Consequently, much research on vdW materials has been demonstrated, such as graphite and GIC wherein considering the vdW interaction is essential. Thus, various investigations using first-principles calculation have been performed on the phenomenon that alkali metals (AMs) and alkaline earth metals (AEs) can be inserted into graphite, except Na (among AMs) and Be and Mg (among AEs); various insights have also been provided . For example, Okamoto reported that the high Na/Na + redox potential is responsible for the lack of Na insertion , while Wang et al. and Liu et al. concluded the binding energy between graphite and the intercalant as the cause. In addition, Moriwake et al. found that Li is rather specific because it creates covalent bonding-like charge density . Lenchuk et al. also reported the formation of stable Liintercalated GIC (Li-GIC) due to the covalent bonding contribution and vdW interaction . However, most of these studies have been limited to the discussion of the formation energies of GIC with AMs and AEs. Moreover, only a few systematic studies of other elements have been reported, along with detailed discussions on the stacking structures of each element.