Accurate approximations of density functional theory for large systems with applications to defects in crystalline solids

TL;DR

This paper introduces controlled, scalable approximations of density functional theory that enable accurate large-scale simulations of defects in crystalline solids, providing insights into their mechanics and physics.

Contribution

It develops systematic, convergent discretization methods for DFT that allow efficient, adaptive, large-scale computations with linear and sublinear scaling, applicable to defect studies.

Findings

Demonstrated numerical efficiency and accuracy of the methods

Provided insights into defect mechanics and physics in crystalline solids

Achieved large system simulations with no additional modeling

Abstract

This chapter presents controlled approximations of Kohn-Sham density functional theory (DFT) that enable very large scale simulations. The work is motivated by the study of defects in crystalline solids, though the ideas can be used in other applications. The key idea is to formulate DFT as a minimization problem over the density operator, and to cast spatial and spectral discretization as systematically convergent approximations. This enables efficient and adaptive algorithms that solve the equations of DFT with no additional modeling, and up to desired accuracy, for very large systems, with linear and sublinear scaling. Various approaches based on such approximations are presented, and their numerical performance demonstrated through selected examples. These examples also provide important insight about the mechanics and physics of defects in crystalline solids.