Localized MP2 method

Fast local-MP2 method with density-fitting for crystals. I. Theory and algorithms " ... 

The incorporation of correlation effects in calculations for periodic solids requires the use of a many-body formalism. Second order many-body perturbation theory, in its MP2 form, should provide the basis of an efficient computational approach to this problem. In particular, the local MP2 methods originally developed for large molecules can be adapted for the treatment of periodic solids. 

One of the most impressive applications of the local correlation methods is their extension to the periodic systems. Having in mind to discuss this extension on the MP2 level in the next section we restrict the discussion here to the consideration of local MP2 methods for molecular systems with closed shells, referring the reader to the papers discussing local CC methods [128,133,134,142,143]. 

In the local MP2 method [131] the occupied canonical MOs of the preceding HF calculation are localized using the Pipek-Mezey [37] localization procedure and keeping the localized orbitals orthonormal. Even though the localization is formally an 0 N ) step, the localization time is negligible for aU the local MP2 calculations. 

Symmetry Exploitation in Local MP2 Method for Periodic Systems... 

There is also a local MP2 (LMP2) method. LMP2 calculations require less CPU time than MP2 calculations. LMP2 is also less susceptible to basis set superposition error. The price of these improvements is that about 98% of the MP2 energy correction is recovered by LMP2. 

The HE, GVB, local MP2, and DFT methods are available, as well as local, gradient-corrected, and hybrid density functionals. The GVB-RCI (restricted configuration interaction) method is available to give correlation and correct bond dissociation with a minimum amount of CPU time. There is also a GVB-DFT calculation available, which is a GVB-SCF calculation with a post-SCF DFT calculation. In addition, GVB-MP2 calculations are possible. Geometry optimizations can be performed with constraints. Both quasi-Newton and QST transition structure finding algorithms are available, as well as the SCRF solvation method. 

The HF method tends to overestimate the barriers, making unstable molecules seem stabler than they really are. Geometries are discussed further in Section 5.5.1. Approximate versions of the MP2 method that speed up the process with little loss of accuracy are available in some program suites LMP2, localized MP2, and RI-MP2, resolution of identity MP2. LMP2 starts with a Slater determinant which has been altered so that its MOs are localized, corresponding to our ideas of bonds and lone pairs (Section 5.2.3.1), and permits only excitations into spatially nearby virtual orbitals [93]. RI-MP2 approximates four-center integrals (Section 5.3.2) by three-center ones [94]. 

Local MP2-based method for estimation of intermolecular interactions in aromatic molecules. Benzene, naphthalene, and pyrimidine dimers. A comparison with canonical MP2 method75... 

Local-MP2 electron correlation method for nonconducting crystals126... 

A difficulty with this local approach to dynamical correlation is that, in Moller-Plesset theory, for example, the zero-order Fock operator is no longer diagonal in the space of the Slater determinants, making the application of such theories slightly more complicated than theories based on canonical orbitals. Currently, the development of local correlation methods is an active area of research [57-63]. The diatomics-inmolecules (DIM) method and the triatomics-in-molecules (TRIM) method, for instance, recover typically 95% and 99.7%, respectively, of the full MP2 correlation energy [63]. By means of a linear scaling local variant of the CCSDT method,... 

Schiitz M, Hetzer G, Werner H-J. Low-order scaling local electron correlation methods. I. Linear scaling local MP2. J Chem Phys 1999 111 5691-5705. 

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