Finding the Best Density Functionals for Water: Benchmarking the Forces

A DFT benchmark on water, including more than 50 functionals from GGA to double-hybrid levels, is reported. The main metric is the accuracy of forces, allowing higher statistical confidence, fewer error sources, and easy extraction of intermolecular interactions. Various aspects of force benchmarking are discussed, including calculating reference data, defining metrics, and comparison with regular energy metrics. The input structures include water clusters of 4-128 molecules, with highly varied yet realistic configurations of water, ice, and their combinations. The B97M-V, ωB97M-V, and revDOD-PBEP86-D4 functionals are found to be best at the mGGA, hybrid, and double-hybrid levels, respectively. No satisfying GGA functionals are found, but comparable accuracy to B97M-V can be obtained by combining BLYP-D4 with a simple correction to O-H bonds. DFT-D has a moderate effect on the intermolecular forces, and its impact on accuracy is mixed.