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J. Phys. Chem. 1983, 87, 1312-1322
pattern resulting from the long-range coupling between two nonequivalent methyl groups. The other isomer is a high-symmetry isomer, as evidenced by the singlet NMR re~onance,~ and it could be one of the two isomers 1 or 3. Previous interpretations assigned the spectrum in terms of the presence of the trans,trans form. However, the above calculations clearly indicate that the cis,cis isomer is the lower energy form and that the higher symmetry isomer observed in the NMR spectra is almost certainly the cis,cis form 1. A similar interpretation is likely in the case of the low-temperature NMR spectra observed for di-tert-butylsulfur diimide. The barrier for rearrangement of the different isomers can be obtained from Tables IV and V and compared to experimental estimates.17 The barrier for the cis,trans to trans,cis isomerization has been estimated to be 13.0 kcal/mol for di-tert-butylsulfur diimide7and 11.9 kcal/mol in the case of bis[4-(dimethylamino)phenyl]sulfurdiimide' by dynamic NMR spectroscopy. The barriers obtained at our best theoretical level are 18.0 kcal/mol for the parent sulfur diimide and 16.0 kcal/mol for the dimethyl derivative. As the barrier apparently drops with increasing bulk of the substituent, it is clear that our results are quite consistent with the experimental findings.'r7 It can be seen from Tables IV and V that the theoretical results implicate the cis,cis isomer as an intermediate on the lowest energy interconversion pathway and that the isomerization pathway is intermediate between rigid rotation and in-plane inversion. The
inclusion of electron correlation in the calculations has little effect on the magnitude of the barriers or on the relative stability of the isomers. Conclusions d functions on S have to be included in the basis set in order to study these compounds a t a reliable theoretical level. The geometries obtained with such basis sets are in good agreement with experiment. The cis,cis isomer is the most stable form of the parent sulfur diimide and the cis,trans isomer is the lowest energy form of dimethylsulfur diimide. The trans,trans isomers for both compounds are considerably higher in energy. The temperature-dependent NMR spectra of dimethylsulfur diimide can be reinterpreted with these points in mind. The isomerization pathway is intermediate between rigid rotation and inplane inversion. The cis,trans to trans,cis interconversion involves the cis,cis isomer as an intermediate and the barrier for interconversion is 18.0 kcal/mol for sulfur diimide and 16.0 kcal/mol for dimethylsulfur diimide. The lowering of the barrier on substitution is consistent with the smaller barriers seen experimentally in compounds with larger substituents.
Acknowledgment. We are indebted to M.-H. Whangbo for several interesting discussions. Registry No. 1 (R = H), 62255-28-1;1 (R = CHJ, 84878-02-4; 2 (R = H), 62255-30-5;2 (R = CHJ, 84878-03-5;3 (R = H), 62255-29-2;3 (R = CHB), 84878-04-6.
Electronic Structure of Scandium Fluoride. A Low-Resolution ab Initio Study James F. Harrlson' Theoretical Chemistry Group, Chemistry Division, Argonne National Laboratory, Argonne, Illinois 60439, and the Chemistry Department, Michigan State Unlversity, East Lansing, Michigan 48824 (Received: June 30, 1982; I n Final Form: October 15, 1982)
Using ab initio GVB and CI techniques, we have studied the electronic structure of ScF in the ground and low-lying excited states. The ground state is predicted to have 1P symmetry with a bond length of 1.811A, a vibrational frequency of 742.3 cm-l, and an anharmonicity constant, uexe,of 4.1 cm-l. The corresponding experimental values are 1.787 A, 735.6 cm-', and 3.8 cm-l. The bonding in this state is ionic and corresponds to Sc+F-. Using the ground-state GVB orbitals (modified slightly via the IVO transformation), we constructed configuration interaction representations as a function of internuclear separation for the 30 lowest electronic states. The internuclear separation and various spectroscopic constants have been calculated for each state and, where possible, molecular orbital occupancies have been assigned. The role of differentialelectron correlation in the accurate description of the molecular energy levels of ScF is emphasized.
Introduction Diatomic molecules containing one transition-metal atom are of considerable importance in high-temperature c h e m i ~ t r y ,as ~ ,constituents ~ of cool stars4and as models for the role5 that d electrons play in chemical bonds in(1)Scientist in Residence, Argonne National Laboratory, 1980/81. Address correspondence to this author a t the Department of Chemistry, Michigan State University, East Lansing, MI 48824. (2) K. D. Carlson and C. R. Claydon, Adu. High Temp. Chem., 1,43 (19671, and other articles in this series. (3) 'High Temperature Science: Future Needs and Anticipated Developments", National Academy of Sciences, Washington, DC, 1979. (4) W. Weltner, Jr., Science, 155, 155 (1967).
