Moller-Plesset convergence issues in computational quantum chemistry

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. Moller-Plesset perturbation theory offers a popular correction strategy: it formally expands eigenfunctions and eigenvalues as power series in a coupling parameter lambda that switches the Hamiltonian continuously between the Hartree-Fock form (lambda=0) and the electron-correlating ``physical{''} Hamiltonian (lambda=1). Recent high-order Moller-Plesset numerical expansions indicate that the series can either converge or diverge at lambda=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 lambda 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). (C) 2000 American Institute of Physics. {[}S0021-9606(00)30222-7].