Fig. 1

Polarizable Lennard–Jones model for gold. a Extension of the simple Lennard–Jones model with dummy electrons to add features of the free electron gas. The virtual electrons rest at the atom core and carry a mass of 1 au. b Visualization of the dummy electrons on the Au (111) surface in the presence of an adsorbed sodium ion in vacuum. The induced charges spread across several atomic layers laterally and beneath the top atomic layer. c The energy expression contains terms for harmonic bond stretching, Coulomb energy, and van-der-Waals energy (Lennard–Jones potential). d The model uses five independent parameters (highlighted in bold) including the mass of the dummy electron m_e, a combination of the charge q and the bond stretching constant k_r, whereby a certain ratio α = q²/(2k_r) determines the magnitude of the image potential, as well as the Lennard–Jones parameters σ, ε_core, and ε_e. The total mass of the gold atom (m_core + m_e) and the rest position of the dummy electron r₀ = 0 Å are constants