On the expansion of molecular wavefunctions in a Gaussian basis set

Abstract

The properties of the expansion of the elliptical function, exp(- alpha lambda )exp(- beta mu ), in an even-tempered basis set of Gaussian functions, exp(- eta r2), are examined analytically. A Laplace transform is used to obtain an integral representation of the elliptical function in terms of Gaussian functions. Numerical quadrature procedures afford a method for obtaining a finite-series expansion of elliptical functions in terms of an arbitrary number of Gaussian-type functions. The Laplace transform provides a prescription for the generation of a systematic sequence of distributed basis sets of Gaussian functions from a sequence of atomic even-tempered sets. Illustrative calculations are reported for the hydrogen molecular ion.