Jumping, Rotating, and Flapping: The Atomic-Scale Motion of

Letter pubs.acs.org/JPCL

Jumping, Rotating, and Flapping: The Atomic-Scale Motion of Thiophene on Cu(111) Barbara A. J. Lechner,*,† Marco Sacchi,‡ Andrew P. Jardine,† Holly Hedgeland,† William Allison,† John Ellis,† Stephen J. Jenkins,‡ Paul C. Dastoor,§ and B. J. Hinch∥ †

Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom § Centre for Organic Electronics, University of Newcastle, Callaghan NSW 2308, Australia ∥ Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, New Jersey 08854, United States ‡

S Supporting Information *

ABSTRACT: Self-assembled monolayers of sulfur-containing heterocycles and linear oligomers containing thiophene groups have been widely employed in organic electronic applications. Here, we investigate the dynamics of isolated thiophene molecules on Cu(111) by combining helium spin-echo (HeSE) spectroscopy with density functional theory calculations. We show that the thiophene/Cu(111) system displays a rich array of aperiodic dynamical phenomena that include jump diffusion between adjacent atop sites over a 59−62 meV barrier and activated rotation around a sulfur−copper anchor, two processes that have been observed previously for related systems. In addition, we present experimental evidence for a new, weakly activated process, the flapping of the molecular ring. Repulsive inter-adsorbate interactions and an exceptionally high friction coefficient of 5 ± 2 ps−1 are also observed. These experiments demonstrate the versatility of the HeSE technique, and the quantitative information extracted in a detailed analysis provides an ideal benchmark for state-of-the-art theoretical techniques including nonlocal adsorbate− substrate interactions. SECTION: Physical Processes in Nanomaterials and Nanostructures he field of organic electronics has developed rapidly over the past decade from a stage of fundamental research to a business market that currently generates around 2.2 billion USD a year and is forecast to reach over 44 billion USD by 2021.1 In the context of an ever-growing investment in discovering new materials for organic light-emitting diodes, organic transistors, ultrahigh density logic memory, displays, and sensors, fundamental scientific research has had a leading role in uncovering the details of the forces that govern bonding, diffusion, and assembly of organic monolayers.2−8 Among the hundreds of organic molecules investigated for optoelectronic applications, thiophene-containing oligo- and polymers have acquired increasing prominence9,10 and are now widely employed in the fabrication of supramolecular organic electronic devices.11,12 Density functional theory (DFT) calculations are paramount in the quest for ever-improved, new organic materials, predicting the fundamental properties such as adsorbate mobility prior to the assembly of monolayers. Due to a lack of experimental data for atomic-scale processes on surfaces, however, many of these theoretical models remain largely unvalidated. The present work presents high-precision helium spin-echo (HeSE) measurements of submonolayer (ML) coverages of thiophene, an important precursor molecule, and uses them as a benchmark for state-of-the-art DFT calculations.

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© 2013 American Chemical Society

In previous studies, small aromatic molecules such as benzene, pyridine, and thiophene adsorbed on single-crystal metal surfaces were used as prototype systems for exploring electronic-level alignment and charge transfer at the metal− organic interface.3,13 Furthermore, thiophene adsorption has been studied to characterize the kinetics of catalytic desulfurization on a range of substrates, such as Au(111),14−18 Cu(111),19−25 Cu(100),26−30 Cu(110),31 and Pt(110),32 to mention only a few. A recurring theme in thiophene adsorption studies has been the molecular orientation on the surface. For example, a near-edge X-ray absorption fine structure (NEXAFS) study on Pt(111) showed a phase transition from a configuration with the ring tilted away from the surface by approximately 40° at temperatures below 180 K to a parallel-bonded geometry at higher temperatures.33 Similarly, Sexton observed a change from flat-lying to tilted adsorbates with increasing coverage of thiophene on Cu(100).29 A range of X-ray absorption studies by Imanishi et al.20 and Milligan et al.21−23 reported that thiophene bonds to atop sites on Cu(111) through the sulfur atom, with the molecular ring adopting an approximately flat-lying geometry at Received: March 22, 2013 Accepted: May 22, 2013 Published: May 22, 2013 1953

