Quantification of finite-temperature effects on adsorption geometries of pi-conjugated molecules

The adsorption structure of the molecular switch azobenzene on Ag(111) is investigated by a combination of normal incidence x-ray standing waves and dispersion-corrected density functional theory. The inclusion of non-local collective substrate response (screening) in the dispersion correction improves the description of dense monolayers of azobenzene, which exhibit a substantial torsion of the molecule. Nevertheless, for a quantitative agreement with experiment explicit consideration of the effect of vibrational mode anharmonicity on the adsorption geometry is crucial. PACS numbers: 68.43.Fg, 68.49.Uv, 71.15.Mb, 68.43.Pq 1 ar X iv :1 40 5. 36 70 v1 [ co nd -m at .m tr lsc i] 1 4 M ay 2 01 4 Precise experimentally determined structures of large organic adsorbates are indispensable — for the detailed understanding of their wide-ranged functionalities, but also for the benchmarking of ab initio electronic structure calculations [1–3]. For large molecules with polarizable π-electron systems, van der Waals (vdW) interactions are substantial and may critically influence the adsorption geometry [4–7]. Accounting for these interactions in ab initio calculations remains a challenge, and different approaches to this problem at varying degrees of accuracy are currently explored [8–14]. Due to the system sizes inherent to large molecular adsorbates, efficient semi-empirical dispersion correction schemes to density-functional theory (SEDC-DFT) are particularly promising [13]. However, their approximate nature makes them even more dependent on reliable experimental benchmark structures. This holds in particular for adsorption at metal surfaces, where the non-local collective substrate response (many-body electronic screening) requires advancements beyond the traditional pairwise summation of vdW interactions in these schemes [14, 15]. With SEDC-DFT now striving for the approximate inclusion of the collective substrate response [14], the accuracy increases to approximately 0.1 Å for the predicted adsorption heights [14, 16–18]. At this level of accuracy, a new issue arises: Experiments for structure determination are often carried out close to room temperature, while in SEDC-DFT the ground state (at 0 K) is normally calculated. The complex internal vibrational structure of large organic adsorbates which may sensitively influence the experimental time-averaged geometry is thus neglected. In this Letter we show that the inclusion of such thermal expansion effects into SEDC-DFT is indeed necessary to reach quantitative agreement between experiment and theory. Hence, benchmarking at the current level of sophistication requires the careful analysis of finite-temperature effects. Otherwise misleading conclusions with respect to the SEDC-DFT accuracy might be obtained. Our experiments have been carried out on azobenzene (AB, cf. Fig. 1a) adsorbed at Ag(111), by the normal incidence x-ray standing wave technique (NIXSW). AB is a widelyused molecular switch [20]. Investigations of its substrate interaction are driven by the challenge to preserve the switching functionality in the presence of a surface. In this context, the knowledge of the adsorption structure is essential. NIXSW is an established method to determine the adsorption geometry (in particular adsorption heights) of large organic adsorbates [21, 22]. The AB/Ag(111) system has been studied by NIXSW before and the results were compared to the SEDC-DFT approaches of the time to conclude on the importance of (then