On Choosing the best Density Functional Approximation.

Andreas Savin

Laboratoire de Chimie Théorique, CNRS, Universite Pierre et Marie Curie, 4 Place Jussieu, F-75252 Paris, France

The relative merits and deficiencies of density functional approximations are often quantified by presenting mean errors and mean absolute errors. However, there are other ways to analyze the data, for example using measures given by robust statistics, less affected by data not following the general pattern. A density functional can be also chosen by applying the same criteria as for voting. Weighting a set of data, or dividing the data into groups (e.g., for identifying the situations when a given approximation is reliable) may also modify the appreciation of the errors. Finally, the proper choice of reference data also plays a role.

These aspects will be illustrated with results obtained for band gaps of solids. It will be shown that different criteria can lead to different choice of functionals, forcing thus to a choice based on decision not based on quantitative criteria.