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Abstract

Van der Waals (vdW) interactions arise from correlated electronic fluctuations in matter and are therefore present in all materials. Our understanding of these relatively weak yet ubiquitous quantum mechanical interactions has improved significantly during the past decade. This understanding has been largely driven by the development of efficient methods that now enable the modeling of vdW interactions in many realistic materials of interest for fundamental scientific questions and technological applications. In this work, the physics behind the currently available vdW methods are reviewed, and their applications to a wide variety of materials are highlighted, ranging from molecular assemblies to solids with and without defects, nanostructures of varying size and dimensionality, as well as interfaces between inorganic and organic materials. The origin of collective vdW interactions in materials is discussed using the concept of topological dipole waves. Focus is placed on the important observation that the full many-body treatment of vdW interactions becomes crucial in the investigation and characterization of materials with increasing complexity, especially when studying their response properties, including vibrational, mechanical, and optical phenomena. Despite significant recent advances, many challenges still remain in the development of accurate and efficient methods for treating vdW interactions that will be broadly applicable to the modeling of functional materials at all relevant length and timescales.