VCl4 revisited: ESR and photolysis in solid hydrogen, neon, and argon; Formation of VH4

Article abstract of DOI:10.1021/jp0020079

Electron-spin-resonance (ESR) spectra of the VCl₄ molecule were observed at low concentrations at 2-4 K in solid H₂, D₂, Ne, and Ar. As previously observed in other matrixes, the spectra of an axial molecule were obtained in H₂, D₂, and Ne, indicative of a Jahn-Teller (JT) distorted molecule with compressed tetrahedral D_2d symmetry. However, in argon, a composite of an axial and a near-isotropic spectrum was observed, and annealing yielded only the isotropic at 4 K. This surprising result is discussed relative to JT dynamic vibronic interaction. Photolysis of VCl₄ in H₂ (and D₂) matrixes yielded a new spectrum assigned to VH₄ (or VD₄), indicating that the tetrahydride is also a JT-distorted ²E ground-state molecule, in accord with earlier ab initio theory.

Full text of DOI:10.1021/jp0020079

9302
J. Phys. Chem. A 2000, 104, 9302-9306
VCl4 Revisited: ESR and Photolysis in Solid Hydrogen, Neon, and Argon; Formation of
VH4
John T. Graham, Li Li, and W. Weltner, Jr.*
Department of Chemistry, UniVersity of Florida, GainesVille, Florida 32611-7200
ReceiVed: June 2, 2000; In Final Form: August 14, 2000
Electron -spin-resonance (ESR) spectra of the VCl4 molecule were observed at low concentrations at 2-4 K
in solid H2, D2, Ne, and Ar. As previously observed in other matrixes, the spectra of an axial molecule were
obtained in H2, D2, and Ne, indicative of a Jahn-Teller (JT) distorted molecule with compressed tetrahedral
D2d symmetry. However, in argon, a composite of an axial and a near-isotropic spectrum was observed, and
annealing yielded only the isotropic at 4 K. This surprising result is discussed relative to JT dynamic vibronic
interaction. Photolysis of VCl4 in H2 (and D2) matrixes yielded a new spectrum assigned to VH4 (or VD4),
indicating that the tetrahydride is also a JT-distorted 2E ground-state molecule, in accord with earlier ab initio
theory.
Introduction
The VCl4 molecule has been experimentally1-8 and
theoretically9-17 studied for more than 30 years with no definite
conclusion as to the degree of vibronic coupling occurring in
2
the ground state. Tetrahedral ligand field theory splits the D
2
term of the d1 configuration into the orbitally degenerate E
lower state and 2T upper state, separated by about 1 eV. These
states are subject to vibronic distortion due to the Jahn-Teller
(JT) effect. In JT terms, it is an E X e type with stabilization of
a distorted tetrahedron in the ground state. (Renewed interest18
in JT systems includes multimode effects in the E X e problem.)
VCl4 was first treated theoretically by Ballhausen and Liehr
in 19619 and subsequently by many workers culminating in the
recent study of Stavrev and Zerner.17 As those authors point
out, the calculated Jahn-Teller stabilization energies given in
the literature “vary from a few tens to a few thousands of
wavenumbers”.
Early electron-spin-resonance (ESR) spectra were measured
by Herring, McDowell, and Nakajima,4 by Pratt,5 and by
Johannesen, Candela, and Tsang.6 The matrixes used in these
cases were solid krypton and xenon,4 solid mineral oil, CCl4,
n-heptane, TiCl4, and SnCl4,5 and solid TiCl4,6 respectively, all
at liquid helium temperatures at several microwave frequencies.
Later (1981) studies by Ammeter et al.7 were made in solid
CCl4, CBr4, cyclohexane, and toluene at 4 K. Those authors
were specifically concerned with the influence of molecular host
lattices on the electronic properties of orbitally (near-) degenerate
transition metal complexes. They conclude that there was little
matrix dependence observed in the case of VCl4. Agresti,
Ammeter, and Bacci (in 1984)8 again note that in a large variety
of host systems showing resolved vanadium hyperfine structure
the ESR spectra of VCl4 are very similar and can be fitted with
an almost axial spin Hamiltonian, whereby g| ) 1.95 ( 0.01,
g ) 1.91 ( 0.01, A| < 50, A ) 105 ( 10 × 10-4 cm-1. (The
spectrum they are referring to is essentially the same as we find
in solid hydrogen, illustrated here in our Figure 1, to be
discussed below.) Pratt5 has probably made the most thorough
ESR studies. The spectra in TiCl4 and SnCl4 were anomalous
in that they were not reproducible, and he concluded that they
were “quite subject to intermolecular effects from the surround-
Figure 1. (a) ESR spectrum of 0.5% VCl4 in a n-H2 matrix at 2 K (ν
) 9.806 GHz). (b) Simulated spectrum using g ) 1.917, g| ) 1.952,
A
) 101 G, A| ) 55 G, and a Gaussian line width of 20 G.
