Density functional theory for van der Waals complexes: Size matters

Over the past 25 years there has been remarkable progress towards accurate description of nonbonded interactions within the context of density functional theory (DFT). Various methods have been devised to capture London dispersion, which is the most exacting contribution to noncovalent interactions; these strategies include both new functionals as well as ad hoc dispersion corrections to existing functionals. At present, it is possible to compute interaction energies for small van der Waals complexes (containing ~20 atoms) to an accuracy of ~0.5 kcal/mol, using a range of dispersion-inclusive DFT methods that are reviewed here. Systematic tests reveal remarkable consistency across different methods, at least for small noncovalent dimers. At the same time, the magnitude of the ad hoc dispersion corrections are systematically smaller than benchmark dispersion energies because some dispersion resides within the semilocal exchange-correlation functional, in a manner that is difficult to disentangle. Despite impressive results for small systems, the best contemporary DFT methods afford larger errors in systems with >~ 100 atoms, approaching 3-5 kcal/mol as compared to ab initio benchmarks for total interaction energies, although the benchmarks themselves have larger uncertainties in systems of this size. Errors for larger systems vary widely from one DFT method to the next, with no discernible systematic trend. Nanoscale van der Waals complexes thus represent the new frontier in development of DFT for noncovalent interactions.