The atomic dipole polarizability, α, and the van der Waals (vdW) radius, R vdW , are two key quantities to describe vdW interactions between atoms in molecules and materials. Until now, they have been determined independently and separately from each other. Here, we derive the quantummechanical relation R vdW = const. × α 1/7 which is markedly different from the common assumption R vdW ∝ α 1/3 based on a classical picture of hard-sphere atoms. As shown for 72 chemical elements between hydrogen and uranium, the obtained formula can be used as a unified definition of the vdW radius solely in terms of the atomic polarizability. For vdW-bonded heteronuclear dimers consisting of atoms A and B, the combination rule α = (αA + αB)/2 provides a remarkably accurate way to calculate their equilibrium interatomic distance. The revealed scaling law allows to reduce the empiricism and improve the accuracy of interatomic vdW potentials, at the same time suggesting the existence of a non-trivial relation between length and volume in quantum systems.

It is an undisputed textbook fact that nonretarded van der Waals (vdW) interactions between isotropic dimers are attractive, regardless of the polarizability of the interacting systems or spatial dimensionality. The universality of vdW attraction is attributed to the dipolar coupling between fluctuating electron charge densities. Here, we demonstrate that the long-range interaction between spatially confined vdW dimers becomes repulsive when accounting for the full Coulomb interaction between charge fluctuations. Our analytic results are obtained by using the Coulomb potential as a perturbation over dipole-correlated states for two quantum harmonic oscillators embedded in spaces with reduced dimensionality; however, the longrange repulsion is expected to be a general phenomenon for spatially confined quantum systems. We suggest optical experiments to test our predictions, analyze their relevance in the context of intermolecular interactions in nanoscale environments, and rationalize the recent observation of anomalously strong screening of the lateral vdW interactions between aromatic hydrocarbons adsorbed on metal surfaces. DOI: 10.1103/PhysRevLett.118.210402 Interactions induced by quantum-mechanical charge density fluctuations, such as van der Waals (vdW) and Casimir forces, are always present between objects with finite dimensions [1][2][3][4]. Such interactions are important not only for many fundamental phenomena throughout the fields of biology, chemistry, and physics but also for the design and performance of micro-and nano-structured devices. While Casimir forces can be both attractive or repulsive, depending on the nature of the fluctuations (quantum and/or thermal) and the spatial structure (topology and/or geometry) of the interacting systems [5][6][7][8], it is undisputed common wisdom that nonretarded vdW interactions between two objects in vacuo are inherently attractive [9][10][11]. The universality of vdW attraction is attributed to the ubiquitous zero-point energy lowering, induced by dipolar coupling between fluctuating electron charge densities [9,10].However, many biological, chemical, and physical phenomena of importance in materials happen in spatially confined environments, as opposed to isotropic and homogeneous vacuum. The confinement can be artificially engineered by applying static or dynamic electromagnetic fields or arise as a result of the encapsulation of molecules in nanotubes, fullerenes, and/or by adsorption on polarizable surfaces. Moreover, in biological systems, proteins are typically confined in an inhomogeneous environment. We remark that even when such confinement entails tiny modification of the electron density (having no apparent effect on the electrostatics), it can visibly affect the interactions stemming from density fluctuations due to their long-range inhomogeneous nature.Here, we demonstrate that the breaking of rotational and/or translational symmetry of 3D vacuum results in repulsive long-range interactions for vdW dimers.The repulsive interaction stems from...

General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Full terms of use are available: http://www.bristol.ac.uk/pure/about/ebr-terms Drude oscillators provide a harmonic description of charge fluctuations, and are widely studied as a model system and for ab initio calculations. In the dipole approximation the Hamiltonian describing the interaction of Drudes is quadratic, so can be diagonalized exactly, but the energy diverges at short range. Here we consider the quantum mechanics of Drude oscillators interacting through the full Coulombic Hamiltonian, for which the interaction energy does not have this defect. This protypical model for interactions between matter includes electrostatics, induction and dispersion. Potential energy curves for rare-gas dimers are very closely matched by Drude correlation energies plus a single exponential function. The exact and accurate results presented here help to delineate between basic properties of the physical model, and effects that arise from the dipole approximation.

Mutual Coulomb interactions between electrons lead to a plethora of interesting physical and chemical effects, especially if those interactions involve many fluctuating electrons over large spatial scales. Here, we identify and study in detail the Coulomb interaction between dipolar quantum fluctuations in the context of van der Waals complexes and materials. Up to now, the interaction arising from the modification of the electron density due to quantum van der Waals interactions was considered to be vanishingly small. We demonstrate that in supramolecular systems and for molecules embedded in nanostructures, such contributions can amount to up to 6 kJ/mol and can even lead to qualitative changes in the long-range van der Waals interaction. Taking into account these broad implications, we advocate for the systematic assessment of so-called Dipole-Correlated Coulomb Singles in large molecular systems and discuss their relevance for explaining several recent puzzling experimental observations of collective behavior in nanostructured materials.