Mo” ller–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. Mo”ller–Plesset perturbation theory offers a popular correction strategy: it formally expands eigenfunctions and eigenvalues as power series in a coupling parameter l that switches the Hamiltonian continuously between the Hartree– Fock form (l50) and the electron-correlating ‘‘physical’’ Hamiltonian (l51). Recent high-order Mo”ller–Plesset numerical expansions indicate that the series can either converge or diverge at l 51 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 l 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!. © 2000 American Institute of Physics. @S0021-9606~00!30222-7#