dx.doi.org/10.1021/jz400639c | J. Phys. Chem. Lett. 2013, 4, 1953−1958

The Journal of Physical Chemistry Letters

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very low coverages. With increasing coverage, Milligan et al. identified two phases where the molecular ring tilts away from the surface at 26 ± 5° and 44 ± 6°, respectively, which they termed α- and β-states.22 Previous DFT calculations of thiophene adsorption on the (110) and (111) surfaces of Cu confirmed that adsorption geometries of small tilt angle are most stable and emphasized the importance of including corrections for dispersion effects in DFT calculations.24,25,31 Here, rather than relying on structural information alone, we present a more critical investigation of the adsorbate dynamics to map out a detailed picture of the processes governing selfassembly and gauge the accuracy of DFT with dispersion force corrections in the case of molecular systems. HeSE spectroscopy probes surface dynamics on pico- to nanosecond time scales by scattering a polarized beam of helium-3 atoms off a surface.34−36 The wave packet of each atom is split into two components of opposite nuclear spin, which interrogate the surface at different times, t and t + tSE, and are then recombined after scattering from the surface. The outgoing wave packets differ as a result of surface motion occurring during the so-called spin-echo time, tSE, between the impact of the two spin components, giving a direct measure of surface correlations through the intermediate scattering function (ISF), which is related to the van Hove pair correlation function by a Fourier transform.37 The measured ISFs for thiophene/Cu(111) appear as an approximately single exponential, of the form a exp(−αtSE) + c. We study the decay rate, α, as a function of momentum transfer, ΔK, coverage, and temperature and interpret our results with the aid of Langevin molecular dynamics (MD) simulations (see the Methods section).37 To investigate the motion of thiophene/Cu(111) in the lowcoverage α-state identified by Milligan et al.,22 we performed HeSE measurements for two different coverages in this regime, 0.015 ML and 0.022 ML, where we define a ML as one adsorbate molecule per substrate atom. Looking first at the temperature dependence of the decay rate, α, shown in Figure 1, we observe two competing activated processes. The abrupt change of gradient at approximately 145 K suggests that α is dominated by one process at low temperatures and by another, more strongly activated one at higher temperatures. The rate of the process with the higher activation barrier increases more rapidly, and the relative process rates thus become dominated by this process at higher temperatures, causing the sharp transition in the curve. At T < 145 K, an apparent activation energy, Ea, of 19 ± 2 meV at 0.015 ML and 21 ± 2 meV at 0.022 ML is observed, while at higher temperatures, Ea is 59 ± 2 meV and 62 ± 4 meV at the respective coverages. Similar behavior has been reported in a related adsorbate system, ethanethiolate on Cu(111), by Paterson et al.,38 where jump diffusion between atop sites was observed at high temperatures, while a more weakly activated process was attributed to rotation of the alkane tail group around the sulfur−copper anchor point at lower temperatures. Comparing the experimental activation barriers with our results from DFT calculations including van der Waals corrections (see the Methods section), we confirm jump diffusion and rotation as the two major competing surface dynamic processes seen experimentally. DFT predicts that thiophene adsorbs preferentially with the sulfur atom approximately on top of a copper atom, in agreement with the literature,22 and the ring over an fcc site. We find a predicted barrier for translational jumps between adjacent atop

Figure 1. Temperature-dependent measurements of the dynamics of thiophene/Cu(111) at 0.7 Å−1 along ⟨112̅⟩ reveal two competing activated processes. The gradient gives an apparent activation barrier for rotation of 19 ± 2 meV at 0.015 ML (green) and 21 ± 2 meV at 0.022 ML (orange), while jump diffusion is more strongly activated with Ea = 59 ± 2 meV at 0.015 ML (blue) and Ea = 62 ± 4 meV at 0.022 ML (red).

sites of 94 meV for the sulfur atom moving through a hcp site and 87 meV through an fcc site (see the Supporting Information), giving a slightly higher diffusion barrier than the experimentally determined one of 59−62 meV, but of similar magnitude. By calculating the adsorption energy for different orientations of the molecular ring while the sulfur atom is anchored to a copper atom, we find a rotational barrier of 29 meV (see the Supporting Information), which is on the same order as the experimental barrier to rotation of 17 ± 2 meV obtained by fitting the Arrhenius plot with the analytical models (see the Methods section). Table 1 summarizes the experimental and calculated activation energies. Table 1. Experimental and Calculated Activation Energies for the Different Types of Dynamics Ea [meV]

