Twelve outstanding problems in ground-state density functional theory: A bouquet of puzzles

Kohn-Sham density functional theory and its many applications constitute perhaps the most populated area of both physics and chemistry. The theory permits calculation of the ground-state density and energy of a many-electron system (e.g., an atom, molecule, or solid) by the selfconsistent solution of a one-electron Schroedinger equation. The theory is exact in principle for these quantities, and in practice the required approximations can be usefully accurate. Here, with few equations and without any claim of optimal selection, we present 12 problems in density functional theory that remain to be solved, with an emphasis on formal problems and on the construction of approximate density functionals. The solutions to some of these problems could go a long way toward deepening understanding of the exact theory and toward improving the accuracy of electronic structure calculations.