Seven Useful Questions in Density Functional Theory

TL;DR

This paper discusses seven key unresolved issues in density functional theory, highlighting their importance for computational accuracy and potential mathematical approaches for resolution.

Contribution

It identifies and explains seven fundamental open problems in density functional theory, providing context and emphasizing their significance for future research.

Findings

Identifies seven critical open problems in DFT.

Highlights the importance of mathematical proofs for DFT accuracy.

Provides background and context for each problem.

Abstract

We explore a variety of unsolved problems in density functional theory, where mathematicians might prove useful. We give the background and context of the different problems, and why progress toward resolving them would help those doing computations using density functional theory. Subjects covered include the magnitude of the kinetic energy in Hartree-Fock calculations, the shape of adiabatic connection curves, using the constrained search with input densities, densities of states, the semiclassical expansion of energies, the tightness of Lieb-Oxford bounds, and how we decide the accuracy of an approximate density.