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

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.