Beyond Energies: Geometries of Nonbonded Molecular Complexes as Metrics for Assessing Electronic Structure Approaches

Electronic structure approaches for calculating intermolecular interactions have traditionally been benchmarked almost exclusively on the basis of energy-centric metrics. Herein, we explore the idea of utilizing a metric related to geometry. On a diverse series of noncovalently interacting systems of different sizes, from the water dimer to the coronene dimer, we evaluate a variety of electronic structure approximations with respect to their abilities to reproduce coupled-cluster-level geometries. Specifically, we examine Hartree-Fock, second-order Møller-Plesset perturbation theory (MP2), attenuated MP2, scaled MP2, and a number of density functionals, many of which include empirical or nonempirical van der Waals dispersion corrections. We find a number of trends that transcend system size and interaction type. For instance, functionals incorporating VV10 nonlocal correlation tend to yield highly accurate geometries; ωB97X-V and B97M-V, in particular, stand out. We establish that intermolecular distance, as measured by, e.g., the center-of-mass separation of two molecules, is the geometric parameter that deviates most profoundly among the various methods. This property of the equilibrium intermolecular separation, coupled with its accessibility via a small series of well-defined single-point calculations, makes it an ideal metric for the development and evaluation of electronic structure methods.