Assessment of higher order correlation effects with the help of Moller-Plesset perturbation theory up to sixth order

For 30 molecules and two atoms, MPn correlation energies up to n = 6 are computed and used to analyse higher order correlation effects and the initial convergence behaviour of the MPn series. Particularly useful is the analysis of correlation contributions E-XY((n)) ... (n = 4, 5, 6; X, Y, ... = 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 effects as described by D, Q, DD, DQ, QQ, DDD, etc., contributions are most important, which are stepwise included at MPn with n = 2,...,6. Class A systems are reasonably described by MPn theory, which is reflected 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 difficult since three- and four-electron correlation effects and couplings between two-, three-, and four-electron correlation effects missing for lower order perturbation theory are significant. MPn methods, which do not cover these effects, simulate higher order with lower order correlation effects 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, diffuse functions added to an unsaturated sp basis lead to an exaggeration of higher order correlation effects, which can cause enhanced oscillations and divergence of the MPn series.