Despite their numerical advantages, GTO basis sets are inherently non-orthogonal and prone to linear dependencies that become more pronounced as the size of the basis increases. In addition, the calculation of relative energies with atomcentered functions suffers from the basis set superposition error (BSSE) because of the completeness mismatch between systems of different sizes, which tends to overstabilize bound clusters relative to single fragments, thus overestimating binding energies. Schemes for estimating the BSSE and correcting for the basis set imbalance are therefore commonly employed, with the most standard approximation being the counterpoise (CP) correction . Nevertheless, it has been argued that such an ad hoc rectification can lead to spurious effects on the final a) Electronic mail: ursula.roethlisberger@epfl.ch accuracy , for instance due to an unequal amount of correction between the entire system and its constituents . As a result, the CP correction applied to the calculation of interaction energies is sometimes viewed more as an estimate. Such an estimate can be considered neither an upper nor a lower bound for the actual BSSE .