Electronic Structure Calculations at Macroscopic Scales using Orbital-Free DFT

Abstract

Recently proposed Quasi-Continuum Orbital Free Density Functional Theory (QC-OFDFT) is a seamless multi-scale scheme that has enabled the computation of electronic structure at macroscopic scales, and has paved the way for an accurate electronic structure study of defects in materials. It combines a real-space formulation of OFDFT with a finite-element discretization that is amenable to coarse-graining. The initial development of QC-OFDFT, for the purpose of demonstration, used Thomas-Fermi-Weizsacker family of kinetic energy functionals. However, more accurate kinetic energy functionals have been proposed in the form of kernel energies that are non-local in real-space. In the first part of this talk, we will present the development of a local variational formulation for these kernel energies through a system of coupled Helmholtz equations. We incorporate these kernel energies into the quasi-continuum framework and investigate the convergence of the method with respect to coarse-graining and cell-size through studies on mono-vacancy and di-vacancies in aluminum. Our results show remarkable cell-size effects in the energetics of vacancies, and suggest much larger computational domains than those considered previously are necessary in electronic structure studies on defects. We further discuss the behavior of vacancies, in their dilute limit, from electronic structure calculations. In the second part of the talk, we will present a mathematical analysis of QC-OFDFT. In particular, by using perturbation method and multiple scale analysis, we provide a formal justification for the validity of the coarsegraining of electronic fields, which is central to the quasicontinuum reduction of OFDFT. Further, we derive the homogenized equations that govern the behavior of electronic fields in regions of smooth deformations. Using Fourier analysis, we determine the far-field solutions for these fields in the presence of local defects, and subsequently estimate cell-size effects in computed defect energies.