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We present a real-space formulation and higher-order finite-differenceimplementation of periodic Orbital-free Density Functional Theory (OF-DFT).Specifically, utilizing a local reformulation of the electrostatic and kernelterms, we develop a generalized framework for performing OF-DFT simulationswith different variants of the electronic kinetic energy. In particular, wepropose a self-consistent field (SCF) type fixed-point method for calculationsinvolving linear-response kinetic energy functionals. In this framework,evaluation of both the electronic ground-state as well as forces on the nucleiare amenable to computations that scale linearly with the number of atoms. Wedevelop a parallel implementation of this formulation using thefinite-difference discretization. We demonstrate that higher-orderfinite-differences can achieve relatively large convergence rates with respectto mesh-size in both the energies and forces. Additionally, we establish thatthe fixed-point iteration converges rapidly, and that it can be furtheraccelerated using extrapolation techniques like Anderson's mixing. We validatethe accuracy of the results by comparing the energies and forces withplane-wave methods for selected examples, including the vacancy formationenergy in Aluminum. Overall, the suitability of the proposed formulation forscalable high performance computing makes it an attractive choice forlarge-scale OF-DFT calculations consisting of thousands of atoms.

Higher-order finite-difference formulation of periodic Orbital-free Density Functional Theory