Numerical evaluation of molecular one- and two-electron multicenter integrals with exponential-type orbitals via the Fourier-transform method

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Abstract
The method of Bonham, Peacher, and Cox for computing molecular multicenter integrals for 1s Slater-type orbitals is generalized to include all states. This was possible by using B functions as basis functions which have the simplest structure under Fourier transformation, compared with other commonly used exponential-type orbitals (ETO’s). Those ETO’s which differ from B functions, like Slater-type orbitals (STO’s), can be expressed by finite linear combinations of B functions. Therefore multicenter integrals occurring in molecular calculations with any of the commonly used ETO basis sets can be represented by integrals with B functions. In the present paper the three-center nuclear attraction integrals and the two-electron multicenter integrals with B functions are evaluated in a unified way via the Fourier-transform method and Feynman’s identity. The resulting expressions require a two- or three-dimensional numerical integration, respectively. The numerical and computational properties of the resulting formulas are discussed and various test values are given. Comparison is made with some values of integrals with STO’s which exist in the literature.