Highly accurate coupled-cluster singlet and triplet pair energies from explicitly correlated calculations in comparison with extrapolation techniques

Coupled-cluster singles and doubles (CCSD) valence shell correlation energies of the systems CH2 (<1A1 state), H2O, HF, N2, CO, Ne, and F2 are computed by means of standard calculations with correlation-consistent basis sets of the type cc-pVxZ (x = D, T, Q, 5, 6) and by means of explicitly correlated coupled-cluster calculations (CCSD-R12/B) with large uncontracted basis sets of the type 19s14p8d6f4g3h for C, N, O, F, and Ne and 9s6p4d3f for H. These CCSD-R12/B calculations provide reference values for the basis set limit of CCSD theory. The computed correlation energies are decomposed into singlet and triplet pair energies. It is established that the singlet pair energies converge as X−3 and the triplet pair energies as X−5 with the cardinal number of the correlation-consistent basis sets, and an extrapolation technique is proposed that takes into account their different convergence behaviour. Applied to the cc-pV5Z and cc-pV6Z results, this new extrapolation yields pair energies with a mean absolute deviation of 0.02 mEh from the CCSD-R12/B reference values. For the seven systems under study, the extrapolated total valence shell correlation energies agree to within 0.2 mEh with the CCSD-R12/B benchmark data.