Application of Perturbation Theory to Open-Shell Systems

Abstract

Open-shell systems are characterized by the fact that the unperturbed energy levels are degenerate. This degeneracy shows itself physically in the general appearance of the optical spectra and in the sensitivity of open-shell systems to the effect of an external field. The degeneracy also affects the way in which perturbation theory is applied to such systems. Since the model space contains several Slater determinants, it is no longer possible to classify the single-particle states into occupied and unoccupied states as in the closed-shell case. We need in addition a third category of states, representing open-shell states or valence states, which are partly occupied in the model space. In order to be able to use the particle-hole formalism developed in the previous chapters, we shall still separate the single-particle states into two categories, which can be referred to as “particle” and “hole” states, respectively. In this formalism we have the option of treating the valence shell(s) either as particles or as holes, which gives some additional flexibility.