M.
Sacchi
*a,
P.
Singh
b,
D. M.
Chisnall
c,
D. J.
Ward
c,
A. P.
Jardine
c,
W.
Allison
c,
J.
Ellis
c and
H.
Hedgeland
d
aDepartment of Chemistry, University of Surrey, Guildford, GU2 7XH, UK. E-mail: m.sacchi@surrey.ac.uk
bThe Perse School, Cambridge, CB2 8QF, UK
cCavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge, CB3 0HE, UK
dSchool of Physical Sciences, The Open University, Walton Hall, Milton Keynes, MK7 6AA, UK
First published on 27th April 2017
We use helium spin-echo spectroscopy (HeSE) to investigate the dynamics of the diffusion of benzene adsorbed on Cu(111). The results of these measurements show that benzene moves on the surface through an activated jump-diffusion process between the adsorption sites on a Bravais lattice. Density Functional Theory (DFT) calculations with van der Waals (vdW) corrections help us understand that the molecule diffuses by jumping through non-degenerate hollow sites. The results of the calculations shed light on the nature of the binding interaction between this prototypical aromatic molecule and the metallic surface. The highly accurate HeSE experimental data provide a quantitatively stringent benchmark for the vdW correction schemes applied to the DFT calculations and we compare the performances of several dispersion interaction schemes.
Notwithstanding the central role of benzene adsorption in surface and interface chemistry, the number of low-coverage, atomically resolved experimental studies of the adsorption of this aromatic molecule on copper and other coinage metal surfaces is relatively limited.11–20 Early STM and DFT studies by Komeda et al.20 and by Lorente et al.19 show that benzene adsorbs in a flat orientation on the Cu(100) surface, with the hollow sites being the preferred adsorption sites.19 On Cu(111) the molecule adsorbs up to a single monolayer coverage with the aromatic ring parallel to the surface17,18 and is able to diffuse freely and form stable islands near the steps at a temperature of 77 K.17,21 The long series of previous computational studies of benzene adsorption on Cu(111), employing both standard DFT generalised gradient approximation (GGA) exchange–correlation (XC) functionals and dispersion-corrected XC functionals, are motivated by the general lack of agreement on some fundamental results, such as the preferred adsorption site, the adsorption energies and the molecule-surface distance at the equilibrium.12 The previous experimental and theoretical studies generally focused on the properties of the C6H6–Cu(111) system in equilibrium at a given surface temperature and coverage. The dynamical aspects of the self-assembly process, in particular the surface mobility, have not been quantitatively explored. The main reason for the lack of information on the barriers for surface diffusion, as well as the friction coefficients, resides in the difficulty in determining the minimum energy adsorption site and, particularly, in measuring with accuracy the diffusion rates of the molecule. For instance, in the case of thiophene on Cu(111),8 three different degrees of freedom – molecular translation, rotation and vertical motion – were individually characterized by DFT and HeSE, giving accurate, quantitative insight into the atomic-scale motion of a heteroaromatic on a surface. In this work we present new theoretical and experimental insights into the adsorption and diffusion of benzene on Cu(111), a paradigmatic surface science system for benchmarking weak dispersion interactions in 2D.
The remaining details of the calculations and convergence criteria have been previously reported and discussed in several recent reports,6–9 but we summarise here the most important computational parameters. The surface has been modelled as a seven-layer slab, with a vacuum layer of ∼20 Å vertically separating the periodically repeated supercells. The cut-off energy of the plane wave basis set was fixed at 11 Hartrees, while the Brillouin zone was sampled with a 4 × 4 × 1 k-point Monkhorst–Pack30 grid. The bottom three layers were kept fixed in the bulk crystal positions while the top four atomic layers were allowed to relax during structural optimisation.
The experiments were performed on a single-crystal Cu(111) sample, mounted in a scattering chamber with a base pressure of 1 × 10−10 mbar and cleaned by repeated cycles of Ar+ sputtering (800 eV, 10 μA, 20 min at 300 K) and annealing (800 K, 30 s). The surface quality was monitored using the sample’s reflectivity to the helium beam (>20%) and the shape of the helium scattering specular peak. Benzene (>99.9% purity, Aldrich), purified by several freeze–evacuate–thaw cycles, was deposited on the surface by backfilling the chamber and monitoring the drop in the specularly reflected helium beam during adsorption. Using the same method as in our recent study of benzene on Cu(001),10 we estimate absolute coverages of 0.03 and 0.1 monolayers (ML) for the low and high coverage measurements, respectively.
