Basis set convergence of the coupled-cluster correction, $\delta _{\text{MP2}}^{\text{CCSD(T)}}$δMP2CCSD(T): Best practices for benchmarking non-covalent interactions and the attendant revision of the S22, NBC10, HBC6, and HSG databases

Abstract

In benchmark-quality studies of non-covalent interactions, it is common to estimate interaction energies at the complete basis set (CBS) coupled-cluster through perturbative triples [CCSD(T)] level of theory by adding to CBS second-order perturbation theory (MP2) a “coupled-cluster correction,” \documentclass[12pt]{minimal}\begin{document}$\delta _{\text{MP2}}^{\text{CCSD(T)}}$\end{document}δMP2CCSD(T), evaluated in a modest basis set. This work illustrates that commonly used basis sets such as 6-31G*(0.25) can yield large, even wrongly signed, errors for \documentclass[12pt]{minimal}\begin{document}$\delta _{\text{MP2}}^{\text{CCSD(T)}}$\end{document}δMP2CCSD(T) that vary significantly by binding motif. Double-ζ basis sets show more reliable results when used with explicitly correlated methods to form a \documentclass[12pt]{minimal}\begin{document}$\delta _{\text{MP2}-{\rm F}12}^{\text{CCSD(T}^*)-{\rm F}12}$\end{document}δMP2−F12CCSD(T*)−F12 correction, yielding a mean absolute deviation of 0.11 kcal mol−1 for the S22 test set. Examining the coupled-cluster correction for basis sets up to sextuple-ζ in quality reveals that \documentclass[12pt]{minimal}\begin{document}$\delta _{\text{MP2}}^{\text{CCSD(T)}}$\end{document}δMP2CCSD(T) converges monotonically only beyond a turning point at triple-ζ or quadruple-ζ quality. In consequence, CBS extrapolation of \documentclass[12pt]{minimal}\begin{document}$\delta _{\text{MP2}}^{\text{CCSD(T)}}$\end{document}δMP2CCSD(T) corrections before the turning point, generally CBS (aug-cc-pVDZ,aug-cc-pVTZ), are found to be unreliable and often inferior to aug-cc-pVTZ alone, especially for hydrogen-bonding systems. Using the findings of this paper, we revise some recent benchmarks for non-covalent interactions, namely the S22, NBC10, HBC6, and HSG test sets. The maximum differences in the revised benchmarks are 0.080, 0.060, 0.257, and 0.102 kcal mol−1, respectively.