Electronic energy Moller-Plesset perturbation theory

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

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. 

In order to improve on the Hartree-Fock model, the use of perturbation theory is common. The first energy correction is obtained at second order and the corresponding method is calles second-order Moller-Plesset perturbation theory (MP2). MP2 calculations provide a first estimate for the correlation energy SE, which turned out to be also useful for estimates of the interaction energy in cases dominated by dispersive interactions (see the next section for an overview on how interaction energies can be calculated from total electronic energy estimates). 

To determine the corrections to the energy it is therefore necessary to determine the wavefunctions to a given order. In Moller-Plesset perturbation theory the unperturbed Hamiltonian j q is the sum of the one-electron Pock operators for the N electrons ... 

Electronic structure calculations have been performed with the system of programs Gaussian94 (G94) [19]. Restricted Hartree-Fock theory (RHF) is used for closed shell systems, and Unrestricted Hartree-Fock theory (UHF) for open shell systems (radicals). The correlation energy corrections are introduced with Moller-Plesset perturbation theory up to second order, and results from spin projected calculations are used (PMP2 and PUMP2). 

In many cases electronic properties calculated at the Hartree-Fock level do not have the accuracy sufficient to make them useful in chemical predictions. For example, as revealed in a recent study,the stability of the cage isomer of the C20 carbon cluster relative to that of the cyclic isomer is underestimated at the Flartree-Fock level by as much as 200 kcal/mol. In such systems, the electron correlation effects have to be taken into account in quantum chemical calculations through application of approximate methods. One such approximate electron correlation methods that has gained a widespread popularity is the second-order Moller-Plesset perturbation theory (MP2). Until recently calculations involving the MP2 approach have used a traditional formulation in which the MP2 energy is evaluated as the sum... 

Second-order Moller-Plesset perturbation theory is the simplest approach to account for electron correlation when starting from a HF-SCF reference determinant. The correlation energy in MP2 is given by... 

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