Systematic Trends in Water Properties Across Jacob's Ladder Density Functionals

Kohn-Sham density functional theory is the workhorse of computational materials science and chemistry, but the optimal choice of exchange-correlation approximation for a given system is often unclear. Traditional benchmark studies typically compare selected density functional approximations (DFAs) against high-level quantum chemistry results for small structures and static energies, rather than against experimental thermodynamic or response properties. Here, we show how machine learning interatomic potentials (MLIPs) allow for molecular dynamics simulations of these properties at scale, thereby providing a thermodynamic benchmark for DFAs. Focusing on the wellstudied but challenging case of bulk water at ambient conditions, we benchmark 11 DFAs spanning the top four rungs of Jacob's ladder (GGA, meta-GGA, hybrid, and double hybrid) with and without empirical dispersion corrections. Using MLIPs trained on each DFA, we compute infrared spectra, heat capacities, radial distribution functions, and diffusivities. We find a general improvement up Jacob's ladder towards double hybrids, though there is substantial variation between DFAs within the same rung and across different properties. Dispersion corrections yield only a modest influence on the computed properties. We elucidate the similarities and hierarchy among DFAs, both based on correlating the DFA energies and forces for the same training configurations, and based on analyzing the finite-temperature observables. Our work thus demonstrates the power of MLIPs for finite-temperature benchmarking of electronic structure methods.