Quadratic Padé approximants and the intruder state problem of multireference perturbation methods

Simple and quadratic Padé resummation methods are applied to high‐order series from multireference many‐body perturbation theory (MR‐MBPT) calculations using various partitioning schemes (Møller–Plesset, Epstein–Nesbet, and forced degeneracy) to determine their efficacy in resumming slowly convergent or divergent series. The calculations are performed for the ground and low‐lying excited states of (i) CH₂, (ii) BeH₂ at three geometries, and (iii) Be, for which full configuration interaction (CI) calculations are available for comparison. The 49 perturbation series that are analyzed include those with oscillatory and monotonic divergence and convergence, including divergences that arise from either frontdoor or backdoor intruder states. Both the simple and quadratic Padé approximations are found to speed the convergence of slowly convergent or divergent series. However, the quadratic Padé method generally outperforms the simple Padé resummation. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005