Moller-plesset many-body perturbation theory

Moller-Plesset many-body perturbation theory taken through second order in the energy is the most commonly used ab initio molecular electronic structure method in contemporary quantum chemistry. For this report on many-body perturbation theory and its application to the molecular electronic structure problem we restricted our survey of applications to second-order Moller-Plesset perturbation theory. Even with this restriction, the nmnber of pubhcations appearing in the period covered by our review - namely, June 1999 to May 2001 - is sizeable. We recorded in the introduction that 883 publications containing the string MP2 in the title or keywords appeared in the year 2000 alone. However, rather than review just a small subset of these publications we decided to try to convey the... 

Highest occupied molecular orbital Intermediate neglect of differential overlap Linear combination of atomic orbitals Local density approximation Local spin density functional theory Lowest unoccupied molecular orbital Many-body perturbation theory Modified INDO version 3 Modified neglect of diatomic overlap Molecular orbital Moller-Plesset... 

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. 

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. 

Published in 2002, the second report covered the period June 1999 to May 2001 and provided an opportunity to review the wide range of applications to which many-body perturbation theory in its simplest form, that is Moller-Plesset perturbation theory through second order, was being put at the turn of the millennium. The main development considered in this second report were ... 

As in my three most recent reviews, "" I have attempted to provide a snapshot of the many applications of many-body perturbation theory in its simplest form, i.e. Moller-Plesset theory designated MP2, during the period under review by performing a literature search for publications with the string MP2 in the title only. During the period covered by the present report, a total of 80 papers were discovered satisfying this criterion. 

This partitioning, when applied in conjunction with the set of canonical Hartree-Fock orbitals (in which is diagonal), corresponds to the Moller-Plesset variant of many-body perturbation theory. A Hartree-Fock determinant, which is an eigenfunction of Pjq, is therefore the natural choice for the zeroth-order wavefunctiond... 

The quantum-mechanical energies and properties are calculated individually for each of the (1 1) structures extracted from the MC simulation of the liquid and for the optimized (1 1) complexes using many-body perturbation theory in second order with the Moller-Plesset partitioning [33], using the MP2/aug-cc-pVDZ theoretical model implemented in the Gaussian 98 program [34]. 

Physicists and chemists have developed various perturbation-theory methods to deal with systems of many interacting particles (nucleons in a nucleus, atoms in a solid, electrons in an atom or molecule), and these methods constitute many-body perturbation theory (MBPT). In 1934, Mpller and Plesset proposed a perturbation treatment of atoms and molecules in which the unperturbed wave function is the Hartree-Fock function, and this form of MBPT is called Moller-Plesset (MP) perturbation theory. Actual molecular applications of MP perturbation theory began only in 1975 with the work of Pople and co-workers and Bartlett and co-workers [R. J. Bartlett, Ann. Rev. Phys. Chem.,31,359 (1981) Hehre et al.]. 

Many-body methods, based on the linked-cluster expansion (LCE), were first developed by Brueckner [1] and Goldstone [2] in the 1950s for nuclear physics problems. Perturbation-theory applications to atomic and molecular systems (in a numerical, one-center frame) were pioneered by Kelly [3] in the early 1960s. Basis sets were later introduced, first in second-order [4] and then in third-order [5]. The 1970s saw a proliferation of molecular applications with basis sets, under the names of many-body perturbation theory (MBPT) [6] or the Moller-Plesset method [7]. Nowadays, many-body methods offer some of the most powerful tools in the quantum chemistry arsenal, in particular the coupled-cluster (CC) method, and are available in many widely used quantum chemistry program packages. 

Moller-Plesset Perturbation Theory. - Many-body perturbation theory with a Moller-Plesset reference hamiltonian is the most widely used approach to the correlation problem in atomic and molecular systems. Second-order theory, which is often designated MP2 and which was the order of theory originally presented by Moller and Plesset, is computationally efficient and facilitates the use of very large basis sets which allows basis set truncation errors to be reduced to a level where other effects, such as relativity, are often more significant... 

Olsen et al. and others rests on the assumption that the utihty of lower-order Moller-Plesset perturbation theory can be inferred from the behaviour of the higher-order terms in the perturbation series. It is widely appreciated that MoUer-Plesset perturbation theory and the equivalent many-body perturbation theory for a single determinantal reference function are not as robust as, for example, configuration interaction. Some care must therefore be exercised in applications to ensure that an appropriate reference function is employed. 

Some Applications of Second-order Many-body Perturbation Theory with a Moller-Plesset Reference Hamiltonian... 

The first approach is Moller-Plesset (MP) many-body perturbation theory. To the Hartree-Fock wavefunction is added a correction corresponding to exciting two electrons to higher energy Hartree-Fock MOs. Second-order, third-order, and fourth-order corrections to the Hartree-Fock total energy are designated MP2, MP3, and MP4, respectively. For double substitutions, i,j (occupied) into m,n (virtual),... 

Theoretical studies have been based on ab-initio molecular orbital calculations performed using either the Gaussian 86 code or, earlier, Gaussian codes on a Cray 1 Computer. The majority of calculations employed a modestly sized basis set (6-31G)to save computational time but a few have been carried out using a larger (6-311G ) basis set and using Moller-Plesset (MP) many-body perturbation theory to second or fourth order. 

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