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 advan- tages 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 meth- ods and variants of the Tkatchenko-Scheffler method. In addi- tion, we compare the performance of these methods for systems ranging from molecules to solids, which have disper- sive to ionic interactions: 128 molecular pairs, 23 molecular crystals, 4 noble gas crystals, 27 two-dimensional layered materials, and 9 ionic crystals.
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