30 November 2001
Chemical Physics Letters 349 (2001) 249±256
www.elsevier.com/locate/cplett
The millimeter/sub-millimeter spectrum of the LiS
radical in its 2Pi ground state
M.A. Brewster, L.M. Ziurys
*
Department of Chemistry, Department of Astronomy and Steward Observatory, University of Arizona,
933 North Cherry Avenue, Tucson, AZ 85721, USA
Received 12 September 2001
Abstract
The pure rotational spectrum of LiS …X2 Pi † has been recorded in the v ˆ 0 and v ˆ 1 states in the region 130±540
GHz using millimeter/sub-millimeter direct absorption methods. This radical was synthesized from lithium vapor and
CS2 in a DC discharge. Transitions arising from the two orbit components were measured, both which exhibited
lambda-doubling and, for the X ˆ 1=2 ladder, hyper®ne interactions. Rotational, lambda-doubling, and hyper®ne
parameters have subsequently been determined. These data prove unambiguously that the ground state of LiS is 2 Pi
and suggest that the A2 R‡ state lies 4300 cm 1 higher in energy. The bonding in this radical appears to be predominantly ionic. Ó 2001 Elsevier Science B.V. All rights reserved.
1. Introduction
Metal oxide species play a major role in a
variety of environments, including high temperature reactions, corrosion processes, catalysis and in
stellar atmospheres [1±3]. Examining the bonding
in these molecules has thus been the topic of much
experimental, e.g., [4±6], and theoretical work,
e.g., [7±9]. Also of interest are the corresponding
metal sul®de species. Although substitution of the
oxygen atom by sulfur produces an isovalent
compound, di€erences in electronegativity and
valence electron con®gurations between these two
elements are thought to generate subtle structural
variations [10,11]. For example, metal monosul®des are predicted to form bonds that are
*
Corresponding author. Fax: +520-621-1532.
E-mail address: [email protected] (L.M. Ziurys).
longer and sometimes weaker than their oxide
counterparts. They also may be more covalent in
certain instances.
One oxide system which has been heavily investigated in the past is the alkali metal group.
These molecules have attracted particular interest
because the ground state term is predicted to
change from 2 P to 2 R as the periodic table is
descended [12,13], with the cross-over occurring
between NaO and KO. Experimentally, it has been
found that both NaO and LiO have 2 P ground
electronic states [14,15], while those of RbO and
CsO are 2 R [5,6]. There is some evidence that KO
has 2 P symmetry in its ground state as well [16].
This change in electronic term and hence electron
con®guration (r2 p3 vs. p4 r1 ) has been attributed
to the competition between electrostatic and exchange interactions [11]. A similar trend is predicted for the alkali sul®des, except the change in
symmetry is calculated to occur later down the
0009-2614/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved.
PII: S 0 0 0 9 - 2 6 1 4 ( 0 1 ) 0 1 2 0 2 - 7
250
M.A. Brewster, L.M. Ziurys / Chemical Physics Letters 349 (2001) 249±256
column. Computations have suggested that KS
and RbS, for example, have 2 P ground states, in
contrast to their oxide counterparts [11].
Naturally, it is of interest to investigate the
electronic ground states of the alkali sul®de species, as well as their bonding properties and other
characteristics, especially in comparison to the
oxides. To achieve this end, we have measured the
pure rotational spectrum of both NaS [17] and KS
[18], using millimeter/sub-millimeter direct absorption methods. These radicals had not been
studied previously by any spectroscopic technique.
The recorded spectra have clearly shown that the
ground state of both molecules is 2 P, in agreement
with theory. Moreover, transitions of both radicals
exhibited large lambda-doubling, signifying the
existence of a nearby 2 R state, also predicted by
theoretical calculations [10]. LiS, on the other
hand, has never been investigated by any spectroscopic method. This sul®de is particularly important because it can be compared most directly
to the hydrogen analog, SH. Despite the fact that
hydrogen and lithium both have one valence
electron, their corresponding analogs are often
predicted to have di€erent electronic ground
states, such as CH (X2 Pr ) and LiC …X4 R† [19].