jumping

rotating

flapping

HeSE experiments DFT calculations

59−62 87−94

17 ± 2 29

11 ± 2 68

To study the two processes in more detail, we performed HeSE measurements at 160 K and 110 K, in the high- and lowtemperature regimes observed in the Arrhenius curve, respectively. Figure 2 shows the measured momentum transfer dependence, α(ΔK), at 160 K along ⟨110̅ ⟩ and ⟨112⟩̅ for coverages of (a) 0.015 ML and (b) 0.022 ML. We observe a periodic shape with a minimum at the first diffraction condition of the substrate, 2.84 Å−1 along ⟨112̅⟩. Such sinusoidal curves are indicative of jumping on a Bravais lattice39 and consistent with center-of-mass diffusion between atop sites. With increasing coverage, two changes are apparent. First, a peak and dip feature at ΔK < 0.5 Å−1 grows in intensity and moves to higher ΔK with increasing coverage (see inset), which is indicative of repulsive inter-adsorbate interactions.40 Due to these interactions, the thiophene molecules thus do not form islands but rather move as isolated species across the large 1954



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dominated by single jumps between adjacent sites, in agreement with the previous observation that the friction of molecular adsorbates is systematically higher than that of atomic adsorbate species.8,43,44 Having found good agreement between experiment and theory in the low-coverage α-state, we extended our measurements into a higher-coverage region where molecules of different tilt angles, that is, in the α- and β-states reported by Milligan et al., coexist.22 As the surface at 160 K saturates before reaching the β-state, we lower the sample temperature to 140 K (putting us near the kink in the Arrhenius plot) and select a coverage of ∼0.1 ML. Figure 3a shows the resulting

Figure 2. α(ΔK) curves for thiophene/Cu(111) along the two main azimuths. (a,b) Data at 160 K for coverages of 0.015 ML (blue dots) and 0.022 ML (red dots) and results from MD simulations (solid lines). (Inset) A peak and dip feature at small ΔK grows with coverage, with the dips marked by arrows. (c) Comparison of measurements at 110 K (green dots) with the effective rate, α, from an analytical model for jump rotation (see the Methods section), shown as a solid line. A deviation from the rotation signature along ⟨11̅0⟩ can be explained by the rate for jump diffusion (scaled from the data at 160 K using Arrhenius’s law, shown as a dashed line) exceeding the rate for rotation at ΔK > ∼1.7 Å−1 and the fitting picking up a combination of both.

terraces of the copper surface (see the Methods section). Second, the magnitude of the α(ΔK) curve increases with coverage, suggesting a coverage-dependent jump rate. We confirm an approximately linear variation of α with coverage by monitoring the jump rate at ΔK = 0.7 Å−1 during the dosing process (not shown). Repeating the 0.015 ML experiments at 110 K, we observe a distinctly different α(ΔK) dependence, shown in Figure 2c. At low ΔK, the curves are largely consistent with the shape predicted for activated rotation on a six-fold lattice, shown as solid lines, corresponding to the ring swinging between adjacent hollow sites over a barrier on bridge sites. We find a systematic deviation from the rotation curve at ΔK > ∼1.7 Å−1 along the ⟨11̅0⟩ direction, attributable to mixing of rotation with jump diffusion in this region, which can be illustrated by scaling the jump diffusion curve measured at 160 K using Arrhenius’s law (dashed line). DFT calculations of the dipole moment, p, of thiophene/ Cu(111) give p = 1.63 D for a coverage of 0.08 ML (corresponding to a (2√3 × 2√3)R30° structure) and p = 0.97 D for 0.14 ML or a (√7 × √7)R19.1° structure. Using the Topping model,41 we relate these values to a polarizability, αp, of 74 Å3 and a zero-coverage dipole moment, p0, of 3.5 D. In Langevin MD simulations,37 we model jump diffusion over a potential energy surface (PES) for adsorption on top sites, describing dipolar interactions by αp and p0. We obtain a good overall description of the experimental data, shown as solid lines in Figure 2a and b, and find a friction coefficient, describing the rate of energy transfer between adsorbate and substrate, of η = 5 ± 2 ps−1. Such an exceptionally high friction42 implies that a frequent energy exchange limits the possible jump distance, resulting in adsorbate trajectories

Figure 3. HeSE measurements of ∼0.1 ML thiophene/Cu(111) in the high-coverage β-state. (a) α(ΔK) curve along the ⟨112̅⟩ azimuth at 140 K with a constant nonzero decay rate at low ΔK values. (b) Arrhenius measurements at 0.05 Å−1 (cyan) and 0.7 Å−1 (black).