ing matrix”. Overall, the ESR evidence at low temperatures find
g| > g , indicating that the JT distortion stabilizes a flattened
tetrahedron (D2d symmetry). At higher temperatures, the spec-
trum reversibly disappears due to spin relaxation.
An electron diffraction study3 has found the V-Cl bond
distance to be 2.14 Å, and several, not entirely conclusive,
infrared and Raman measurements have been made.1,2 The
frequency most relevant to this research is ν2 (the e bending)
estimated3 to be 97 ( 9 cm-1
.
The motivations for this ESR research on the VCl4 molecule
were the following: (1) to observe the molecule in the least
perturbing solid environments, not previously employed; (2) to
observe the spectra at higher resolution and possibly detect
chlorine hyperfine structuresthis latter was not realized; (3) to
explore further ESR in the solid hydrogens;19-21 and (4) to take
10.1021/jp0020079 CCC: $19.00 © 2000 American Chemical Society
Published on Web 09/20/2000

ESR and Photolysis in Solid Hydrogen, Neon, and Argon
J. Phys. Chem. A, Vol. 104, No. 41, 2000 9303
advantage of the strong absorption of visible light by VCl4 to
anneal the matrixes and ultimately to photolyze the molecule.
Here we compare X-band ESR spectra of VCl4 in hydrogen,
deuterium, neon, and argon matrixes prepared at 2 or 4 K. The
usual axial spectrum was obtained in most matrixes, but
annealing and photolysis provided some interesting new results.
Experimental Section
Vanadium tetrachloride is a volatile red/brown liquid with a
melting point of -26 °C. The VCl4 was purified by pumping
on the sample during freeze/thaw cycles to remove chlorine and
hydrogen chloride impurities. This was achieved using a
methyloxybenzene (anisole) slush bath at -37.5 °C where the
vapor pressure of VCl4 is ∼0.1 Torr. Premixed samples of 4
and 0.5 mol % VCl4 with host gases were prepared in 5 L bulbs,
passed up through the ESR cavity and deposited onto the copper
rod at 2 K or 4 K. Gas mixtures were prepared and used the
same day. Another procedure involved the co-deposition of the
VCl4 and the matrix gas. The VCl4 was introduced into the
flowing matrix gas through a PTFE needle valve with the VCl4
liquid at room temperature or cooled with either the anisole
slush or the ice water slush. When co-deposited, the concentra-
tion of VCl4 in the matrix could only be judged approximately
by comparison of the observed ESR spectrum with the premixed
spectra.
The matrixes were prepared on a copper rod (spatula-shaped)
at 2-4 K, which was then lowered into a Bruker (ESP 300 E)
X-band cavity. The ESR apparatus and accompanying cryogen-
ics have been previously described.22,23
Samples isolated in neon or argon matrixes were annealed
by either restricting the flow of liquid helium or by irradiating
the sample with diffused unfiltered light from a 1 kW Xe/Hg
lamp (Oriel) through the slotted side of the X-band cavity.
During the annealing cycles ESR spectra were recorded at
various temperatures. Photolysis, and the appearance of new
spectral features, resulted when the lamp was focused on the
cavity.
Vanadium tetrachloride was purchased from Aldrich with a
purity of >98% based on chlorine analysis. Research grade
argon (99.999%) was from B. O. C., neon (99.9995%) from
Matheson, deuterium (99.6%) from Cambridge Isotope Labo-
ratories, and hydrogen (99.9995%) from Matheson.
Figure 2. ESR spectrum of 0.5% VCl4 in an argon matrix at 4 K (ν
) 9.8064 GHz). (a) Prior to annealing; (b) after annealing to about 30
K; (c) Difference spectrum.
absorption from the Xe/Hg lamp. The spectrum in Figure 2
could be simulated as a composite of the anisotropic and
isotropic spectrum, as that figure indicates. Since this isotropic
spectrum had apparently not been observed before in any other
matrix, it is significant and needs rationalization.
