  The projector-augmented wave (PAW) method is one of the approaches that are
widely used to approximately treat core electrons and thus to speed-up
plane-wave basis set electronic structure calculations. However, PAW involves
approximations and it is thus important to understand how they affect the
results. Tests of precision of PAW data sets often use properties of isolated
atoms or of atomic solids. While this is sufficient to identify problematic PAW
data sets, little information has been gained to understand the origins of the
errors and suggest ways to correct them. Here we show that interaction energies
of molecular dimers are very useful not only to identify problematic PAW data
sets but also to uncover the origin of the errors. Using dimers from the S22
and S66 test sets and other dimers we find that the error in the interaction
energy is composed of a short range component with an exponential decay and a
long range electrostatic part caused by error in the total charge density. We
propose and evaluate a simple improvable scheme to correct the long range error
and find that even in its simple and readily usable form, it is able to reduce
the interaction energy errors to less than one half on average for hydrogen
bonded dimers.
