Basis set dependence of the doubly hybrid XYG3 functional

In the present study, we investigated the basis set dependence of XYG3, a newly developed doubly hybrid functional [Y. Zhang, X. Xu, and W. A. Goddard III, Proc. Natl. Acad. Sci. U.S.A. 106, 4963 (2009)], in prediction of (1) heats of formation (HOFs), (2) bond dissociation enthalpies (BDEs), (3) reaction barrier heights (RBHs), and (4) nonbonded interactions (NBIs). We used basis sets of triple-zeta quality starting from 6-311+G(d,p) with increasing completeness of the polarization functions to the largest Pople-type basis set 6-311++G(3df,3pd) and found that there was a continued improvement with larger basis sets. We showed that while HOF predictions were prone to basis set deficiencies, the basis set dependences in calculating BDEs, RBHs, and NBIs were mild. All of them converged fast with the increase of basis set size. We extended XYG3 to propose the XYG3o functional which was specifically optimized for a particular basis set in order to enhance its performance when using basis set of moderate size. With the 6-311+G(2df,p) basis set, XYG3o led to MADs of 2.56 kcal/mol for HOFs of the G3/99 set, 1.17 kcal/mol for BDEs of the BDE92/07 set, 1.11 kcal/mol for RBHs of the NHTBH38/04 and HTBH38/04 sets, and 0.40 kcal/mol for NBIs of the NCIE31/05 set, being comparable to those obtained by using XYG3/6-311++G(3df,3pd).