Overlapping and non-overlapping integrals in molecular calculations

Abstract

The “auxilliary basis fuctions” method is specifically adapted to the case of two-electron integrals involving non-overlapping charge distributions. Complementary sets of irregular solid harmonics are introduced to represent tha Gaussian potentials in the long-range limit and the corresponding expansion coefficients are found by minimizing the mean-square deviation with respect to the true potentials within the molecular region. Analytic formulae are given for the necessary integrals. The degree od accuracy obtainable and the corresponding saving in the construction of Coulomb-type operators are discussed, also in connection with a simple model system.