0022-365418312087-1312$01.50/0
volving transition elements. Of these diatomics the transition-metal monohalides are of particular interest because of the small number of electrons involved in the bonding (the metal-halogen bond is presumably a single bond) and the relatively large amount of spectroscopic data6 available. The object of this study is the smallest, and presumably simplest, transition-metal monohalide, ScF. (5) P. R. Scott and W. G. Richards, "Specialist Periodical Reports: Molecular Spectroscopy", Vol. 4, The Chemical Society, London, 1976, p 70. (6) See the compilation by K. P. Huber and G. Herzberg, 'Molecular Spectra and Molecular Structure. IV. Constants of Diatomic Molecules", Van Nostrand-Rheinhold, New York, 1979.
1983 American Chemical Society
The Journal of Physical Chemistty, Vol. 87, No. 8, 1983 1313
Electronlc Structure of Scandium Fluorlde D(ScF) =140.8?3kcal/mol
5.0 -
4.5-
H '7
G
'7
4.0 -
3.5-
F '7
9 3@
-
3.0
3A(uncerta~n)
3
E '7
Y
w 2.5-
a
2.0-
1.5-
dh
c 'C+
c
3@
B'l7
-
1.0
0.50.00
-
X'C'
0%
Figure 1. Experimental energy levels of ScF.
(3A 1
311. These alternatives are shown in Figure 2 along with the suggested spectroscopic constants we and wexe. There have been several qualitative models suggested for the electronic structure of the oxides and halides of the transition"-13 elements and they have proved helpful in providing a model within which one can discuss the electronic configurations associated with the observed spectroscopic states. There have been two reported ab initio studies of ScF, both at the LCAO-MO level. The first by Carlson and Moser14studied the lowest lZ+ and 3Ar states. Although their ScF result predicted the 3Ar to be the ground state, they argued convincingly that the differential in the correlation energy would preferentially lower the lZ+ state. They estimated this differential semiempirically and concluded that the lZ+ was indeed the ground state but only by 461 cm-'. The second study, by Scott and Richards,15was concerned primarily with the atomic orbital composition of the highest occupied K orbital in the lowest 3@ state. In addition, these authors reported calculated spectroscopic parameters for the a3Arand B'H as well as the 3@ state. These calculations and their conclusions will be discussed later. The presence of singlet and triplet states in the observed spectra and the near constancy of the experimental bond lengths attest to the presence of at least two electrons which are not crucial to the bonding and which may occupy the 49, 4p, and 3d orbitals on Sc. This suggests strongly that there are many low-lying states of ScF which have not been seen because of the dipole selection rules. The goal of the present study is to provide a global view of the low-lying (45.00 eV) electronic states of ScF while simultaneously obtaining insight into the character of the individual states via several low-resolution ab initio calculations. The calculations are characterized as low resolution because all states are treated at the same theoretical level notwithstanding our awareness that differential correlation effects are important in determining the correct energy level ordering in transition-metal atoms16 and diatomics14J7containing a transition element. Although this uniform treatment guarantees a nonuniform accuracy in the calculated levels and spectroscopic constants, we anticipate that by observing the systematics in the degree of disagreement we will identify problem areas which can be addressed by more focused studies.
:__ :+I (591.0,233)
a 'A BARROW et. al.
GURVICH and SHENYAVSKAYA (514.0, 1.98)
Flgure 2. Two interpretations of the spectroscopic feature at 2.719 eV. The numbers in parentheses are the values (in cm-') of u, and uexeobtained on the basis of assignment.
The experimental information that we have available is collected in Figure 1. We know from the high-temperature (2000 K) studies of Barrow et al.' that there is a lZ+ state and a 3Ar state close enough in energy to participate in absorption with comparable intensities. We know also from the low-temperature (4 K) matrix isolation studies of McLeod and Weltne? that the lZ+ is the ground state. The dissociation energy has been measured by Zmbov and Margravegvia a high-temperature mass-spectrometric study of the equilibrium between CaF, Sc, Ca, and ScF. The resulting value of 140.8 f 3.2 kcal/mol is large and characteristic of the strong bonds associated with a transition element and one from the main groups of the periodic table. There seems to be some question as to the nature of the feature at 2.719 eV. When seen in absorption by Barrow et a1.I it was assigned as a 3A 3A. When seen in emission by Gurvich and ShenyavskayalO it was assigned as 3Z+
-
-
(7) R. F. Barrow, M. W. Bastin, D. L. G. Moore, and C. J. Pott, Nature (London),215, 1072 (1967). (8) D. McLeod and W. Weltner, J. Phys. Chem., 70, 3293 (1966). (9) K. F. Zmbov and J. L. Margrave, J. Chem. Phys., 47,3122 (1967).
