Structure and energetics of benzene adsorbed on transition-metal surfaces: density-functional theory with van der Waals interactions including collective substrate response

Abstract

The adsorption of benzene on metal surfaces is an important benchmark system for hybrid inorganic/organic interfaces. The reliable determination of the interface geometry and binding energy presents a significant challenge for both theory and experiment. Using the Perdew-Burke-Ernzerhof (PBE), PBE+vdW (van der Waals) and the recently developed PBE+vdW surf (densityfunctional theory with vdW interactions that include the collective electronic response of the substrate) methods, we calculated the structures and energetics for benzene on transition-metal surfaces: Cu, Ag, Au, Pd, Pt, Rh and Ir. Our calculations demonstrate that vdW interactions increase the binding energy by more than 0.70 eV for physisorbed systems (Cu, Ag and Au) and by an even larger amount for strongly bound systems (Pd, Pt, Rh and Ir). The collective response of the substrate electrons captured via the vdW surf method plays a significant role for most substrates, shortening the equilibrium distance by 0.25 Å for Cu and decreasing the binding energy by 0.27 eV for Rh. The reliability of our results is assessed by comparison with calculations using the random-phase approximation including renormalized single excitations, often hard to interpret, or even lacking. For example, due to the relative difficulty of controlling and measuring weakly bound systems, no experimental adsorption height has been reported so far for Bz physisorbed on noble metals. The only experimentally deduced adsorption height, to the best of our knowledge, was determined for the disordered Bz chemisorbed on the Pt(111) surface at a coverage close to or less than one [36].The binding energy, which reflects the strength of the interaction between an adsorbate and the substrate, is another key parameter for the description of HIOS. Experimental binding energies are mainly obtained by temperature-programmed desorption (TPD) [22][23][24][25]27] and microcalorimetry measurements [32,[37][38][39]. TPD is the most extensively used method for determining the kinetic and thermodynamic parameters of desorption processes and decomposition reactions. The desorbing molecular species are selected by their mass, while the amount of adsorbate is determined by integrating the peaks of the desorption spectrum. The Redhead formula is typically used to calculate the adsorption energy based on three parameters: the desorption temperature, the heating rate and a pre-exponential factor [40]. The wide range of empirical pre-exponential factors (10 13 -10 19 s −1 ) that are typically used for molecular desorption may cause a notable uncertainty in the determined binding energy [41][42][43]. TPD experiments have been carried out to study the interaction of Bz with the Cu [13], Ag [24] and Au surfaces [29]. However, special attention must be paid to the interpretation of TPD spectra for the Pd, Pt and Rh surfaces, because the adsorbed Bz molecules may decompose during heating, in particular at low coverage [44]. Here, we revisit the adsorption energies from the measured TPD spectra for Bz on Cu(111), A...

Electronic charge rearrangement at metal/organic interfaces induced by weak van der Waals interactions

“…This molecule has been highly used and studied as an adsorbate on Ag(111) [42,49,50] and is considered a model system for larger hydrocarbons. Here, Bz is adsorbed in a flat configuration [49] at a distance of 2.96Å [9]. The binding energies, obtained with both PBE + vdW surf and PBE + vdW surf sc (Table I), indicate a rather weak physisorption.…”

“…In this context, the long-range van der Waals (vdW) interactions-while absent in standard DFT exchangecorrelation (XC) functionals-have been proven of fundamental importance in determining the structure and the cohesive energies of layered systems, such as molecules adsorbed on metal surfaces [3,[7][8][9][10][11][12][13][14]. On the other hand, the long-range vdW energy represents only a small fraction (0.001%) of the total electronic energy for a wide range of systems [15], from small dimers (e.g., diatomic dimers, water dimer) to complex hybrid inorganic/organic systems, passing through large molecular systems and metal surfaces.…”

Versatile van der Waals Density Functional Based on a Meta-Generalized Gradient Approximation

“…[53]. Unfortunately, none of them simultaneously predicts the correct E ad and Δ z , with the best results coming from PBE þ vdW surf [53], which still overestimates the adsorption for the case of Cu and apparently cannot apply to general geometries. The recent rev-vdW-DF2 [7] is close to SCANþrVV10 based on its results for benzene on Cu(111), but more thorough calculations are needed for confirmation.…”

“…To be a successful general-geometry density functional, SCANþrVV10 should pass more stringent tests, where both strong local atomic bonds and weak vdW interactions need to be well described. We first consider the widely studied benzene ring adsorbed on the (111) surface of coinage metals [51][52][53][54][55][56]. This is also one of the most common systems for benchmarking a vdW functional's capability to simultaneously describe the vdW bonding and the metallic bonding.…”

“…The results from other methods, including PBE, PBE þ vdW, PBE þ vdW surf , MP2, vdW-DF1, DFTþD, and M06-L, etc., have been compiled in Ref. [53]. Unfortunately, none of them simultaneously predicts the correct E ad and Δ z , with the best results coming from PBE þ vdW surf [53], which still overestimates the adsorption for the case of Cu and apparently cannot apply to general geometries.…”