Reliable Structures and Electronic Energies of Small Water Clusters Using Density Functional and Local Correlation Coupled Cluster Model Chemistries

In this paper we have assessed the ability of the domain-based local pair natural orbital (DLPNO)-CCSD(T) method to match the explicitly correlated CCSD(T) relative energies of (H₂O)_n=3–7 isomers along with the impact of the level of theory utilized to optimize the water cluster geometries. The benchmark structures were optimized using a 2-body:Many-body procedure in which all of the 1- and 2-body contributions are computed using CCSD(T) while all of the higher-order many-body interactions are computed using MP2 (denoted CCSD(T):MP2). Benchmark relative energies were computed for these CCSD(T):MP2 optimized geometries with explicitly correlated CCSD(T)-F12b single point energies (SPEs) using the cc-pVQZ-F12 and cc-pV5Z-F12 basis sets augmented with diffuse functions on the O atoms. The benchmark structures and energies were used to gauge the performance of less demanding computational protocols. For example, DLPNO–CCSD(T) computations on the 31 benchmark structures with the analogous family of correlation consistent basis sets (cc-pVNZ for H and aug-cc-pVNZ for O, or simply haNZ where N = D-6) were used to estimate relative energies at the complete basis set (CBS) limit via three-point extrapolations. When compared to the CCSD(T)-F12 benchmark data, the mean absolute differences (MADs) were ≤ 0.13 kcal/mol when triple-ζ and larger basis sets were employed. Using these DLPNO–CCSD(T) results, we demonstrate that 2 less-demanding geometry optimization procedures, specifically the ωB97X-D density functional theory (DFT) method paired with the 6–31++G(d,p) basis set and the density-fitted MP2 method paired with the haTZ basis set, give structures that yield nearly identical relative energies (MADs of only 0.07 and 0.02 kcal/mol, respectively, when comparing DLPNO–CCSD(T)/ha6Z data). In addition, we show how the presence or absence of diffuse functions in the basis sets used for DLPNO–CCSD(T) SPEs impact the quality of the relative energies. The protocol that combines ωB97X-D/6–31++G(d,p) optimized structures with DLPNO–CCSD(T) SPEs using triple-ζ or higher Dunning basis sets that include augmentation with diffuse functions on the oxygen atoms provides a fast and accurate method for determining the relative electronic energies of (H₂O)_n=3–7 water cluster isomers.