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

Abstract

The 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.

SVECV‐f12: Benchmark of a composite scheme for accurate and cost effective evaluation of reaction barriers

“…Thus, only DZ and TZ basis sets are needed for obtaining a good extrapolated energy and the less demanding basis sets compensate for the more expensive calculation method. Varandas has recently performed a very complete comparison of the CCSD(T) and CCSD(T)-F12 convergence toward the CBS limit which is worth mentioning [51]. Nevertheless, this point will be further explored in this paper.…”

“…Admittedly, this can introduce an error which has not been investigated further in this work. The papers of Helgaker et al [53], Hill et al [54], and Varandas [51,55], among many others cited there, can be explored for other extrapolation options. It is however worthwhile to notice (see Table 6) that the MUD of the energy difference between the CCSD(T)-F12/ CBS//M06-2X-D3/aug-cc-pVTZ and CCSD(T)-F12/cc-pVQZ-F12//CCSD(T)-F12/cc-pVQZ-F12 calculations is only 0.82 kcal mol À1 , with the former always lower than the latter except in the case of the all-hydrogen reaction R05.…”

Optimized Structural Data at the Complete Basis Set Limit via Successive Quadratic Minimizations

“…For example, if the x 1 basis set provides poor results for the optimized geometry, it is likely that the CBS limit produced by the SQM protocol will be harmed. This can hopefully be remedied via post-CBS extrapolation, − an issue to be explored elsewhere.…”

“…In previous work, − we discussed how the complete basis set limit (CBS) of the correlation and SCF (HF and CASSCF) energies can be obtained via low-cost extrapolation methods; the reader is addressed elsewhere , for reviews. The extrapolation procedure is based on the re-hierarchization of the cardinal numbers used to define the basis set quality and has been shown to be applicable to any ansatz.…”

Can the quasi‐molecule concept help in deciphering planarity? The case of polycyclic aromatic hydrocarbons

“…In all cases, single-reference (SR) methods are utilized [28]. Already expensive in many cases, no attempt is made to attain the highest affordable accuracy with the methods nowadays at our disposal [29][30][31] (and references therein). For the quasi-tetratomics, that is required, and the sort of accuracy previously reported [2] is judged to be enough.…”