Convergence behavior of the symmetry-adapted perturbation theory for states submerged in Pauli forbidden continuum

The polarization expansion and the symmetry-adapted perturbation theory (SAPT) in the symmetrized Rayleigh-Schrodinger (SRS) and the Hirschfelder-Silbey (HS) formulations are applied through high order to the medium- and long-range interaction of the ground-state lithium and hydrogen atoms. The interaction energies obtained by perturbation theory are compared with the counterpoise-corrected full configuration interaction results. It is shown that the SRS and HS expansions diverge as a result of the presence of the Pauli forbidden continuum in which the physical eigenstates of the perturbed Hamiltonian are submerged. Despite this divergence, the SAPT expansions give accurate results in low orders and excellent results when summed up in a standard way of assigning a sum to an asymptotically convergent series. The polarization expansion is found to diverge as well, with its asymptotic limit equal to the arithmetic mean of singlet and triplet energies. Unlike the case of simpler systems, for the interaction of lithium and hydrogen atoms the Hirschfelder-Silbey method does not provide any improvement over the much simpler SRS approach. (C) 2001 American Institute of Physics.