J. Phys. Chem. 1993,97, 3171-3175
3171
Electronic Structure, Spectroscopic Properties, and State Ordering of the Isoelectronic ScO, TIN, and VC Diatomics Saba M. Mattar Department of Chemistry, University of New Brunswick, Bag Service No. 45222, Fredericton, New Brunswick, Canada E3B 6E2 Received: July 28, 1992
Local density functional computations, which take into account electron exchange-correlation and employ large one-particle Gaussian basis sets, are used to study the electronic structure and bonding of the of ScO, TiN, and VC low-lying states. While both ScO and TiN have 21+ ground states, arising from the 9af37rX23?r,2 electronic configuration, the VC diatomic is predicted to have a 2A ground state. The VC 2A ground state (8~~3~,~3?r,216,t) is the same as that suggested from EPR matrix-isolation experiments. The spectroscopic parameters ue,WeXe, Be, a,, and p and its derivatives are also computed for the three lowest 2Z+, ZA, and 211 states, Introduction The symmetry and geometry of trapping sites play a subtle but important role in matrix-isolation spectroscopy. For example, in the case of some atoms these effects are quite prominent and can be monitored by electron paramagnetic resonance (EPR),1-2 magnetic circular dichroism3-s and electronic a b ~ o r p t i o n ~ - ~ spectroscopies. In principle, diatomic molecules that possess orbitally degenerate 211or 2A ground states are not detectable by EPRIO since their principal perpendicular g-tensor components are
+
g,,= 2(\kl(Li 2Si)19) = 0 (1) where i = x, y and \k = 211, ?A. However, atom-molecule interactions may be sufficiently strong to lower the molecular symmetry and quench and orbital angular momentum of the diatomic, which results in EPR active complexes.I1-l3 The first important example of orbital angular momentum quenching in diatomics by rare gas atoms was recently reported by Hamrick and Weltner.14 The EPR spectra of the isoelectronic NbC, NbSi, VSi, and VC were found to exhibit large g,, anisotropies. Furthermore, the hyperfine splittings varied considerably with the type of matrix gas used. Hamrickand Weltner suggested that the diatomics initially have highly ionic 2Aground states and possess large electric dipole moments. These dipole moments will interact with a nonaxial polarizable rare-gas matrix atom, via dipole-induced dipole interactions, to form a new complex of lower symmetry.I4 The assumption that VC has a 2A ground stateI4 is based on the following experimental facts. The ScO diatomic has a ground state and the two lowest excited states are the 2A and 211, lying approximately 16 000 cm-1 higher in energy.Is-l7 In comparison to ScO, the TiN diatomic also has a ground state butthe2Astatedrops toabout 6000cm-1.18.19 Thusit is plausible to assume that in the VC case the 2A state continues to drop below the 2 z + state, yielding a 2A ground state.I4 The purpose of this paper is to verify the ordering of the ground and low-lying excited states of VC by using the local density approximation (LDA). The structure-bonding relationships are also analyzed in terms of itsvalenceone-electronmolecular orbitals and Mulliken population analysis. In addition, the electronic structures of ScO and TIN are also computed and compared with previous computations by using ab initio Hartree-Fock selfconsistent field configuration interaction (HF-SCF-CI) techniques.2g22 The agreement between the LDA and HF-SCF-CI computationsin theScO and TiN cases should support the present VC results.
