The Mpller-Plesset Approach to Electron Correlation

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. 

4M0ller-Plesset the Norwegian letter 0 is pronounced like French eu or German o. 

We could write Fmpi = Fj j p1 = mpo + E where mpo is the sum of one-electron energies and intemuclear repulsions and En is the J, K correction (corresponding respectively to the two terms in Eqs. 5.85 and 5.90), regarding the second term as a kind of perturbational correction to the sum of one-electron energies. 

MP2 is the first MP level to go beyond the HF treatment it is the first real Mpller-Plesset level. The MP2 energy is the HF energy plus a correction term (a perturbational adjustment) that represents a lowering of energy brought about by allowing the electrons to avoid one another better than in the HF treatment  

The HF term includes intemuclear repulsions, and the perturbation correction E(2) is a purely electronic term. E1 2 is a sum of terms each of which models the promotion of pairs of electrons. So-called double excitations from occupied to formally unoccupied MOs (virtual MOs) are required by Brillouin s theorem [89], which says, essentially, that a wavefunction based on the HF determinant Z plus a determinant corresponding to exciting just one electron from Dl cannot improve the energy. 

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