Multicenter Integrals in Quantum Mechanics. I. Expansion of Slater-Type Orbitals about a New Origin

Abstract

Convenient and accurate formulas have been found which implement the spherical‐harmonic expansion of a Slater‐type orbital about a point displaced from the orbital's center. These formulas include, as a special case, the expansion of spherically symmetric orbitals which has been reported previously. The results are presented in algebraic form, suitable for machine computation, and have been tested for the transformation of any Slater‐type orbital with n≤7, l≤3, | m |≤l to an arbitrary space‐fixed point. By the use of this analysis, in conjunction with the properties of the rotation group, it is now possible to evaluate directly, the general multicenter electron‐repulsion integral expressed in terms of Slater‐type orbitals. The convenience of this direct approach suggests that previous analyses in terms of Gaussian orbitals or Gaussian approximations to Slater‐type orbitals, replete with their poor radial dependence, may no longer offer any computational advantages.