011
20.023
20.014
25.5←24.5
26.5←25.5
27.5←26.5
28.5←27.5
463 753.209
463 758.461
463 762.413
463 767.261
0.026
0.040
0.015
20.008
26.5←25.5
27.5←26.5
28.5←27.5
29.5←28.5
480 795.409
480 800.686
480 804.652
480 809.477
20.011
0.028
20.026
20.041
27.5←26.5
28.5←27.5
29.5←28.5
30.5←29.5
497 823.025
497 828.351
497 832.347
497 837.126
20.022
0.067
0.008
20.023
28.5←27.5
29.5←28.5
30.5←29.5
31.5←30.5
514 835.556
514 840.697
514 844.828
514 849.736
0.013
20.081
20.034
0.094
In MHz; residuals are from fit not using g s.
good case ~b! molecule. The total separation of the quartets
is 13.7 MHz for the N519→20 transition, and the splitting
only increases slightly at higher N. The components also do
not cross each other in the range of N519– 30 studied here;
this behavior is again typical in the case ~b! limit, where at
higher N, the F 1 and F 4 (J5N63/2) levels approach one
energy, and the F 2 and F 3 (J5N61/2) levels approach another energy. The separation of these two energy limits is 4
times the spin–spin constant l. Hence, a regular quartet pat-
J. Chem. Phys., Vol. 110, No. 10, 8 March 1999
J. Xin and L. M. Ziurys
4799
resolved, labeled by the appropriate J quantum number. This
spectrum covers 80 MHz in frequency and was recorded in
about 50 s.
These spectra were analyzed using nonlinear, leastsquares methods with the following effective Hamiltonian,
which consists of molecular frame rotation, spin–spin, and
spin–rotation interactions terms:
Ĥ eff5Ĥ rot1Ĥ ss1Ĥ sr .
~1!
The first term in this expression concerns the rotational constant B and centrifugal distortion corrections D and H,
namely,
Ĥ rot5BN2 2DN4 1HN6 .
~2!
The fine structure interactions involve l, the spin–spin parameter, and g, the spin–rotation term, as well as both of
their centrifugal distortion corrections l D and g D , i.e.,
FIG. 1. A rotational energy level diagram for a 4 S electronic state in a case
~b! coupling scheme. Each rotational level, indicated by quantum number N,
is split into four sublevels due to spin–spin and spin–rotation interactions.
These four levels are specified by quantum number J, where J5N61/2
(F 2 ,F 3 ) and J5N63/2 (F 1 ,F 4 ). The strongest electric-dipole-allowed
transitions are when DN5DJ561, as shown, such that four strong components should be present per rotational line.
tern is expected, although at very low N the levels can cross
and revert to a case ~a! coupling scheme. ~The term value
formulas for these fine structure levels can be found in Ref.
20!. No evidence of hyperfine interactions were observed in
the data, which would arise from the potassium 39K nuclear
spin of I53/2. It might be detectable at lower N. Moreover,
no lines of the potassium-41 isotope of KC were detected,
which is not unexpected given the 39K: 41K abundance ratio
of 0.93:0.07.
A typical spectrum recorded for KC is shown in Fig. 2.
These data are the N527→28 rotational transition near
480.8 GHz. The four fine structure components are clearly
Ĥ ss52/3l ~ 3S 2Z 2S2 ! 12/3l D ~ 3S 2Z 2S2 ! N2 ,
~3!
Ĥ sr5 g ~ N•S! 1 g D ~ N•S! N2 .
~4!
Although the rotational and spin–rotation terms are easy to
evaluate in a case ~b! basis uNJS&, the spin–spin Hamiltonian,
as written, involves S Z , an operator not defined in this coupling scheme. In a case ~b! basis, Ĥ ss takes on a complicated
form in Cartesian coordinates, and is more easily expressed
in the following spherical tensor notation, where q refers to
molecule-fixed components:
Ĥ ss52/3A6lT 2q50 ~ S,S! 11/3A6l D @ T 2q50 ~ S,S! ,N2 # 1 .
~5!
