The evaluation of integrals occurring in the theory of molecular structure. Parts I & II

Abstract

Part I : A new technique is developed for evaluating the integrals which occur in molecular theory. The method is based on the expansion of exponentials in terms of the so-called £ functions. These involve modified Bessel functions. In this part we list the properties of these £ functions needed for the two-centre integrals. A table is provided of the I ’s and K ’s used in their tabulation. An account is given of the properties of certain integrals of the £ functions and some numerical examples are provided. Part II : Methods are described for the evaluation of the two-centre, one-electron Coulomb, overlap and resonance integrals, for the two-electron Coulomb and hybrid (Coulomb-exchange) integrals, and for the penetration integrals. Formulae are listed for more than 180 distinct integrals.