Here we present the ®rst experimental study of
the LiS radical. The pure rotational spectrum of
this species has been recorded using millimeter/
sub-millimeter direct absorption methods. Observation of both spin±orbit components (X ˆ 1=2
and 3/2) and their lambda-doubling interactions
con®rms that the electronic ground state of this
species is indeed 2 Pi . Hyper®ne splittings, arising
from the 7 Li nucleus, were also observed. In this
Letter we present our spectroscopic measurements
and analysis for this molecule, compare these results with those obtained previously for NaS and
KS, and discuss the implications for bonding in
alkali sul®de compounds.
2. Experimental
The measurements were conducted with one of
the millimeter/sub-millimeter direct absorption
spectrometers of the Ziurys group. Details can be
found in [20]. Brie¯y, this instrument consists of a
phase-locked Gunn oscillator/varactor multiplier
radiation source, a 0.5 m long double-pass reaction cell containing a Broida-type oven, and an
InSb hot electron bolometer detector. Phase-sensitive detection is carried out using source modulation.
Lithium sul®de was generated in a DC glow
discharge in a mixture of 5±8 mTorr CS2 , 15±20
mTorr argon, and K 1 mTorr of Li vapor. The
metal vapor was produced by the Broida-type
oven. Carbon disul®de and argon were mixed together prior to introduction into the reaction
chamber. They were then ¯owed into the cell beneath the oven to assist in carrying the metal vapor
into the discharge region, located about 5 cm
above the oven itself. The discharged gas mixture
exhibited a bright magenta color, likely due to
emission of atomic lithium.
An approximate rotational constant of LiS was
initially estimated from theoretical studies [19],
which predicted bond lengths. Based on this value,
extensive regions in frequency space … 5±6 GHz†
were continuously searched to locate the LiS signals. Once the rotational pattern had been established and both spin±orbit components identi®ed,
only scans 100 MHz in frequency coverage were
required to ®nd additional transitions. The LiS
signals were in general suciently intense such that
transition frequencies could be obtained from an
average of one scan taken in increasing frequency
and another in decreasing frequency. However,
below 250 GHz, the presence of hyper®ne splittings required as many as 20 such scan averages to
obtain reasonable signal levels. Typical linewidths
varied from 470±1300 kHz.
3. Results and analysis
Table 1 presents the transition frequencies
measured for LiS. Forty-three individual lines
were recorded for this radical in its v ˆ 0 vibrational state, and 18 in the v ˆ 1 level. As is evident
in the table, both spin±orbit components were
observed in each state. In the X ˆ 3=2 ladder, the
lambda-doubling was found to be on the order of
3±35 MHz, with the splitting increasing with increasing J; it was considerably larger … J 5 GHz†
Table 1
Observed transition frequencies for LiS (X2 Pi )a
vˆ0
2
J 00
3.5
3.5
3.5
3.5
3.5
3.5
3.5
3.5
4.5
4.5
4.5
4.5
4.5
4.5
4.5
4.5
6.5
6.5
7.5
7.5
8.5
8.5
9.5
9.5
10.5
10.5
11.5
11.5
12.5
12.5
13.5
13.5
14.5
14.5
Parity
f
f
f
f
e
e
e
e
f
f
f
f
e
e
e
e
f
e
f
e
f
e
f
e
f
e
f
e
f
e
f
e
f
e
F 00
4
3
2
1
4
3
2
1
5
4
3
2
5
4
3
2
b
F0
5
4
3
2
5
4
3
2
6
5
4
3
6
5
4
3
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
mobs
mo
b
132 017.458
±
±
±
132 015.776b
±
±
±
169 724.380b
±
±
±
169 721.147b
±
±
±
245 107.485
245 100.373
282 779.366
282 769.888
320 435.329
320 423.146
358 073.178
358 058.025
395 690.866
395 672.283
±
±
470 856.876
470 830.649
508 400.979
508 370.429
±
±
c
)0.160
0.192
)0.057
0.098
0.028
0.022
0.006
)0.005
0.001
)0.022
)0.035
)0.003
0.000
)0.046
)0.007
)0.015
0.029
0.022
2
P1=2
mobs
mo
135 072.592
135 073.530
135 073.876c
135 073.876c
130 203.366
130 204.165c
130 204.165c
130 204.165c
172 954.484
172 954.955
172 955.173c
172 955.173c
