Toward the Exact Exchange–Correlation Potential: A Three-Dimensional Convolutional Neural Network Construct

A deep neural network is constructed to yield in principle exact exchange–correlation potential. It requires merely the electron densities of small molecules and ions and yet can determine the exchange–correlation potentials of large molecules. We train and validate the neural network based on the data for H₂ and HeH⁺ and subsequently determine the ground-state electron density of stretched HeH⁺, linear H₃⁺, and H–He–He–H²⁺. Moreover, the deep neural network is proven to model the van der Waals interaction by being trained and validated on a data set containing He₂. Comparisons to B3LYP are given to illustrate the accuracy and transferability of the neural network.