Sixth-order many-body perturbation theory. IV. Improvement of the M�ller-Plesset correlation energy series by using Pad�, Feenberg, and other approximations up to sixth order

Abstract

Three different ways of getting reliable estimates of full configuration interaction (FCI) correlation energies are tested, namely (a) by Padé approximants [k, k] and [k, k − 1], (b) by using extrapolation formulas, and (c) by Feenberg scaling of Møller-Plesset (MP) correlation energies. By using MPn energies up to sixth order, i.e., MP2, MP3, MP4, MP5, and MP6, it was possible to test the convergence behavior of the Padé series [1, 0], [1, 1], [2, 1], [2, 2] and the Feenberg series up to sixth order where in the latter case a scaling factor λ(5) (scaling of the second-order wave function, FE2) rather than the previously tested λ(3) (scaling of the first-order wave function, FE1) was considered. Investigation of 26 different correlation energies for systems with monotonic convergence in the MPn series (class A systems) or initially oscillatory convergence behavior (class B systems) indicates that Padé approximants lead in some cases to reasonable estimates of FCI correlation energies, but in other cases, in particular for class B systems, they give too negative correlation energies. Both monotonic and oscillatory behavior for the Padé series is observed where it is possible to predict its convergence behavior on the basis of calculated MPn energies. The best estimates of the FCI correlation energy are obtained by FE2 scaling. At sixth-order FE2, values for atoms and molecules with equilibrium geometry differ on the average by just 0.146 mhartree from FCI correlation energies. The FE2 correlation energies all converge monotonicly. Also, FE2 scaling reduces the exaggeration of MP6 correlation energies for class B systems. However, surprisingly good estimates of FCI energies are also obtained by simple extrapolation formulas based on MP4, MP5, and MP6 correlation energies. © 1996 John Wiley & Sons, Inc.