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

Abstract

We propose a local real-space formulation for orbital-free DFT with density dependent kinetic energy functionals and a unified variational framework for computing the configurational forces associated with geometry optimization of both internal atomic positions as well as the cell geometry. The proposed real-space formulation, which involves a reformulation of the extended interactions in electrostatic and kinetic energy functionals as local variational problems in auxiliary potential fields, also readily extends to all-electron orbital-free DFT calculations that are employed in warm dense matter calculations. We use the local real-space formulation in conjunction with higher-order finite-element discretization to demonstrate the accuracy of orbital-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 range of properties and benchmark calculations. Finally, we investigate the cell-size effects in the electronic structure of point defects, in particular a mono-vacancy in Al. We unambiguously demonstrate that the cell-size effects observed from vacancy formation energies computed using periodic boundary conditions underestimate the extent of the electronic structure perturbations created by the defect. On the contrary, the bulk Dirichlet boundary conditions, accessible only through the proposed real-space formulation, which correspond to an isolated defect embedded in the bulk, show cell-size effects in the defect formation energy that are commensurate with the perturbations in the electronic structure. Our studies suggest that even for a simple defect like a vacancy in Al, we require cell-sizes of ∼ 10 3 atoms for convergence in the electronic structure.

Energetics of intrinsic point defects in aluminium via orbital-free density functional theory

“…The convergence of E f v with respect to N s was already found in the previous literatures [19,21,22,58]. For WGC-KEDF, Ho et al [19] found that the formation energy is converged within 3 meV by 4 × 4 × 4 supercell, which is also confirmed by Gavini's group [21,22,58] and our calculation (see Figure 1).…”

“…In particular, the WGC-KEDF converges more rapidly than the WT-KEDF, and the LDA-XCDF performed better than the GGA-XCDF. Note that the WGC-KEDF plus LDA-XCDF performed extremely well and was chosen in the previous literatures [19,21,22]. In order to model the convergent tendency, we used a simple exponential…”

“…Gavini's group [17,[20][21][22] proposed the non-periodic real-space formulation for OF-DFT and used this formulation to calculate the vacancy formation energy and also the unrelaxed case. The size effect is also considered here.…”

Orbital-free density functional theory study of the energetics of vacancy clustering and prismatic dislocation loop nucleation in aluminium

“…The density-dependent Wang-Govind-Carter (WGC) kinetic energy functional (Wang et al, 1999) is the most widely used model for T s in solid-state orbital-free DFT calculations on materials systems whose electronic structure is close to a free-electron gas, and is employed in this work. Numerical studies have indicated that this is a transferable model for Al, Mg and Al-Mg materials systems with accuracies commensurate with Kohn-Sham DFT calculations on a wide range of materials properties (Carling & Carter, 2003;Ho et al, 2007;Das et al, 2015). The functional form of the WGC kinetic energy functional is given by…”

“…In the present work we employ a real-space formulation of orbital-free density functional theory and the quasi-continuum reduction technique to conduct electronic structure calculations on multi-million atom systems. In particular, we employ the Wang Govind Carter (WGC) orbital-free kinetic energy functional (Wang et al, 1999) which has been shown to be accurate for aluminum for a wide range of properties (Carling & Carter, 2003;Das et al, 2015). We begin our study by computing the binding energies of divacancies in aluminum.…”