We worried that it might be due to an impurity; however,
this seems to be unlikely. First, it was completely reproducible
through several runs where diligence was paid to the freeze-
thaw of the VCl4 liquid just before the experiment. Then, any
impurity would have to be derived from the argon, which is
research grade. Also, the axial VCl4 signal is initially of the
same order of intensity as the isotropic, and it appears that
warming to just 30 K causes it to be converted to isotropic.
This small temperature change is not conducive to chemical
reaction but is to rearrangement of the argon matrix. The
implication is that the sites for VCl4 have altered in the matrix,
leading to effectively an alteration of its JT behavior, indeed,
almost to an isotropic spectrum of a tetrahedral VCl4 radical!
This is supported by the results in solid neon where some degree
of annealing was successful. The original axial spectrum was
altered with a narrowing of the spectra and the appearance of
isotropic features (see Figure 3).
Photolysis of VCl4 in Solid H2 and D2. Direct exposure to
the focused light from the Xe/Hg lamp led to rapid photolysis,
either the appearance of new spectra (in H2, D2) or only the
disappearance of the VCl4 spectrum (in Ne, Ar). Also, photolysis
of VCl4 in a 5% mixture of H2/Ar led only to the gradual
disappearance of VCl4 signals, but a new spectrum was not
observed. The immediately noticeable effect of photolysis on
Results
All of the ESR spectra in H2, D2, and Ne, upon trapping at
2 K, were similar to that shown in Figure 1, which is also similar
to previously measured spectra. The spectrum in solid H2 was
simulated as an axial doublet radical using Gaussian-shaped lines
of line width 20 G, with g ) 1.917 and g| ) 1.952 and 51V (I
) 7/2) hyperfine pattern of eight lines yielding A ) 101 G
and A| ) 55 G. These parameters are in general accord with
earlier observations along with those derived from the spectra
in other matrixes. Annealing of these solids on the Cu rod is
difficult and usually led to the loss of the matrixes in the cases
of H2 and D2, however, an effect was observed in neon (see
below).
The ESR spectrum of 4% VCl4 in argon at 4 K is the usual
axial spectrum but with broadened lines. However, 0.5% VCl4
in argon at 4 K yielded the more complicated spectrum shown
in Figure 2. Upon annealing, this spectrum is revealed to be a
composite of the axial spectrum (similar to Figure 1) and the
narrower, nearly-isotropic spectrum shown in Figure 2 again
measured at 4 K. This “isotropic” spectrum was obtained after
either thermal annealing at ∼30 K or after diffuse light

9304 J. Phys. Chem. A, Vol. 104, No. 41, 2000
Graham et al.
Figure 3. ESR spectrum of 0.5% VCl4 in a neon matrix at 2 K (ν )
9.8057 GHz). (a) Prior to annealing; (b) after annealing. The feature at
about 3200 G is a background signal.
the ESR spectrum was the appearance of three weak phase-
down lines at high fields (between 3900 and 4400 G), two
medium intensity lines phase-up at low field (between 2950
and 3200 G), an intense line mostly phase-up at ∼ 3350 G,
and two medium strength phase-up lines separated by 90 G
between 3550 and 3700 G. The low-field and high-field lines
have the form of “parallel” lines in matrixes containing randomly
oriented radicals (see Figure 4).24 These lines appear in both
solid H2 and solid D2, slightly shifted between the two matrixes.
The photolysis also produces H (and D) atom signals. The D
atom signals are seen as the three sharp lines separated by about
80 G in Figure 4.
Figure 4. (a) ESR spectrum of 0.5% VCl4 in a D2 matrix at 2 K (ν )
9.8055 GHz). (b) Spectrum produced after photolysis of the matrix
with a Xe/Hg lamp for 15 min. The three lines split by 80 G are due
to D atoms, and (*) the sharp lines are due to CH3 radicals. (•) Lines
are believed to be unreacted VCl4. (c) Spectrum produced by annealing
to about 4 K.