21
According to Hougen, for a S state with even multiplicity, S21/2 spin–spin parameters and S11/2 spin–
rotation constants are necessary in the effective Hamiltonian,
not considering centrifugal distortion corrections. For a 4 S
state, this general rule means one spin–spin parameter ~l!
and two spin–rotation parameters are required to model the
data. As discussed by Brown and Milton22 and Nelis, Brown,
and Evenson,23 the second spin–rotation parameter ~after g!
involves a third order spin–orbit interaction and is given the
symbol g s . In spherical tensor notation, this term has the
form:23
Ĥ ~sr3 ! 5 ~ 10/ A6 ! g s T 3 ~ L2 ,N! •T 3 ~ S,S,S! .
FIG. 2. Spectrum of the N527→28 rotational transition of KC in its X 4 S 2
ground state near 480.8 GHz observed in this work. The four expected fine
structure components ~see Fig. 1! are clearly visible, and are indicated by
quantum number J. These data cover 80 MHz in frequency and were recorded in one scan with a duration of about 50 s.
~6!
The actual matrix elements for this spin–rotation contribution in a case ~b! basis are given in Nelis et al.,23 and only
those with DN50, 62 are nonzero for a 4 S state. According
to Brown and Milton, the third order term may be necessary
in high precision measurements for states with quartet and
higher multiplicity.
In the analysis carried out for KC in this work, the data
were fitted with a Hamiltonian that included the third order
spin–rotation correction g s and one without it. The results of
these two separate fits are given in Table II. As shown, in the
analysis not using the third-order spin–rotation interaction,
the rotational constants B, D, and H and fine structure parameters l, l D , g, and g D were necessary to fit the data. All
seven parameters are well defined, and the rms of the fit is 30
kHz, which is excellent. Moreover, all residuals v obs – v calc
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J. Chem. Phys., Vol. 110, No. 10, 8 March 1999
TABLE II. Spectroscopic constants for KC (X 4 S 2 ). a
Without Ĥ sr(3)
Value
Parameter
B0
D0
109 H 0
g
gD
l
lD
8619.8957~44!
0.021 779 9~68!
8.0~3.4!
5.268~58!
20.000 095~24!
17 033.2~9.8!
0.002 22~23!
B0
D0
109 H 0
g
gD
gS
l
lD
rms of fit
a
0.030
TABLE III. Bond lengths for metal carbide species.
With Ĥ sr(3)
Parameter
J. Xin and L. M. Ziurys
Value
8619.8964~58!
0.021 780 6~89!
8.2~4.4!
5.16~19!
20.000 067~55!
20.019~30!
17 059~43!
0.002 13~33!
0.029
All values in MHz; errors are 3 sigma and apply to the last quoted decimal
places.
~see Table I! are less than 95 kHz. In the analysis including
the second spin–rotation term, the fit did not significantly
improve ~the rms of the fit was 29 kHz!, and g s was not well
defined with a value of 219630 kHz. All other constants
have slightly higher errors, as well.
IV. DISCUSSION
The spectra and analysis of KC indicate that this radical
has a 4 S 2 ground state. To our knowledge, there are no
theoretical studies existing for KC, but several calculations
have been done for the alkali carbide LiC.24,25 These computations have suggested that LiC has a 4 S 2 ground electronic state arising from a s 1 p 2 configuration. Such a configuration also results in 2 S 1 and 2 S 2 terms, but the 4 S 2
state lies lowest in energy. The first excited electronic state
for LiC is predicted to be a 2 P state, which arises from a
s 2 p 1 orbital occupancy. According to Ricca and
Bauschlicher,25 covalently bonded carbides favor the s 2 p 1
configuration and a 2 P ground state, such as in CH, while
more ionic species prefer the s 1 p 2 occupation and a 4 S 2
ground state. KC is thus following the trend predicted for
LiC ~i.e., a s 1 p 2 configuration!, as opposed to being similar
to CH. The ground state electron configuration in KC is
therefore (7 s ) 2 (8 s ) 1 (3 p ) 2 .
