The characteristic polynomial approach to the solution of quantum chemical perturbation problems

Abstract

An approach to the solution of finite-dimensional quantum chemical perturbation problems based on the ‘characteristic polynomial’ is developed and discussed. Using the successive derivatives of the polynomial, an ordered perturbation sequence is constructed. From this sequence, perturbation series for individual eigenvalues are determined. Applications of this method are illustrated for cases of non-degenerate eigenvalues, two-fold energy degeneracy lifted in first order, andq-fold energy degeneracy. A re-derivation of the well-known Rayleigh-Schrodinger perturbation formulae from their corresponding characteristic polynomial expressions is presented, and an additional illustration is made of the use of the reduced characteristic polynomial by considering a benzene molecule with three adjacent carbon atoms ‘perturbed’ in some way.