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 C6-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 this manuscript, we provide simple models and sets of parameters for commonly used solvents, atoms, and small molecules.
Highlights
Van der Waals forces are the fundamental interactions between two neutral and polarisable particles [1, 2, 3]
We show that a single point Gauss quadrature leads to the intuitive result that the vacuum van der Waals C6 coefficient is screened by the permittivity squared of the environment evaluated near to the resonance frequencies of the interacting particles
It can be observed that the C6-coefficient (7) depends on dispersion of the implicit environmental medium via an integration along the imaginary frequency axis. This fact motivated us to develop a simple model that takes into account the screening of the van der Waals interaction with a similar numerical effort as ordinary density functional theory (DFT) simulations in vacuum would require
Summary
Van der Waals forces are the fundamental interactions between two neutral and polarisable particles [1, 2, 3]. This pairwise separation of the dispersion energy corresponds to the Hamaker approach [33] (or first-order Born series expansion [34]) in macroscopic quantum electrodynamics Such models are commonly used in modern van-der-Waals–density-functional-theory simulations with tabled vacuum C6-coefficients for the different interacting constituents. It can be observed that the C6-coefficient (7) depends on dispersion of the implicit environmental medium via an integration along the imaginary frequency axis This fact motivated us to develop a simple model that takes into account the screening of the van der Waals interaction with a similar numerical effort as ordinary DFT simulations in vacuum would require. As the deformation of the particle’s electron density in commonly considered in the form of Eq (10), the local-field corrections as expressed via excess polarizability models [18] in the form of Eq (3), we neglect the explicit consideration of these effects within this manuscript
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