Calculation of Geometrical Derivatives in Molecular Electronic Structure Theory

Abstract

The analytical calculation of geometrical derivatives in molecular electronic structure theory is reviewed. The simplifications arising from the use of variational wave functions (Wigner’s 2n+l rule) are described and it is shown how energies for non-variational wave functions may be written in a variational form to take advantage of these simplifications. After a discussion on Hamiltonian derivatives, general expressions are given for the molecular gradients and Hessians for the following ab initio electronic structure techniques: self-consistent field (SCF) and multiconfigurational (MC) SCF wave functions, configuration interaction (CI) and coupled cluster (CC) wave functions, and Moller-Plesset (MP) perturbation theory. Finally, use of translational and rotational symmetries is discussed.