Method Calibration or Data Fitting?

We
investigate by explicit parameter optimization to what extent
basis sets of polarized double-ζ quality can introduce compensating
errors in five different density functional methods. It is shown that
minor changes in the contraction coefficients of the valence functions
in the basis sets can have a significant impact and allow different
density functional methods to achieve very similar performances. This
holds for nuclear magnetic shielding constants and for isomerization
energies, barrier heights, and noncovalent interactions. It is furthermore
shown that errors due to neglect of vibrational and solvent effects
can be absorbed in the combined method and basis set errors. These
findings hold for data sets consisting of 50–150 data points.
This raises the question of whether the common practice of identifying
combinations of density functional methods and basis sets that have
a good performance against a selected set of reference data should
be considered as data fitting in the combined parameter space spanned
by the method and basis set.