Series Expansion for Two-Center Noninteger-n Coulomb Integrals

Abstract

A series in the internuclear distance R is derived for the two-center Coulomb integral between noninteger-n Slater-type charge distributions. There are in general two types of terms: R2N+λ and Rn1+n2+3+N, (N=0, 1, 2, ···; λ = |l1—l2|, |l1—l2| + 1, ···, l1+l2). Most of the coefficients are found from the coefficients of the overlap series by exploiting {∇2 (Coulomb integral) = −4π (overlap integral)}. When n1 and n2 are not integers but n1+n2 is, the series contains logarithmic terms. The series is for general values of n1, n2, l1, l2, m1, m2, ζ1, ζ2, and R, and it converges for R<∞.