Analytical evaluation of multicenter molecular integrals over Slater-type orbitals using expanded Löwdin alpha functions

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Abstract
The Löwdin alpha functions, which are the functions associated with the spherical-harmonic expansion of a displaced Slater-type orbital, are expressed using C matrices to represent the polynomials in terms of the displacement distance a and the radial distance r. These polynomials are multiplied by the sum and difference of exponentials. The expansion of the exponentials leads to the use of E and F matrices. By keeping only the r variable identifiable, further simplifications of the alpha functions are possible, which makes for easy programming of all multicenter integrals. Also, no singularities appear in these developments. Everything is demonstrated by using 1s orbitals as prototypes.