On the Evaluation of Exponential (Slater) Type Integrals

Abstract

Molecular electronic structure calculations are usually based upon the LCAO-MO approach in which the molecular orbitals (MO’s) are represented by linear combinations of atomic orbitals (AO’s). For the quantum mechanical calculation of energies and properties of molecules one has to evaluate the matrix elements of the Hamiltonian. With the AO’s being centered at the various atomic nuclei in the molecule under consideration, these matrix elements become the infamous multicenter molecular integrals: The use of AO’s which resemble physically meaningful one-electron wave functions for the one-nucleus one-electron Coulomb problem (i.e. the hydrogen atom) like exponentially decaying Slater-type orbitals (STO’s) leads to multicenter integrals which are notoriously difficult to evaluate for poly-atomic molecules.