α(ΔK) curve, exhibiting a shape intermediate between the lowand high-temperature curves shown in Figure 2a and c, indicating that both translational and rotational motion are measured simultaneously at this temperature. More importantly, however, the decay rate does not tend to zero for small ΔK but rather levels off at α ≈ 0.005 ps−1. Such behavior is characteristic for confined diffusion perpendicular or parallel to the surface, such as frustrated perpendicular motion or rotation.36 In order to study the process in more detail, we performed temperature-dependent measurements at this coverage, comparing the activation barrier at the positions indicated 1955



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≥99.5%) was purified by repeated freeze−thaw cycles in high vacuum and dosed onto the sample at 160 K in a line-of-sight method positioning a dosing tube in front of the sample. The purity of the dosed species was confirmed in a quadrupole mass spectrometer and the coverage determined by relating the specular helium signal during uptake to the position of the de Gennes dips in Figure 2.48 Analytical models predict a single exponential for jump diffusion on a Bravais lattice39 and a sum of exponentials for activated rotational motion,38 which give a complex experimental lineshape when combined. However, we observe only small deviations from a single exponential in our experiments. For a similar system, Paterson et al. have demonstrated that a description of all processes by a single exponential is the most reliable approach to interpret such lineshapes;38 hence, we apply the same method here, analyzing all data by fitting a exp(−αtSE) + c to the data at tSE > 25 ps and extracting a single decay rate, α. At T > 145 K, α relates directly to the jump diffusion rate, and Ea can thus be extracted from the Arrhenius plot. In the low-temperature region, however, α gives an effective rate only, which we interpret by fitting the lineshapes predicted by analytical models38,49 with a single exponential to get a theoretical effective α. Using the rotation model 5(a) of ref 49, we describe thiophene by two equally weighted scattering centers, one above the anchored S atom and one above the rotating ring, which moves on a circle of radius r = 3.0 ± 0.2 Å by hopping between the six hollow sites around the S−Cu anchor point with a jump rate of β = 10 ± 3 ns−1 (see the Supporting Information). In order to account for a temperature dependence in the ratio of the different exponentials,49 we optimize the combined jump diffusion and rotation model to reproduce the Arrhenius results at T < 145 K, obtaining a barrier for rotation of Ea = 17 ± 2 meV. Detailed analysis of the jump diffusion was obtained by performing center-of-mass MD simulations, modeling the adsorbate motion in the classical Langevin equation.37 A PES for jump diffusion between atop sites with a 75 ± 3 meV barrier was created using the appropriate Fourier components, employing the method described in refs 37 and 47. The simulated ISFs were analyzed with the same method as the experimental data. In the theoretical part of this study, all energies were calculated using CASTEP, a plane wave periodic boundary condition density functional theory code.50 As in recent works,8,43 we employed the Perdew Burke Ernzerhof51 exchange−correlation functional with a kinetic energy cutoff for the plane wave basis of 300 eV. The electronic energy tolerance of our calculations was 10−6 eV, and the force tolerance for structural calculations was 0.05 eV/Å. The Brillouin zone was sampled with a (4 × 4 × 1) k-point grid. The Cu(111) surface was modeled by a seven-atomic-layers slab in which the atoms on the bottom three layers were frozen. We employed the dispersion force correction method introduced by Tkatchenko and Scheffler (TS method)52 and implemented by McNellis et al.,53 in which the C6 interatomic coefficients are calculated directly from the electron density of the system. We recently tested the combination of DFT and TS vdW corrections on the pyrrole/Cu(111) system, obtaining good agreement between HeSE experiments and the diffusion barrier calculated by DFT. 43 In the same work, we demonstrated the importance of including the zero-point energies (ZPE) in DFT calculations of molecular adsorbate systems.43 As these calculations are computationally expensive,

