X-ray Electron Density Investigation of van der Waals Gap Interaction in TiS₂

Van der Waals (vdW) gap interaction is decisive for many extraordinary properties in vdW gap materials. However, it is a strong challenge for theory to model the vdW gap interaction since vdW force is not described in ground states. The experimental observation of the vdW gap interaction can be useful to understand the vdW gap and for theory to develop functionals that accurately model the long-range electron correlations. In this study, we observed the vdW gap bonding in layered TiS₂ using accurate experimental electron density (ED). The ED was determined from high-resolution X-ray diffraction data using the Hansen-Coppens multipole model. The experimental ED was evaluated quantitatively by Bader's topological analysis. The obtained ED and the topological measures were compared with DFT calculations using vdW functionals, e.g. SCAN+rVV10. Quantitative agreement is observed for the covalent Ti-S interaction. On the other hand, significant difference is observed for the vdW gap interaction with experiment revealing a more covalent bonding situation than the DFT. Therefore, the present work provides an experimental benchmark for testing theoretical models of vdW gap iteraction.