Effective screening of medium-assisted Van der Waals interactions between embedded particles

TL;DR

This paper derives simple, effective formulas to account for medium effects on Van der Waals interactions between particles, showing how the environment's permittivity screens these forces, especially in transparent media.

Contribution

It introduces a straightforward approximation method using Gauss quadrature to evaluate medium screening effects on Van der Waals interactions, applicable to various solvents and molecules.

Findings

Vacuum $C_6$ coefficients are scaled by the square of the medium's permittivity.

The approximation is most accurate when the medium is transparent at resonance frequencies.

Provides models and parameters for common solvents, atoms, and molecules.

Abstract

The effect of an implicit medium on dispersive interactions of particle pairs is discussed and simple expressions for the correction relative to vacuum are derived. We show that a single point Gauss quadrature leads to the intuitive result that the vacuum van der Waals $C_6$ coefficient is screened by the permittivity squared of the environment evaluated near to the resonance frequencies of the interacting particles. This approximation should be particularly relevant if the medium is transparent at these frequencies. In the manuscript, we provide simple models and sets of parameters for commonly used solvents, atoms and small molecules.