This work reviews the increasing evidence that many-body van der Waals (vdW) or dispersion interactions play a crucial role in the structure, stability and function of a wide variety of systems in biology, chemistry and physics. Starting with the exact expression for the electron correlation energy provided by the adiabatic connection fluctuation–dissipation theorem, we derive both pairwise and many-body interatomic methods for computing the long-range dispersion energy by considering a model system of coupled quantum harmonic oscillators within the randomphase approximation. By coupling this approach to density functional theory, the resulting many-body dispersion (MBD) method provides an accurate and efficient scheme for computing the frequency-dependent polarizability and many-body vdW energy in molecules and materials with a finite electronic gap. A select collection of applications are presented that ascertain the fundamental importance of these non-bonded interactions across the spectrum of intermolecular (the S22 and S66 benchmark databases), intramolecular (conformational energies of alanine tetrapeptide) and supramolecular (binding energy of the ‘buckyball catcher’) complexes, as well as molecular crystals (cohesive energies in oligoacenes). These applications demonstrate that electrodynamic response screening and beyond-pairwise many-body vdW interactions—both captured at the MBD level of theory—play a quantitative, and sometimes even qualitative, role in describing the properties considered herein. This work is then concluded with an in-depth discussion of the challenges that remain in the future development of reliable (accurate and efficient) methods for treating many-body vdW interactions in complex materials and provides a roadmap for navigating many of the research avenues that are yet to be explored.

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Many-body van der Waals interactions in molecules and condensed matter.

The Cl35 pure quadrupole resonance frequency has been observed in polycrystalline CH2Cl2, CHCl3, CCl4, (CH3)3CCl, and CH3CCl3 at temperatures of 77°K and above. In all cases, the resonance frequency decreases at higher temperatures, in qualitative agreement with Bayer's theory for the torsional motions of the molecules. However, a quantitative comparison of the theory with experiment, including Livingston's results at 4 and 20°K, reveals significant discrepancies which are discussed and attributed mainly to the decrease in torsional frequencies at higher temperatures. The resonance was found to ``fade out'' at temperatures below the transition points in those solids, CCl4, (CH3)3CCl, and CH3CCl3, where internal or molecular reorientations are known to occur. In the other compounds the resonance was observable up to the melting point. The origin of this phenomenon is discussed briefly.

Temperature Dependence of the Chlorine Pure Quadrupole Resonance Frequency in Molecular Crystals

Chemical shifts in the phosphorus nuclear magnetic resonance absorption have been measured in twenty compounds. The shifts arise from differences in the magnetic shielding of the phosphorus nuclei by electrons, and the values observed are interpreted qualitatively in terms of the molecular electronic structures. The range in shifts in 7×10—4 which is somewhat larger than observed for fluorine on which more extensive data are available. The phosphorus resonance shifts fall into two distinct groups one of which contains compounds with trivalent phosphorus and the other, pentavalent. The shifts in pentavalent compounds fall in a relatively narrow range, generally with greater nuclear magnetic shielding than in the trivalent. The resonance shifts between similar or homologous compounds can be accounted for by considering changes in the importance of ionic and double‐bonded electronic structures.

Electron Distribution in Molecules. IV. Phosphorus Magnetic Resonance Shifts

Nuclear quadrupole resonance in inorganic chemistry

The nuclear quadrupole resonance spectrum of Cl in chloranil and in the 1: 1 complex of chloranil with hexamethylbenzene was obtained at 77 tained K and room temperature. The results are used to estimate the upper limit for charge transfer in the complex from chloranil to hexamethylbenzene. Complexes of picrylchloride: hexamethylbenzene and parachloroaniline: sym-trinitrobenzene were also studied but no resonances were detected. (D. L.C.)

H. S. Gutowsky

Papers

Chlorine Pure Quadrupole Resonances