Basis set convergence of CCSD(T) equilibrium geometries using a large and diverse set of molecular structures

We examine the basis set convergence of the CCSD(T) method for obtaining the structures of the 108 neutral first- and second-row species in the W4-11 database (with up to five non-hydrogen atoms). This set includes a total of 181 unique bonds: 75 H-X, 49 X-Y, 43 X=Y, and 14 X≡Y bonds (where X and Y are first- and second-row atoms). As reference values, geometries optimized at the CCSD(T)/aug'-cc-pV(6+d)Z level of theory are used. We consider the basis set convergence of the CCSD(T) method with the correlation consistent basis sets cc-pV(n+d)Z and aug'-cc-pV(n+d)Z (n = D, T, Q, 5) and the Weigend-Ahlrichs def2-nZVPP basis sets (n = T, Q). For each increase in the highest angular momentum present in the basis set, the root-mean-square deviation (RMSD) over the bond distances is decreased by a factor of ∼4. For example, the following RMSDs are obtained for the cc-pV(n+d)Z basis sets 0.0196 (D), 0.0050 (T), 0.0015 (Q), and 0.0004 (5) Å. Similar results are obtained for the aug'-cc-pV(n+d)Z and def2-nZVPP basis sets. The double-zeta and triple-zeta quality basis sets systematically and significantly overestimate the bond distances. A simple and cost-effective way to improve the performance of these basis sets is to scale the bond distances by an empirical scaling factor of 0.9865 (cc-pV(D+d)Z) and 0.9969 (cc-pV(T+d)Z). This results in RMSDs of 0.0080 (scaled cc-pV(D+d)Z) and 0.0029 (scaled cc-pV(T+d)Z) Å. The basis set convergence of larger basis sets can be accelerated via standard basis-set extrapolations. In addition, the basis set convergence of explicitly correlated CCSD(T)-F12 calculations is investigated in conjunction with the cc-pVnZ-F12 basis sets (n = D, T). Typically, one "gains" two angular momenta in the explicitly correlated calculations. That is, the CCSD(T)-F12/cc-pVnZ-F12 level of theory shows similar performance to the CCSD(T)/cc-pV(n+2)Z level of theory. In particular, the following RMSDs are obtained for the cc-pVnZ-F12 basis sets 0.0019 (D) and 0.0006 (T) Å. Overall, the CCSD(T)-F12/cc-pVDZ-F12 level of theory offers a stellar price-performance ratio and we recommend using it when highly accurate reference geometries are needed (e.g., in composite ab initio theories such as W4 and HEAT).