Mpller-Plesset third-order perturbation theory

Perturbative approximation methods are usually based on the Mpller-Plesset (MP) perturbation theory for correcting the HF wavefunction. Energetic corrections may be calculated to second (MP2), third (MP3), or higher order. As usual, the open- versus closed-shell character of the wavefunction can be specified by an appropriate prefix, such as ROMP2 or UMP2 for restricted open-shell or unrestricted MP2, respectively. 

There is also a hierarchy of electron correlation procedures. The Hartree-Fock (HF) approximation neglects correlation of electrons with antiparallel spins. Increasing levels of accuracy of electron correlation treatment are achieved by Mpller-Plesset perturbation theory truncated at the second (MP2), third (MP3), or fourth (MP4) order. Further inclusion of electron correlation is achieved by methods such as quadratic configuration interaction with single, double, and (perturbatively calculated) triple excitations [QCISD(T)], and by the analogous coupled cluster theory [CCSD(T)] [8],... 

MP3 Third-order Mpller-Plesset perturbation theory... 

Figure 1 Angular variation of components of the two-body interaction energy in (HF)3 in a planar Cii, configuration. SCF components are labeled as follows ES = electrostatic, EX = exchange, def = deformation energy (AE - - ES - EX). The dispersion energy 6cjisp ° computed by perturbation theory is denoted disp. The curve representing the complete two-body interaction through third-order Mpller-Plesset perturbation theory is labeled as full. All terms have been computed in the dimer-centered basis set. (Data taken from ref. 120.)...

The second modern geminals-based approach was developed by Szalewicz and co-workers in the early 1980s. These authors are mostly interested in the closed-shell CCD method, its linearized version (LCCD), and the second-(MP2) and third-order (MP3) Mpller-Plesset perturbation theory approaches, which are contained in LCCD, In single-reference CCD theory, the wave function is written in the exponential form... 

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