Systematic Evaluation of Counterpoise Correction in Density Functional Theory

Abstract

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.

Origins of Offset-Stacking in Porous Frameworks

“…DFT calculations in Table were performed using the def2-ma-SVP basis set and include counterpoise correction. This procedure affords negligible basis-set convergence errors in supramolecular DFT calculations, and tests on (half-COF1) 2 in Table S2 demonstrate that counterpoise-corrected DFT/def2-ma-SVP interaction energies are converged to within ≲1 kcal/mol of DFT/def2-TZVPD results. Basis set effects are somewhat larger (∼3 kcal/mol) at the XSAPT+MBD level (Table S3), although the energetic ordering of various structures is conserved upon enlarging the basis set from def2-ma-SVP to def2-ma-TZVP.…”

“…First, it is not clear how large the basis-set superposition error (BSSE) might be, or where it appears in the various components of E int when the periodic EDA developed in ref is applied. Although BSSE is often a minor concern at the DFT/triple-ζ level, it does grow with system size and we have documented examples where the BSSE in a DFT/def2-TZVP calculation can be as large as 7–8 kcal/mol for systems with ∼300 atoms . For a layered material, BSSE should be size-extensive and will therefore increase in larger models of COF-1.…”

Supramolecular Diversity, Theoretical Investigation and Antibacterial Activity of Cu, Co and Cd Complexes Based on the Tridentate N,N,O-Schiff Base Ligand Formed In Situ

“…In some cases, the half-counterpoise correction [ 10 , 51 ] or extrapolation to the basis set limit was found to better describe the reference data [ 52 , 53 ]. Although the BSSE largely affects the small (double-ζ) basis sets [ 54 , 55 ], the DFT scheme used herein for geometry optimizations (ωB97X-D4/ma-def2-TZVP) may suffer from the BSSE when calculating binding energies [ 54 ], also because estimation of the absolute electronic energy is a known weak point of the DFT. However, the geometrical parameters of the S66 models calculated at the DFT level are close to those obtained at the ab initio level ( Table S8 ), while the DLPNO-CCSD(T) correction of the final energy allows approaching the reference BE values.…”

Adjusting the balance between hydrogen and chalcogen bonds

“…Basis set superposition error was then removed from E int by the standard counterpoise protocol. 85 A recent investigation 86 concluded that combining this correction with a double- ζ basis like aug-cc-pVDZ provides results in excellent agreement with complete basis set calculations within a DFT framework. Bond paths, and the density at their bond critical points, were elucidated by the QTAIM method 87–89 by the use of the AIMAll program.…”