2z+
2z+
0022-3654/93/2097-317 1$04.00/0
Computational Details The description of the local-density functional linear combination of atomic orbitals (LDF-LCAO) method have been previously reported.23-28 The basis sets for the transition metals are derived from Wachters' 14~/9p/Sdprimitivescontractedto [62111111/3312/ 32].29 They are further augmented b y p and d functions. Their exponents are 0.0833 and 0.0278 for Sc, 0.0951 and 0.0317 for Ti, and 0.1051 and 0.0350 for V.30 For C, N, and 0 the 13s/8p basissetsdevelopedbyvanD~ijneveldt,~' contracted to [6211111/ 421 11 and augmented by p and d polarization functions,32 are used. The SCF iterations are continued until the relative change in both the charge density and exchangwrrelation potential is less than l t 5 . A complete Mulliken population analysis iscarried out for the three molecules in their ground states. To estimate the binding energies, the total energy of the constituent atoms in their ground states was also computed. The same C,, symmetry adapted basis sets of the diatomics were used in the atomic c o m p ~ t a t i o n s . ~Two ~ J ~nonlinear least-squares fitting programs are used to estimate the spectroscopicparameters we,uexc,Be,a,, andp and its derivatives, from the total energy and dipole moment curves.33 Normally, 25 values for the total energy and dipole moment in a 0.25-au range around the minimum are used in the fitting procedures. Results and Discussion The LDF-LCAO computations of the ScO and TiN molecules indicate that their ground states are 2Z+with the corresponding 9uf37rX237ry2 electronic configuration. This is in accordance with previous experimental's-l9and results. A summary of the properties for both the ScO and TiN are given in Tables I and 11, respectively. These tables show that the equilibrium distances, Re, computed by the LDF-LCAO method are very close to those found experimentally or computed via the HFSCF-CI techniques. Since the rotational constant, Be,is related to Re by the simple relation34 h Be = 8n2cqRe2
it is not surprising to find that the Be values are also in good agreement with the experimental and theoretical results shown in Tables I and 11. In eq 2, the reduced mass of the dimer is denoted by in order not to confuse it with the dipole moment P.
The LDF-LCAO we values are within f50 cm-I of the experimental values for the ScO ground and excited states. In the 0 1993 American Chemical Society
Mattar
3172 The Journal of Physical Chemistry, Vol. 97, No. 13, 1993
TABLE I: Eauilibrium Distances, Binding Energies, and Spectroscopic Constants for the ScO Diatomic' X?C+
A?A
A'%
9.09 7.01 6.38
1.666 1.668 1.646 1.675 1.630 1.703 1.726 1.709 1.741 1.735 1.685 1.686 1.661 1.69 1 1.672
5.21
9.430 4.200
994. I 964.9 1042.0 930.0 1 120.0 894.9 845.9 902.0 772.0 748.0 897.2 876.0 914.0 853.0 887.0
0.0 0.0 0.0 0.0 0.0 14300.8 15029.0 14792.0 14883.0 16500.0 15419.6 16489.3 16768.0 16789.0 17500.0
0.514 0.513
15.99 33.00
3.83
3.51
3.55 3.18
4.62 2.32
7.11
3.34
8.99 6.65
5.19 -2.03
3.96 4.20 4.41 3.66
4.39
b 17
-1.290
c
d e
4.644 4.900
0.492 0.479
16.20
-2.397
b 17 c
d e
11.425 5.00
0.503 0.502
16.97 37.00
b 17
-7.817
6.78 2.75
C
d e
The units of we, w,xe, and B, are cm-I. a, is in IOw4cm-I, while those of pIR., ap/aR, and a2p/8R2are D, D/bohr, and D/bohr2, respectively. h This work. Reference 21, using HF-SCF-SDCI. Reference 21, using the C P F approximation. Reference 22, using pseudopotential S C F followed by MRSDCI.
TABLE 11. Equilibrium Distances, Binding Energies, and Spectroscopic Constants for the TiN Diatomic' state ReqrA De, eV T,cm-I wc WeXe Be a, PIR. ap/aR XZZ+ A?A Af2n
1.568 1.582 1.630 1.602 1.690 1.571 1.596 1.650
8.05 6.87 3.78
1139.2 1049.0 1010.0 990.1 1020.0 1080.6
0.0 0.0
0.0 8354.9 6400.0 15711.1 16197.0 16200.0
-1.403
0.633 0.620
21.07
2.453
0.605
22.21
7.896
0.630
22.03
950.0
3.65 3.56 3.05 6.83 7.86 4.30 4.63 4.48
@p/dR2
ref
3.32
-1.756
1.24
-3.317
b 19 c b
3.60
-1.877
C
b 19 c
Units are defined in Table 1. This work. Reference 20, using CAS-SCF-CI.
