Variational Approach to Perturbation Theory. I. Application to the Calculation of Atomic Polarizabilities

A variational approach to perturbation theory is derived which establishes the relationship between variational and conventional approaches that utilize expansions in terms of atomic or molecular eigenfunctions. This approach is based upon the observation that the variational approach to perturbation theory is formally equivalent to a variational method for constructing a special set of excited-state wavefunctions. A mathematical demonstration of this equivalence has been formulated. With the use of this new approach to perturbation theory, we have calculated both the static and dynamic polarizabilities of the two-electron helium isoelectronic series, H−, He, and Li+ and a four-electron system represented by the beryllium atom. Multiconfiguration open-shell wavefunctions were employed. These flexible wavefunctions permit a quantitative analysis of the near-degenerate s—p orbital mixing in the ground state of the beryllium atom. The inclusion of this orbital degeneracy effect results in a substantial reduction in the calculated polarizability.