Prediction of full CI energies with the help of sixth-order Moller-Plesset (MP6) perturbation theory

The sixth-order Moller-Plesset (MP6) correlation energy is analysed by using first-and second-order cluster operators and distinguishing between connected and disconnected operator products. Each product is described by simplified Brandow diagrams that help to characterize the associated energy contributions in terms of orbital relaxation, pair correlation, three-electron correlation or four-electron correlation effects. The importance of the various correlation terms and their coverage at MP2, MP3, MP4, MP5, and MP6 are analysed to understand and to predict the convergence behaviour of the MPn series, which strongly depends on the electronic structure of the atoms and molecules investigated. Adjusting existing extrapolation procedures to the convergence behaviour of the MPn series leads to improved predictions of full CI (FCI) energies based on MP6 correlation energies. The best results are obtained by a combination of first-order and second-order Feenberg scaling, which produces the results of higher order Feenberg scaling. The mean absolute deviation of predicted FCI energies from exact values is found to be 0.07 mhartree for atoms and molecules in their equilibrium geometry and 1.03 mhartree for molecules with stretched geometries and, thereby, considerable multi-reference character. Reasonable FCI energies can also be obtained with approximate MP6 methods, the most economic method of which is MP6(M7) which scales with O(M-7) (M is the number of basis functions). Mean absolute deviations of FCI energies based on MP6(M7) are 0.40 and 1.88 mhartree for equilibrium and stretched geometries, respectively. (C) 1997 Elsevier Science B.V. (C) 1997 Elsevier Science B.V.