A local environment descriptor for machine-learned density functional theory at the generalized gradient approximation level

We propose a grid-based local representation of electronic quantities that can be used in machine learning applications for molecules, which is compact, fixed in size, and able to distinguish different chemical environments. We apply the proposed approach to represent the external potential in density functional theory with modified pseudopotentials and demonstrate its proof of concept by predicting the Perdew-Burke-Ernzerhof and local density approximation electronic density and exchange-correlation potentials by kernel ridge regression. For 16 small molecules consisting of C, H, N, and O, the mean absolute error of exchange-correlation energy was 0.78 kcal/mol when trained for individual molecules. Furthermore, the model is shownto predict the exchange-correlation energy with an accuracy of 3.68 kcal/mol when the model is trained with a small fraction (4%) of all 16 molecules of the present dataset, suggesting a promising possibility that the current machine-learned modelmay predict the exchange-correlation energies of an arbitrary molecule with reasonable accuracy when trained with a sufficient amount of data covering an extensive variety of chemical environments. Published by AIP Publishing.