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

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