Explicitly correlated atomic orbital basis second order Møller–Plesset theory

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The scope of problems treatable by ab initio wavefunction methods has expanded greatly through the application of local approximations. In particular, atomic orbital (AO) based wavefunction methods have emerged as powerful techniques for exploiting sparsity and have been applied to biomolecules as large as 1707 atoms [S. A. Maurer, D. S. Lambrecht, D. Flaig, and C. Ochsenfeld, J. Chem. Phys. 136, 144107 (2012)]. Correlated wavefunction methods, however, converge notoriously slowly to the basis set limit and, excepting the use of large basis sets, will suffer from a severe basis set incompleteness error (BSIE). The use of larger basis sets is prohibitively expensive for AO basis methods since, for example, second-order Møller-Plesset perturbation theory (MP2) scales linearly with the number of atoms, but still scales as O(N(5)) in the number of functions per atom. Explicitly correlated F12 methods have been shown to drastically reduce BSIE for even modestly sized basis sets. In this work, we therefore explore an atomic orbital based formulation of explicitly correlated MP2-F12 theory. We present working equations for the new method, which produce results identical to the widely used molecular orbital (MO) version of MP2-F12 without resorting to a delocalized MO basis. We conclude with a discussion of several possible approaches to a priori screening of contraction terms in our method and the prospects for a linear scaling implementation of AO-MP2-F12. The discussion includes concrete examples involving noble gas dimers and linear alkane chains.