A new expansion of the Coulomb potential and linear $r_{ij}$ terms

Abstract

In this work a new expansions of Coulomb potential and interparticle distance, linear term $r_{12}$ are proposed. Except the singularities, the expansions converge to the exact value in the whole coordinate space including the vicinity of the singularities or correlation cusps points. The disadvantage of the expansion is, that it leads to complicated goniometric functional forms. Anyway, for their simplification, we used the method of their expansion developed by the author in the past.