TABLE I V Mulliken Population Analysis for the Sc Component in ScO
TABLE 111. Mulliken Population Analysis for the ScO and TIN *E+Ground States ~
~~
orbital anal. scandium orbital overlap 7af
7al 9a 8a1 80
3n" 3711 totals
-0.05 -0.05 0.01 0.01 -0.01 0.32 0.29
S 0.02 0.02 0.01 0.01 0.84
P 0.06 0.06 0.03 0.02 0.08 0.04 0.03 0.90 0.32
d 0.03 0.03 0.23 0.22 0.07 0.41 0.37 1.36
S 0.89 0.89 0.03 0.03 0.00
P 0.00 0.00 0.70 0.72 0.00 1.55 1.59 1.84 4.56
titanium 70' 7a 8n1 98 8a/ 3r" 3*,1 totals
0.03 0.03 0.04 0.03 -0.24 0.40 0.38
0.04 0.04 0.00
0.00 0.89
0.97
ref
oxygen d occupation no. 0.00 1 1 0.00 0.00 1 0.00 1 0.00
1
0.01 0.01 0.02
2 2
0.08 0.08 0.38 0.36 0.07 0.75 0.70
0.85 0.85 0.05 0.06 0.03
0.29
2.42
1.84
0.00 0.00 0.52 0.54 0.00 1.20 1.25
0.00 0.00 0.00
3.51
0.04
0.00
0.00 0.02 0.02
22
a
1.16 0.82 0.20 0.02 0.55 0.62
1.36 0.76 0.00 0.08 0.58 0.78
1.38 0.90 0.25 0.07 0.58 0.78
This work.
nitrogen
0.04 0.04 0.05 0.04 0.06 0.03 0.03
3d 4s 4PU 4P77 3da 3dn
21
1 1 1 1 1
2 2
case of TiN the LDF-LCAO procedure predicts an we that is 90 cm-' larger than the experimental value. The T, values for the 2A and 211low-lying states of ScO and TiN, given in Tables I and 11, are well within the f1000-cm-I error expected from CASSCF-CI computations for such systems.20 Only few experimental dipole moment measurements of the of ScO and TIN have been performed. Tables I and I1 reveal that the dipole moments, computed at the equilibrium distances by the LDF-LCAO method, are quite close to all those previously measured experimentally (TiN 2Z+ and 211states, ScO 211state). The computed dipole moment derivatives, in these tables, also agree reasonably well with those computed by the HF-SCF-CI methods.2C-22
The detailed Mulliken population analyses for ScO and TiN in their ground states are given in Table 111. In the TiN case, a population analysis was also performed by Bauschlicher.*OThe HF-SCF-CI calculations predict that the total Ti s, p, and d valence character is 0.87, 0.28, and 2.45, respectively.20 The LDF-LCAO numbers in Table I11 are in very good agreement with these results. In addition, the HF-SCF-CI computationsZo predict that the total nitrogen 2p character is 3.44 as compared with 3.51 obtained by the LDF-LCAO method. In the ScO case, two population analyses have been done previously.*IJZ The results for the S c component obtained by the two CI methods are compared with the present LDF-LCAO results in Table IV. Except for the 4pa contribution, the LDFLCAO results are in full agreement with those of Jeung and Koutecky,22 which utilizea pseudopotential SCFscheme followed by multireference configuration interaction due to single and doubleexcitations (MRDCI). Furthermore, Table IVshows that the agreement between the LDF-LCAO results and the CASSCF-CI results of Bauschlicher21 is also good. One may then conclude that the LDF-LCAO method gives a reasonable picture of the electronic structure and bonding for the ScO and TiN diatomics. The properties obtained by this method are comparable to those determined experimentally or computed by using sophisticated HF-SCF-CI techniques. Contrary to the ScO and TiN cases that have ground states, the VC ground state is a 2A with an 8~23r,~3r~216,,,f
2x+
Isoelectronic ScO, TiN, and VC Diatomics -0.05
1'
'
"
"
'
"
'
'
"
The Journal of Physical Chemistry, Vol. 97, No. 13, 1993 3173
"
"
"
''4
r 70 T 6
1.2
1.4
1.6 R vc
1.a
2.0
2.2
(A)
Figure 1. Relative energy of VC states as a function of the internuclear bond distance, R. The energy scale is relative to the sum of the groundstate energies of C(,P) and V(4F).
