The löwdin α function and its application to the multi-center molecular integral problem over slater-type orbitals

Abstract In this paper we trace the evolution of the Lowdin α-function method in its application to multicenter molecular integrals over Slater-type orbitais (STOs). As is well-known, any STO displaced from the origin can be expanded in an infinite series of spherical harmonics; the functional coefficients have been designated as Lowdin α functions. These a functions can be represented as exponentials multiplied by polynomials in the displacement distance and the radial distance. The polynomials are used to construct a C matrix with integer elements. To avoid cancellation errors in some cases, the exponentials are expanded to obtain E matrices for interior regions and F matrices for exterior regions. We believe that this careful approach to molecular integrals will succeed in producing accurate and rapid evaluation of the integrals needed in STO basis-set methods or quantum chemistry.

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