# Unifying microscopic and continuum treatments of van der Waals and Casimir interactions

## TL;DR

This paper introduces a unified approach combining atomistic and continuum models to accurately compute van der Waals and Casimir interactions at mesoscopic scales, accounting for complex shapes and many-body effects.

## Contribution

It develops a novel theoretical framework that integrates density functional theory with electromagnetic scattering to capture shape-dependent and many-body effects in vdW interactions.

## Key findings

- Interactions can be significantly modified by shape and retardation effects.
- The approach captures many-body and multiple scattering effects to all orders.
- Compared to previous models, the new method predicts orders-of-magnitude differences in vdW forces.

## Abstract

We present an approach for computing long-range van der Waals (vdW) interactions between complex molecular systems and arbitrarily shaped macroscopic bodies, melding atomistic treatments of electronic fluctuations based on density functional theory in the former, with continuum descriptions of strongly shape-dependent electromagnetic fields in the latter, thus capturing many-body and multiple scattering effects to all orders. Such a theory is especially important when considering vdW interactions at mesoscopic scales, i.e. between molecules and structured surfaces with features on the scale of molecular sizes, in which case the finite sizes, complex shapes, and resulting nonlocal electronic excitations of molecules are strongly influenced by electromagnetic retardation and wave effects that depend crucially on the shapes of surrounding macroscopic bodies. We show that these effects together can modify vdW interactions by orders of magnitude compared to previous treatments based on Casimir--Polder or non-retarded approximations, which are valid only at macroscopically large or atomic-scale separations, respectively.