In explicitly correlated coupled-cluster singles and doubles [CCSD(F12)] calculations, the basis set incompleteness error in the double excitations is reduced to such an extent that the error in the Hartree-Fock energy and the error in the single excitations become important. Using arguments from perturbation theory to systematically truncate the coupled-cluster singles and CCSD(F12) Lagrangians, a series of coupled-cluster models are proposed and studied that reduce these basis set incompleteness errors through additional single excitations into a complementary auxiliary basis. Convergence with model and size of complementary basis is rapid and there appears to be no need to go beyond second-order models. Our iterative second-order approach is a slight improvement over the existing noniterative approach, but its main advantage is that it is suitable for response theory.
