Explicitly correlated second-order perturbation theory using density fitting and local approximations.

Three major obstacles in electronic structure theory are the steep scalings of computer time with respect to system size and basis size and the slow convergence of correlation energies in orbital basis sets. Three solutions to these are, respectively, local methods, density fitting, and explicit correlation; in this work, we combine all three to produce a low-order scaling method that can achieve accurate MP2 energies for large systems. The errors introduced by the local approximations into the R12 treatment are analyzed for 16 chemical reactions involving 21 molecules. Weak pair approximations, as well as local resolution of the identity approximations, are tested for molecules with up to 49 atoms, over 100 correlated electrons, and over 1000 basis functions.