168 088.874
168 089.273c
168 089.273c
168 089.273c
248 685.234
243 828.882
286 529.426
281 679.080
324 356.743
319 513.274
362 164.999
357 329.151
399 951.941
395 124.590
437 715.408
±
475 453.219
470 645.365
513 163.161
508 366.301
±
±
)0.017
0.197
0.175
0.164
)0.062
0.377
0.055
)0.229
)0.020
0.056
0.062
0.033
0.078
0.290
0.098
)0.096
0.015
)0.002
)0.025
)0.023
)0.046
0.009
)0.032
)0.021
)0.040
)0.035
)0.032
c
0.007
)0.010
0.059
0.024
2
P3=2
mobs
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
391 439.150
391 420.950
428 630.017
428 608.196
465 796.520
465 770.796
502 936.521
502 906.573
540 047.926
540 013.414
mo
c
0.038
0.013
0.006
)0.027
)0.014
)0.019
)0.027
)0.007
0.010
0.030
P1=2
mobs
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
390 820.585
±
428 185.187
470 354.374
465 525.114
507 656.253
502 838.220
544 928.253
540 122.233
mo
c
0.006
)0.004
0.003
)0.013
)0.004
0.016
0.002
)0.065
M.A. Brewster, L.M. Ziurys / Chemical Physics Letters 349 (2001) 249±256
2.5
2.5
2.5
2.5
2.5
2.5
2.5
2.5
3.5
3.5
3.5
3.5
3.5
3.5
3.5
3.5
5.5
5.5
6.5
6.5
7.5
7.5
8.5
8.5
9.5
9.5
10.5
10.5
11.5
11.5
12.5
12.5
13.5
13.5
J0
vˆ1
2
P3=2
a
In MHz.
Blend of all hf components.
c
Blended lines.
b
251
252
M.A. Brewster, L.M. Ziurys / Chemical Physics Letters 349 (2001) 249±256
in the X ˆ 1=2 sub-level, and in this case the
splitting decreased with increasing J. The X ˆ 3=2
lines were also found to be stronger in intensity
than the other ladder, verifying the inverted nature
of the P term. In addition, in the lower rotational
transitions of the X ˆ 1=2 ladder, hyper®ne
structure was partially resolved, which arises from
the lithium 7 nuclear spin of I ˆ 3=2. The hyper®ne interactions in principle should split each
lambda-doublet into four strong components, but
in the case of LiS, only two features were typically
observed. One such feature appeared to be the
strongest hf component, for example, the
F ˆ 5 ! 6 line in the J ˆ 7=2 ! 9=2 transition
(see Table 1), and the second was composed of the
other three components (F ˆ 4 ! 5, 3 ! 4, and
2 ! 3). Usually, these three hf transitions were
totally collapsed, but in certain cases, one component appeared as a shoulder on the line comprising the other two, and its frequency could be
measured separately. Hyper®ne interactions were
not observed in the X ˆ 3=2 ladder, and at higher
J, the hf splitting in the X ˆ 1=2 sub-level was
completely collapsed as well. Hence, in these cases
Fig. 2. Spectra of the J ˆ 5=2 ! 7=2 transition of LiS (X2 Pi :
v ˆ 0), showing both the X ˆ 3=2 spin±orbit ladder near 132
GHz (top panel) and the X ˆ 1=2 sub-level near 130±135 GHz
(bottom panel). The X ˆ 3=2 transition consists of two lines
which are lambda-doublets, indicated by parity designations e
and f. The X ˆ 1=2 transition, on the other hand, is split by
both lambda-doubling (see e and f labeling) and hyper®ne interactions. Each lambda-doublet therefore appears as two features which result from four hf components, indicated by
quantum number F . The approximate positions and relative
intensities of these hyper®ne components are shown under each
spectrum. The top spectrum is an average of 20, 5 MHz scans,
each lasting 10 s in duration; the bottom spectra are 16 scan
averages, also 5 MHz in frequency coverage and with 10 s scan
time.
Fig. 1. A section of the 25=2 ! 27=2 rotational transition of
LiS (X2 Pi : v ˆ 0) near 508.4 GHz, showing the lambda-doublets of the X ˆ 3=2 sub-level (labeled e and f) and the e parity
component in the X ˆ 1=2 ladder. The X ˆ 3=2 doublets are
split by 30 MHz, while those of the X ˆ 1=2 sub-level are
separated by almost 5 GHz. The stronger intensities of the
X ˆ 3=2 lines indicate that the P state is inverted. This spectrum was obtained as a single, 100 MHz scan, lasting approximately 1 min.
there is only a single feature observed for each
lambda-doubling component.