Basis Sets and Molecular Codes The scandium basis is Wachters'ls 14s,9p,5d augmented with two p functions optimized for the lowest 4Fstate by Dunninglg and one diffuse d as recommended by Hay.*O The Sc basis was contracted to 5s, 4p, 3d by using the
(10) L. V. Gurvich and E. A. Shenyavskaya, Opt. Spectrosc. (Engl. Transl.), 14, 161 (1963). (11) R. A. Berg and 0. Sinanoglu, J. Chem. Phys., 32, 1082 (1960). (12) C. K. Jorgensen, Mol. Phys., 7, 417 (1964). h Chem... 1.64 (13) C. J. Cheetham and R. F. Barrow. Ado. H i ~ Temo. . (igii7j. (14) K. D. Carlson and C. Moser, J . Chem. Phys., 46, 35 (1967). (15) P. R. Scott and W. G. Richards, Chem. Phys. Lett., 28,101 (1974). (16) C. Froese Fischer in "Proceedings of the Sixth Conference on Atomic Physics, Riga, USSR", Plenum Press, New York, 1978; M. Guse, N. S. Ostlund, and G . D. Blyholder, Chem. Phys. Lett., 61, 526 (1979); T. H. Dunning, Jr., B. H. Botch, and J. F. Harrison, J . Chem. Phys., 72, 3419 (1980); R. L. Martin, Chem. Phys. Lett., 75, 290 (1980); C. W. Bauschlicher, Jr., J. Chem. Phys., 73, 2510 (1980); C. W. Bauschlicher, Jr., and S. P. Walch, ibid., 74,5922 (1981);B. H. Botch, T. H. Dunning, Jr., and J. F. Harrison, ibid., 75,3466 (1981);C . Froese Fischer, ibid., 76, 1934 (1982). (17) S. Walch and C. Bauschlicher, Jr., Chem. Phys. Lett., 86, 66 (1982). (18) A. J. Wachters, J . Chem. Phys., 52, 1033 (1970). (19) T. H. Dunning, Jr., private communication. (20) P. J. Hay, J. Chem. Phys., 66, 4377 (1977).
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The Journal of Physical Chemistty, Voi. 87, No. 8, 1983
TABLE I: C o m p a r i s o n of C a l c u l a t e d GVB and E x p e r i m e n t a l S p e c t r o s c o p i c Parameters for S c F D e , kcalimol Re. I L ~ ,cm * W e X e , cm B e . cm a,, cm
exptl
GVB
140 1787, 735 6 38 0.3950 0 00266
100 1819 727 6 40 0.3815 0 00266
+20
1
Sc-F 'E'
-10
-20
S C ( ~ DSCF ) vectors (the energy is -759.7251 au) and the Raffenetti21general contraction scheme. The fluorine basis is Huzinaga's229s,5p contracted to 3s, 2p on the basis of the 2p SCF vectors and Wfenetti's recommendation. The fluorine basis was augmented by one diffuse p (exponent= of 0.074) and a diffuse d (exponent = 0.5). The d exponent was optimized in a GVB calculation on the lowest lZ+ state a t the experimental equilibrium bond length. The SCF energy of F in this basis is -99.398 19 au. The total number of basis functions is 53 but only 49 were used in the molecular calculation. (The symmetric sum of the 3d functions was excluded in both the atomic and molecular calculations.) All calculations were carried out a t Argonne National Laboratory by using the collection of codes maintained by the Theoretical Chemistry Group. The authors of these codes are acknowledged in the companion paper on ScLi.
Generalized Valence Bond Study of the XIZ+ State The argon core of the Sc atom and the Is and 2s orbitals of F will be the core orbitals of ScF and although variationally determined will always remain doubly occupied. Explicitly, we have core = la22a23a24a25a26a27azla42a4 If the F(2P) approaches the S C ( ~ Dwith ) its singly occupied 2p, orbital along the internuclear line, the GVBZ4 function which correlates the bond and separates into the SCF atom is = A(core)(802- X9u2)3a410a2
Harrison
(1)
The energy calculated with this ansatz is presented in Figure 3 (relative to the asymptotic energy -859.1233 au). The calculated properties along with their experimental6 counterparts are presented in Table I. With the exception of the dissociation energy the agreement with experiment is rather good. At very large separations X = 1 and the natural orbitals corresponding to the bond orbitals 8a and 9a are given by 2p,(F) f 3d,(Sc). The 3a is the 2p,(F) and the 10a is the uncorrelated 4s(Sc). As the atomic separation is reduced to the equilibrium value, X decreases to
