Analytical evaluation of two-centre Coulomb, hybrid and one-electron integrals for Slater-type orbitals

Abstract

A general formula has been established for the expansion of the product of two normalized associated Legendre polynomials centred on the nuclei a and b. This formula has been utilized for the calculation of two-centre integrals with Slater-type orbitals. For the two-centre Coulomb, hybrid and one-electron integrals (overlap integrals and nuclear attraction integrals) with an arbitrary combination of quantum numbers, analytical formulae have been obtained in a closed form; new auxiliary functions have been introduced, determined by polynomials according to the parameters of Slater atomic orbitals, by means of which all these integrals are expressed in the form of a linear combination. Useful recurrence relations have also been established for these auxiliary functions.