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 α- and β-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 α- and
β-tin and electronic valence densities similar to those obtained
with semilocal PP.