Page 206 - Strategies and Applications in Quantum Chemistry From Molecular Astrophysics to Molecular Engineer

FSGO Hartree-Fock Instabilities of Hydrogen in External Electric Fields

J.M. ANDRE, G. HARDY, D. H. MOSLEY and L. PIELA
Facultés Universitaires Notre-Dame de la Paix, Laboratoire de Chimie Théorique
Appliquée, 61 rue de Bruxelles, B-5000 Namur, Belgium and University of Warsaw,
Quantum Chemistry Laboratory, Pasteura 1, 02-093 Warsaw, Poland

1. Introduction

In the early sixties, it was shown by Roothaan [1] and Löwdin [2] that the symmetry
adapted solution of the Hartree-Fock equations (i.e. belonging to an irreducible
representation of the symmetry group of the Hamiltonian) corresponds to a specific
extreme value of the total energy. A basic fact is to know whether this value is associated
with the global minimum or a local minimum, maximum or even a saddle point of the
energy. Thus, in principle, there may be some symmetry breaking solutions whose energy
is lower than that of a symmetry adapted solution.

The Hartree-Fock description of the hydrogen molecule requires two spinorbitals, which
are used to build the single-determinant two-electron wave function. In the Restricted
Hartree-Fock method (RHF) these two spinorbitals are created from the same spatial
function (orbital) but differ only by its multiplication by the a or spin basis functions.

It is common knowledge that, in the case of the hydrogen molecule studied in a minimal
basis set, the correlation error can be explained by the existence of ionic species in the
hydrogen dissociation products:

This is an artefact due to the non-zero probability of the restricted wave-function of
finding two electrons of opposite spins at the same spatial position.
FSGO's (Floating Spherical Gaussian Orbital) were introduced by Frost [3] in the mid
1960s. With FSGO's one abandons the idea of atomic orbitals centred on nuclear
positions to arrive at an even more compact basis set than a minimal one. FSGO's
correspond to s-type Gaussians that are not fixed at the atomic centers but are able to
"float" in space so as to optimally represent each localized pair of electrons. Because only
one function is needed for each electron pair, the basis set used is often referred to as
being "subminimal".
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Y. Ellinger and M. Defranceschi (eds.), Strategies and Applications in Quantum Chemistry, 189–202.
© 1996 Kluwer Academic Publishers. Printed in the Netherlands.