Moller-Plesset theory linear scaling

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,... 

Ayala PY, Scuseria GE. Linear scaling second-order Moller-Plesset theory in the atomic orbital basis for large molecular systems. J Chem Phys 1999 110 3660-3671. 

Werner, H.-J. Manby, F. R. Knowles, P. J. Fast linear scaling second-order Moller-Plesset perturbation theory (MP2) using local and density fitting approximations, 7. Chem. Phys. 2003,118, 8149-8160. 

Two relevant topics have been ignored completely in this short chapter the treatment of electron correlation with more sophisticated methods than DFT (that remains unsatisfactory from many points of view) and the related subject of excited states. Wave function-based methods for the calculation of electron correlation, like the perturbative Moller-Plesset (MP) expansion or the coupled cluster approximation, have registered an impressive advancement in the molecular context. The computational cost increases with the molecular size (as the fifth power in the most favorable cases), especially for molecules with low symmetry. That increase was the main disadvantage of these electron correlation methods, and it limited their application to tiny molecules. This scaling problem has been improved dramatically by modern reformulation of the theory by localized molecular orbitals, and now a much more favorable scaling is possible with the appropriate approximations. Linear scaling with such low prefactors has been achieved with MP schemes that the... 

Low-order scaling local correlation methods II Splitting the Coulomb operator in linear scaling local second-order Moller-Plesset perturbation theory ... 

H.-J. Werner, F. R. Manby, and P. J. Knowles,/. Chem. Phys., 118, 8149-8160 (2003). Fast Linear Scaling Second-Order Moller-Plesset Perturbation Theory (MP2) using Local and Density Fitting Approximations. 

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