Representative spectra illustrating these e€ects
are presented in Figs. 1 and 2. Fig. 1 shows the
lambda-doublets in the X ˆ 3=2 sub-level of the
J ˆ 25=2 ! 27=2 transition of LiS (v ˆ 0) near
M.A. Brewster, L.M. Ziurys / Chemical Physics Letters 349 (2001) 249±256
508.4 GHz. The doublets, labeled by the parity
designation e and f, are separated in this transition
by about 30 MHz. Also present in the spectrum is
the e component of the X ˆ 1=2 sub-level; its
matching doublets lies 5 GHz higher in frequency. The X ˆ 3=2 lines are clearly stronger in
intensity than the X ˆ 1=2 feature, evidence for a
2
Pi ground state.
In Fig. 2, a low frequency transition
…J ˆ 5=2 ! 7=2† in both X ladders is shown at 132
GHz …X ˆ 3=2† and at 130±135 GHz …X ˆ 1=2†.
Both lambda-doublets in the X ˆ 1=2 sub-level
(lower panel) are additionally split into two features because of lithium hyper®ne interactions.
One feature is attributable to the F ˆ 4 ! 5
transition, and the other is a blend of the
F ˆ 3 ! 4, 2 ! 3, and 1 ! 2 lines. One of these
components …F ˆ 3 ! 4† appears as a shoulder on
the left side of the f parity line, making it broader
by about 300 kHz than the expected linewidth. The
positions and relative intensities of the four hf
components that compose the e and f transitions
are indicated beneath the respective spectrum. At
higher frequencies, these two features merge together and eventually form a single line. In the
X ˆ 3=2 spectrum (top panel) there is little evidence of hf splittings in the closely spaced lambdadoublets.
The data were analyzed using a standard
Hund's case (a) Hamiltonian consisting of molecular frame rotation, spin±orbit interaction,
lambda-doubling, and hyper®ne coupling, including centrifugal distortion corrections [21]:
H^eff ˆ H^rot ‡ H^so ‡ H^LD ‡ H^hf :
…1†
The v ˆ 0 and v ˆ 1 data sets were ®t separately. Because there had been no previous spectroscopic studies of LiS, an estimate of the
spin±orbit constant A was not available for the
data ®t. Consequently, that of NaS was used as an
initial value ()8000 GHz [17]). The spin±orbit
constant was allowed to vary in the ®t and a reasonably de®ned value was obtained.
Analysis of the hyper®ne interaction in the
v ˆ 0 state proved somewhat problematic because
it was observed only in one X ladder, and, even in
this sub-level, it was not completely resolved. (No
hf splittings were recorded for the v ˆ 1 state.)
253
Hence, all four hf parameters (a, b, c, and d) could
not be independently determined. Because there
was a noticeable di€erence between the hyper®ne
splittings in the e and f parity components in the
X ˆ 1=2 ladder, the d constant could be established. Also, the a parameter appeared necessary
for a reasonable ®t. A signi®cant correlation, on
the other hand, was found between b and c, and
consequently in the ®nal ®t, only the value …b ‡ c†
could be determined. The v ˆ 0 transition frequencies were ®t as one data set, even though the
hf splittings were collapsed for levels with
J > 11=2, and for all X ˆ 3=2 transitions. Parity
was chosen to match that of KS [18], which consequently made the hf constant d positive.
The spectroscopic constants resulting from this
analysis are presented in Table 2 for both the v ˆ 0
and v ˆ 1 vibrational states of LiS …X2 Pi †, as well
as the individual rms of the data ®ts. As shown in
the table, all constants are well determined and the
rms of the ®ts are well below the estimated experimental uncertainty of 100 kHz. The residuals
are given in Table 1. (Those listed for the transitions where the hyper®ne splitting was totally
collapsed are an average over the four individual
residuals given for each hf component.) As is evident in the table, centrifugal distortion corrections
were found necessary for the spin±orbit constant
and lambda-doubling parameter p.