Discussion
In solid hydrogen, presumably the least perturbing matrix,
an axial spectrum is obtained. at 2 K. Thus, VCl4 is a distorted
JT molecule, which at 2 K is static, implying that EJT > hω;
how much greater is the question. This behavior is apparently
true in most other solids: mineral oil, CCl4, cyclohexane,
heptane. However, it is not true in argon and neon where both
the anisotropic and the isotropic spectrum are observed at 2-4
K (as shown in Figures 2 and 3). Thus, contrary to earlier
generalities, VCl4 is influenced by the environment. Annealing
in solid argon, and less certainly in neon, produces new sites in
which dynamic effects appear.
“Isotropic” Spectrum in Argon. The spectrum is like that
of a slowly tumbling molecule with increasing line width at
the higher fields (or higher mI values). It can be simulated using
g ) 1.93 and A ) 69 G, and with the estimated line widths
varying quadratically with mI according to
cubic lattice is 3.16 or 3.76 Å, respectively,25 much too small
to accommodate a VCl4 molecule. p-H2 crystallizes in a
hexagonal-closed-packed lattice with 3.78 Å as the nearest-
neighbor distance.26 It is clear that VCl4 would not fit into any
of these crystalline lattices, and it is either accommodated by
the packing of matrix atoms about it or fitted in the spaces
between crystallities in the polycrystalline matrix. At 4 K it is
then unlikely that rotational motion could occur.
O’Brien27 has shown that the Jahn-Teller effect can also
produce line-width variations at low temperatures, also depend-
ing upon ∆g ) g| - g and ∆A ) A| - A . She has considered
the relaxation due to transitions between vibronic levels where
the “relaxation process will take the system from the ground
state in one potential minimum to another by way of the excited
states, even if the probability of direct transitions is small. At
each of these transitions, the Larmor frequency of the system
is changed but the electron spin is not turned over.” Furthermore,
if this relaxation process is dominant, she finds that the width
of each of the ESR lines should be a multiple of
22 - 1.5mI + 0.5mI2
However, it is unlikely that VCl4 is slowly tumbling in Ar at 4
K.
τ[(g| - g )âH + (Az - Ax)Iz]2/h2
VCl4 is a large molecule relative to substitutional sites in any
of these matrix lattices. The V-Cl bond distance3 is 2.14 Å,
but a van der Waals radius for Cl must be added to that. If this
is assumed to be 1 Å, the diameter of a VCl4 sphere is about 6
Å. The diameter of a neon or argon atom in the face-centered-
where τ is the relaxation time, i.e., a quadratic function of the
mI values (as in slow tumbling). (∆g is positive here but ∆A is
negative.) Her discussion is related to the change in the

ESR and Photolysis in Solid Hydrogen, Neon, and Argon
J. Phys. Chem. A, Vol. 104, No. 41, 2000 9305
TABLE 1: Analysis of the ESR Spectra Assigned to VH4
and VD4 as Axially Distorted Molecules at 2 K in the Solid
Hydrogens
anisotropic spectrum to an isotropic one as the temperature is
changed. Here, there is no temperature change (the spectra are
all measured at 2-4 K), but an environmental change in the
matrix. One then postulates that annealing has either lowered
the barriers between the three troughs or has changed the site
where one trough is lower in energy, i.e., favored (sometimes
referred to as nonrandom strain), to equalize all three and
effectively allow tunneling to produce the “isotropic” spectra.
parallel
lines (G)
perpendicular
lines (G)
MI (51V)
obsd
calcd
obsd
calcd
VH4 (ν ) 9.8052 GHz)a
+7/2
+5/2
+3/2
+1/2
-1/2
-3/2
-5/2
-7/2
2974.3
2974.6
3170.9
3369
3569
3771
3975
4180
4389
3243
3301
3365
3436.5
3515
3600
3692
3791
3170.6
3363.1
3579.4
3301
The warping, due to second-order effects, resulting in three
troughs in the lower potential curve of the “Mexican hat”, is
characterized by a parameter â such that 2â is the height of the
barrier between troughs.28,29 â depends on both the linear and
nonlinear vibronic coupling and is difficult to estimate in
general, and more so for VCl4 since there are no analogies as
occur among ionic crystals. These matrixes, as originally formed,
are usually “strained” as is evident by the change in the spectrum
of a dopant after annealing. The relaxation of the matrix atoms
about the isolated dopant often leads to loss of some sites and
strengthening of more stable ones. These changes effect the
change from the axial spectrum to the isotropic one in Figure
2, which apparently also occurs in neon.