-2.0
1
- Bo
-3.0
90 i--
Figure 3. Vanadium carbide contour diagram for the 701 orbital. Contour values are 0.01, 0.02,0.03,0.04,0.05,0.06,0.07, and 0.08 for contours 1-8. The corresponding negative contours are drawn as dashed lines. The zero contour is denoted by a 0. Units are (e-/ao3)I/*.
-
3n 1
180
u
.......1..
.
3%
,'
. .
_...__..
7
.
0
x
-10.0 -1 1 .o I
I
Spin u Spin I3 Figure 2. Spin-unrestricted valence molecular orbital diagram for the ground-state configuration of vanadium carbide.
electronic configuration. The total energy curves for the ground and lowest two excited states (211and for this molecule are given in Figure 1. The minima of the three curves and their binding energy values, given in Table V, indicate that all three states are stable. The equilibrium bond distances, dipole moments, and their first and second derivatives are also listed in Table V. The valence molecular orbitals for the VC ground state are shown in Figure 2 and the Mulliken population analyses are given in Table VI. The extent of bonding or antibonding within a molecular orbital may be determined by examining the population and distribution of the component atomic orbitals in this table. Figure 3 shows the contour diagram for the 7ut orbital. This orbital results from an in-phase interaction of the 2s(C) atomic orbital with an sd,i(V) hybrid. The 2s(C) orbital is the major component (73%) while the sdLI(V)is only 22%. The population analysis in Table VI indicates that this orbital arises from the donation of approximately 0.26 electrons from the 2s(C) to the vanadium 3d22,4s, and 4p orbitals. The total overlap value of 0.19 between the two atoms is large, indicating a strong bond. Similar arguments also apply to the 701 orbital. The 3 r molecular orbitals are due to the bonding interaction of the 3d,,(V), 3d,,(V), 2p,.(C) and 2p,(C) atomic orbitals. This typeof bonding isclearly illustrated in Figure4 for the 3atorbital. The populations in Table VI for the 3rt and 3771 show that the electrons are shared among the two atoms. The large overlap values for the 3 r orbitals indicate that they are strongly bonding and that significant delocalization of charge has occurred in the
2c+)
II
6 4
Figure 4. Contour diagram for the 3 d orbital. Contour values are listed in Figure 3.
