We derived the necessary conditions to which the vector coupling coefficients (vcc) a:; and bt!,, describing atomic L,S-multiplets of the configurations d N (1 c N S 9), should satisfy. Special attention is paid to the states of non-Roothaan type for which vcc depend on the choice of degenerate d-orbitals basis set determined within the accuracy up to an orthogonal transformation u. It is shown that for such states the direct sum of matrices //aiA/l and llbi$/ must be the nonsymmetric matrix. Obtained vcc were used for the ab initio calculations (basis set (14s9p5d)

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A new semiempirical SCF MO procedure available for prediction of the transition-metal complexes' binding energy and molecular geometry is developed. The features of the method are (i) an explicit account of the orthogonality of the basis set; (ii) use of a new formula for the resonance integral; and (iii) an effective account of the Coulomb correlation of electrons in the calculation of the two-electron integrals based on approach of a model Coulomb hole function. The parameterization for H, C, N, 0, Co, and Ni atoms is presented. The results of NDDO/MC (NDDO for Metal Compounds) calculations of molecular geometries and binding energies for a number of organic compounds and more than 30 cobalt and nickel complexes are compared with the available experimental and ab initio data. The average absolute errors for the binding energies of organic molecules and metal complexes are 8.8 and 5.0 kcal/mol, respectively. 6

Cluster model DFT calculations of CO adsorption on various possible forms of gallium in Ga/HZSM-5 zeolites have been performed. CO was found to only weakly interact with Ga + , (GaO) + , and (Ga(OH) 2-n H n ) + (n ) 1, 2) cationic clusters. The resulting shifts of the CO stretching frequency (∆ν CO ) are only very small. On the other hand, CO coordination to small mononuclear and binuclear Ga 3+ hydride/hydroxide/oxide species results in positive shifts in the stretching frequency in the range ∆ν CO ) 20-40 cm -1 . Larger shifts (∆ν CO ) 70-90 cm -1 ) are associated with CO coordination to Ga ions at the corners of small three-dimensional Ga-oxide clusters. The experimentally observed changes in the infrared spectrum of adsorbed CO over Ga/HZSM-5 zeolites upon reductive and oxidative treatments are interpreted with these insights. Possibilities for the formation of such polynuclear oxide species in the zeolite micropore space are discussed. On the basis of recent literature insights, we suggest that large shifts derive from CO coordination to oligomeric Ga cationic complexes stabilized by the negative zeolite charge.

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The bonding of atomic oxygen to ferrous iron was studied using the Fe(OH)2 system as a model of the ferrous iron center. All lowest triple, quintet, and septet states of OFe(OH)2 were studied at the complete active-space self-consistent-field theory level augmented by multireference second-order-perturbation theory. In addition the density functional theory with three-parameter exchange functional of Becke and correlation functional of Lee, Yang, and Parr has been applied to this system. The ground state has been found to have A51 symmetry. The electron configuration responsible for this state is similar to that of molecular oxygen: there are the doubly occupied σ and π shells and singly occupied π* orbitals. The only difference revealed in this study is the presence of nonbonding half-filled dδ orbitals.

Different methods of averaging of energy over the states of electronic configurations yN (nr = I , 2, 3 and N = 1, 2 , . . . , 2n, -1) leading to Roothaan' energy expression are considered. The consequent values of vector coupling coefficients (vcc) in energy functionals for various states as well as for average values of energy are presented.It is shown also that in molecular systems of cubic and tetragonal symmetry having electronic configurations tN (N = 2-4) and e z there exist states for which vcc are dependent on the choice of basis set of degenerate open-shell molecular orbitals. The origin of such "non-Roothaan" terms and peculiarities of its calculation by the restricted Hartree-Fock method are discussed.

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