Systematic corrections to the equivalent core model

Abstract

The widely used equivalent core model (ECM) describes core hole states in systems with atomic charge Z by considering corresponding states with fully occupied core in systems with increased charge Z+1. When calculating energies of Z-core hole states, the valence energy of these states often has been assumed to equal the valence energy of the (Z+1) ground state. This approach misses several points: most importantly, the different spin symmetry of the corresponding states. The behavior of core hole states is governed by an effective 2×2 matrix Hamiltonian due to the two possible spin states of the core hole. A recently introduced diagonalization gives rise to a scalar core hole Hamiltonian. Both the ECM and the core hole Hamiltonian act in valence space. This allows establishment of a connection between these two approaches. By expressing the core hole Hamiltonian in the (Z+1) orbital basis, we systematically derive corrections to the ECM. Those corrections, including the one arising because of the different spin symmetry of the corresponding states, are presented in second order of Møller–Plesset perturbation theory (MP2). Hence, they can be implemented very easily so that ground-state calculations in a (Z+1) system may directly provide the core hole state energy in the original Z system.