Explicitly correlated combined coupled-cluster and perturbation methods

Coupled-cluster singles and doubles (CCSD) or coupled-cluster singles, doubles, and triples (CCSDT) with noniterative, perturbation corrections for higher-order excitations have been extended to include the basis functions that explicitly depend on interelectronic distances (r(12)) in the wave function expansions with the aim of dramatically accelerating the basis-set convergence of correlation energies. The extension has been based on the so-called R12 (or F12) scheme and applied to a second-order triples correction to CCSD [CCSD(2)(T)-R12], a second-order triples and quadruples correction to CCSD [CCSD(2)(TQ)-R12], a third-order triples correction to CCSD [CCSD(3)(T)-R12], and a second-order quadruples correction to CCSDT [CCSDT(2)(Q)-R12]. A simplified R12 treatment suggested by Fliegl [J. Chem. Phys. 122, 084107 (2005)] has been combined with some of these methods, introducing CCSD(2)(T)(R12) and CCSD(2)(TQ)(R12). The CCSD(T)-R12 method has also been developed as an approximation to CCSD(2)(T)-R12. These methods have been applied to dissociation of hydrogen fluoride and double dissociation of water. For the molecules at their equilibrium geometries, molecular properties predicted by these methods converge extremely rapidly toward the complete-correlation, complete-basis-set limits with respect to the cluster excitation rank, perturbation order, and basis-set size. Although the R12 scheme employed in this work does not improve the basis-set convergence of connected triples or quadruples corrections, the basis-set truncation errors in these contributions have roughly the same magnitude as small residual basis-set truncation errors in the connected singles and doubles contributions even in the dissociation of hydrogen fluoride. In the double dissociation of water, the basis-set truncation errors in the connected triples contribution can be a few times as great as those in the connected singles and doubles contributions.