Mqller-Plesset perturbation theory

It is an attractive feature of ab initio wave function theory that there is a clear hierarchy of methods leading from Hartree-Fock to the exact solution of the Schrodinger equation. Post-Hartree-Fock methods can be divided into three main categories [88]. The first is based on (Mqller-Plesset) perturbation theory [89] and referred to as MPn where n is the order of the perturbation. MPn is excellent when Hartree-Fock already is giving a reasonable description, as is often the case for complexes involving Ad and 5d elements. Otherwise, it fails or might only converge slowly with the order n. MP2 can be used for medium size systems of 100-200 atoms. 

All calculations in Ref. [22] were performed utilizing the Gaussian-98 code [30]. The potential energy scan was performed by means of the Mqller-Plesset perturbation theory up to the fourth order (MP4) in the frozen core approximation. The electronic density distribution was studied within the population analysis scheme based on the natural bond orbitals [31,32], A population analysis was performed for the SCF density and MP4(SDQ) generalized density determined applying the Z-vector concept [33]. 

Mqller-Plesset perturbation theory (p. 648) multiconfigurational SCF (MC SCF) methods (p. 624) multireference methods (p. 623) natural orbitals (p. 621)... 

Similar transition expectation values can also be defined for other non-variational methods like Mqller-Plesset perturbation theory, where one defines a Lagrangian by adding the equations for the correlation coefficients as extra conditions multiplied with Lagrangian multipliers to the respective MP energy expression (Hattig and Hefi, 1995 Aiga and Itoh, 1996). 

The restricted Mqller-Plesset description of the dissociation process is improved as we go to higher orders in perturbation theory, in particular at the MP4 level. However, as for all methods based on the dominance of a single electronic configuration, the description deteriorates as the OH bonds are stretched, although the MP4 curve is quite satisfactoiy for bond distances up to 3.5oo- For sufficiently large distances, the restricted potential-energy curves diverge at all levels of theory. 

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