Neural network representation for non-interacting kinetic energy for atoms and ionic species

Abstract

A correct functional expression for the non-interacting kinetic energy Ts[ρ] in terms of the electron density function ρ(r) continues to be a significant problem in OF-DFT. An approximation such as Thomas-Fermi theory will provide a good guess for the value of the kinetic energy, but it will not reproduce the shell structure of an atom, i.e., the various K, L, M, and N shells. The following report presents the construction of a deep learning based algorithm to approximate the Pauli potential vNN θ ([ρ]; r) using seven input variables such as the nuclear charge (Z), logarithmic density, and radial Laplacians and gradients of reduced density. The neural network architecture utilized has seven inputs and predicts the Pauli potential. In order to ensure physical consistency in the predictions made by the model, the following are three crucial considerations that were taken into account. Firstly, the use of SiLU as an activation function ensures smooth predictions. Secondly, the use of Soft plus on the output layer ensures that the Pauli potential will always be positive as dictated by physical laws. Lastly, the 1/Z weighting was employed during training to account for both light and heavy atoms.