Computer Physics Communications 73 (1992) 192—196 Computer Physics North-Holland Communications On the use of a model function of Coulomb hole approximation for evaluation of the Coulomb integrals in semiempirical SCF MO methods M.J. Filatov, I.L. Zilberberg and G.M. Zhidomirov Institute of CatalysLs, Novosibirsk 630090, Russian Federation In order to evaluate the Coulomb and exchange integrals in the semiempirical SCF MO methods over an spd-basis of orbitals, an approximation of the model function of the Coulomb hole is used. The procedure of calculating mono- and bicentric Coulomb integrals based on the properties of Fourier transform is developed. 1. Introduction When one performs quantum chemical calculations, several kinds of integrals computed over the basis functions must be evaluated. Among them are Coulomb integrals of the form (~ttkrr) = ~ X~(2)). Here x~(i) is the j~th basis function depending on the coordinates of the ith electron. In the semiempirical SCF MO methods one must evaluate mono- and bicentric integrals only [1]. These integrals could be evaluated by the following way: monocentric Coulomb integrals from the data on atomic spectra and bicentric integrals by empirical fomulae. These empirical formulae sew together two asymptotes: (i) in the long-range limit integrals must behave as interacting multipoles and (ii) at the point Rab = 0 bicentric integrals must go into corresponding monocentric ones [2,31. A possibility of evaluating the monocentric integrals from the data on atomic spectra enables some allowance of the correlation effects in atoms [41. The bicentric integrals evaluated by empirical formulae take correlation effects into account too. This allowance of interatomic and molecular correlation energies is extremely important in the case of d-element compounds, when these energies become comparable with the promotion and metal-ligand binding energies, respectively [5]. Usually in the methods based on the NDDO assumption [1], the multipole expansion of interacting charge distributions is used to evaluate the bicentric integrals [3,6]. Since this procedure is rigorous only in the long-range limit, one must use some mathematical expedients [3,61to avoid incorrect behavior of integrals at short and intermediate distances. In this work an alternative possibility of the Coulomb integrals evaluation based on the approximation of a model Coulomb hole function [7,81 is used. In line with Clementi’s proposals [81 we choose the Correspondence to: M.J. Filatov, Institute of Catalysis, Novosibirsky 630090, Russian Federation. Elsevier Science Publishers B.V.