A new method of deriving higher order MP(n) correlation energies is presented. Application of this method to MP6 leads to the derivation of the total correlation energy E((6)) and its dissection into 36 energy terms E(ABC)((6)). For 33 electron systems, for which full CI (FCI) correlation energies are known E((6)) and E(ABC)((6)) values together with the corresponding MP5 and MP4 energies are computed and used to analyze the initial convergence behavior of the MPn series. Two classes of systems can be distinguished, namely systems with monotonic convergence of the MPn series (class A systems) and systems with initial oscillations in the MPn series (class B systems). Analysis of E(A)((4)), E(AB)((5)) and E(ABC)((6)) values reveals that oscillations in the MPn series are caused by similar oscillations in the T contributions. For class A systems, the T contributions are of minor importance and decrease monotonically with order n as do also the SDQ contributions. For class B systems, one observes a significantly increased importance of the T contributions and alternation in the sign of the T energy for n = 4, 5, 6. Results indicate that class A systems are electron systems with well separated electron pairs. The most important correlation effects are pair correlations while three-electron correlations and couplings between pair correlations are relatively small. The latter become important when electrons cluster in certain regions of an atom or molecule. Clustering of electrons always means increased electron correlation and a more complicated correlation pattern including three-electron and pair-coupling effects. In this case, MP theory strongly exaggerates correlation effects at even orders n, which is corrected by positive correlation contributions, in particular three-electron contributions at odd orders thus leading to the oscillations observed for class B systems. Once the electron structure of an atom or molecule is understood, it is possible to identify the system as a class A or class B system and to predict the convergence behavior of the corresponding MPn series. If extrapolation formulas are used that do not distinguish between class A and class B systems, the mean deviation from FCI correlation energies is 12 mhartrees. If however, different extrapolation formulas are applied for class A and class B systems, the mean deviation obtained for the same set of molecules decreases to 0.3 mhartree, which corresponds to an improvement of FCI estimates by a factor of 36.