On choosing the best density functional approximation

1.1 Aim of the paper Density functional approximations have been very successful for describing properties of molecules and crystals when these depended on their electronic structure. However, a multitude of approximations exists, the values for the properties produced by them can differ significantly, and some criterion must be used in order to choose a given functional to predict a given property. Most often, density functional approximations are evaluated against some benchmark data sets, and quantities like the mean error and mean absolute error are indicated in order to asses the validity of the approximation. Moreover, in many approximations, the exchange-correlation functional may contain parameters that are determined by optimizing some statistical measures like those mentioned above on a training set of data. In such a case, the approximation itself is evidently dependent on the choice of the measure used. The aim of the present paper is to show that the ‘‘best approximation’’ can be a different one, depending upon the criterion used for defining the closeness of the approximation to the reference data.