Because two vibrational states were investigated, equilibrium rotational constants could
be derived. These values are presented in Table 3.
Table 2
Spectroscopic constants for LiS (X2 Pi )a
Parameter
vˆ0
vˆ1
A
AD
BV
DV
p
q
pD
a
b‡c
d
rms of ®t
)8 222 000 (90 000)
)2.69 (94)
18 906.2805 (31)
0.090507 (12)
4 860.84 (27)
)6.73 (20)
)0.08569 (52)
3.92 (69)
)7.7 (1.4)
3.6 (2.1)
0.086
)8 185 000 (81 000)
)2.17 (83)
18 702.7044 (37)
0.089923 (10)
4 883.68 (35)
)6.58 (17)
)0.08910 (57)
±
±
±
0.016
a
In MHz; errors are 3r.
254
M.A. Brewster, L.M. Ziurys / Chemical Physics Letters 349 (2001) 249±256
di€erent rotational spectrum from what has been
observed. As discussed in various theoretical
works [11,19], there is competition between electrostatic and exchange forces, the former favoring
the r2 p3 con®guration, and the latter p4 r1 . For
most of the lighter alkali oxides and sul®des, it has
been found that the electrostatic forces dominate,
as in the case of LiS.
Although, the 2 P term is the ground state for
the lighter alkali species, the nearest excited state is
predicted to be 2 R, and results from promotion of
a r electron into a p orbital. As the periodic table
is descended, this A2 R state is calculated theoretically to move closer in energy to the X2 Pi state,
until the P state is overtaken, and the energy ordering reverses. These theoretical energies are given in Table 4 for the alkali sul®des and oxides.
Many of the alkali oxides and sul®des have only
been studied by pure rotational spectroscopy.
Hence, measurements of the A2 R‡ excited state
energies are generally not available. However,
these energies can be estimated from rotational
data using the lambda-doubling constant p, assuming pure precession [22]:
Table 3
Equilibrium constants for LiS (X2 Pi )a
Parameter
This work
Theoryb
Be
ae
De
be
xe
re
19 008.0681 (39)
203.5761 (48)
0.090799 (14)
)0.000584 (16)
580 cm 1
2.1497 A
±
±
±
±
597 cm 1
2.147 A
a
b
In MHz, unless indicated otherwise.
From [19].
From Be and De , the harmonic vibrational frequency was also estimated using the relationship
3 1=2
4Be
xe ˆ
:
…2†
De
The frequency obtained is xe 580 cm 1 , close
to that predicted from ab initio calculations
(xe ˆ 597 cm 1 [19]. Furthermore, an equilibrium
was debond length for LiS of re ˆ 2:1497 A
termined from Be , also similar in value to that
[19]).
derived theoretically (re ˆ 2:147 A
4. Discussion
pˆ
This work is the ®rst spectroscopic observation
of LiS, and analysis of its pure rotational spectrum
has veri®ed that the electronic ground state of this
radical is 2 Pi . The electron con®guration of this
molecule in this state is therefore 1r2 2r2 1p3 . Another possible con®guration for LiS is 1r2 1p4 2r1 ,
which would have resulted in a 2 R state, and a
4AB
:
EP ER
…3†
Using the p constant derived in this work, the
A2 R‡ state is estimated to lie 4268 cm 1 above
the ground state ± close to that predicted by ab
initio calculations ( 5000 cm 1 ; see Table 4).
Using data from [18,19], the 2 R energies have also
been estimated for NaS and KS. These values are
Table 4
Lowest-lying 2 R energies for alkali sul®des and oxidesa
EP (experimental)b
Molecule
ER
LiS
NaS
KS
LiO
NaO
KO
4268
3342
1900
2565
2050
200
a
In cm 1 .
Derived assuming pure precession hypothesis (see text).
c
QCISD (T)/6-311+G (2df) calculation.
d
SDCI calculation.
e
MRCI calculation.
b
ER
EP (theory)
4970c , 5088d
4046d
1834d
2400e
1902e
)46e
Reference
[11,19]
[17,11]
[18,11]
[14,12]
[15,12]
[16,12]
M.A. Brewster, L.M. Ziurys / Chemical Physics Letters 349 (2001) 249±256
ER EP 3342 and 1900 cm 1 , respectively, also
reasonably close to ab initio predictions (see Table
4). In contrast, the energies of the R state for LiO
and NaO are 2565 and 2050 cm 1 , based on pure
precession [14,15], and that of KO is 200 cm 1
[16]. Again, these values are close to those calculated theoretically, though there is disagreement in
the case of KO concerning which state actually lies
lowest [12]. (Theory predicts the 2 R state to be
lower by 46 cm 1 .) In general, the R±P separation
is about a factor of two larger in the sul®des than
in the oxides.
