Density Functional Analysis of Noncovalent 2- and 3-Body Interactions in Trimolecular Clusters

The performance of several density functionals for the description of 3-body interactions was evaluated on three benchmark data sets: 3B-69, S22(3), and 3BHET. Only a few DFT methods achieve consistent accuracy, notably B97-based functionals (ωB97X-V, ωB97X-D, and B97M-V) and double hybrids such as PBE-QIDH-D3(BJ) and B2-PLYP-D3(BJ). If dispersion corrections are essential for describing 2-body interactions, accurate 3-body energies require the presence of a significant fraction of Hartree-Fock exchange. Among dispersion models, those casting information from the electron density, like VV10, XDM, and MBD, provide the best performance. These last models also provide a qualitative agreement with the classical Axilrod-Teller-Muto model for trimers in the S22(3) data set, an indication that they provide a reasonable description of the long-range dispersion component of the 3-body interactions. Overall, these data sets remain more challenging than standard noncovalent benchmarks due to the subtle electronic effects governing many-body interactions.