Orbital-free density functionals based on real and reciprocal space separation

We introduce a general class of orbital-free density functionals (OF-DFT) decomposed into a local part in coordinate space and a local part in reciprocal space. As a demonstration of principle, we choose for the former the Thomas-Fermi-von Weizsäcker (TFW) kinetic energy density functional (KEDF) and for the latter a form derived from the Lindhard function, but with the two system-dependent adjustable parameters. These parameters are machine-learned from Kohn-Sham data using Bayesian linear regression with a kernel method, which employs moments of the Fourier components of the electronic density as the descriptor. Through a number of representative cases, we demonstrate that our machine-learned model provides more than an order-of-magnitude improvement in the accuracy of the frozen-phonon energies compared to the TFW KEDF, with negligible increase in the computational cost. Overall, this work opens an avenue for the construction of accurate KEDFs for OF-DFT.