Hamiltonian Expansion in Geometrical Distortions

Abstract

In this paper we consider the geometry dependence of the molecular Hamiltonian. The Hamiltonian is constructed in a geometry-dependent orbital representation. Orbital connections are introduced to link such representations at different geometries, and it is shown how orthogonal connections lead to geometry-independent density elements. Derivative expressions of the Hamiltonian are given in terms of one-index transformations of the integrals. It is illustrated how the Hellmann-Feynman theorem may be applied directly to SCF and limited CI wave functions once the right orbital connections have been chosen. Some computational aspects are considered and finally the relation to covariant derivatives in differential geometry is discussed.