The 4 S 2 ground state for KC invites the question of the
degree of ionic character in the bonding in this radical. Theoretical calculations suggest that 0.72e2 is transferred from
the lithium atom to carbon in LiC,25 such that the Li1C2
resonance structure should dominate. Such a proposed electron transfer means that the ground state should correlate
with Li1 and C2 at large internuclear separation; instead, it
correlates with Li2S(2s 1 )1C3P(2s 2 2p p2 ), because of
avoided crossings. Such a correlation suggests that there is
some covalent character to the LiC bond, as might be found
in KC.
Comparison with other carbides that have been studied
experimentally should bring some insight to the bonding issue, although these all involve transition metals. Transition
metal carbides appear to be primarily covalently bonded. For
example, theoretical calculations for RuC26 suggest only
0.27e2 is transferred from the metal to the carbon atom, and
that the Ru–C bond is a triple bond with one s and two p
Molecule
CoC
NiC
FeC
KC
Ground state
1
S
S1
3
D
4 2
S
2
1
r 0 ~M–C! ~Å!
1.5612
1.631
1.593
2.513
bonds. FeC also has a similar triple bond,7,16 and to account
for the 2 S 1 ground state of CoC,6 a triple bond is possible as
well. The triple bonds are reflected in the bond lengths given
for third row metal carbides, listed in Table III. The bond
lengths for FeC, CoC, and NiC ~M. Morse, private communication! are all quite similar at 1.5–1.6 Å, and relatively
short. They are also about 0.5 Å shorter than predicted from
covalent radii.
In contrast, the KC bond is considerably longer: 2.513
Å, also shown in Table III. ~This number was calculated
from B 0 listed in Table II, and is an r 0 bond length.! Such
lengthening might suggest a transition from covalent to ionic
bonding in KC. However, there are other effects which may
account for this change. For example, the three unpaired
electrons in KC suggest some degree of sp 3 hybridization of
the carbon, and the presence of a single bond to potassium.
The single bond in KC should be longer than the triple bond
in transition metal carbides. In addition, the atomic radius of
potassium ~2.27 Å! is considerably larger than those of iron,
nickel, or cobalt ~; 1.25 Å!.27 It is also comparable to the
K–C bond length in KCCH, which is 2.540 Å19 and presumably has non-negligible covalent character. Therefore, the increased bond length in KC is consistent with covalent trends
of the transition metal carbides. It should also be noted that
the ionic radius of C2 is 2.6 Å, suggesting an even longer
bond length for a very ionic KC.
The pure rotational spectrum of potassium carbide is one
of the few obtained for a species in a 4 S 2 ground electronic
state. As the analysis done here suggests, use of the thirdorder spin–rotation interaction does not appear to be necessary for KC. Including this term in the Hamiltonian did not
improve the fit and the spin–rotation term g s in the end was
not well defined. Examining the use of this parameter in
other studies, it clearly was necessary in analyzing electronic
spectra of the C 4 S 2 state of VO, but not for the X 4 S 2
ground state.28 It was additionally used for fitting LMR rotational data of the a 4 S 2 state of CH,23 although the value
calculated was small and no better defined than our parameter ( g s 50.15460.279 MHz, 3s error!. On the other hand,
g s was not used to analyze pure rotational spectra of the
X 6 S 1 states of CrCl29 and CrH.30 It may be that this third
order correction becomes more significant in excited states
where there are more close-by perturbing states.
It is also significant that the spin–rotation term g in KC
is quite small @5.268~58! MHz#, suggesting that the nearest
4
P states lie at high energies. Although there is no information available on excited states of KC, experimental or theoretical, calculations for LiC25 suggest that this may indeed
be the case. For LiC, all 4 P states are repulsive and lie
J. Chem. Phys., Vol. 110, No. 10, 8 March 1999
J. Xin and L. M. Ziurys
considerably higher in energy than numerous other doublet
states.
The value of l for potassium carbide, on the other hand,
is relatively large ~17 033 MHz!, and actually greater in
value than B, the rotational constant. The spin–spin constant
consists of two contributions, direct spin–spin coupling and
a second-order spin–orbit contribution, i.e.,
l eff5l ss1l so.
~7!