internuclear region. This strong covalent interaction results from the coincidence in energy of the 3d,,(V), 3d,,(V), 2p,(C), and 2p,(C) one-electron atomic orbitals. The 80. orbitals are responsible for the transfer of electronic charge from the 3d2z(V) to an empty sp carbon hybrid orbital. Although 2p,(C) and 3d,z(V) are in phase and provide a backdonation pathway, the overall sp carbon hybrid orbital points away from the V atom, leading to a molecular orbital that is slightlyantibonding. This is illustrated in Figure 5 for thecontour diagram of the 8uf orbital. The highest occupied molecular orbital (HOMO) is the 16,t orbital. It is entirely 3d,(V) in character, is nonbonding, and has no overlap with the carbon atom. The overall analysis indicates that VC has one u-bond and two a-bonds, which is also similar to the TiN case.20 However, these are further weakened by the antibonding natureof the 80 orbitals. In the first-row transition-metal diatomics, such as hydrides and oxides, the electronic configurationresponsible for the bonding may be 3dn4s2,3dn+I4p1,3d"+2, 3d"4s14p', or 3dn+14s1.20 The total populations listed in Table VI reveal that vanadium has a valence population of 3d4.164s0.*84p0.20, while the carbon has a 2s' 832~2.50valence orbital occupation. Furthermore, the gross atomic populations indicate that 0.386 electrons have been transferred from the vanadium to the carbon atom. From the present analysis of the valence one-electron molecular orbitals and the greater stability of the vanadium 3d44s1configuration as compared to the 3d44pl configuration,35 one may qualitatively conclude that the vanadium 3d44s1and the carbon 3s22p2states participate in the bonding of the ground-state molecule. The
Mattar
3114 The Journal of Physical Chemistry, Vol. 97, No. 13, 1993
TABLE V state X2A A?C+ A'ZII (I
Euuilibrium Distances, Binding Energies, and Spectroscopic Constants for the VC Diatomic' Re,, A D,, eV T, cm-' We WCXC Bc a, ulx aulaR 1.577 1.572 1.564
0.0 2580.1 17326.4
6.77
1054.0 1064.5 1065.2
.
18.167 1.944 4.495
0.698 0.702 0.709
27.65 27.77 28.24
5.94 3.14 4.21
-0.25 2.37 2.52
awaR2 -1.938 -1.675 -1.503
ref b b b
Units are defined in Table I. This work.
TABLE VII: Dipole Moment' Analysis for ScO,
TABLE VI: Mullien Population Analysis for the VC fA Ground State
TIN. and VC
orbital anal. vanadium orbital overlap
7a1 7a 881 80, 3rt1 3~,,1 16 totals
0.19 0.15 -0.01 -0.19 0.61 0.47 0.00
sco carbon
s
p
d
s
p
d
0.10 0.09 0.03 0.06
0.04 0.03 0.01 0.03 0.04 0.05
0.12 0.10 0.54 0.35 1.13 0.92 1 .oo
0.73 0.78 0.15 0.17
0.01 0.00 0.27 0.39 0.81 1.02
0.00 0.00 0.00 0.00 0.02 0.02 0.00
occupation no.
6' 6, 7r1
0.28 0.20 4.16 1.83 2.50 0.04
01
vc 64.41 1
Electronic Component -48.178 -52.832
-58.469
irreducible Representation 0.000 0.000 0.000 0.000 -10.990 -12.924 -10.733 -12.594 -16.543 -16.736 -9.912 -10.578
-3.774 0.000 -15.600 -14.035 -12.815 -12.245
total dipole moment positive charge centroidb negative charge centroidh net charge transfer'
8ot
TiN
Nuclear Component 52.003 56.484
3.825 0.706 0.654 0.578
3.652 0.766 0.7 17 0.401
5.942 0.874 0.793 0.386
Dipolemoment unitsindebye. Computedat theequilibriumdistances of the ground states. Centroid positions in bohrs along the z axis. Net electronic charge transfer from the transition-metal computed from the gross atomic populations.