in Figure 3b, in the low (dashed line) and high (dash−dotted line) momentum transfer regions. Due to the difficulty in separating jump diffusion and rotation at this temperature, the activation energy at 0.7 Å−1 falls in between that observed for the two processes in the low-coverage measurements (cf. Figure 1). At 0.05 Å−1, however, an activation energy of 11 ± 2 meV is evident, which is lower than either barrier observed in the αstate, thus indicating that it is not due to a “mixing” effect. If the constant decay rate at small ΔK was due to rotation, one would expect the activation energy to match that found for rotational motion; if it was due to a process coupled to jump diffusion, on the other hand, the activation energy at small ΔK should be equal to that for jump diffusion. We can therefore conclude that a third process occurring on similar time scales is present (see the Supporting Information). We propose that this process corresponds to a flapping of the molecular ring between states of different tilt angles, that is, the α- and β-states observed by Milligan et al., which is only weakly activated due to the large distance between the ring and substrate in the tilted configuration. Indeed, DFT calculations of adsorption geometries with different tilt angles between the molecular plane and surface confirm this idea, showing two local minima at 4° and 23° and a 68 meV barrier in between (see the Supporting Information). In conclusion, we have provided a complete experimental investigation of the motion of thiophene/Cu(111) and have compared the results with state-of-the-art DFT calculations. We observe a wide range of aperiodic adsorbate dynamics, including jump diffusion between adjacent atop sites, rotation around a sulfur−copper anchor, and a flapping of the molecular ringwhich has previously only been observed in unbound molecules 45as well as an exceptionally high friction coefficient and lateral adsorbate interactions, demonstrating the remarkable range of dynamical phenomena at a molecular level that can be identified simultaneously using the HeSE technique. We have used each of these results as a benchmark for DFT calculations with dispersion force corrections and found good general agreement across the observed dynamics. Our work demonstrates that state-of-the-art DFT calculations identify all dynamical processes accurately and give remarkably good agreement of experiment and calculations in the ratio between the energy barriers for translational and rotational motion. The small discrepancy in the absolute values and the overestimate of the barrier for ring flapping can most likely be attributed to the predominantly covalent character of the adsorbate−substrate interactions, resulting in a strong directional bond, thus increasing the uncertainty of the DFT results. Overall, our work validates these theoretical calculations as a powerful tool for predicting and interpreting adsorbate motion.

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METHODS All experiments were performed using the Cambridge HeSE spectrometer, which is described in detail elsewhere,34,35 with a beam energy of 8.2−8.3 meV. A single-crystal Cu(111) sample (Surface Preparation Laboratory, The Netherlands) was mounted in a vacuum chamber with a background pressure of 5 × 10−11 mbar and cleaned by Ar+ sputtering (800 eV, 10 μA, 300 K) and annealing to 800 K for 30 s. Surface cleanliness was confirmed using the specular helium reflectivity, which was greater than 37%. At such a high reflectivity, the crystal surface exhibits large terraces, thus minimizing step edge effects.46 Azimuthal alignment was obtained using the known diffraction pattern of a CO overlayer.47 Thiophene (Fluka, puriss. 1956



