On the Coulson–Fischer wave function for the X 1A′ H+3 molecular ion: parametrisation using distributed Gaussian basis sets

Abstract

Coulson–Fischer theory is applied to the ground electronic state of the simplest polyatomic molecule, the H+3 molecular ion. The Coulson–Fischer orbitals are parametrised in terms of a distributed Gaussian basis set of s-type functions with variationally optimised exponents and positions. The efficacy of these basis set is demonstrated by performing matrix Hartree–Fock calculations which can be compared with previous studies using alternative methods of basis set construction. The ground-state potential energy surface is explored for a range of equilateral, isosceles and scalene triangular geometries for which a number of authors have reported the results of accurate calculations. It is demonstrated that the Coulson–Fischer wave function supports a global approximation to the ground-state potential energy surface of the H+3 system. The Coulson–Fischer orbitals afford a simple picture of the molecular wave function which provide a simple description of the bonding for all geometries. The distributed Gaussian basis set affords a more efficient method of approximation than some other techniques, such as, for example, the more widely used expansions in terms of atom-centred basis functions.