Moller-Plesset perturbation theory order

To obtain an improvement on the Hartree-Fock energy it is therefore necessary to use Moller-Plesset perturbation theory to at least second order. This level of theory is referred to as MP2 and involves the integral J dr. The higher-order wavefunction g is... 

A number of types of calculations begin with a HF calculation and then correct for correlation. Some of these methods are Moller-Plesset perturbation theory (MPn, where n is the order of correction), the generalized valence bond (GVB) method, multi-conhgurational self-consistent held (MCSCF), conhgu-ration interaction (Cl), and coupled cluster theory (CC). As a group, these methods are referred to as correlated calculations. 

Correlation can be added as a perturbation from the Hartree-Fock wave function. This is called Moller-Plesset perturbation theory. In mapping the HF wave function onto a perturbation theory formulation, HF becomes a hrst-order perturbation. Thus, a minimal amount of correlation is added by using the second-order MP2 method. Third-order (MP3) and fourth-order (MP4) calculations are also common. The accuracy of an MP4 calculation is roughly equivalent to the accuracy of a CISD calculation. MP5 and higher calculations are seldom done due to the high computational cost (A time complexity or worse). 

MP2 2 Order Moller-Plesset Perturbation Theory Through 2nd derivatives... 

MP4 4 Order Moller-Plesset Perturbation Theory (including Singles, Doubles, Triples and Quadruples by default) Energies only... 

Thus, the value of E the first perturbation to the Hartree-Fock energy, will always be negative. Lowering the energy is what the exact correction should do, although the Moller-Plesset perturbation theory correction is capable of overcorrecting it, since it is not variational (and higher order corrections may be positive). 

MP2 second-order Moller-Plesset perturbation theory... 

As can be seen from Table I, the C-C bond distance as described by LDF is closer to experiment than the corresponding HF value obtained with a 6-3IG basis. Including correlation via second and third order Moller-Plesset perturbation theory and via Cl leads to very close agreement with experiment. The C-H bond length is significantly overestimated in the LDF calculations by almost 2%. The HCH bond angle is reasonably well described and lies close to all the HF and post-HF calculations. Still, all the theoretical values are too small by more than one degree compared with experiment the deviation from experiment is particularly pronounced for the semi-empirical MNDO calculation. 

Ten-no, S. New implementation of second-order Moller-Plesset perturbation theory with an analytic Slater-type geminal. J. Chem. Phys. 2007, 126, 014108. 

Manby, F.R. Density fitting in second-order linear-r12 Moller-Plesset perturbation theory. J. Chem. Phys. 2003, 119, 4607-13. 

Higher level calculations, based on higher orders of Moller-Plesset perturbation theory, can also be performed, albeit with the consumption of much more computer time. For example, an MP4SDTQ calculation uses fourth-order Moller-Plesset perturbation theory, includes excitations through quadruples, and gives better energies than MP2 does. 

Moller-Plesset perturbation theory (MPPT) aims to recover the correlation error incurred in Ilartree- Fock theory for the ground state whose zero-order description is ,. The Moller-Plesset zero-order Hamiltonian is the sum of Fock operators, and the zero-order wave functions are determinantal wave functions constructed from HF MOs. Thus the zero-order energies are simply the appropriate sums of MO energies. The perturbation is defined as the difference between the sum of Fock operators and the exact Hamiltonian ... 

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

---