Nuclear attraction and electron interaction integrals of exponentially decaying functions and the Poisson equation

Abstract

The technique proposed by O-Ohata and Ruedenberg (J Math Phys 7:547 (1966)) and by Silver and Ruedenberg (J Chem Phys 49:4306 (1968)) of computing nuclear attraction and electron interaction integrals by solving an inhomogeneous Laplace equation can also be applied ifB functions (Filter E, Steinborn EO (1978) Phys Rev A 18:1) are used as basis functions in atomic and molecular calculations. It is shown that because of the remarkable mathematical properties ofB functions the derivation of compact explicit expressions for the multicenter integrals mentioned above is particularly simple. These results are also of interest in the context of other exponentially decaying functions, since all the other commonly occurring exponentially decaying functions as, for instance, Slater functions or bound state hydrogen eigenfunctions can be expressed as simple linear combinations ofB functions. Consequently, their multicenter integrals can also be expressed in terms of multicenter integrals ofB functions.