Moeller-Plesset second-order perturbation

WFT treatment such as Moeller-Plesset second-order perturbation theory (MP2) or coupled-cluster with single and double excitations (CCSD(T)) with correlation energy [51]. This approximation works fairly well for large interfragment distances but is obscured for shorter bonds by exchange and intrafragment correlation effects. 

Shi Z, Boyd RJ, Intrinsic barriers of some model SN2 reactions second-order Moeller-Plesset perturbation calculations, J Am Chem Soc, 113, 2434-2439 (1991) and refs therein... 

Shi, Z. Boyd, R. J. An ab initio Study of model Sf 2 reactions with inclusion of electron correlation effects through second-order Moeller-Plesset perturbation calculations, J. Am. Chem. Soc. 1990,112, 6789-6796. 

MBPT(2) stands for second-order many-body perturbation theory, which is also known by the Hamiltonian partitioning scheme it employs, Moeller-Plesset (see references 68 and 69). 

The data are obtained from large basis set calculations (see Table 7.6) which include electron correlation (second-order Moeller-Plesset perturbation theory) and which are corrected for basis set superposition error (BSSE), (Boys and Bernardi 1970). While the results for the stronger hydrogen bonds are qualitatively the same with or without the inclusion of correlation, the weaker interactions require the better description of the wave function. 

The first choice seems to be more natural since, H() being invariant, the partitioning scheme remains untouched of Moeller-Plesset type. The price to be paid for this principal simplicity, however, is high in calculational details, as the well-developed, systematic many-body graphical algorithms are not applicable if the unperturbed eigenfunctions bear a complicated structure. In a series of papers [44-48], Pulay and Ssebo developed formulas for the second- and third -and fourth-order perturbative corrections with localized orbitals using a CEPA-... 

We can apply for the diagonal elements of the self-energy matrix, X(ft>,) in the Moeller-Plesset (MP) many body perturbation theory (MBPT) in the second order (MP2) approximation... 

Moeller-Plesset Perturbation Theory. After having computed the quasi one-electron orbitals q>j and quasi one electron energies e,- one can apply (following Rice and Handy113,114) the MP/2 expression of the second order correlation correction of the quasi total energy for given , a), t, Est and 0. In this case the Moeller-Plesset perturbation will be... 

P. Pulay and S. Saebo, Theor. Chim. Acta, 69, 357 (1986). Orbital-invariant Formulation and Second-Order Gradient Evaluation in Moeller-Plesset Perturbation Theory. 

As first step second order Moeller-Plesset perturbation theory (MP2) /20/ has been applied for different chains with small unit cells (see point 3). The MP2 correction to the Hartree-Fock energy can be written with the help of (15) in the simple form, ... 

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