Simple coupled-cluster singles and doubles method with perturbative inclusion of triples and explicitly correlated geminals:: The CCSD(T)(R12)over-bar model

To approach the complete basis set limit of the "gold-standard" coupled-cluster singles and doubles plus perturbative triples [CCSD(T)] method, we extend the recently proposed perturbative explicitly correlated coupled-cluster singles and doubles method, CCSD(2)((R12) over bar) [E. F. Valeev, Phys. Chem. Chem. Phys. 8, 106 (2008)], to account for the effect of connected three-electron correlations. The natural choice of the zeroth-order Hamiltonian produces a perturbation expansion with rigorously separable second-order energy corrections due to the explicitly correlated geminals and conventional triple and higher excitations. The resulting CCSD(T)((R12) over bar) energy is defined as a sum of the standard CCSD(T) energy and an amplitude-dependent geminal correction. The method is technically very simple: Its implementation requires no modification of the standard CCSD(T) program and the formal cost of the geminal correction is small. We investigate the performance of the open-shell version of the CCSD(T)((R12) over bar) method as a possible replacement of the standard complete-basis-set CCSD(T) energies in the high accuracy extrapolated ab initio thermochemistry model of Stanton [J. Chem. Phys. 121, 11599 (2004)]. Correlation contributions to the heat of formation computed with the new method in an aug-cc-pCVXZ basis set have mean absolute basis set errors of 2.8 and 1.0 kJ/mol when X is T and Q, respectively. The corresponding errors of the standard CCSD(T) method are 9.1, 4.0, and 2.1 kJ/mol when X=T, Q, and 5. Simple two-point basis set extrapolations of standard CCSD(T) energies perform better than the explicitly correlated method for absolute correlation energies and atomization energies, but no such advantage found when computing heats of formation. A simple Schwenke-type two-point extrapolation of the CCSD(T)((R12) over bar)/aug-cc-pCVXZ energies with X=T,Q yields the most accurate heats of formation found in this work, in error on average by 0.5 kJ/mol and at most by 1.7 kJ/mol. (C) 2008 American Institute of Physics.