Non-parametric Local Pseudopotentials with Machine Learning: a Tin Pseudopotential Built Using Gaussian Process Regression

We present novel non-parametric representation math for local pseudopotentials (PP) based on Gaussian Process Regression (GPR). Local pseudopotentials are needed for materials simulations using Orbital-Free Density Functional Theory (OF-DFT) to reduce computational cost and to allow kinetic energy functional (KEF) application only to the valence density. Moreover, local PPs are important for the development of accurate KEFs for OF-DFT as they are only available for a limited number of elements. We optimize local PPs of tin (Sn) using GP regression to reproduce the experimental lattice constants of {\alpha}- and \b{eta}-Sn, the energy difference between these two phases as well as their electronic structure and charge density distributions, which are obtained with Kohn-Sham Density Functional Theory employing semi-local PPs. The use of a non-parametric GPR-based PP representation avoids difficulties associated with the use of parametrized functions and has the potential to construct an optimal local PP independent of prior assumptions. The GPR-based Sn local PP results in well-reproduced bulk properties of {\alpha}- and \b{eta}-tin, and electronic valence densities similar to those obtained with semi-local PP.