Two-Center Exchange Integrals between Slater-Type Atomic Orbitals

A novel general formula is developed which expresses two-center charge distributions over Slater-type atomic orbitals as expansions over terms of the form (ξ − 1)k(ξ2 − 1)M/2ex(− αξ)Ylm(η,φ), where (ξ, η, φ) are elliptic coordinates. The formula is applied to derive compact expressions for the calculation of two-center exchange integrals arising from large basis sets. The program structure is discussed and computing times are quoted for these type integrals.