Numerical Methods for the Evaluation of the Löwdin α-Function

Abstract

The problem of expanding an angular momentum wave function centered at one point in terms of angular momentum wave functions centered at another point is analysed. The emphasis is on obtaining methods that can be applied to functions that are defined numerically, in contrast to analytic methods. Three numerical approaches are described, and it is found that one leads to extremely accurate results. The question of the rate of convergence of the resulting series is discussed, and results of the application of the expansion to the calculation of nuclear attraction three-center integrals, and electron-electron four-center integrals are presented.