Electronic structure methods Moller-Plesset perturbation

A few quantum-chemical ab initio calculations dealt with the electronic structure and some molecular parameters of PH". Accordingly, the ground state, derived from that of the neutral molecule by adding a 2n (P3p7r) electron, is KL (4a)2 (5o) (2n), X rij [7]. The best theoretical value so far for the total molecular energy at the equilibrium internuclear distance, Et = -341.46363 Eh, was obtained from a recent G2 calculation by using a method that treats the electron correlation by Moller-Plesset perturbation theory (MP4) and quadratic configuration interaction (QCI) [8]. 

The Seetion on More Quantitive Aspects of Electronic Structure Calculations introduees many of the eomputational ehemistry methods that are used to quantitatively evaluate moleeular orbital and eonfiguration mixing amplitudes. The Hartree-Foek self-eonsistent field (SCF), eonfiguration interaetion (Cl), multieonfigurational SCF (MCSCF), many-body and Moller-Plesset perturbation theories. 

Local correlation methods represent an importantnew class of correlated electronic structure methods that aim at computing molecular properties with the same accuracy as their conventional counterparts but at a significantly lower computational cost. We discuss the challenges of parallelizing local correlation methods in the context of local second-order Moller-Plesset perturbation theory, illustrating a parallel implementation and presenting benchmarks as well. 

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... 

Although a wide variety of theoretical methods is available to study weak noncovalent interactions such as hydrogen bonding or dispersion forces between molecules (and/or atoms), this chapter focuses on size consistent electronic structure techniques likely to be employed by researchers new to the field of computational chemistry. Not stuprisingly, the list of popular electronic structure techniques includes the self-consistent field (SCF) Hartree-Fock method as well as popular implementations of density functional theory (DFT). However, correlated wave function theory (WFT) methods are often required to obtain accmate structures and energetics for weakly bound clusters, and the most useful of these WFT techniques tend to be based on many-body perturbation theory (MBPT) (specifically, Moller-Plesset perturbation theory), quadratic configuration interaction (QCI) theory, and coupled-cluster (CC) theory. 

In general, second-order Moller-Plesset perturbation theory (a specific case of second-order many-body perturbation theory) is the workhorse of electronic structure techniques for weakly bound systems because the method tends to provide a reliable description of a wide range of weak interactions. For most hydrogen-bonding scenarios, MP2 energetics are extremely accurate and nearly identical to those from CCSD(T) computations with the same basis set. In fact, a recent study revealed that MP2 interaction energies obtained with an appropriate triple- basis set agree favorably with CCSD(T) CBS... 

On the theoretical side the H20-He systems has a sufficiently small number of electrons to be tackled by the most sophisticated quantum-chemical techniques, and in the last two decades several calculations by various methods of electronic structure theory have been attempted [77-80]. More recently, new sophisticated calculations appeared in the literature they exploited combined symmetry - adapted perturbation theory SAPT and CCSD(T), purely ab initio SAPT [81,82], and valence bond methods [83]. A thorough comparison of the topology, the properties of the stationary points, and the anisotropy of potential energy surfaces obtained with coupled cluster, Moller-Plesset, and valence bond methods has been recently presented [83]. 

Density-functional theory (DFT) is one of the most widely used quantum mechanical approaches for calculating the structure and properties of matter on an atomic scale. It is nowadays routinely applied for calculating physical and chemical properties of molecules that are too large to be treatable by wave-function-based methods. The problem of determining the many-body wave function of a real system rapidly becomes prohibitively complex. Methods such as configuration interaction (Cl) expansions, coupled cluster (CC) techniques or Moller Plesset (MP) perturbation theory thus become harder and harder to apply. Computational complexity here is related to questions such as how many atoms there are in the molecule, how many electrons each atom contributes, how many basis functions are... 

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