Analytic continuation in exchange perturbation theory

It has been shown that the divergence or pathologically slow convergence of perturbation expansions involving a weak or none symmetry forcing (Murrell–Show–Musher–Amos, symmetrized polarization or polarization expansions) can be circumvented by using a simple analytic continuation procedure. When applied to the interaction of a hydrogen atom with a proton this procedure provides accurate values of the exchange energy from the knowledge of the polarization series alone. When the ungerade symmetry is forced the symmetrized polarization series is shown to converge to a spurious, unphysical interaction energy. The true interaction energy can only be recovered by the analytic continuation procedure. This procedure provides us also with the information about location of singularities of the analytic functions defined by the perturbation series. Such information turns out to be sufficient for an understanding of peculiar convergence properties of the perturbation expansions and their Pade approximants.