Moller-Plesset, second-order accuracy

Correlation can be added as a perturbation from the Hartree-Fock wave function. This is called Moller-Plesset perturbation theory. In mapping the HF wave function onto a perturbation theory formulation, HF becomes a hrst-order perturbation. Thus, a minimal amount of correlation is added by using the second-order MP2 method. Third-order (MP3) and fourth-order (MP4) calculations are also common. The accuracy of an MP4 calculation is roughly equivalent to the accuracy of a CISD calculation. MP5 and higher calculations are seldom done due to the high computational cost (A time complexity or worse). 

Second-order Moller-Plesset perturbation theory (MP2) is the computationally least expensive and most popular ab initio electron correlation method [4,15]. Except for transition metal compounds, MP2 equilibrium geometries are of comparable accuracy to DFT. However, MP2 captures long-range correlation effects (like dispersion) which are lacking in present-day density functionals. The computational cost of MP2 calculations is dominated by the integral transformation from the atomic orbital (AO) to the molecular orbital (MO) basis which scales as 0(N5) with the system size. This four-index transformation can be avoided by introduction of the RI integral approximation which requires just the transformation of three-index quantities and reduces the prefactor without significant loss in accuracy [36,37]. This makes RI-MP2 the most efficient alternative for small- to medium-sized molecular systems for which DFT fails. 

In many cases electronic properties calculated at the Hartree-Fock level do not have the accuracy sufficient to make them useful in chemical predictions. For example, as revealed in a recent study,the stability of the cage isomer of the C20 carbon cluster relative to that of the cyclic isomer is underestimated at the Flartree-Fock level by as much as 200 kcal/mol. In such systems, the electron correlation effects have to be taken into account in quantum chemical calculations through application of approximate methods. One such approximate electron correlation methods that has gained a widespread popularity is the second-order Moller-Plesset perturbation theory (MP2). Until recently calculations involving the MP2 approach have used a traditional formulation in which the MP2 energy is evaluated as the sum... 

The question for a more systematic inclusion of electronic correlation brings us back to the realm of molecular quantum chemistry [51,182]. Recall that (see Section 2.11.3) the exact solution (configuration interaction. Cl) is found on the basis of the self-consistent Hartree-Fock wave function, namely by the excitation of the electrons into the virtual, unoccupied molecular orbitals. Unfortunately, the ultimate goal oi full Cl is obtainable for very small systems only, and restricted Cl is size-inconsistent the amount of electron correlation depends on the size of the system (Section 2.11.3). Thus, size-consistent but perturbative approaches (Moller-Plesset theory) are often used, and the simplest practical procedure (of second order, thus dubbed MP2 [129]) already scales with the fifth order of the system s size N, in contrast to Hartree-Fock theory ( N ). The accuracy of these methods may be systematically improved by going up to higher orders but this makes the calculations even more expensive and slow (MP3 N, MP4 N ). Fortunately, restricted Cl can be mathematically rephrased in the form of the so-called coupled clus-... 

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. 

One of the most dramatic changes in the standard theoretical model used most widely in quantum chemistry occurred in the early 1990s. Until then, ab initio quantum chemical applications [1] typically used a Hartree-Fock (HF) starting point, followed in many cases by second-order Moller-Plesset perturbation theory. For small molecules requiring more accuracy, additional calculations were performed with coupled-cluster theory, quadratic configuration interaction, or related methods. While these techniques are still used widely, a substantial majority of the papers being published today are based on applications of density functional theory (DFT) [2]. Almost universally, the researchers use a functional due to Becke, whose papers in 1992 and 1993 contributed to this remarkable transformation that changed the entire landscape of quantum chemistry. 

Accuracy of the SLG approximation can be improved by perturbation theory. Second quantization provides us a powerful tool in developing a many-body theory suitable to derive interbond delocalization and correlation effects. The first question concerns the partitioning of the Hamiltonian to a zeroth-order part and perturbation. LFsing a straightforward generalization of the Moller-Plesset (1934) partitioning, the zeroth-order Hamiltonian is chosen as the sum of the effective intrabond Hamiltonians ... 

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