Some Problems in Density Functional Theory

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.

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• Artificial Intelligence for Science in Quantum, Atomistic, and Continuum Systems
• A Snapshot of Time-Dependent Density-Functional Theory
• Kohn-Sham inversion with mathematical guarantees
• Solution of the v-representability problem on a one-dimensional torus
• v-representability and Hohenberg-Kohn theorem for non-interacting Schrödinger operators with distributional potentials in the one-dimensional torus
• Exchange-only virial relation from the adiabatic connection
• A rigorous formulation of Density Functional Theory for spinless fermions in one dimension
• Regularised density-potential inversion for periodic systems: application to exact exchange in one dimension