Correlation effects. Perturbation theory

There are a number of methods that take into account correlation effects perturbation theory, random phase approximation with exchange, method of incomplete separation of variables, so-called extended method of calculation, superposition-of-configurations, multi-configuration approach, etc. The first two methods have so far been applied only to comparatively simple systems (e.g. configurations having few electrons above the closed shells). 

Correlation effects. Perturbation theory 29.3 Perturbation theory... 

Whenever the Hartree-Fock wave function provides a good zero-order description of the electronic system, it is natural to investigate the possibility of treating dynamical correlation by perturbation theory rather than by coupled-cluster theory. In this manner, we may hope to recover the most important effects of dynamical correlation at a cost lower than that of coupled-cluster theory. 

It is well known that Hartree-Fock (HF) theory not only has been proven to be quite suitable for calculations of ground state (GS) properties of electronic systems, but has also served as a starting point to develop many-parti-cle approaches which deal with electronic correlation, like perturbation theory, configuration interaction methods and so on (see e.g., [1]). Therefore, a large number of sophisticated computational approaches have been developed for the description of the ground states based on the HF approximation. One of the most popular computational tools in quantum chemistry for GS calculations is based on the effectiveness of the HF approximation and the computational advantages of the widely used many-body Mpller-Plesset perturbation theory (MPPT) for correlation effects. We designate this scheme as HF + MPPT, here after denoted HF -f- MP2. ... 

There have also been methods designed for use with perturbation theory and MCSCF calculations. Correlation effects are necessary for certain technically difficult molecules, such as CO, N2, HCN, F2, and N2O. 

Correct the base energy for residual correlation effects (to countera known deficiencies of truncating perturbation theory at fourth order) 1 computing the QCISD(T)/6-311G(d,p) energy. Subtract E from th energy to produce AE ... 

Things have moved on since the early papers given above. The development of Mpller-Plesset perturbation theory (Chapter 11) marked a turning point in treatments of electron correlation, and made such calculations feasible for molecules of moderate size. The Mpller-Plesset method is usually implemented up to MP4 but the convergence of the MPn series is sometimes unsatisfactory. The effect... 

If we except the Density Functional Theory and Coupled Clusters treatments (see, for example, reference [1] and references therein), the Configuration Interaction (Cl) and the Many-Body-Perturbation-Theory (MBPT) [2] approaches are the most widely-used methods to deal with the correlation problem in computational chemistry. The MBPT approach based on an HF-SCF (Hartree-Fock Self-Consistent Field) single reference taking RHF (Restricted Hartree-Fock) [3] or UHF (Unrestricted Hartree-Fock ) orbitals [4-6] has been particularly developed, at various order of perturbation n, leading to the widespread MPw or UMPw treatments when a Moller-Plesset (MP) partition of the electronic Hamiltonian is considered [7]. The implementation of such methods in various codes and the large distribution of some of them as black boxes make the MPn theories a common way for the non-specialist to tentatively include, with more or less relevancy, correlation effects in the calculations. 

Electron correlation was treated by the CIPSI multi-reference perturbation algorithm ([24,25] and refs, therein). The Quasi Degenerate Perturbation Theory (QDPT) version of the method was employed, with symmetrisation of the effective hamiltonian [26], and the Maller-Plesset baricentric (MPB) partition of the C.I. hamiltonian. 

Perturbative methods (CASPT2 [17], NEVPT2 [18]) add the dynamical correlation in an effective way, using multiconfigurational second-order perturbation theory on the CASSCF input states. These methods have proved to be suitable for studying problems in spectroscopy, photochemistry, and so on [19, 20]. 

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