In Fig. 2e, we present the temperature dependency of the dephasing rate as an Arrhenius plot, at a coverage of 0.03 ML and momentum transfer of 0.3 Å−1 in the [11] direction. From the Arrhenius plot, we find an effective activation energy of 35 ± 1 meV, a value approximately one third of that measured for benzene adsorbed on the (001) facet of copper, but very similar to the 41 ± 1 meV measured for five-membered aromatic cyclopentadienyl on the same Cu(111) surface.9
In addition to the slow decay that is caused by the diffusive motion of the adsorbate, and which we have analysed above, a typical polarisation measurement also shows an initial rapid drop within the first one or two picoseconds. The much smaller and more rapid decay here is associated with the intracellular motion of the adsorbate molecule when it is localised within a particular adsorption hollow.32 In the polarisation curves we present in Fig. 2, it may be noticed that the data at 0.1 ML has two data points taken at smaller times than those shown in the 0.03 ML curves. These two data points are excluded from the subsequent exponential fit illustrated by the black lines, in order to ensure that there is no influence from the initial drop. Once these points are excluded, the slow decay can be considered independently from the fast decay as it occurs on such a different time scale.
In our previous work we benchmarked the performance of the original TS scheme, as implemented in CASTEP, on several aromatic systems: pyrrole/Cu(111),7 thiophene/Cu(111)6 and benzene/Cu(001).6 For pyrrole and thiophene the surface translational/rotational barriers are in very good agreement with the experimental results obtained by HeSE spectroscopy. Taking into account that supramolecular self-assembled systems on metal surfaces have to be modelled with supercells containing hundreds of atoms, the computational-cost advantage of the TS-scheme, when compared to the vdW-DFT functionals, is significant. In this work we have employed the TS and the TSSCS method, which adds self-consistent screening to the original correction scheme, and is thought to be capable of generally improving the performance of the method in adsorbate systems.
The adsorption energy of benzene on the high-symmetry sites on a Cu(111)-(2√3 × 2√3) surface cell is reported in Fig. 3 and Table 1 and compared with selected DFT results from the recent studies of Carter and Rohl.37 First of all, it is clear that both the TS and the TSSCS methods agree in indicating the hollow site as the minimum energy adsorption site for benzene. The diffusion barrier is slightly lower for the TSSCS calculations (18 meV instead of 21 meV) and both the TS and TSSCS fall below the experimental results (35 meV), although the difference might be considered to be within reasonable chemical accuracy. The oldest and most primitive correction scheme (G06, ref Grimme et al.24) also assigns the position of the global minimum to the HCP-R site, but shows a more pronounced difference in the angular dependence of the adsorption energy on TOP sites (0.111 eV). In general, one would not expect Zero Point Energy (ZPE) corrections to be important in the case of a physisorbed aromatic molecule in a completely flat configuration. For this study we calculated the ZPE contributions to the barrier height using DFT with TS vdW corrections. The effect of the ZPE contribution is essentially to shift the minimum energy adsorption site from the HCP to FCC sites, marginally lowering the barrier height between the hollows and BR sites from 21 meV to 17 meV. The HCP and TOP sites are now 86 meV and 180 meV higher in energy than the FCC site. In this paper we will not discuss further the effects of ZPE corrections and the relative accuracy of each pairwise correction scheme for evaluating vibrational frequencies since this will be the subject of future works.
