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We propose a local real-space formulation for orbital-free DFT with densitydependent kinetic energy functionals and a unified variational framework forcomputing the configurational forces associated with geometry optimization ofboth internal atomic positions as well as the cell geometry. The proposedreal-space formulation, which involves a reformulation of the extendedinteractions in electrostatic and kinetic energy functionals as localvariational problems in auxiliary potential fields, also readily extends toall-electron orbital-free DFT calculations that are employed in warm densematter calculations. We use the local real-space formulation in conjunctionwith higher-order finite-element discretization to demonstrate the accuracy oforbital-free DFT and the proposed formalism for the Al-Mg materials system,where we obtain good agreement with Kohn-Sham DFT calculations on a wide rangeof properties and benchmark calculations. Finally, we investigate the cell-sizeeffects in the electronic structure of point defects, in particular amono-vacancy in Al. We unambiguously demonstrate that the cell-size effectsobserved from vacancy formation energies computed using periodic boundaryconditions underestimate the extent of the electronic structure perturbationscreated by the defect. On the contrary, the bulk Dirichlet boundary conditions,accessible only through the proposed real-space formulation, which correspondto an isolated defect embedded in the bulk, show cell-size effects in thedefect formation energy that are commensurate with the perturbations in theelectronic structure. Our studies suggest that even for a simple defect like avacancy in Al, we require cell-sizes of $\sim 10^3$ atoms for convergence inthe electronic structure.

Real-space formulation of orbital-free density functional theory using finite-element discretization: The case for Al, Mg, and Al-Mg intermetallics