Density functional theory (DFT) has become an enormously successful tool for electronic structure calculations. The Kohn-Sham scheme is now used in over 10,000 papers per year. Literally hundreds of distinct approximations are now available in modern electronic structure codes in both chemistry and materials science. The best of these are non-empirical interpolations among known limits of quantum mechanics; the worst are mere fits of empirical data.
Up to and beyond the middle of last century, strong connections were developed between density functional approximations and semiclassical methods. The original work of Thomas and Fermi has this flavor, as do early attempts to derive the gradient expansion corrections to both the kinetic and exchange energies. But this connection became somehow more obscure with the introduction of the Kohn-Sham scheme.
Along different lines, the direct approximation of the functional, such as in Thomas-Fermi theory and its extensions, proved very amenable to methods of functional analysis. This approach was championed by Lieb and many others, and is still producing useful results today. But such works are largely disconnected from modern DFT practice, again due to the difficulties in dealing with the Kohn-Sham scheme. Occasional results, such as the Lieb-Oxford bound, have crossed this divide.
Recent work has sought to re-examine the link between DFT, semiclassical approximations, and functional analysis. Numerical and heuristic results suggest a close (but subtle) underlying link. Understanding of these links, and using them to build new and more powerful approximations, could have tremendous impact in modern electronic structure calculations. The aim of this workshop is to reunite these disparate strands and begin a conversation among the different communities, including researchers from mathematics, physics, and theoretical chemistry.