Effective screening of van der Waals interactions in continuous environments

Computational investigations of supramolecular ordering under electrochemical conditions required density functional theory (DFT) studies of inter-molecular potentials in aqueous environment [1]. These interactions are partly of van der Waals (vdW) type where corrections to the usual DFT functionals have to be applied. While the aqueous environment can be conveniently included through a continuum solvent model, the vdW corrections lack this information. Starting from the Casimir-Polder Integral [2], we derive simple expressions for the correction of the vdW contribution relative to vacuum. Single point Gauss quadrature leads to the intuitive result, where the vacuum van der Waals C₆ coefficient is screened by the squared environment's permittivity evaluated near to the resonance frequencies of the interacting particles.

[1] Hartl, Shubham Sharma, Oliver Brugner, Stijn F. L. Mertens, Michael Walter, and Gerhard Kahl J. Chem. Theory Comput. 2020, 16, 5227−5243
[2] Johannes Fiedler, Priyadarshini Thiyam, Anurag Kurumbail, Friedrich A. Burger, Michael Walter, Clas Persson, Iver Brevik, Drew F. Parsons, Mathias Bostrom, and Stefan Y. Buhmann J. Phys. Chem. A 2017, 121, 9742−9751