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.

广泛存在的观念认为，Boys-Bernardi函数对比对（CP）方法会对超分子相互作用能产生过度校正，这种过度校正通常是由于基组重叠误差所导致的，这在关联波函数方法中尤为明显。然而，在密度泛函理论（DFT）的背景下，基组收敛性问题通常并不突出，这个问题尚未得到系统的考虑。本研究对一组代表性的泛函和基组进行了系统的评估，同时考虑了小二聚体和较大的超分子复合物（如具有约150个原子的层状复合聚合物和约300个原子的配体-蛋白模型）的基准数据集。结果表明，在采用CP校正的情况下，仅使用双ζ基组即可获得接近完整基组质量的分子间相互作用能，这与未采用CP校正的三ζ基组相比，成本更低。与未校正的能量相比，CP校正后的相互作用能对扩散基函数的存在更为不敏感，这对于扩散函数昂贵且在大系统中经常出现数值问题具有重要意义。我们的研究结果推翻了CP校正会导致基组不完整性“过度校正”的传统观点。在小基组中，CP校正对于证明结果并非基于误差抵消是必不可少的。