and electron, respectively. N is the total number of electrons, while A is the total number of nuclei. In the case of a diatomic molecule, only the z components of the centroids do not vanish and the effective distance between the charges is d = (R:"' Table VI1 shows that, as expected, the charge transfer in VC is less than in TIN, which in turn is less than in ScO. However, VC has the largest dipole moment because it has the largest distance, d, between the separated charges. If the orbital angular momentum of the VC diatomic is to be quenched via dipole-induced dipole interaction with a rare gas atom then it must possess a large dipole moment and the rare-gas atom must have a large polarizability, a. Indeed the VC zA ground state has a dipole moment that is larger than both the ScO and TiN *C+ ground states, leading to a large dipole-induced dipole interaction, -pa/+. Recently Morse has detected two transitions for the VC dimer in thegas phase.36 The first is in thenear-infrared region (1 1 988 cm-I) and the second in the visible region (16 805 cm-I). One easily identifies the latter as the transition from the X2A ground state to the A'211 state listed in Table V. However, the agreement between the near-infrared transition, 11 988 cm-I, and the forbidden XzA to A2C+ transition (Table V) is poor. The 11 988-cm-I transition may be due to the excitation from the ground state to an excited 2A or 2@ state. A multideterminant HF-SCF-CI computation that includes single and double excitationsshould givea much better prediction of these higher excited states and their transition energies in this case. This work is presently under way. The detailed expressions for the hyperfine splittings of the 2A VC molecule perturbed by a nonaxial rare-gas atom are given by Hamrick and Weltner.I4 Unfortunately, to reproduce the effect of the rare-gas atom and the quenching of orbital angular momentum by LDF-LCAO computations, one has to compute not only the VC diatomic but the loosely bound triatomics Ne- -VC, Ar- -VC,etc. This is beyond the scope of this paper. From the difficulty in resolving the rotational lines in Morse's preliminary spectral gas-phase results, the VC molecule is believed to have some 4s(V) character, leading to a significant hyperfine ~plitting.)~ This hyperfine interaction may be induced from core
ry).
Figures. Vanadiumcarbidecontourdiagramforthe8ajorbital. Contour values are listed in Figure 3.
participation of the vanadium atom ground-state electronic configuration 3d34s2, in the bonding is highly unlikely. This is very similar to TiN where the Ti 3d34s1and not the 3d24s2 configuration if involved in the bonding.20 Hamrick and Weltner proposed that the VC unpaired electron occupies a db orbital instead of a d r , leading to a 2A3/2 ground state. l 4 The contour diagrams in Figures 3-5 and the one-electron molecular orbital occupations determined by the LDF-LCAO method support these experimental findings. Table VI1 contains a detailed analysis of the ScO, TiN, and VCdipole moments. Thecontribution to the total dipole moments from the nuclear and electronic components is tabulated separately. The table also includes the electronic contributions from every irreducible representation. In a diatomic molecule the dipole moment depends on the amount of charge transferred from one atom to another and the actual distance between separated charges. To estimate this distance the Cartesian coordinates of the positive and negative charge centroids, which are defined as A
A
RYuc= x Z i R i j / x Z i
(3)
i= I
i= I
and N
relet = (*AI-xrij2A)/N J
(4)
i= I
respectively, are also computed and given in Table VII. In eqs 3 and 4, Ri, and r,, represent the jth coordinate of the ith nucleus
Isoelectronic ScO, TiN, and VC Diatomics polarization effects and may be estimated from a spin-unrestricted com~utation.~~ For thevanadium nucleus the isotropiccomponent of the hyperfine splitting is"JJ3J7
where xm,JV) and x,,,,.p(V) represent the occupied spin-up and spin-down orbitals, respectively, g, is the gyromagnetic ratio of the vanadium nucleus, and ON its nuclear magneton. Comparison may be made with the hyperfine values obtained from trapping VC in a Ne matrix. The results for a Ne matrixI4 are chosen since Ne has the smallest polarizability of the Ar, Kr, and Xe rare gases, Consequently the hyperfine values obtained in a Ne matrix should be theclosest to the gas-phasevalues. Theisotropic hyperfine splitting constant for the V center may be estimated from its parallel and perpendicular components as
+
Aistr(V)= '/3[A,I(V) 2A,(V)] From Hamrick and Weltner's results for the vanadium hyperfine parallel and perpendicular components(Neon-Site 1)14 one obtains a value of 618.53 MHz. By use of eq 5 , the corresponding computedvalue is found to be 48 1.O MHz. The theoretical results seem reasonable since the error bar associated with AII(V)may be as large as 60 MHz (ref 14, Figure 7). In the present computations, the ground-state wave function is a single Slater determinant and may be contaminated with states of higher multiplicity. Previously when computing the Sc isotropic hyperfine splittings in ScNi diatomic this did not pose a problem, since there were no low-lying quartet states.33 However, in the VC case thecomputation of thevertical excitation energiespredict a 411 state, lying approximately 24 399 cm-' above the ground state and arising from the 8ut9ut3?ryfelectronic configuration. This state is similar to the one found by Jeung and Koutecky for S C O . ~There ~ will undoubtedly be some spin contamination to the 2A VC ground state from the 411state, which will affect the computed hyperfine splittings to some extent. Finally, one would like to add that the binding energies, computed by the LDF method and listed in Tables I, 11, and V, are overestimated. This is a well-known consequence of the LDF appro~imation.38~~ The overbinding, in some cases, may be as large as several electronvolts. Addition of nonlocal effect^^^.^'^^ to the local density approximation, whether implemented variationally within the SCF cycles or as a post SCF correction, should help reduce the overestimation of the binding energies.
