Mpller-Plesset perturbation theory applications

The next two papers (6.3 and 6.4) deal with the application of an ab initio quantum mechanical method (the Mpller-Plesset perturbation theory) to large binary clusters formed by water with methane or methanol. The molecules of methane or methanol were selected because they represent two extreme types of molecules 1) methane, an entirely hydrophobic molecule and 2) methanol, which has both hydrophobic and hydrophilic parts and, in addition, can form H-bonds with water. These calculations allow one to analyze the changes in the H-bond network of water in the vicinity of both molecules when they are inserted into pure water. These two cases might be helpful in understanding much more complex molecules such as proteins. 

Nonadditive effects in open-shell clusters have been investigated only recently and relatively little information is available on their importance and physical origin. From the theoretical point of view, open-shell systems are more difficult to study since the conventional, size-consistent computational tools of the theory of intermolecular forces, like the Mpller-Plesset perturbation theory, coupled cluster theory, or SAPT, are less suitable or less developed for applications to open-shell systems than to closed-shell ones. Moreover, there are many types of qualitatively different open-shell states, exhibiting different behavior and requiring different theoretical treatments. 

This review surveys the implementation and application of a relativistic multireference Mpller-Plesset perturbation theory for many-electron systems which takes a general class of multiconfiguration Dirac-Fock SCF wavefunctions as reference functions. 

The least expensive and conceptually simplest correlation treatment that can be applied to medium-size molecules is the second-order Mpller-Plesset perturbation theory (MP2), which is the most popular single-reference approach for the low-level treatment of electron correlation [21]. Higher order MP perturbation theory such as MP3 and MP4 are typically less useful in particular, results coming from MP3 level are inferior to MP2 because of the characteristically oscillatory convergence of perturbation theory. MP4, MP5, and MP6 offer some improvements, but the high computational costs required prevent their routine application [22]. 

Basis Sets Correlation Consistent Sets Configuration Interaction Coupled-cluster Theory Density Functional Applications Density Functional Theory Applications to Transition Metal Problems G2 Theory Integrals of Electron Repulsion Integrals Overlap Linear Scaling Methods for Electronic Structure Calculations Localized MO SCF Methods Mpller-Plesset Perturbation Theory Monte Carlo Quantum Methods for Electronic Structure Numerical Hartree-Fock Methods for Molecules Pseudospectral Methods in Ab Initio Quantum Chemistry Self-consistent Reaction Field Methods Symmetry in Hartree-Fock Theory. 

Configuration Interaction PCI-X and Applications Coupled-cluster Theory Density Functional Applications Density Functional Theory (DFT), Hartree-Fock (HF), and the Self-consistent Field Mpller-Plesset Perturbation Theory Self-consistent Reaction Field Methods Spin Contamination Transition Metal Chemistry Transition Metals Applications. 

We now consider the use of perturbation theory for the case where the complete operator A is the Hamiltonian, H. Mpller and Plesset (1934) proposed choices for A and V with this goal in mind, and the application of their prescription is now typically referred to by the acronym MPn where n is the order at which the perturbation theory is truncated, e.g., MP2, MP3, etc. Some workers in the field prefer the acronym MBPTn, to emphasize the more general nature of many-body perturbation theory (Bartlett 1981). 

The type of correlated method that has enjoyed the most widespread application to H-bonded systems is many-body perturbation theory, also commonly referred to as Mpller-Plesset (MP) perturbation theory This approach considers the true Hamiltonian as a sum of its Hartree-Fock part plus an operator corresponding to electron correlation. In other words, the unperturbed Hamiltonian consists of the interaction of the electrons with the nuclei, plus their kinetic energy, to which is added the Hartree-Fock potential the interaction of each electron with the time-averaged field generated by the others. The perturbation thus becomes the difference between the correct interelectronic repulsion operator, with its instantaneous correlation between electrons, and the latter Hartree-Fock potential. In this formalism, the Hartree-Fock energy is equed to the sum of the zeroth and first-order perturbation energy corrections. 

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.]. 

During the 1960s, Kelly [37-43] pioneered the application of what is today the most widely used approach to the description of correlation effects in atomic and molecular systems namely, the many-body perturbation theory [1,2,43 8]. The second-order theory using the Hartree-Fock model to provide a reference Hamiltonian is particularly widely used. This Mpller-Plesset (mp2) formalism combines an accuracy, which is adequate for many purposes, with computational efficiency allowing both the use of basis sets of the quality required for correlated studies and applications to larger molecules than higher order methods. 

The application of many-body perturbation theory to molecules involves the direct application of the Rayleigh-Schrodinger formalism with specific choices of reference Hamiltonian. The most familiar of these is that first presented by Mpller and Plesset... 

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