Electron Moller-Plesset perturbation theory

The Seetion on More Quantitive Aspects of Electronic Structure Calculations introduees many of the eomputational ehemistry methods that are used to quantitatively evaluate moleeular orbital and eonfiguration mixing amplitudes. The Hartree-Foek self-eonsistent field (SCF), eonfiguration interaetion (Cl), multieonfigurational SCF (MCSCF), many-body and Moller-Plesset perturbation theories. 

Another approach to electron correlation is Moller-Plesset perturbation theory. Qualitatively, Moller-Plesset perturbation theory adds higher excitations to Hartree-Fock theory as a non-iterative correction, drawing upon techniques from the area of mathematical physics known as many body perturbation theory. 

So far, we ve presented only general perturbation theory results.We U now turn to the particular case of Moller-Plesset perturbation theory. Here, Hg is defined as the sum of the one-electron Fock operators ... 

We state without further derivation that the electronic energy corrected to second order in Moller-Plesset perturbation theory, mp2 is... 

Using MP2(full)/6-31+G geometries (second-order Moller-Plesset perturbation theory with core electrons included in the perturbation treatment). 

Using a single determinant to derive the Hartree-Fock wavefunction does not take into account the correlation between electrons of different spins. If the wavefunction is described by a linear combination of determinants, then configuration interaction is incorporated. Another method to model correlation energy involves Moller-Plesset perturbation theory. A more detailed description of this may be found in Ref. 41. 

One of the inherent problems with ab initio calculations is that they do not take full account of electron correlation, which arises from electrons keeping away from the vicinity of other electrons. This can make a significant contribution to the energy and is especially significant for accurate calculations of reaction energies and bond dissociation. One early method used for adding the effects of electron correlation to the Hartree-Fock method incorporated Moller-Plesset perturbation theory and led to methods labeled MP2, MP3, MP4, etc. 

The Moller-Plesset perturbation theory is a popular and most extensively used method to incorporate electron correlation to the HF theory [26, 34], In this method the HF Hamiltonian is treated in a perturbative way. Thus, the total Hamiltonian is written as ... 

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