### Abstract

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-n ZVPP 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-n ZVPP 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).

Published by AIP Publishing.

Received 11 June 2016
Accepted 20 August 2016
Published online 12 September 2016

Supplementary Material:
See supplementary material for an overview of the 246 bonds in the W4-11-GEOM dataset (Table S1); overview of the basis-set convergence of the CCSD(T) method for the first-row molecules in the GEOM-AV6Z dataset (Table S2); squared correlation coefficients between the bond distances obtained with the CCSD(T)/A′ V6Z level of theory and the CCSD(T)/VnZ and CCSD(T)/A′ VnZ levels of theory (Table S3); overview of the basis-set convergence of the CCSD(T) and CCSD(T)-F12 methods for the H—X, X—Y, X=Y, and X≡Y bonds in the GEOM-AV6Z dataset (Table S4); overview of the basis-set convergence of the CCSD(T) and CCSD(T)-F12 methods for the H—X, X—Y, X=Y, and X≡Y bonds involving only first-row elements in the GEOM-AV6Z dataset (Table S5); effect of CCSD(T) and CCSD(T)-F12 reference geometries on molecular energies calculated at the CCSD(T)/CBS level of theory for the molecules in the GEOM-AV6Z database (Table S6); overview of the basis-set convergence of the CCSD(T) method for pathologically multireference systems (Figures S1 and S2); geometries for all the optimized structures are available on the website of the Karton group http://www.chemtheorist.com.
Acknowledgments:
We gratefully acknowledge the system administration support provided by the Faculty of Science at UWA to the Linux cluster of the Karton group, the financial support of Danish National Research Foundation (Center for Materials Crystallography, DNRF-93) to P.R.S., and an Australian Research Council (ARC) Discovery Early Career Researcher Award to A.K. (Grant No. DE140100311).

Article outline:

I. INTRODUCTION
II. COMPUTATIONAL METHODS
III. RESULTS AND DISCUSSION
A. Overview of the molecules in the W4-11 database and reference geometries
B. Basis set convergence of bond distances
1. Basis set convergence of conventional CCSD(T) calculations against CCSD(T)/A′V6Z reference geometries
2. Basis set convergence of explicitly correlated CCSD(T)-F12 calculations
3. Accelerating the basis set convergence of CCSD(T) and CCSD(T)-F12 calculations
4. Basis set convergence for subsets of the GEOM-AV6Z dataset
5. Basis set convergence for the entire W4-11-GEOM dataset
6. Energetic consequences of the level of theory used for optimizing the geometries
IV. CONCLUSIONS
SUPPLEMENTARY MATERIAL

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