An alternative method for expanding the product of two slater wave functions

Abstract

A method is outlined by which the product of two Slater wave functions based on two nuclei A and B is expanded as an integral of charge distributions centered on points P lying on the axis AB. These distributions are most easily derived by means of Gaussian transforms; their Fourier transforms are known from the work of Bonham, Shavitt and Karplus. They can be expressed in terms of modified Bessel functions and they become weaker and at the same time more concentrated as P approaches A or B. The new representation provides useful guidelines for the optimization and partial circumvention of numerical quadratures arising in the computation of four-center integrals with the use of Gaussian transforms and also for the derivation of efficient approximation formulas.