Conclusions The LDF-LCAO calculations predict that VC has a bound 2A ground state similar to experimental VC results in rare-gas matrices. The VC HOMO is totally nonbondingand theunpaired electron resides entirely on the V atom. This is in agreement with the suggestions of Hamrick and Weltner, based on their EPR experiments.I4 The VC molecule has some ionic character originating from the donation of 2s(C) to the 3d(V) (7u orbitals) and back-donation from themetal to thecarbon atom (Iuorbitals). The covalent component of the bonding arises from *-bonds of the 3* orbitals. Although the ionic character in the molecule causes a net charge transfer from V to C, the large dipole moment is rationalized in terms of the large distance between the separated positive and negative charge centroids. The hyperfine splitting in this molecule, in its ground state, is most likely due to core polarization effects. The agreement between the computed vanadium isotropic hyperfine splittings and those found in a Ne matrix is reasonable. The present ScO, TiN, and VC and previous S C N ~VNi, , ~ ~and TiV results17 suggest that the LDF-LCAO method may adequately describe the geometry, electronic structure, and charge distributionsof transition-metal diatomics. It is hoped that these
The Journal of Physical Chemistry, Vol. 97, No. 13, 1993 3175 theoretical results will encourage further experimental determinations of diatomic spectroscopic parameters such as dipole moments, vibrational frequencies, anharmonicities,and hyperfine and g tensors for the ground and low-lying excited states.
Acknowledgment. The Natural Sciences and Engineering Research Council of Canada (NSERC) is acknowledged for its continued financial support and assistance. I am also grateful to Professor M. D. Morse, University of Utah, for the preliminary VC gas-phase results. References and Notes ( I ) Graham, W. R. M.; Weltner, W., Jr.J. Chem. Phys. 1976.65, 1516. (2) Ammeter, J. H.; Schlosnagle, D.C. J. Chem. Phys. 1973,59,4784. (3) Pellow, R.; Eyring, M.; Vala, M. J . Chem. Phys. 1989, 90, 1440. (4) Lund. P. A,; Smith, D.; Williamson, 9. E.; Schatz, P. N. J . Phys. Chem. 1984.88, 3 I . ( 5 ) Weinert, C. M.; Fortsmann, F.; Grinter, R.; Kolb, D. M. Chem. Phys. 1983, 80, 95. (6) Kuppelmaier, H.; Stockmann, H. J.; Steinmetz, A.; Gorlach, E.; Ackermann, H. Phys. Lett. 1983, 98A, 187. (7) Hormes, J.; Schiller, J. Chem. Phys. 1983, 74, 433. (8) Ossicini, S.; Fortsmann, F. J . Chem. Phys. 1981, 75. 2076. (9) Balling, L. C.; Havey, M. D.; Dawson, J. F. J . Chem. Phys. 1978, 69, 1670.
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