Local explicitly correlated second-order perturbation theory for the accurate treatment of large molecules

A local explicitly correlated LMP2-F12 method is described that can be applied to large molecules. The steep scaling of computer time with molecular size is reduced by the use of local approximations, the scaling with respect to the basis set size per atom is improved by density fitting, and the slow convergence of the correlation energy with orbital basis size is much accelerated by the introduction of terms into the wave function that explicitly depend on the interelectronic distance. The local approximations lead to almost linear scaling of the computational effort with molecular size without much affecting the accuracy. At the same time, the domain error of conventional LMP2 is removed in LMP2-F12. LMP2-F12 calculations on molecules of chemical interest involving up to 80 atoms, 200 correlated electrons, and 2600 contracted Gaussian-type orbitals, as well as several reactions of large biochemical molecules are reported.