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. From a physical science perspective, it is far from clear whether those problems are of major import. For context, we provide an outline of the basic structure of DFT as it is presented and used conventionally in physical sciences, note some unresolved mathematical difficulties with those conventional demonstrations, then pose several questions regarding both the time-independent and time-dependent forms of DFT that could benefit from attention in applied mathematics. Furthermore, progress on any of these would aid in development of better approximate functionals and in interpretation of DFT.