Nonparametric Local Pseudopotentials with Machine Learning: A Tin Pseudopotential Built Using Gaussian Process Regression

We present novel nonparametric 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, but they are only available for a limited number of elements. We optimize local PPs of tin (Sn) represented with GPR to reproduce the experimental lattice constants of alpha- and beta-Sn and 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 semilocal PPs. The use of a nonparametric 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 beta-tin and electronic valence densities similar to those obtained with semilocal PP.