On the Equivalence of Two-Point Basis-Set Extrapolations and Robust Parameterization for Coupled-Cluster and Double-Hybrid DFT Methods

Basis-set extrapolation (BSE) to the complete basis set (CBS) limit is a cornerstone of several high-accuracy thermochemical computational schemes. In this study, we assess some of the approximations that are commonly made when using BSE. While the extrapolation parameters are typically fitted using coupled-cluster methods, there are cases where these same parameters are applied to other computational methods. While there can be significant differences in the fitted parameters, when applied to two benchmark datasets the difference in performance between the coupled-cluster and method-specific fitted parameters is small. While there are a number of schemes for two-basis-set extrapolations to the CBS limit, it is shown that three common extrapolations─exponential, exponential–square root, and inverse power─reduce to a Schwenke-style correction to the larger basis set of the scaled difference between two sequential basis sets (ECBS = En + f·(En – En–1)). Moreover, this reduction means that the differences between the methods is mathematically meaningless, and given the extrapolation parameter of one scheme one can find both the Schwenke-type extrapolation factor f and the extrapolation factors of the other two schemes and vice versa. Finally, Schwenke-type two-point extrapolation parameters are given for a selection of basis sets for coupled-cluster and selected double-hybrid density functional theory exchange–correlation functionals.