Assessing Exchange-Correlation Functionals for Accurate Densities of Solids.

The success of Kohn-Sham density functional theory in predicting electronic properties from first-principles is key to its ubiquitous presence in condensed matter research. Central to this theory is the exchange-correlation functional, which can only be written in an approximate form using a handful of exact constraints. A recent criticism of these approximations is that they are designed to give an accurate description of the energy at the expense of a poor representation of the density, which is contrary to the spirit of density functional theory.

Strategies to build functionals of the density, or functionals of Green's functions: what can we learn?

The many-body problem cannot in general be solved exactly, and one of the most prominent approximations is to build perturbation expansions. A huge variety of expansions are possible, which differ by the quantity to be expanded, the expansion variable, the starting point, and ideas of how to re-sum or terminate the series. Although much has been discussed and much has been done, some choices were made for historical reasons, in particular, limited computation or storage capacities.