Convergence Behavior of Symmetry-Adapted Perturbation Expansions for Excited States. A Model Study of Interactions Involving a Triplet Helium Atom

Abstract

The convergence behavior of symmetry-adapted perturbation theory (SAPT) expansions is investigated for an interacting system involving an excited, open-shell monomer. By performing large-order numerical calculations for the interaction of the lowest, 1s2s, triplet state of helium with the ground state of the hydrogen atom we show that the conventional polarization and symmetrized Rayleigh-Schrödinger expansions diverge in this case. This divergence is attributed to the continuum of intruder states appearing when the hydrogen electron is falling on the helium 1s orbital and the 2s electron is ejected from the interacting system. One of the dimer states resulting from the interaction becomes then a resonance, which presents a hard case to treat by a perturbation theory. We show that the SAPT expansions employing the strong symmetry-forcing procedure, such as the Eisenschitz-London- Hirschfelder-van der Avoird or the Amos-Musher theories, can cope with this situation and lead to convergent series when the permutational symmetry of the bound, quartet state is forced. However, these theories suffer from a wrong asymptotic behavior of the second- and higher-order energies when the interatomic distance R grows to infinity, which makes them unsuitable for practical applications. We show that by a suitable regularization of the Coulomb potential and by treating differently the regular, long-range and the singular, short-range parts of the interatomic electron-nucleus attraction terms in the Hamiltonian one obtains a perturbation expansion which has the correct asymptotic behavior in each order and which converges fast for a wide range of interatomic distances.