Another isovalent molecule that presumably
could have either a 2 Pi or 2 R‡ ground state, depending on its electron con®guration, is the SH
radical. Like the lighter alkali halides, SH has been
found to have a 2 Pi ground state, but its ®rst excited state …A2 R‡ † lies 31 000 cm 1 higher in
energy [19]. This energy is considerably larger than
for any of the alkali sul®des or oxides. SH is certainly a very covalent molecule, and therefore, the
R±P separation may indirectly indicate the degree
of covalent character. Covalent bonding is favored
in the 2 Pi : 1r2 p3 con®guration as opposed to the
2 ‡
R : p4 r1 con®guration because an electron pair in
a sigma orbital can be shared between the two
atoms in the P case, but only a single electron in
the R case [7]. This property is also apparent in the
alkali species. Based on electronegativity arguments, the alkali oxides must be fairly ionic and
hence their R±P energy separation is relatively
small. Because sulfur is less electronegative, the
sul®des have more covalent character than the
oxides, and the R±P energy separation is signi®cantly larger.
Despite having more covalent character than
lithium oxide, LiS is still partly an ionic
molecule. Evidence for ionicity lies in the spin±
orbit
constant
for
LiS,
which
is
A ˆ 8222 GHz. This constant is fairly close in
value to that of S (3p5 ): f ˆ 9773 GHz [23].
Therefore, the resonance structure Li‡ S must
contribute substantially to the bonding in this
molecule.
A further comparison of ionic vs. covalent
character can be made by examining the hyper®ne constants derived for LiS. This interaction
arises from the unpaired electron spin coupling
255
with the 7 Li nuclear spin …I ˆ 3=2† and hence is a
measure of the electron density near the lithium
nucleus. The Fermi contact term in fact traces the
electron density at the nucleus. Consequently, the
magnitude of hyper®ne constants will indicate
the degree of deviation from the Li‡ S structure,
where the unpaired electron lies exclusively on the
sulfur atom. The hyper®ne constants established
for LiS in fact are quite small in value, with the
Fermi contact term near zero. (The parameter
…b ‡ c† ˆ 7:7 (1.4) MHz.) In contrast, the
atomic Fermi contact term for 7 Li is 409 MHz, a
considerably larger number [24]. Hence, there is
little electron density at the lithium nucleus.
Furthermore, the Fermi contact term has been
measured in SH to be (bF ˆ 73:5 MHz [25]. In
this molecule, the nuclear spin arises from the
hydrogen atom (I ˆ 1=2). The electron density is
clearly greater on the hydrogen nucleus in SH
than on lithium in SLi. (Both hydrogen and lithium have comparable magnetic moments so a
direct comparison can be made.) The unpaired
electron is thus shared more evenly in SH than
LiS, and thus the bonding is more covalent in the
hydride.
5. Conclusion
Measurements of the pure rotational spectrum
of LiS have demonstrated that this species has a
2
Pi ground state, as do NaS, KS, and SH. Analysis
of the lambda-doubling interactions suggests that
the A2 R‡ state in this radical lies 4300 cm 1
above ground state. Although this energy separation suggests that the bonding in LiS is more
covalent in character than in LiO, this molecule is
still very ionic. Evidence for this ionicity is found
in the spin±orbit constant, which is similar to that
of S , and in the small values of the lithium hyper®ne parameters. Observation of the v ˆ 0 and
v ˆ 1 states of LiS has allowed for calculation of
equilibrium constants re and xe , which are in good
agreement with ab initio calculations. These measurements have demonstrated that, though alkali
sul®des and oxides are isovalent, there are noticeable di€erences in their bonding and electronic
structure.
256
M.A. Brewster, L.M. Ziurys / Chemical Physics Letters 349 (2001) 249±256
Acknowledgements
This research is supported by NSF Grant CHE98-17707.
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