Local explicitly correlated coupled-cluster methods: Efficient removal of the basis set incompleteness and domain errors

We propose an explicitly correlated local LCCSD-F12 method in which the basis set incompleteness error as well as the error caused by truncating the virtual orbital space to pair-specific local domains are strongly reduced. This is made possible by including explicitly correlated terms that are orthogonalized only to the pair-specific configuration space. Thus, the contributions of excitations outside the domains are implicitly accounted for by the explicitly correlated terms. It is demonstrated for a set of 54 reactions that the reaction energies computed with the new LCCSD-F12 method and triple-zeta basis sets deviate by at most 2.5 kJ/mol from conventional CCSD complete basis set results (RMS: 0.6 kJ/mol). The local approximations should make it possible to achieve linear scaling of the computational cost with molecular size.