Neural-Network Implementation of Transferable Kohn-Sham Exchange-Correlation Functionals

The accuracy of Kohn-Sham density functional theory [1] depends crucially on its approximated exchange-correlation functional. Structures of conventional density functionals depend on, however, combination of a number of physical constraints, making thereby the construction technically demanding and systematic improvement of their accuracy difficult. In order to overcome this difficulties, we present a new strategy free from the use of complicated physical constraints: representing the functional structure with Neural-network (NN), which is an extremely flexible function with a large number of parameters.
We demonstrate two types of NN-based functional. (i)Non-local functionals, which is made to reproduce the exact exchange-correlation potential of 1D model systemsconsisting of two electronsapplied with various external potentials [2], (ii)Semi-local functionals, which is made to reproduce densities provided by an accurate quantum chemical calculation of only a few molecules [3]. We show potentials of the NN-based functionals for high accuracy and out-of-training transferability.

[1]W.Kohn and L. J. Sham, Phys Rev. 140, A1133-A1138(1965).
[2]RN, R. Akashi, S. Sasaki, and S. Tsuneyuki, J. Chem. Phys. 148, 241737 (2018).
[3]RN, R. Akashi, O. Sugino, in preparation.