  Density functional theory (DFT) is one of the primary approaches to get a
solution to the many-body Schrodinger equation. The essential part of the DFT
theory is the exchange-correlation (XC) functional, which can not be obtained
in analytical form. Accordingly, the accuracy improvement of the DFT is mainly
based on the development of XC functional approximations. Commonly, they are
built upon analytic solutions in low- and high-density limits and result from
quantum Monte Carlo or post-Hartree-Fock numerical calculations. However, there
is no universal functional form to incorporate these data into XC functional.
Various parameterizations use heuristic rules to build a specific XC
functional. The neural network (NN) approach to interpolate the data from
higher precision theories can give a unified path to parametrize an XC
functional. Moreover, data from many existing quantum chemical databases could
provide the XC functional with improved accuracy. In this work, we develop NN
XC functional, which gives both exchange potential and exchange energy density.
Proposed NN architecture consists of two parts NN-E and NN-V, which could be
trained in separate ways, which adds additional flexibility. We also show the
suitability of the developed NN XC functional in the self-consistent cycle when
applied to atoms, molecules, and crystals.
