First-Principles Models for van der Waals Interactions in Molecules and Materials: Concepts, Theory, and Applications

Noncovalent van der Waals (vdW) or dispersion forces are ubiquitous in
nature and influence the structure, stability, dynamics, and function of molecules and
materials throughout chemistry, biology, physics, and materials science. These forces are
quantum mechanical in origin and arise from electrostatic interactions between
fluctuations in the electronic charge density. Here, we explore the conceptual and
mathematical ingredients required for an exact treatment of vdW interactions, and
present a systematic and unified framework for classifying the current first-principles
vdW methods based on the adiabatic-connection fluctuation−dissipation (ACFD)
theorem (namely the Rutgers−Chalmers vdW-DF, Vydrov−Van Voorhis (VV),
exchange-hole dipole moment (XDM), Tkatchenko−Scheffler (TS), many-body
dispersion (MBD), and random-phase approximation (RPA) approaches). Particular
attention is paid to the intriguing nature of many-body vdW interactions, whose
fundamental relevance has recently been highlighted in several landmark experiments.
The performance of these models in predicting binding energetics as well as structural,
electronic, and thermodynamic properties is connected with the theoretical concepts and provides a numerical summary of the
state-of-the-art in the field. We conclude with a roadmap of the conceptual, methodological, practical, and numerical challenges
that remain in obtaining a universally applicable and truly predictive vdW method for realistic molecular systems and materials.