The quest for a universal density functional: The accuracy of density functionals across a broad spectrum of databases in chemistry and physics

Kohn-Sham density functional theory is in principle an exact formulation of quantum mechanical electronic structure theory, but in practice we have to rely on approximate exchange-correlation (xc) functionals. The objective of our work has been to design an xc functional with broad accuracy across as wide an expanse of chemistry and physics as possible, leading-as a long-range goal-to a functional with good accuracy for all problems, i.e., a universal functional. To guide our path toward that goal and to measure our progress, we have developed-building on earlier work in our group-a set of databases of reference data for a variety of energetic and structural properties in chemistry and physics. These databases include energies of molecular processes such as atomization, complexation, proton addition, and ionization; they also include molecular geometries and solid-state lattice constants, chemical reaction barrier heights, and cohesive energies and band gaps of solids. For the present paper we gather many of these databases into four comprehensive databases, two with 384 energetic data for chemistry and solid-state physics and another two with 68 structural data for chemistry and solid-state physics, and we test 2 wave function methods and 77 density functionals (12 Minnesota meta functionals and 65 others) in a consistent way across this same broad set of data. We especially highlight the Minnesota density functionals, but the results have broader implications in that one may see the successes and failures of many kinds of density functionals when they are all applied to the same data. Therefore the results provide a status report on the quest for a universal functional.
Comment: APR 18 2013: Final revision, accepted version to be published in Phil. Trans. R. Soc. A as part of a theme issue on 'DFT for Physics, Chemistry and Biology', guest edited by Tanja van Mourik, Michael Buehl, and Marie-Pierre Gaigeot. JUL 21 2013: Updated version where we corrected a few typos in the tables and in the references. SEP 06 2013: Correction of a few typos