Equivariant graph neural networks for fast electron density estimation of molecules, liquids, and solids

Electron density rho((r) over right arrow) is the fundamental variable in the calculation of ground state energy with density functional theory (DFT). Beyond total energy, features and changes in rho((r) over right arrow) distributions are often used to capture critical physicochemical phenomena in functional materials. We present a machine learning framework for the prediction of rho((r) over right arrow). The model is based on equivariant graph neural networks and the electron density is predicted at special query point vertices that are part of the message-passing graph, but only receive messages. The model is tested across multiple datasets of molecules (QM9), liquid ethylene carbonate electrolyte (EC) and LixNiyMnzCo(1-y-z)O2 lithium ion battery cathodes (NMC). For QM9 molecules, the accuracy of the proposed model exceeds typical variability in rho((r) over right arrow) obtained from DFT done with different exchange-correlation functionals. The accuracy on all three datasets is beyond state of the art and the computation time is orders of magnitude faster than DFT.