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(10) Dang, M. T.; Hirsch, L.; Wantz, G. P3HT:PCBM, Best Seller in Polymer Photovoltaic Research. Adv. Mater. 2011, 23, 3597−3602. (11) Mishra, A.; Ma, C. Q.; Baeuerle, P. Functional Oligothiophenes: Molecular Design for Multidimensional Nanoarchitectures and Their Applications. Chem. Rev. 2009, 109, 1141−1276. (12) Nogueira, A. F.; Lomba, B. S.; Soto-Oviedo, M. A.; Correia, C. R. D.; Corio, P.; Furtado, C. A.; Hümmelgen, I. A. Polymer Solar Cells Using Single-Wall Carbon Nanotubes Modified with Thiophene Pedant Groups. J. Phys. Chem. C 2007, 111, 18431−18438. (13) Witte, G.; Lukas, S.; Bagus, P. S.; Wöll, C. Vacuum Level Alignment at Organic/Metal Junctions: “Cushion” Effect and the Interface Dipole. Appl. Phys. Lett. 2005, 87, 263502−263502. (14) Zhou, J.; Yang, Y.; Liu, P.; Camillone, N., III; White, M. Electronic Structure of the Thiophene/Au(111) Interface Probed by Two-Photon Photoemission. J. Phys. Chem. C 2010, 114, 13670− 13677. (15) Ito, E.; Noh, J.; Hara, M. Adsorption States and Thermal Desorption Behaviors of Thiophene Derivative Self-Assembled Monolayers on Au(111). Surf. Sci. 2008, 602, 3291−3296. (16) Dishner, M. H.; Hemminger, J. C.; Feher, F. J. Formation of a Self-Assembled Monolayer by Adsorption of Thiophene on Au(111) and Its Photooxidation. Langmuir 1996, 12, 6176−6178. (17) Nambu, A.; Kondoh, H.; Nakai, I.; Amemiya, K.; Ohta, T. Film Growth and X-ray Induced Chemical Reactions of Thiophene Adsorbed on Au(111). Surf. Sci. 2003, 530, 101−110. (18) Liu, G.; Rodriguez, J. A.; Dvorak, J.; Hrbek, J.; Jirsak, T. Chemistry of Sulfur-Containing Molecules on Au(111): Thiophene, Sulfur Dioxide, and Methanethiol Adsorption. Surf. Sci. 2002, 505, 295−307. (19) Richardson, N. V.; Campuzano, J. C. The Adsorption of Thiophene on a Cu(111) Surface. Vacuum 1981, 31, 449−451. (20) Imanishi, A.; Yokoyama, T.; Kitajima, Y.; Ohta, T. Structural and Electronic Properties of Adsorbed Thiophene on Cu(111) Studied by S K-Edge X-ray Absorption Spectroscopy. Bull. Chem. Soc. Jpn. 1998, 71, 831−835. (21) Milligan, P.; McNamarra, J.; Murphy, B.; Cowie, B. C. C.; Lennon, D.; Kadodwala, M. A NIXSW and NEXAFS Investigation of Thiophene on Cu(111). Surf. Sci. 1998, 412/413, 166−173. (22) Milligan, P. K.; Murphy, B.; Lennon, D.; Cowie, B. C. C.; Kadodwala, M. A Complete Structural Study of the Coverage Dependence of the Bonding of Thiophene on Cu(111). J. Phys. Chem. B 2001, 105, 140−148. (23) Milligan, P. K.; Murphy, B.; Lennon, D.; Cowie, B. C. C.; Kadodwala, M. Effects of Substituents on the Structure and Bonding of Thiophene on Cu(111). J. Phys. Chem. B 2001, 105, 5231−5237. (24) Tonigold, K.; Groß, A. Adsorption of Small Aromatic Molecules on the (111) Surfaces of Noble Metals: A Density Functional Theory Study with Semiempirical Corrections for Dispersion Effects. J. Chem. Phys. 2010, 132, 224701. (25) Callsen, M.; Atodiresei, N.; Caciuc, V.; Blügel, S. Semiempirical Van Der Waals Interactions Versus Ab Initio Nonlocal Correlation Effects in the Thiophene-Cu(111) System. Phys. Rev. B 2012, 86, 085439. (26) Imanishi, A.; Yagib, S.; Yokoyama, T.; Kitajima, Y.; Ohta, T. Structural and Electronic Properties of Adsorbed C4H4S on Cu(100) and Ni(100) Studied by S K-XAFS and S-1s XPS. J. Electron Spectrosc. Relat. Phenom. 1996, 80, 151−154. (27) Gaudioso, J.; Ho, W. Single-Molecule Vibrations, Conformational Changes, and Electronic Conductivity of Five-Membered Heterocycles. J. Am. Chem. Soc. 2001, 123, 10095−10098. (28) Rodriguez, J. A. The Adsorption of Pyrazine, Hydrogen Sulfide and Thiophene on Copper: A Quantum-Chemical Study. Surf. Sci. 1990, 234, 421−438. (29) Sexton, B. A. A Vibrational and TDS Study of the Adsorption of Pyrrole, Furan and Thiophene on Cu(100): Evidence for π-Bonded and Inclined Species. Surf. Sci. 1985, 163, 99−113. (30) Orita, H.; Itoh, N. Adsorption of Thiophene on Ni(100), Cu(100), and Pd(100) Surfaces: Ab Initio Periodic Density Functional Study. Surf. Sci. 2004, 550, 177−184.

the full results given here do not include ZPEs. However, we have validated the key activation barriers by repeating the calculations including ZPEs and found that the effect on the translational, rotational, and flapping activation energies is ≤3 meV and thus can be neglected in this particular system. All energy barriers that we report here were calculated by constrained relaxation and for a (2√3 × 2√3)R30° supercell, corresponding to a coverage of 0.08 ML. A more detailed account of the results is provided as Supporting Information.

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ASSOCIATED CONTENT

S Supporting Information *

(1) Signature of motion perpendicular to the surface in the amplitude of the decay rate. (2) Potential energy landscape from density functional theory calculations. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors are grateful to Suzanne Paterson for useful discussion of the rotation models and also wish to thank the EPSRC [EP/E004962/1 (H.H., J.E., W.A., A.P.J., B.A.J.L.) and EP/J01643/1 (M.S., S.J.J.)], the Austrian Academy of Sciences (B.A.J.L.), the NSF [CHE 1124879 (B.J.H.)], and the Royal Society (A.P.J.) for financial support. The University of Newcastle Special Studies Program is gratefully acknowledged for sabbatical funding (P.C.D.).

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REFERENCES

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Jumping, Rotating, and Flapping: The Atomic-Scale Motion of

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