Binding Energy of Adsorbates on a Noble-Metal Surface: Exchange and Correlation Effects

We discuss the adsorption of xenon and of PTCDA on the silver (111) surface within a first-principles approach, focusing on the adsorbate-substrate interaction energy as a function of distance. We combine exact exchange with correlation energy from the adiabatic-connection fluctuation-dissipation theorem. At a large distance $Z$ from the surface, the correlation causes a van der Waals attraction [$\sim -C_3/(Z-Z_0{)}^3$]. At a closer distance, the attraction deviates from its asymptotic form and, combined with the repulsive exact-exchange energy, yields an equilibrium in close agreement with experiment.

Figure 1

Binding energy of adsorbates on the Ag(111) surface. Panel (a) is for a Xe atom (located on top of a Ag atom). Panel (b) refers to a PTCDA molecule [located above a Ag(111) bridge site [3]]. Structural relaxation of the substrate is neglected. The solid lines show our results for the correlation-free interaction energy ($\Delta E_{\mathrm{EXX}}$, upper curve in each panel), for the correlation ($\Delta E_C$, lower curve), and for the sum of both. Most correlation data employed here are obtained from the $\mathrm{\text{jellium}}+4d$ model approach (see text). The open squares in (a) result from an ab initio calculation of $\Delta E_C$ [cf. Fig. 2a]. For comparison, the dashed curves show the DFT interaction energy resulting from two common exchange-correlation functionals (LDA and PBE).

Figure 2

Upper panel (a): Correlation interaction energy $\Delta E_C$ between a Xe atom and the Ag(111) surface. The squares are obtained from an ab initio calculation (see text) while the circles result from a jellium model ($\leftrightarrow \mathrm{Ag}$ $5s$ electrons) to the surface electronic structure, also including the polarizability of the Ag $4d$ electrons (see text). The inset shows the same data on a nonlinear vertical scale, i.e., $1/\sqrt[3]{-\Delta E_C}$. On this scale, the expected asymptotic behavior at a large distance [$\Delta E_C\sim -C_3/(Z-Z_0{)}^3$] [12, 13, 14] would show up as linear behavior, which is indeed the case (see the dashed line as a guide to the eye). The $\mathrm{\text{jellium}}+4d$ model yields $C_3=3.7\mathrm{eV}{\AA }^3$ and a reference-plane position of $Z_0=1.5\AA$. Lower panel (b): The same for PTCDA on Ag(111).