Many-body perturbation approach

In the matter of electron correlation, there are a number of procedures that have been developed over the years. A prime advantage of a many-body perturbation approach, such as Mqller-Plesset for dealing with complexes... 

All the above mentioned functionals generally provide atomic or molecular properties with a reasonable precision, so that conventional DF methods are claimed to deliver results comparable to those obtained by second-order many body perturbation approaches (MP2). From a purely formal point of view, the reasons for such good performances are not yet evident. 

Rayleigh-Schrodinger many-body perturbation theory — RSPT). In this approach, the total Hamiltonian of the system is divided or partitioned into two parts a zeroth-order part, Hq (which has... 

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. 

Pipek J, Bogar F (1999) Many-Body Perturbation Theory with Localized Orbitals - Kapuy s Approach. 203 43-61... 

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. 

S. A. Kucharski and R. J. Bartlett, Fifth-Order Many-Body Perturbation Theory and Its Relationship to Various Coupled-Cluster Approaches, Volume 18 of Advances in Quantum Chemistry Wiley, Hoboken, NJ, 1986, p. 281. 

Ei=i n F(i), perturbation theory (see Appendix D for an introduction to time-independent perturbation theory) is used to determine the Cj amplitudes for the CSFs. The MPPT procedure is also referred to as the many-body perturbation theory (MBPT) method. The two names arose because two different schools of physics and chemistry developed them for somewhat different applications. Later, workers realized that they were identical in their working equations when the UHF H is employed as the unperturbed Hamiltonian. In this text, we will therefore refer to this approach as MPPT/MBPT. 

The second step of the calculation involves the treatment of dynamic correlation effects, which can be approached by many-body perturbation theory (62) or configuration interaction (63). Multireference coupled-cluster techniques have been developed (64—66) but they are computationally far more demanding and still not established as standard methods. At this point, we will only focus on configuration interaction approaches. What is done in these approaches is to regard the entire zeroth-order wavefunc-tion Tj) or its constituent parts double excitations relative to these reference functions. This produces a set of excited CSFs ( Q) that are used as expansion space for the configuration interaction (Cl) procedure. The resulting wavefunction may be written as... 

---