The Coulson–Fischer wave function: parametrisation using distributed Gaussian basis sets

Abstract

A ‘generalised’ Coulson–Fischer wave function, in which the orbitals are approximated by means of a linear expansion in distributed Gaussian s-type basis functions, is used to determine a complete potential energy curve for the ground state of the hydrogen molecule by ab initio methods. A distributed basis set is developed in which both the positions and the exponents of Gaussian s-type functions are determined by invoking the variation principle. This basis set supports a sub-μhartree level of accuracy and provides a reference with respect to which calculations can be assessed, where the exponents are generated using an even-tempered prescription and an anharmonic model is employed to distribute the basis functions along the internuclear axis. This basis set also supports energy expectation values of a sub-μhartree level of accuracy.