An expansion for four-center integrals over Slater-type orbitals

A new expression is given for the electron repulsion integral over Slater-type orbitals on four different centers. It is based on the asymptotic expansion derived from the bipolar expansion of a previous paper. The expression has the form where q_p = {n_p, l_p, m_p}. Both F and σ are closed expressions. The quantity F is a combination of incomplete gamma functions, Laguerre polynomials and spherical harmonics. It depends upon the relative coordinates of a point P on the AB axis and a point Q on the CD axis. The functions σ_nlm(A, B) depend on the charge distribution (χ_Aχ_B); they have the character of overlap integrals and are of the form