A simple algebraic derivation of the Obara–Saika scheme for general two-electron interaction potentials

Abstract

A new derivation is presented for the recursion relation of Obara and Saika (OS) for two-electron integrals over Gaussian basis functions for general interaction potentials g(r₁₂), where r₁₂ denotes the interelectronic distance. The decisive vertical OS recursion is proved directly from the recursion relation for Gaussian basis functions and the structure of the primitive integral expression for s functions. The resulting simple formulae greatly facilitate extensions of OS-based codes for Coulomb interactions to general g, which has already proved useful in implementations. The present derivation further extends the validity of the OS recursion beyond interactions covered so far.