For heavier molecules, it is thought that l .l , as might
be the case for KC. For this molecule, a major contribution
to l so would likely come from the first excited 2 P state,
which has the s 2 p 1 configuration. Another term affecting
l so is the iso-configurational 2 S 1 state. Judging from the
theoretical calculations for LiC,25 these two states lie close to
each other in energy. Hence, their energies above the ground
4 2
S state are comparable.
The energy of the 2 P state above the X 4 S 2 state can be
predicted from its spin–orbit constant A and the spin–orbit
contribution to l, with the following approximate formula:23
so
l so.
A 2~ 2P !
.
12DE ~ 2 P2 4 S 2 !
ss 31
~8!
Similarly, the energy of the nearest 2 S 1 state can be estimated from l so by the relationship:31
l so.
A 2~ 2P !
.
6DE ~ 2 S 1 2 4 S 2 !
~9!
Because DE( 2 S 1 2 4 S 2 ) is roughly comparable to DE( 2 P
2 4 S 2 ), these two expressions for l so can be combined to a
single equation:
l so.
A 2~ 2P !
.
4DE ~ 2 P2 4 S 2 !
~10!
The spin–orbit constant A of the P state can be estimated
from that of atomic carbon with a single electron in a 2 p
orbital. This value is z 527.5 cm21. 23
If l eff;lso, as might be the case for a heavier molecule,
then Eq. ~10! suggests that the energy separation of the
ground X 4 S 2 and 2 P excited states is 333 cm21. This number is low, since the fundamental stretching frequency of KC
is ;360 cm21, derived using the relationship v 2 ;4B 3e /D e ,
where B 0 ;B e and D 0 ;D e . Moreover, the separation between the a 4 S and X 2 P states in CH is 6030 cm21,23 and
the theoretical estimate for this energy difference in LiC is of
order 10 000 cm21. Because KC is heavier than LiC, the
4 2 2
S 2 P energy difference for potassium carbide will be
less than 10 000 cm21. To predict a value, energies of other
lithium and potassium species can be compared. For example, the energy difference between the A – X states of LiH
is on the order of 26 500 cm21, while the same separation in
KH is 19 050 cm21.32 Using these two values to derive a
scaling factor, the estimated energy above ground state for
the 2 P state in KC is ;7000 cm21. Comparing with alkaline
earth monomethyl species,33 the same scaling factor is about
0.5, corresponding to an energy of 5000 cm21 for the 2 P
state. Hence, assuming a lower limit to the energy difference
of 1000 cm21 is reasonable. Using this value, the spin–orbit
contribution is calculated to be < 5700 MHz. The effective
2
4801
spin–spin parameter l itself is ; 17 000 MHz. Consequently, spin–spin dipolar interactions appear to contribute
significantly to the l parameter in the 4 S 2 ground state of
KC. A similar situation is found for the a 4 S 2 state of CH.23
In contrast, for molecules of comparable weight, namely
SeO, SeS, and SO, the l ss term accounts for less than 5% of
l eff.31 The presence of only s valence electrons in potassium
may account for the smaller spin–orbit interactions in KC.
Clearly other alkali carbide molecules need to be studied to
examine this trend.
V. CONCLUSIONS
Alkali monocarbide species have rarely been investigated in the past, theoretically or experimentally, although
they are obvious case studies because of the importance of
the alkali metals in organic synthesis. Our measurements of
the pure rotational spectrum of KC has demonstrated that
this radical has a 4 S 2 ground electronic state that may have
a non-negligible covalent component to its bond, although
extrapolation from theoretical predictions for LiC indicates a
largely ionic one. Determination of the fine structure constants for KC show that direct-spin dipolar interactions play
a significant role in the spin–spin term. Spin–orbit coupling
is not as important for KC as it is in the transition metal
species. The third-order spin–orbit contribution to the spin
rotation term was not found necessary in the analysis, also an
indication of this effect. Finally, this study suggests that
other alkali carbide species can be synthesized in the gas
phase using Broida-oven or similar techniques. Their investigation should result in new insights into how carbon bonds
to main group metals.
ACKNOWLEDGMENTS
This research was supported by NSF Grant AST-9503274, CHE-95-31244, and NASA Grant NAG5-3785.
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