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.