Long-Range Repulsion Between Spatially Confined van der Waals Dimers

Abstract

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...

Sadhukhan and Tkatchenko Reply:

“…Similarly, PJ's analysis of oscillators confined in 2D and quasi-3D spaces disagrees with our analytical results [1]. Our result for the quasi-3D confinement scales as R −5 , contradicting PJ.…”

“…Sadhukhan and Tkatchenko Reply: In our Letter [1], we investigated the interaction between a pair of 3D Drude oscillators (charge-separated, overall-neutral quantum harmonic oscillators), coupled by a Coulomb potential in reduced spatial dimensions, utilizing a novel perturbation expansion based on Ref. [2] and correlated dipolar oscillator states.…”

“…We generalize our expression [1] for two 1D oscillators with different charges (q A=B ), masses (m A=B ), and frequencies (ω A=B ). Diagonalization of the dipole-coupled potential matrix in coordinates…”

“…[1,6], without the frequency dependence claimed by PJ [7]. Additionally, for N arbitrary oscillators, the repulsive energy [1] cannot be expressed in terms of oscillator densities only, highlighting its quantum-mechanical origin. This inconsistency in PJ's expression arises since it describes interaction between negative charge densities.…”

Quantum-Mechanical Relation between Atomic Dipole Polarizability and the van der Waals Radius

“…Many properties of real atoms can be captured by physical models based on Gaussian wave functions [18]. Among them, the quantum Drude oscillator (QDO) model [19][20][21] serves as an insightful, efficient, and accurate approach [11][12][13][22][23][24][25] for the description of the dispersion interaction. It provides the dipole polarizability α ≡ α 1 = q 2 /µω 2 expressed in terms of the three parameters [21]: the charge q, the mass µ, and the characteristic frequency ω modeling the response of valence electrons.…”