6TH-ORDER MANY-BODY PERTURBATION-THEORY .4. IMPROVEMENT OF THE MOLLER-PLESSET CORRELATION-ENERGY SERIES BY USING PADE, FEENBERG, AND OTHER APPROXIMATIONS UP TO 6TH ORDER

Three different ways of getting reliable estimates of full configurati on interaction (FCI) correlation energies are tested, namely (a) by Pa de approximants [k, k] and [k, k - 1], (b) by using extrapolation form ulas, and (c) by Feenberg scaling of Moller-Plesset (MP) correlation e nergies. 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 Pade 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 lambda((5)) (scaling of the second-order wave function, FE2) rather than the previ ously tested lambda((3)) (scaling of the first-order wave function, FE 1) was considered. Investigation of 26 different correlation energies for systems with monotonic convergence in the MPn series (class A syst ems) or initially oscillatory convergence behavior (class B systems) i ndicates that Pade approximants lead in some cases to reasonable estim ates of FCI correlation energies, but in other cases, in particular fo r class B systems, they give too negative correlation energies. Both m onotonic and oscillatory behavior for the Pade series is observed wher e it is possible to predict its convergence behavior on the basis of c alculated MPn energies. The best estimates of the FCI correlation ener gy are obtained by FE2 scaling. At sixth-order FE2, values for atoms a nd molecules with equilibrium geometry differ on the average by just 0 .146 mhartree from FCI correlation energies. The FE2 correlation energ ies all converge monotonicly. Also, FE2 scaling reduces the exaggerati on of MP6 correlation energies for class B systems. However, surprisin gly good estimates of FCI energies are also obtained by simple extrapo lation formulas based on MP4, MP5, and MP6 correlation energies. (C) 1 996 John Wiley & Sons, Inc.