Van der Waals interaction between an atom and a solid surface

TLDR

The constant C in the atom–solid polarization potential is derived from Lifshitz’s earlier work. The paper develops a theory of the long‑range atom–solid polarization force and the reference plane Z₀ for physisorption applications. The authors use the leading terms of the asymptotic expansion to define a V_pol = −C(Z−Z₀)⁻³ potential, derive Z₀ for jellium and dipole‑dipole crystals, and compute polarization energies for rare‑gas atoms on noble‑metal surfaces. The calculated polarization energies agree with experimental adsorption energies.

Abstract

This paper contributes to the theory of the long-range attractive polarization force between a neutral atom and a crystalline solid surface in the nonrelativistic limit. The first two terms in the asymptotic expansion of the polarization energy are used to define an atom-solid potential of the form ${V}_{\mathrm{pol}}=\ensuremath{-}C{(Z\ensuremath{-}{Z}_{0})}^{\ensuremath{-}3}$. The constant $C$ appearing in this expression is known from the earlier work of E. M. Lifshitz. The present paper gives a theory of the position of the "reference plane," ${Z}_{0}$, which is important in applications to physisorption. An explicit expression for ${Z}_{0}$ is first derived for atoms interacting with a jellium metal and with an insulating crystal consisting of atoms which interact via dipole-dipole forces. These model calculations are then incorporated into a computation of the polarization energies of rare-gas atoms physisorbed on noble-metal surfaces. The computed energies are found to be consistent with observed adsorption energies.