Some Problems in Density Functional Theory

TL;DR

This paper discusses unresolved mathematical issues in density functional theory (DFT), highlighting their importance for improving functional approximations and understanding in various scientific fields.

Contribution

It provides an overview of fundamental mathematical problems in DFT and poses questions aimed at advancing the theory and its applications.

Findings

Identification of key mathematical problems in DFT

Highlighting the importance of resolving these issues for better functionals

Encouraging further research in DFT mathematical foundations

Abstract

Though calculations based on density functional theory (DFT) are used remarkably widely in chemistry, physics, materials science, and biomolecular research and though the modern form of DFT has been studied for almost 60 years, some mathematical problems remain. For context, we provide an outline of the basic structure of DFT, then pose several questions regarding both its time-independent and time-dependent forms. Progress on any of these would aid in development of better approximate functionals and in interpretation.