3976.1
4180.5
4389.0
3600
3692.5
3791
+7/2
+5/2
+3/2
+1/2
-1/2
-3/2
-5/2
-7/2
2962.9
3245
3244
3302
3367
3438
3517
3602
3693
3792
A feature that is brought out by the simulation of this near-
isotropic spectrum is the necessity of using Lorentzian rather
than Gaussian line shapes, particularly to reproduce the outer
wings of the spectrum. This is unusual in matrixes where lines
are usually inhomogeneously broadened by the overlap from
several sites. It implies that the spectrum is observed of
molecules in uniform sites in the annealed argon matrix or
perhaps that the dynamics have produced such an effect.
a A| ) 202 G, g| ) 1.901, A ) 78 G, g ) 1.984. b A| ) 198.4 G,
g| ) 1.914, A ) 78 G, g ) 1.985.
calculated lines are listed in Table 1, along with the derived
magnetic parameters.
Conclusions
The observation of a reproducible almost-isotropic spectrum
of VCl4 is solid argon at 4 K indicates a dynamic Jahn-Teller
effect. It suggests that the JT energy (and warping of the lower
potential trough) is weak, i.e., comparable with the zero-point
vibrational energy.
Excitation of VCl4 in a hydrogen matrix leads to complete
loss of the chlorine atoms, presumably to form HCl, and
formation of VH4. Theory34 predicts VH4 has a 2E ground state,
therefore, also subject to the Jahn-Teller effect. ESR measure-
ments at 2 K confirm this by observation of the spectrum of an
axial molecule, as expected of distorted VH4 subject to a static
JT effect.
One can suggest that the barrier to fluxional behavior in VCl4
is actually sensitive to the surroundings. Note that argon and
neon are the least polar and polarizable of the matrixes in which
VCl4 has been studied. Solid p-H2 would provide an even less
perturbing environment, but normal H2 was used here as a
matrix. n-H2 contains 75% o-H2 molecules which possess an
electric quadrupole moment.
Formation of VH4. The photolysis of VCl4 in H2 or D2
caused its disappearance and the appearance of a characteristic
spectrum of another tetrahedral tetravalent molecule distorted
to D2d symmetry by the Jahn-Teller effect. The emerging
spectrum in Figure 4 has the same features as V(NEt)4,30
V(OBu)4,31 and NbD4.32 This has been discussed rather thor-
oughly in our paper on the niobium tetrahydride.32 Because of
the disappearance of the VCl4 spectrum, the appearance of
atomic H, and the matrix environment of only solid hydrogen,
the photolysis product is assigned to VH4. (Note that the
spectrum of VH2 has been observed,33 and it is not present.)
Ab initio theory by Hood, Pitzer, and Schaefer34 predicted (in
Infrared spectra of these species in these matrixes are needed
to verify these conclusions.
Acknowledgment. We thank Professor David Pratt for
sending us a copy of his extensive early research on VCl4, and
Professor C. A. McDowell for a copy of the article in ref 4.
This research was supported by the National Science Foundation
(Grant CHE-9726297). Acknowledgment is also made to the
donors of the Petroleum Research Fund, administered by the
American Chemical Society, for support of this research (ACS-
PRF Grant 34820-AC6).
2
1979) a E ground state for VH4 with re ) 1.637 Å and that
“VH4 could be prepared in the laboratory.”
Most of the parallel lines in Figure 4, and in the corresponding
spectrum in H2, can be assigned, yielding A| ) 203(1) G, g| )
1.901(5) for VH4 and 198.4 (2) G, g| ) 1.914(5) for VD4. The
perpendicular lines are grouped between 3250 and 3750 G for
VH4; the intensity of the line at 3350 G is attributed to the near
coincidence of the mI ) +3/2 parallel and perpendicular lines
(similar to the strength of that line in VCl4; this similarity is
considered to be completely fortuitous.) The splittings among
the perpendicular lines appear to increase in increasing magnetic
field, i.e., the second-order terms are significant. A = 78(1)
G, g = 1.985(5). Here as is NbH4, g > g|, not as in VCl4.
That anomaly for VCl4 has been noted earlier and attributed to
different couplings to excited states.32,34 The observed and
References and Notes
(1) Dove, M. F.; Creighton, J. A.; Woodward, L. A. Spectrochim. Acta
1962, 18, 267.
(2) Grubb, E. L.; Belford, R. L. J. Chem. Phys. 1963, 39, 244.
