DFT: A Theory Full of Holes?

TL;DR

This paper provides a quirky overview of density functional theory, focusing on its theoretical foundations, the development of approximations, and the tension between empirical and non-empirical methods, including applications to warm dense matter.

Contribution

It highlights how approximations in DFT can be systematically derived non-empirically and surveys its application to warm dense matter.

Findings

Systematic derivation of non-empirical approximations

Historical perspective on DFT development

Survey of DFT applications to warm dense matter

Abstract

This article is a rough, quirky overview of both the history and present state of the art of density functional theory. The field is so huge that no attempt to be comprehensive is made. We focus on the underlying exact theory, the origin of approximations, and the tension between empirical and non-empirical approaches. Many ideas are illustrated on the exchange energy and hole. Features unique to this article include how approximations can be systematically derived in a non-empirical fashion and a survey of warm dense matter.