van der Waals Interactions in Material Modelling

Van der Waals (vdW) interactions stem from electronic zero-point fluctuations and are often critical for the correct description of structure, stability, and response properties of molecules and materials, including biomolecules, nanomaterials, and material interfaces. Here, we give a conceptual as well as mathematical overview of the current state of modeling vdW interactions,focusing in particular on the consequences of different approximations for practical applications. We present a systematic classification of approximate first-principles models based on the adiabatic-connection fluctuation-dissipation theorem, namely the nonlocal density functionals, interatomic methods, and methods based on the random-phase approximation. The applicability of these methods to different types of materials and material properties is discussed in connection with availability of theoretical and experimental benchmarks. We conclude with a roadmap of the open problems that remain to be solved to construct a universal, efficient, and accurate vdW model for realistic material modeling.