Series Expansion for Two-Center Noninteger-n Overlap Integrals

Abstract

A series in the internuclear distance R is derived for the two-center overlap integral between noninteger-n Slater-type orbitals. There are in general two types of terms: R2N+λ and Rn1+n2+1+N, (N=0,1,2,···; λ = |l1—l2|, |l1—l2| + 1, ···, l1+l2). When n1+n2 is an integer while n1 and n2 are not integers, logarithmic terms arise. The series is for general values of n1, n2, l1, l2, m1, m2, ζ1, and ζ2, and it converges absolutely for R<∞.