1.1. Density Functional Theory for Noncovalent Interactions. The description of noncovalent interactions within density functional theory (DFT) has improved dramatically over the past two decades, relative to a starting point where generalized gradient approximations (GGAs) predict interaction potentials that are unbound for dispersion-dominated complexes such rare-gas dimers or even (C 6 H 6 ) 2 . The first functionals to deal with this problem in a generally effective way were those with empirical atom-atom dispersion potentials added ad hoc. These dispersion-corrected or "DFT+D" methods remain tremendously important in contemporary DFT, and modern versions of the dispersion corrections resemble proper atomic C 6 coefficients in the separated-atom limit. (Double-counting of correlation effects at van der Waals contact distances does remain an issue, however. ) Early versions of the DFT+D approach were quickly followed by semiempirical meta-GGA functionals that significantly outperformed GGAs for van der Waals complexes, 9-12 although not always for the right reasons. Rather, because the semilocal meta-GGA framework has a much longer range in real space, due to its dependence on the density Laplacian and the kinetic energy density, meta-GGAs afford non-vanishing interactions in the region of non-bonded close contacts (unlike typical GGAs), and noncovalent interactions may therefore emerge upon sufficient parameterization. Separately, the development of nonlocal correlation functionals, which have the * herbert@chemistry.ohio-state.edu right physics to describe dispersion from first principles, has paved the way for a new generation of empirical functionals based on the B97 model. At present, these B97-based functionals are among the best performers for noncovalent interactions, with accuracy approaching 1-2 kcal/mol for standard benchmark data sets. Other methods attempt to extract in situ atomic C 6 (or C 8 , C 10 , . . .) coefficients from a DFT density, for a first-principles approach to modeling dispersion. Examples include the Becke-Johnson exchange-hole dipole moment method and the Tkatchenko-Scheffler atomsin-molecules polarizability approach. Finally there is double-hybrid (DH-) DFT, in a fraction of the second-order Møller-Plesset (MP2) correlation energy is introduced. These functionals can also describe dispersion from first principles, though it is worth mentioning that MP2 itself is not a benchmark-quality method for dispersion interactions. In DFT, noncovalent interaction energies ∆E int are typically computed via the supramolecular approach: