Mpller-Plesset perturbation theory convergence

Things have moved on since the early papers given above. The development of Mpller-Plesset perturbation theory (Chapter 11) marked a turning point in treatments of electron correlation, and made such calculations feasible for molecules of moderate size. The Mpller-Plesset method is usually implemented up to MP4 but the convergence of the MPn series is sometimes unsatisfactory. The effect... 

The other area in which projection of an unrestricted result has received attention is projected Mpller-Plesset perturbation theory, the PUMPn methods [31], where n is the order of the perturbation theory. In cases in which the UHF approximation is a poor starting point (considerable spin contamination, for example), the convergence of the MP perturbation expansion can be slow and/or erratic. The PUMP methods apply projection operators to the perturbation expansion, although usually not full projection but simply annihilation of the leading contaminants. This approach has met with mixed success again, it represents a rather expensive modification to a technique that was originally chosen partly for its economy — seldom a recipe for success. 

The least expensive and conceptually simplest correlation treatment that can be applied to medium-size molecules is the second-order Mpller-Plesset perturbation theory (MP2), which is the most popular single-reference approach for the low-level treatment of electron correlation [21]. Higher order MP perturbation theory such as MP3 and MP4 are typically less useful in particular, results coming from MP3 level are inferior to MP2 because of the characteristically oscillatory convergence of perturbation theory. MP4, MP5, and MP6 offer some improvements, but the high computational costs required prevent their routine application [22]. 

As noted above, the theoretical challenges to be overcome include the validation of existing theories as well as the development of new theories. One of the surprises in electronic structure theory in the 1990s was the finding that Mpller-Plesset perturbation theory, the most widely used means to include electron correlation effects, does not lead to a convergent perturbation expansion series. This... 

The elongation method with the regional localization scheme as it is implemented in GAMESS program package has been used for ab initio treatment with STO-3G basis set. The optimization calculation of structures, used in CPU check, has been done by means of Mpller-Plesset perturbation theory with 6-31G(d) basis set. The SCF density convergence criteria has been set up to 10 . 

Mpller-Plesset perturbation theory represents a useful approach to the calculation of size-extensive correlation energies for systems dominated by a single electronic configuration. The MP2 model, in particular, represents a successful compromise between computational cost and accuracy. Higher-order corrections may also be calculated, but it should be emphasized that the M0ller-Plesset series does not converge unconditionally. 

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