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

Abstract

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.

Application of computational methods to the design and characterisation of porous molecular materials

“…13,14 In addition, discrete cage molecules can be assembled via a modular synthetic approach providing a facile pathway to a b As with conventional framework materials, PMMs can be described using quantum mechanical methods including density functional theory (DFT). 24 These methods are, potentially, highly accurate, as long as care is taken to properly account for dispersion interactions, 25,26 and can elucidate geometric and energetic properties resulting from the molecular electronic structure. Alternatively, structures can be simulated using model potentials, which are less computationally demanding than quantum mechanical methods.…”

Perturbed path integrals in imaginary time: Efficiently modeling nuclear quantum effects in molecules and materials

“…In this regard, the ab initio quantum chemical and density functional methods provide a systematic route toward attaining this goal and have therefore become an essential tool in many fields of research. [17][18][19] In fact, state-ofthe-art density-functional theory (DFT) approximations [20][21][22] that simultaneously reduce self-interaction error while treating the many-body nature of non-covalent interactions [23][24][25] are now able to furnish predictions for the binding energies of small molecules 26 and supramolecular systems 27 with so-called "chemical accuracy" (i.e., with errors less than 1 kcal mol 1 ), thereby extending the regime of applicability of such high-accuracy approaches to systems that contain 1000s of atoms. Other methods that are quite useful for treating significantly larger systems include the classical force fields, in which the quantum mechanical description of the electronic degrees of freedom is mapped onto an analytical (and therefore computationally efficient) interatomic/interfragment potential.…”

Quantum Theory of the Electron Transfer Coefficient

“…Experienced scientists thoroughly explore mathematical concepts and procedures necessary for an accurate treatment of VWF interactions, and a systematic and unified framework for classifying the first current principles for calculating VWF. [1] Some authors define the banned band or bandgap (BG) as the separation between HOMO-LUMO between molecules of the same chemical species. They tell us that in general for polycyclic aromatic hydrocarbons a BG <1.3 has a very high chemical reactivity.…”