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 the precision of PAW data sets often use the properties of isolated atoms or 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 the 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 an 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 half on average for hydrogen-bonded dimers.

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