Evaluation of B3LYP, X3LYP, and M06-Class Density Functionals for Predicting the Binding Energies of Neutral, Protonated, and Deprotonated Water Clusters

In this paper we assess the accuracy of the B3LYP, X3LYP, and newly developed M06-L, M06-2X, and M06 functionals to predict the binding energies of neutral and charged water clusters including (H2O)(n), n = 2-8, 20), H3O+(H2O)(n), n = 1-6, and OH-(H2O)(n), n = 1-6. We also compare the predicted energies of two ion hydration and neutralization reactions on the basis of the calculated binding energies. In all cases, we use as benchmarks calculated binding energies of water clusters extrapolated to the complete basis set limit of the second-order Moller-Plesset perturbation theory with the effects of higher order correlation estimated at the coupled-cluster theory with single, double, and perturbative triple excitations in the aug-cc-pVDZ basis set. We rank the accuracy of the functionals on the basis of the mean unsigned error (MUE) between calculated benchmark and density functional theory energies. The corresponding MUE (kcal/mol) for each functional is listed in parentheses. We find that M06-L (0.73) and M06 (0.84) give the most accurate binding energies using very extended basis sets such as aug-cc-pV5Z. For more affordable basis sets, the best methods for predicting the binding energies of water clusters are M06-L/aug-cc-pVTZ (1.24), B3LYP/6-311++G(2d,2p) (1.29), and M06/aug-cc-PVTZ (1.33). M06-L/aug-cc-pVTZ also gives more accurate energies for the neutralization reactions (1.38), whereas B3LYP/6-311++G(2d,2p) gives more accurate energies for the ion hydration reactions (1.69).