(3) Morino, Y.; Uehara, H. J. Chem. Phys. 1966, 45, 4543.
(4) Herring, F. G.; McDowell, C. A.; Nakajima, H. Colloq. Int. C. N.
R. S. 1966, 164, 395.
(5) Pratt, D. W. Lawrence Radiation Laboratory Report UCRL-17406;
University of California, Berkeley: California, 1967.
(6) Johannesen, R. B.; Candela, G. A.; Tsang, T. J. Chem. Phys. 1968,
48, 5544.
(7) Ammeter, J. H.; Zoller, L.; Bachmann, J.; Baltzer, P.; Gamp, E.;
Bucher, R.; Deiss, E. HelV. Chim. Acta 1981, 64, 1063.
(8) Agresti, A.; Ammeter, J.; Bacci, M. J. Chem. Phys. 1984, 81, 1861.

9306 J. Phys. Chem. A, Vol. 104, No. 41, 2000
Graham et al.
(9) Ballhausen, C. J.; Liehr, A. D. Acta Chem. Scand. 1961, 15, 775.
(10) Ballhausen, C. J. Introduction to Ligand Field Theory; McGraw-
Hill: New York, 1962; particularly p 196.
(11) Ballhausen, C. J.; DeHeer, J. J. Chem. Phys 1966, 43, 4304.
(12) Coulson, C. A.; Deb, B. M. Mol. Phys. 1969, 16, 545.
(13) Becker, C. A. L.; Dahl, J. P. Theor. Chim. Acta (Berlin) 1970, 19,
135.
(14) Copeland, D. A.; Ballhausen, C. J. Theor. Chim. Acta (Berlin) 1971,
20, 317.
(15) Lu¨thi, H. P.,; Almhoff, J. J. Chem. Phys. 1987, 87, 3702.
(16) Truax, D. R.; Geer, J. A.; Ziegler, T. Theor. Chim. Acta 1974, 33,
299.
(23) Van Zee, R. J.; Baumann, C. A.; Weltner, W., Jr. J. Chem. Phys.
1985, 82, 5604.
(24) Weltner, W., Jr. Magnetic Atoms and Molecules; Dover: New York,
1989.
(25) Pollack, G. L. ReV. Mod. Phys. 1964, 36, 748.
(26) Silvera, I. F. ReV. Mod. Phys. 1980, 52, 393.
(27) O′Brien, M. C. M. Proc. R. Soc. London, Ser. A 1964, 281, 323.
(28) See Reinen, D.; Atanasov, M. Magn. Reson. ReV. 1991, 15, 167,
for a recent review.
(29) Bersuker, I.; Polinger, V. Vibronic Interactions in Molecules and
Crystals; Springer: Heidelberg, 1989.
(17) Stavrev, K. K.; Zerner, M. C. Chem. Phys. Lett. 1996, 263, 667.
(18) Electron-Phonon Dynamics and Jahn-Teller Effect. In Proc. XIV
Intern. Symp.; Bevilacqua, G.; Martinelli, L.; Terzi, N., Eds.; Erice, Italy,
July 7-13, 1998; World Scientific: Singapore, 1999.
(19) Graham, J. T.; Weltner, W., Jr. J. Phys. Chem. A 1999, 103, 4594.
(20) Van Zee, R. J.; Li, S.; Weltner, W., Jr. J. Phys. Chem. 1993, 97,
9087.
(30) Holloway, C. E.; Mabbs, F. E.; Small, W. R. J. Chem. Soc. A 1968,
2980.
(31) Kokoszka, G. F.; Allen, H. C., Jr.; Gordon, G. Inorg. Chem. 1966,
5, 91.
(32) Van Zee, R. J.; Li, S.; Weltner, W., Jr. J. Chem. Phys. 1995, 102,
4367.
(33) Weltner, W., Jr.; Van Zee, R. J.; Li, S. J. Phys. Chem. 1995, 99,
6277.
(21) Van Zee, R. J.; Williams, A. P.; Weltner, W., Jr. J. Chem. Phys.
1997, 107, 4756.
(22) Van Zee, R. J.; Ferrante, R. F.; Zeringue, K. J.; Weltner, W., Jr. J.
Chem. Phys. 1988, 88, 3465.
(34) Hood, D. M.; Pitzer R. M.; Schaefer, H. F., III J. Chem. Phys.
1979, 71, 705.