Basis Set Limit of CCSD(T) Energies: Explicit Correlation Versus Density-Based Basis-Set Correction.

A thorough comparison is carried out for explicitly correlated and density-based basis-set correction approaches, which were primarily developed to mitigate the basis-set incompleteness error of wave function methods. An efficient implementation of the density-based scheme is also presented, utilizing the density-fitting approximation. The performance of these approaches is comprehensively tested for the second-order Møller-Plesset (MP2), coupled-cluster singles and doubles (CCSD), and CCSD with perturbative triples [CCSD(T)] methods with respect to the corresponding complete basis set references. It is demonstrated that the density-based correction together with complementary auxiliary basis set (CABS)-corrected Hartree-Fock energies is highly robust and effectively reduces the error of the standard approaches; however, it does not outperform the corresponding explicitly correlated methods. Nevertheless, what still makes the density-corrected CCSD and CCSD(T) methods competitive is that their computational costs are roughly half of those of the corresponding explicitly correlated variants. Additionally, an incremental approach for standard CCSD and CCSD(T) is introduced. In this simple scheme, the total energies are corrected with the CABS correction and explicitly correlated MP2 contributions. As demonstrated, the resulting methods yield surprisingly good results, below 1 kcal/mol for thermochemical properties even with a double-ζ basis, while their computational expenses are practically identical to those of the density-based basis-set correction approaches.