Mpller-Plesset first derivatives

The Mpller-Plesset (MP) treatment of electron correlation [84] is based on perturbation theory, a very general approach used in physics to treat complex systems [85] this particular approach was described by M0ller and Plesset in 1934 [86] and developed into a practical molecular computational method by Binkley and Pople [87] in 1975. The basic idea behind perturbation theory is that if we know how to treat a simple (often idealized) system then a more complex (and often more realistic) version of this system, if it is not too different, can be treated mathematically as an altered (perturbed) version of the simple one. Mpller-Plesset calculations are denoted as MP, MPPT (M0ller-Plesset perturbation theory) or MBPT (many-body perturbation theory) calculations. The derivation of the Mpller-Plesset method [88] is somewhat involved, and only the flavor of the approach will be given here. There is a hierarchy of MP energy levels MPO, MP1 (these first two designations are not actually used), MP2, etc., which successively account more thoroughly for interelectronic repulsion. 

Mpller and Plesset were the first to derive the formula for the second-order correlation energy. Calculation of the MP2 correlation energy requires just O(M ) operations and, therefore, MP2 calculations represent one of the cheapest ways of getting correlation corrections. As shown before, D excitations de.scribe pair correlation effects and, therefore, the MP2 correction covers the largest part of the correlation energy defined... 

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