@MISC{He00assessmentof, author = {Yuan He and Dieter Cremer}, title = {Assessment of higher order correlation eŒects with the help of Mù ller ± Plesset perturbation theory up to sixth order}, year = {2000} }

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Abstract

For 30 molecules and two atoms, MPn correlation energies up to n ˆ 6 are computed and used to analyse higher order correlation e ects and the initial convergence behaviour of the MPn series. Particularly useful is the analysis of correlation contributions E…n†XY... …n ˆ 4;5;6; X;Y;... ˆ S, D, T, Q denoting single, double, triple, and quadruple excitations) in the form of correlation energy spectra. Two classes of system are distinguished, namely class A systems possessing well separated electron pairs and class B systems which are characterized by electron clustering in certain regions of atomic and molecular space. For class A systems, electron pair correlation e ects as described by D, Q, DD, DQ, QQ, DDD, etc., contributions are most important, which are stepwise included at MPn with n ˆ 2;...;6. Class A systems are reasonably described by MPn theory, which is re ¯ ected by the fact that convergence of the MPn series is monotonic (but relatively slow) for class A systems. The description of class B systems is di cult since three- and four-electron correlation e ects and couplings between two-, three-, and four-electron correlation e ects missing for lower order perturbation theory are signi ® cant. MPn methods, which do not cover these e ects, simulate higher order with lower order correlation e ects thus exaggerating the latter, which has to be corrected with increasing n. Consequently, the MPn series oscillates for class B systems at low orders. A possible divergence of the MPn series is mostly a consequence of an unbalanced basis set. For example, di use functions added to an unsaturated sp basis lead to an exaggeration of higher order correlation e ects, which can cause enhanced oscillations and divergence of the MPn series. 1.