Comparison of the DFT and field approaches to Van der Waals interactions in planparallel geometry

TL;DR

This paper compares the density functional theory and field approach methods for calculating van der Waals interactions in a parallel-plate geometry, highlighting their theoretical equivalence but numerical differences.

Contribution

It establishes a general equivalence between the DFT and field approaches for van der Waals interactions and compares their numerical implementations in a specific geometry.

Findings

The two methods are theoretically equivalent.

Their numerical implementations differ in practice.

Discussion of advantages of each approach.

Abstract

We establish a general equivalence between van der Waals interaction energies within the formalism of the non-local van der Waals functional of the density functional theory and within the formalism of the field approach based on the secular determinants of the electromagnetic field modes. We then compare the two methods explicitly in the case of a planparallel geometry with a continuously varying dielectric response function and show that their respective numerical implementations are not equivalent. This allows us to discuss the merits of the two approaches and possible advantages of either method in a simple model calculation.