Structure and Energetics of Azobenzene on Ag(111): Benchmarking Semiempirical Dispersion Correction Approaches

We employ normal-incidence x-ray standing wave and temperature programed desorption spectroscopy to derive the adsorption geometry and energetics of the prototypical molecular switch azobenzene at Ag(111). This allows us to assess the accuracy of semiempirical correction schemes as a computationally efficient means to overcome the deficiency of semilocal density-functional theory with respect to long-range van der Waals (vdW) interactions. The obtained agreement underscores the significant improvement provided by the account of vdW interactions, with remaining differences mainly attributed to the neglect of electronic screening at the metallic surface.

Figure 1

(a) Structure formula of azobenzene and schematic adsorption model in a butterfly geometry (side view) with key structural parameters $\tilde{\omega }$ and $d_{\mathrm{N}\mathrm{\text{−}}\mathrm{Ag}}$ (see text). (b) Experimental photoemission spectra of $\mathrm{\text{azobenzene}}/\mathrm{Ag}(111)$ (blue ●) and clean Ag(111) (○). For $\mathrm{\text{azobenzene}}/\mathrm{Ag}(111)$, the corresponding fit is also displayed (blue solid line). For clean Ag(111), the three component lines of the fit are plotted as solid black lines. The fit of $\mathrm{\text{azobenzene}}/\mathrm{Ag}(111)$ requires two additional components, one of them shaded in blue ($\mathrm{N}1s$) and the other displayed as a dashed line (see text). (c) Extracted PEY curves as a function of photon energy relative to the Bragg energy (2.635 keV, ●) and the corresponding fits (solid lines) [12]. Each curve is an average of three NIXSW data sets taken at different positions on the crystal. (d) Argand diagram of $d_c$ and $f_c$ for $\mathrm{N}1s$ (blue ●) and $\mathrm{C}1s$ (green ●), and corresponding average points (○). The red spiral represents calculated $d_c$ and $f_c$ for $\mathrm{C}1s$ as $\tilde{\omega }$ sweeps from $-5°$ to 90°. The vector sum of the six phenyl C atoms that contribute to this is illustrated in the bottom left part (zoomed by a factor of 3) for $\tilde{\omega }=13°$.

Figure 2

Thermal desorption spectra at different relative coverages $\theta$ in ML recorded with a linear heating rate of $1\mathrm{K}/\mathrm{s}$ at the fragment mass of 77 amu (${\mathrm{C}}_6{\mathrm{H}}_5^{+}$). 1 ML is defined as the coverage corresponding to the saturated desorption peak. The inset plots the desorption rate $\ln (d\theta /dt)$ against the reciprocal temperature at $\theta =0.075\mathrm{ML}$. The slope of the line, $-E_{\mathrm{des}}/R$ with $R$ the gas constant, then determines the activation energy for desorption at this coverage, here $E_{\mathrm{des}}(0.075\mathrm{ML})=1.08\pm 0.05\mathrm{eV}$.

Figure 3

ZPE-corrected desorption energy curves, computed with bare DFT-PBE and the two discussed DFT-D schemes. The black data point marks the experimental values and errors. Also shown is the curve computed with the TS correction reduced to the topmost layer Ag atoms (see text).