Machine-learning approach for one- and two-body corrections to density functional theory: Applications to molecular and condensed water

We show how machine learning techniques based on Bayesian inference can be used to enhance the computer simulation of molecular materials, focusing here on water. We train our machine-learning algorithm using accurate, correlated quantum chemistry, and predict energies and forces in molecular aggregates ranging from clusters to solid and liquid phases. The widely used electronic-structure methods based on density functional theory (DFT) by themselves give poor accuracy for molecular materials like water, and we show how our techniques can be used to generate systematically improvable one- and two-body corrections to DFT with modest extra resources. The resulting corrected DFT scheme is considerably more accurate than uncorrected DFT for the relative energies of small water clusters and different ice structures and significantly improves the description of the structure and dynamics of liquid water. However, our results for ice structures and the liquid indicate that beyond-two-body DFT errors cannot be ignored, and we suggest how our machine-learning methods can be further developed to correct these errors.