Systematic Evaluation of Counterpoise Correction in Density Functional Theory

A widespread belief persists that the Boys-Bernardi function counterpoise (CP) procedure "overcorrects" supramolecular interaction energies for the effects of basis-set superposition error. To the extent that this is true for correlated wave function methods, it is usually an artifact of low-quality basis sets, but the question has not been considered systematically in the context of density functional theory (DFT) where basis-set convergence is generally less problematic. We present a systematic assessment of the CP procedure for a representative set of functionals and basis sets, considering both benchmark data sets of small dimers as well as larger supramolecular complexes including layered composite polymers with ~150 atoms and ligand--protein models with ~300 atoms. We find that intermolecular interaction energies approaching complete-basis quality can be obtained using only double-zeta basis sets, provided that CP correction is applied. This is less expensive as compared to using triple-zeta basis sets without CP correction. CP-corrected interaction energies are also less sensitive to the presence of diffuse basis functions as compared to uncorrected energies, which is important given that diffuse functions are expensive and often numerically problematic for large systems. Our results upend the conventional wisdom that CP "overcorrects" for basis-set incompleteness. In small basis sets, CP correction is mandatory in order to demonstrate that the results do not rest on error cancellation.