Extremely compact formulas for molecular two-center one-electron integrals and Coulomb integrals over Slater-type atomic orbitals

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Abstract
Extremely compact analytical formulas are derived for molecular two-center one-electron integrals and Coulomb integrals, which occur in linear-combination-of-atomic-orbitals calculations with Slater-type orbitals (STO's). The derivation is based on the connection of the STO's with the reduced Bessel functions (RBF's) and makes use of the convolution theorems of RBF's. The final results are of a surprisingly simple structure and are, therefore, especially useful for practical applications.