Seven methods, including three van der Waals density functionals (vdW-DFs) and four different variants of the Tkatchenko-Scheffler (TS) methods, are tested on the A24, L7, and Taylor et al.’s “blind” test sets. It is found that for these systems, the vdW-DFs perform better that the TS methods. In particular, the vdW-DF-cx functional gives binding energies that are the closest to the reference values, while the many-body correction of TS does not always lead to an improvement in the description of molecular systems. In light of these results, several directions for further improvements to describe van der Waals interactions are discussed.

Density functional theory (DFT) calculations using sixteen different approaches, fourteen of which were designed to include dispersion interactions [DFT + D and van der Waals (vdW)-DF methods], were performed for a set of sixteen framework compounds with either SiO₂ or AlPO₄ composition. The compounds include four dense structures (α-quartz, α-cristobalite, and their AlPO₄ analogues), eight all-silica zeolites, and four aluminophosphate zeotypes (AlPOs). We analyzed the performance in reproducing the equilibrium structure for all systems, and computed bulk moduli and relative stabilities were compared to experiments for those compounds where experimental data are available. We found that the results obtained with functionals that take into account dispersive interactions are closer to experiments than those obtained with a bare generalized gradient functional. However, the variation among individual methods is considerable, and functionals that perform well for one quantity may give rather large deviations for another. Taking together the whole body of results, it appears that the Perdew-Burke-Ernzerhof functional including a many-body dispersion correction and the rev-vdW-DF2 methods present the best performance for the description of SiO₂ and AlPO₄ materials.

Van der Waals (vdW) interactions are important in numerous physical, chemical, and biological systems. However, traditional density functional theory (DFT) within local or semi-local approximations can hardly treat this interaction. Among various attempts to handle vdW interactions in DFT, semi-empirical correction methods are known to present the advantages of low additional computational costs and easy implementation in conventional DFT codes. In this review, we summarize the state-of-the-art semi-empirical vdW correction methods based on pairwise summations within the atoms-in-molecules scaling framework, such as the Grimme's D3 methods and variants of the Tkatchenko-Scheffler method. In addition, we compare the performance of these methods for systems ranging from molecules to solids, which have dispersive to ionic interactions: 128 molecular pairs, 23 molecular crystals, 4 noble gas crystals, 27 two-dimensional layered materials, and 9 ionic crystals.