On choosing the best density functional approximation

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 that do not follow the general pattern). Weighting the data of the set, 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 choices for the “best functional”. To decide which specific density functional approximation should be used can thus be made only by introducing some supplementary, external, possibly personal criterion.