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. The question
has not been considered systematically in the context of density functional
theory, however, 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 and larger supramolecular complexes. The latter
include layered composite polymers with ∼150 atoms and ligand–protein
models with ∼300 atoms. Provided that CP correction is used,
we find that intermolecular interaction energies of nearly complete-basis
quality can be obtained using only double-ζ basis sets. This
is less expensive as compared to triple-ζ basis sets without
CP correction. CP-corrected interaction energies are less sensitive
to the presence of diffuse basis functions as compared to uncorrected
energies, which is important because 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.