Seven useful questions in density functional theory

• Published in: Letters in mathematical physics Vol. 113; no. 2
• Main Authors: Crisostomo, Steven, Pederson, Ryan, Kozlowski, John, Kalita, Bhupalee, Cancio, Antonio C., Datchev, Kiril, Wasserman, Adam, Song, Suhwan, Burke, Kieron
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 09.04.2023; Springer
• Subjects: Complex Systems; Geometry; Group Theory and Generalizations; Mathematical and Computational Physics; Mathematical Physics and Numerical Simulation of Many-Particle Systems; Physics; Physics and Astronomy; Theoretical; Density functional theory; 81; Semiclassical physics; Electronic structure theory; Quantum chemistry; Quantum physics
• ISSN: 1573-0530; 1573-0530
• DOI: 10.1007/s11005-023-01665-z

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.