Perturbation Theory for the Electron Propagator

Abstract

As in the familiar Rayleigh-Schrödinger perturbation theory (RSPT) for the N-electron ground state discussed in Appendix A.1, the starting point for perturbation theory is a division of the original hamiltonian (3.1) into two parts, ˆ H = ˆ T + ˆ V = ˆ H 0 + ˆ H I (4.1) wherê H 0 , defining the zeroth-order part, is a one-particle hamiltonian associated with non-interacting particles, andˆH andˆ andˆH I = ˆ H − ˆ H 0 = ˆ W + ˆ V (4.2) is the interaction part, comprising the bare electron repulsion, ˆ V , and, possibly, a remainder of the one-particle part of the hamiltonian, ˆ W = ˆ T − ˆ H 0 = w rs c † r c s (4.3) In the so-called Møller-Plesset (MP) partitioning, ˆ H 0 = r c † r c r (4.4) is the Hartree-Fock (HF) hamiltonian, based on the solutions of the HF equations, t rs + k V rk[sk] n k = r δ rs (4.5) where n k = 1, 0 denotes the usual (HF) ground-state occupation numbers. Accordingly , the matrix elements of the one-particle interaction partˆWpartˆ partˆW are given by w rs = t rs − r δ rs = − k V rk[sk] n k (4.6) © Springer Nature Switzerland AG 2018 J. Schirmer, Many-Body Methods for Atoms, Molecules and Clusters, Lecture Notes in Chemistry 94, https://doi.