Density Functional Theory: learning from the past, looking to the future
Magnus-Haus, Am Kupfergraben 7, Berlin, Germany
(We cannot accept further participants due to limited space at the conference venue. We apologize for this.)
Density functional theory (DFT) is a universal formally exact approach to the electronic many-body problem which had enormous practical successes due to its widespread applications in chemistry and physics. Nevertheless, the field of DFT is at a crossroads, facing important but stubborn problems (such as reliably reaching chemical accuracy for molecules, or describing strongly correlated systems), while the path forward is unclear. The evolution of the field seems to have led to an increase in empiricism in the construction and choice of exchange-correlation functionals. This calls for a paradigm shift. This workshop will focus on fundamental questions and on identifying promising new strategies to advance the field of DFT.
Over the last decades, DFT [1,2] had a profound impact in many fields of science, most importantly in physics and chemistry. Its balance between reasonable accuracy and modest computational cost has made DFT the method of choice for calculating the electronic structure of materials. With increasingly powerful, computational resources ever larger systems (consisting of hundreds and even thousands of atoms) come within reach of a full DFT description.
The accuracy and success of DFT hinges on the availability of accurate approximations to the exchange-correlation functional. While LDA has been the workhorse approximation during the first decades of DFT [3,4], the advent of GGA's in the 80's [5-8] may be considered as a first “quantum leap” in the development of improved approximations, followed shortly thereafter by the development of hybrid functionals [9,10] which have been particularly successful in chemistry. However, these approximations still have their limitations such as, the lack of a correct description of long-range van der Waals interactions or a cure for the self-interaction error. Despite important advances in development of improved functionals in recent years (such as meta-GGA's , non-local functionals designed to capture van-der-Waals interactions [12,13], range-separated hybrids , or functionals based on the RPA ), there appears to exist no consensus in the community on which direction to go. In fact, a whole zoo of approximate exchange-correlation functionals has been proposed and we are in a situation where users may choose that functional which gives the best result for their particular application. This, of course, is not in the original spirit of DFT, which rests on the universality of the functional of Hohenberg, Kohn, and Sham [1,2].
The promise of the universality of the Hohenberg-Kohn functional definitely has not yet been reached, and seems more elusive than ever. This becomes particularly clear when considering the enormous difficulties of DFT to correctly describe strongly correlated systems. Although recently there has been some (limited) progress in the DFT description of strongly correlated lattice models [16-20], it is not clear at all how to translate these insights into a practical approximate functional for an accurate DFT treatment of real physical systems showing signs of strong correlation.
One of the most dramatic failures of the standard approximations of DFT is the incorrect prediction of a metallic ground state for the strongly correlated Mott insulators, of which transition metal oxides such as NiO and MnO may be considered as prototypical. It is well known experimentally that these materials are insulating even at elevated temperatures, which indicates that magnetic ordering is not the driving mechanism for the gap. The prediction of an insulating state for these strongly correlated materials is a challenge for all ab initio theories. Recently, reduced density-matrix functional theory (RDMFT) has shown potential for correctly treating Mott insulators [21-23]: it not only improves upon the Kohn-Sham band gaps for insulators in general, but also predicts transition metal oxides as insulators, even in the absence of long range spin-order. In fact recently it was demonstrated that RDMFT is not only capable of treating strong correlations at ambient pressure but also captures the rich phenomena of Mott insulator to metal phase transitions. This clearly points towards its ability to capture physics well beyond the reach of most modern day ground-state methods.
Many extensions of the original DFT formulation have been suggested dealing with, e.g., finite temperatures , systems in magnetic fields , superconducting systems , and other situations. Probably the single-most successful extension of DFT is time-dependent DFT (TDDFT) . So far, TDDFT found its most widespread applications in the calculation of excitation spectra of molecules and solids in the regime of linear response. However, more and more the truly time-dependent aspect of TDDFT is being explored by following the time evolution of the Kohn-Sham wave functions to explore physical phenomena such as, e.g., matter in strong laser fields, optimal (femto- or attosecond) control of electron dynamics, or coupled electron-ion dynamics (for an overview, see ); in the strong-field regime there are few alternative methods that can capture electron correlation while remaining computationally feasible.
Of course, as in static DFT, the success of TDDFT depends on the quality of the approximation used for the exchange-correlation potential. The standard approach for most TDDFT applications is the adiabatic approximation, which uses ground-state exchange-correlation functionals evaluated at time-dependent densities; the most notable example is the adiabatic LDA (ALDA). There has been considerable progress in understanding under which conditions the standard functionals such as ALDA can be expected to give reasonable results or, maybe even more importantly, when it will fail . These latter cases include, e.g., double excitations , long-range charge transfer excitations , and electron dynamics in the presence of strong electromagnetic fields . Aside from the approximation for the exchange-correlation functional, approximations are also required to extract the observables of interest from the Kohn-Sham system . Based on the experience with ground-state DFT, nonadiabatic functionals whose construction in one way or another starts from the uniform electron gas have been suggested, most notably the Gross-Kohn  and Vignale-Kohn [34,35] functionals. However, the success of these functionals seems to be limited to a certain class of physical situations and, in particular for finite systems, the gain in accuracy over ALDA is limited .
Antonio Sanna ( Max Planck Institute of Microstructure Physics, Halle ) - Organiser
Sangeeta Sharma ( Max Planck Institute of Microstructure Physics ) - Organiser
Stefan Kurth ( University of the Basque Country UPV/EHU ) - Organiser
Attila Cangi ( Sandia National Laboratories ) - Organiser
Neepa Maitra ( Hunter College of the City University of New York ) - Organiser
Carsten Ullrich ( University of Missouri ) - Organiser