Behavior of counterpoise correction in many-body molecular clusters of organic compounds: Hartree–Fock interaction energy perspective

The counterpoise (CP) correction by Boys and Bernardi has been well accepted as a reliable strategy to account for basis set superposition error (BSSE) in intermolecular complexes. The behavior of the CP correction was thoroughly studied in individual molecules of molecular complexes. This work studies the performance of the CP correction in many-body clusters including three-body clusters of organic compounds in the 3B-69 dataset. Additionally, we used crystal structures of polymorphs of benzene, aspirin, and oxalyl dihydrazide (ODH) to construct a many-body cluster dataset, abbreviated as the MBC-36 dataset, consisting of two, four and eight molecules, and 16 molecules in the case of benzene. A series of Dunning's basis sets—cc-pXZ and aug-cc-pXZ (X = D and T)—were used to predict CP-corrected Hartree–Fock (HF) interaction energies of the 3B-69 and MBC-36 datasets. The CP-corrected interaction energies were found to be basis-set independent, whereas the non-CP corrected interaction energies were found not to a follow a smooth exponential fitting as previously found for electronic energies of individual molecules. This observation was attributed to the presence of non-additive induction forces in some clusters. Two 2 × 2 × 2 supercells of benzene polymorphs were constructed to explore the local nature of BSSE effects. A cut-off radius of 10 Å was demonstrated to be sufficient to fully recover these effects. Although the behavior of CP correction was found to be non-conventional in many-body clusters of organic compounds, the use of a small basis set such as cc-pVDZ showed excellent performance in the prediction of HF interaction energies.