Canonical versus explicitly correlated coupled cluster: Post‐complete‐basis‐set extrapolation and the quest of the complete‐basis‐set limit

AbstractThe concept of post‐complete‐basis‐set (pCBS) extrapolation is introduced. It is shown that pCBS extrapolation of the CCSD(T) correlation energy calculated with conventional theory and up to quadruple‐ζ basis sets yields nearly as accurate values as if done with explicitly correlated CCSD(T)‐F12 theory and its preferred VXZ‐F12 ansätze, also up to quadruple‐ζ. Applied to the popular A24 test set of moderate‐sized non‐covalent interactions, all pCBS energies share the same asymptote up to an average error of 0.06 kcal mol−1, possibly the accuracy of the theory itself. For the 13 first complexes of A24 (A13/24), the best converged due to the severe computational demands of most A24 systems, the corresponding mean signed and unsigned plus standard deviations are MSD = (−0.027 ± 0.14) kcal mol−1 and MUD = (0.101 ± 0.10) kcal mol−1 at canonical CCSD(T)/VXZ and MSD = (−0.010 ± 0.05) kcal mol−1 and MUD = (0.042 ± 0.03) kcal mol−1 at CCSD(T)‐F12b/VXZ‐F12 levels of theory when using as reference the extrapolated values from raw energies calculated with the two largest affordable (typically (5,6) for canonical CCSD(T) and (T,Q) for CCSD(T)‐F12) basis sets. Amid such results, CCSD(T)/AVXZ calculations run with up to quintuple‐ζ basis sets, followed by CBS and pCBS extrapolations, show a MUD only slightly larger by 0.14 kcal mol−1, but at a comparatively higher cost. Both canonical and F12 coupled cluster approaches can therefore be considered for the first time to yield results of similar accuracy when pCBS extrapolated from basis sets of formally similar rungs. The above pattern is found to hold generally in A24.