Electronic Structure Calculations at Macroscopic Scales using Orbital-free DFT

In this chapter we provide an overview of the recently developed coarse-graining technique for orbital-free density functional theory that enables electronic structure calculations on multi-million atoms. The key ideas involved are: (i) a local real-space formulation of orbital-free density functional theory; (ii) a finite element discretization of the formulation; (iii) a systematic means of adaptive coarse-graining of the finite-element basis set using quasi-continuum reduction. The accuracy and effectiveness of the computational technique is demonstrated by studying the energetics of monoand di-vacancies in multi-million atom aluminum crystals.