Optimal Small Basis Set and Geometric Counterpoise Correction for DFT Computations.

In the present study, we have examined the performance of the various small basis sets and their geometric counterpoise (gCP) corrections for DFT computations. The original gCP correction scheme includes four adjustable parameters tailored for each method and basis set, but we find that the use of a single scaling parameter also yields fair results. We term this simplified scheme unity-gCP, which can be straightforwardly applied for devising a reasonable correction for an arbitrary basis set. With the use of unity-gCP, we have examined a systematic set of medium-sized basis sets, and we find 6-31+G(2d) to be the optimal balance between accuracy and computational efficiency. On the other hand, less balanced basis sets, even larger ones, can show significantly worse accuracy; the inclusion of gCP may even lead to severe overcorrections. Thus, sufficient validations would be imperative before the general application of gCP for a particular basis set. For 6-31+G(2d), a welcoming finding is that its gCP has small magnitudes, and thus, it also yields adequate results without gCP corrections. This observation echoes that for the ωB97X-3c method, which uses an optimized double-ζ basis set (vDZP) without the inclusion of gCP. In an attempt to improve vDZP by mimicking the somewhat better-performing 6-31+G(2d), we partially decontract the outer functions of vDZP. The resulting basis set, which we termed vDZ+(2d), generally yields improved results. Overall, the vDZP and the new vDZ+(2d) basis sets pave a way for obtaining reasonable results more efficiently for a wide range of systems than the practice of using a triple- or quadruple-ζ basis set in DFT calculations.