Mo/ller–Plesset convergence issues in computational quantum chemistry

Abstract

The Hartree–Fock self-consistent-field approximation has provided an invaluable conceptual framework and a standard computational procedure for atomic and molecular quantum theory. Its shortcomings are significant however, and require remediation. Mo/ller–Plesset perturbation theory offers a popular correction strategy: it formally expands eigenfunctions and eigenvalues as power series in a coupling parameter λ that switches the Hamiltonian continuously between the Hartree–Fock form (λ=0) and the electron-correlating “physical” Hamiltonian (λ=1). Recent high-order Mo/ller–Plesset numerical expansions indicate that the series can either converge or diverge at λ=1 depending on the chemical system under study. The present paper suggests at least for atoms that series convergence is controlled by the position of a singularity on the negative real λ axis that arises from a collective all-electron dissociation phenomenon. Nonlinear variational calculations for the two-electron-atom ground state illustrate this proposition, and show that series convergence depends strongly on oxidation state (least favorable for anions, better for neutrals, better yet for cations).