Relative stability of intercalation against surface adsorption in van der Waals materials and a predictive descriptor

The layered structure of van der Waals (vdW) materials is expected to enable efficient ion intercalation, making them potentially valuable for applications in the energy storage field. In order to understand the interaction mechanism of intercalation atoms in the vdW materials, we investigate the surface adsorption and interlayer intercalation behaviors of alkali metal (IA), alkaline earth metal (IIA), and halogen (VIIA) atoms in three representative vdW materials, namely insulating h-BN, gapless graphene, and semiconducting 2H-MoS₂, using density functional theory with vdW corrections. Through systematic analysis of binding energies and charge transfer characteristics at various sites, we reveal stabilization mechanisms of surface adsorption and interlayer intercalation that arise from the interplay of structural deformation, charge transfer, and vdW interactions. The relative stability ΔE between intercalation and adsorption can be efficiently predicted by the descriptor -(eQ)²/2z, where Q represents the charge transfer and z is the adsorption height both of which are extracted from the surface-adsorption of a monolayer vdW material calculation. The results provide a unified framework for understanding and predicting atom-substrate interactions in layered materials, providing valuable insights into material selection for energy storage applications.