Fig. 3 Potential energy surfaces derived from the DFT calculations with (a) G06,24 (b) OBS,25 (c) TS26 and (d) TSSCS33 vdW corrections. |
Table 2 reports the optimised structure of benzene on the hollow, bridge and top sites. The distance between the molecule and surface at the proposed adsorption site (2.958 Å) is in very good agreement with the reported height of 0.29 nm derived from the work function change measurements.38 The accurate position of the molecule on the surface, and therefore the geometrical corrugation of the PES along the x, y plane,39 is the single most important factor in determining the quality of a molecule/surface potential. Our calculations confirm, as previously observed by Carrasco et al.40 for benzene on transition metal surfaces, that the interaction between benzene and the terraces of the single crystal metal surface is reasonably accurately captured by the original TS scheme and by its related methods. We note that, without vdW corrections, the potential energy curve will become completely unrealistic (see Eads-GGA results in Table 2); all the calculated adsorption energies are positive, therefore no binding between benzene and the surface is predicted. The TSSCS corrections, by including the self-consistent screening, also result in good agreement with the experimentally derived adsorption height, while the internal structure of the adsorbate (average C–C bond length, and C–H angle) is essentially identical to the TS values. The moderate downward tilting of the essentially unpolarised C–H bonds does not contribute overall to the stabilisation of the system, by reducing the surface-molecule dipole system, as this is dominated by the binding of the aromatic ring. As described by Witte et al.,41 the so-called cushion effect is clearly visible in Fig. 4, which shows the electron density-difference plot for benzene adsorbed on the HCP-R site, with a region of electron depletion just above the surface atoms underneath the adsorbate. This quantum chemical effect governs the electronic density of states redistribution between the organic and metal surfaces and it is caused by the Pauli repulsion between the electron density in the layer immediately above the topmost (111) plane and the approaching electron-rich π-system of the aromatic ring. The displaced electron density cloud forms a three-dimensional “cushion” that holds the molecule at approximately 3 Å, causing a total shift of the work-function in the opposite direction to the predictions of the simplistic electrostatic models. A comparison between our results and those reported by Witte et al.41 shows that the cluster model used in early calculations clearly overestimates the total charge redistribution due to the localised nature of the cluster compared with the periodically repeated surface model employed in the present study. Nevertheless, the understanding of the binding mechanism of benzene on Cu(111) captured by Witte and co-authors within the cushion effect model is essentially correct, especially in predicting the sign of the dipole moment change and consequently the lowering of the work function of the metal surface upon the adsorption of benzene. Witte et al. calculated a work function change of −1.08 eV, in excellent quantitative agreement with our calculations (Table 3) at low coverage (1/12 ML), where we found that benzene causes a shift of the work function of 0.99 eV, within 6% of the experimental measurements.41 Comparing these results with the work function change induced by the adsorption of Cp on the same surface, as calculated by Sacchi et al.,8 we notice some similarities, but also a striking difference. We find that the change in the work function does not significantly change when the benzene coverage is increased above 0.11 ML, which is similar to Cp adsorption, where ΔΦ changed by only 5% when the coverage was increased from 0.11 to 0.14 ML. Again, we observe some degree of depolarisation in the benzene overlayer when the molecules are compressed beyond a certain critical distance, although it is not clear how far the molecules could be compressed before a critical change in the adsorption angle may occur.18
Surface Site | E ads-vdW (eV) | E ads-GGA (eV) | Height (Å) | Charge (e) | C–H angle (degrees) |
---|---|---|---|---|---|
BR-I | −1.027 | 0.023 | 2.959 | −0.59 | −0.663 |
BR-R | −1.029 | 0.038 | 2.972 | −0.56 | −0.183 |
FCC-I | −1.018 | 0.009 | 2.955 | −0.59 | −0.777 |
FCC-R | −1.040 | 0.031 | 2.967 | −0.60 | −0.211 |
HCP-I | −1.030 | 0.016 | 2.960 | −0.59 | −0.380 |
HCP-R | −1.050 | 0.003 | 2.958 | −0.58 | −0.313 |
TOP-I | −0.926 | 0.098 | 2.971 | −0.48 | −1.444 |
TOP-R | −0.940 | 0.093 | 3.174 | −0.60 | −1.437 |
Coverage (ML) | Δμ (D) | ΔΦ (eV) |
---|---|---|
0.08 | 1.8 | −0.99 |
0.11 | 2.3 | −1.70 |
0.14 | 1.7 | −1.62 |
The position of the lowest energy structure and the measured barrier for jump diffusion are entirely consistent with the previous measurements on Cp/Cu(111). In principle, one would not expect such a similarity in the behaviour of these two molecules, given the different symmetry groups (D6h and D5h). It is observed that the substrate reduces the symmetry of both molecules and the extent of charge backtransfer in Cp more than compensates for the larger dispersion interaction between the six-membered ring and surface. The slightly higher barrier for the jump diffusion of cyclopentadienyl on the same surface can be partly rationalised by an increase in the ionic binding, combined with the reduced symmetry compatibility between the pentagonal aromatics and hexagonal substrate. The local adsorption site (hollow hcp) has a reduced three-fold symmetry with respect to the six-fold rotational symmetry of the clean surface and the reduced overlap between the dz orbitals of the three Cu atoms with the π-system of benzene is clearly visible in the density difference plot of Fig. 4. The molecular orbital mismatch between the substrate and molecule (Fig. 4 and 5) reduces the height of the rotational barrier compared to what we observed for benzene on Cu(001), where the experimental and theoretical activation energy are a factor of 3 and 35 higher than for the Cu(111) surface, respectively. The much greater energetic corrugation of the Cu(100) surface is therefore captured by the vdW-corrected DFT simulations, but with a clear DFT overestimation of the barrier height for the jump diffusion (hollow to hollow site) for Cu(100). It is also worth discussing the charge transfer between the substrate and adsorbate in different locations on the PES. For smaller molecules, the extent of donation and backdonation determines the intensity of the binding energy. However, for benzene on Cu(111), the charge transfer from the surface to the molecule does not seem to be correlated to either the distance between the molecule and the surface, or the adsorption energy. Still, it is worth noting that the highest energy local minimum (TOP-I) does show the lowest degree of electron backdonation (−0.4 e) from the substrate.
It is evident from Fig. 5, which shows the Kohn–Sham orbitals (KS-MOs) at the gamma point for benzene adsorbed on a hollow hcp site, that the extremely low chemical interaction between the Cu(111) surface and the adsorbate does not translate into a negligible mixing between the surface and molecular orbitals. In fact, if we concentrate our attention on the frontier orbitals of the system (a selection of these, the HOMO, HOMO−1 and LUMO are represented in Fig. 5), the high degree of mixing between the surface state and molecular π states is immediately visible in the Kohn–Sham orbital representations of these states. For instance, in the HOMO−1 the lower lobes of the π2 and π3 orbitals extend to the copper atoms surrounding the hollow site, while the character of the π4 and π5 orbitals in the LUMO is completely mixed with the surface states connecting adjacent molecules. Furthermore, the calculations show that the π1 and (π2, π3) orbitals are blue shifted in energy by 6.7 eV and 3.8 eV respectively to become part of the HOMO and HOMO−1 bands.
Comparing the results of the calculations with those reported by Carter et al., we can observe a substantial agreement between our data and the results of optB88-vdW, revPBE (vdW-DF) and rPW86 (vdW-DF2). In particular, the molecule-surface height is very similar to that which Carter et al. reported for the vdW-DF (optB88-vdW) calculations (2.93 Å) and the barrier height is also entirely consistent with the results of the vdW-DF calculations (in the 0–30 meV range).37 The binding energy calculated by the TS and TSSCS methods overestimates the experimental adsorption energy (by about 0.4 eV) in the same way as less accurate correction schemes OBS and G06. The barrier for diffusing from HCP over the BR site is about 20 meV, with FCC lying around 10 meV higher than HCP. The energetics of the diffusion pathway do not seem to change significantly with the choice of the vdW corrections with TS, TSSCS, G06 and OBS schemes resulting in barriers in the 11–26 meV range.
All four schemes also result in energetic differences between the HCP and FCC hollows of only 10–14 meV. The experimental data supports adsorption to the non-degenerate hollow sites as the ISFs did not show the additional decay that would be expected in the degenerate case. However, there is a further subtlety. The measurements were carried out at 170 K, corresponding to a thermal energy of 15 meV. If the energetic differences were indeed as small as 10–14 meV, we would expect to have to consider the contribution from jumps from the FCC sites, which would then be reasonably occupied. The ratio of jump rates from the HCP to FCC and FCC to HCP sites is given by λ = exp(ΔE/kBT) where ΔE is the energy difference of the two sites. For the calculated energies, λ is in the range of 2–3. Tuddenham et al. illustrate that for λ = 2 (equivalent to a 10 meV difference), a second exponential term would still be expected, but would become most apparent at slightly higher momentum transfers (around 1.8 Å−1), an effect that is not seen in Fig. 2d. Due to the exponential nature of λ, the strength of the second exponential term rapidly falls away in magnitude as ΔE increases, which suggests that the calculations are probably underestimating the difference between the two sites to a similar degree to the diffusion barrier, where the calculations are 10–25 meV lower than the experiment. A FCC–HCP difference in energy of just 25 meV would be indiscernible within the present experimental data from the greater difference.
The small energetic difference between the I and R rotational states (11–23 meV on the energetically preferred site) would lead to the occurrence of both rotational states at the temperatures of the experiment. However, if we consider the energies presented in Table 2, although these states will be present frequently, they do not affect the rate-limiting barrier, which is from HCP-R to BR-R for TS and TSSCS, HCP-R to FCC-R for G06 and HCP-I to BR-I for OBS. The population of the rotated states would be expected to affect the pre-exponential factor for diffusion, rather than the Arrhenius activation energy that was considered in this work. A typical molecule’s trajectory across the surface would be expected to involve rotation as well as translation, but without the degree of coupling between the two that might be described in terms of quasi-static steering10 where the molecule must rotate to pass over the rate-limiting barrier.42
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