aa r X i v : . [ c ond - m a t . m t r l - s c i ] S e p Unoccupied states of individual silver clusters and chains on Ag(111)
A. Sperl, J. Kr¨oger, ∗ N. N´eel, H. Jensen, and R. Berndt
Institut f¨ur Experimentelle und Angewandte Physik,Christian-Albrechts-Universit¨at zu Kiel, D-24098 Kiel, Germany
A. Franke and E. Pehlke
Institut f¨ur Theoretische Physik und Astrophysik,Christian-Albrechts-Universit¨at zu Kiel, D-24098 Kiel, Germany
Size-selected silver clusters on Ag(111) were fabricated with the tip of a scanning tunneling mi-croscope. Unoccupied electron resonances give rise to image contrast and spectral features whichshift toward the Fermi level with increasing cluster size. Linear assemblies exhibit higher resonanceenergies than equally sized compact assemblies. Density functional theory calculations reproducethe observed energies and enable an assignment of the resonances to hybridized atomic 5 s and 5 p orbitals with silver substrate states. PACS numbers: 68.37.Ef,68.47.De,73.20.At,73.22.-f,81.16.Ta
I. INTRODUCTION
Metal clusters at the nanometer scale which are sup-ported by surfaces or thin films are currently of signifi-cant interest. Transport properties, catalytic efficiency and selectivity, as well as magnetic response dependstrongly on the size of these assemblies. Moreover, un-derstanding the influence of the substrate on the elec-tronic structure of clusters is important for new cluster-based materials with tailored optical, catalytic, or mag-netic properties. To this end, clusters may be decoupledfrom a metal surface by introducing an oxide thin filmbetween the substrate and the deposited clusters. Confinement of electrons to a small region leads to theformation of a discrete spectrum of their eigenstates. Incondensed matter physics, spectroscopic studies of thediscrete spectrum of individual samples has been ratherdemanding owing to difficulties in preparing and address-ing suitable single particles. A major step forward wasachieved with micro-fabrication techniques used to en-gineer semiconductor quantum dots, the levels of whichcould be resolved in a low temperature range by single-electron tunneling spectroscopy. Metals, however, owingto Fermi wavelengths which are of the order of a fewtenths of a nanometer require extremely small particlesizes down to atomic-scale dimensions in order to renderquantization phenomena observable. These sizes can beroutinely obtained nowadays.
Besides the requiredsmall cluster sizes the fabrication of assemblies with anarrow size distribution is another challenging experi-mental task. Several approaches to this goal are known,for instance, the manipulation of thermodynamic param-eters which dictate a particular growth mode.
While lithography or etching-based fabrication are ex-ceptionally challenging techniques buffer-layer-assistedgrowth was shown to lead to particularly narrow sizedistributions of deposited clusters. The ”soft-landing”of mass-selected clusters requires a complex apparatus and faces the possibility of fragmentation, morphological changes and diversity. Early scanning tunneling microscopy (STM) imagingof gold and silver clusters was reported by Abraham etal. and Sattler. Pioneering scanning tunneling spec-troscopy studies of nanometer-sized clusters of gold and iron on GaAs(110) and of size-selected Si onAu(100) have been published already in 1989. For-mation of states in the GaAs band gap was observed inthe former cases while a variety of cluster images wereobtained in the latter case despite the deposition of size-selected clusters. An important step forward was an ex-periment reported in Ref. 26. Mass-selected clusters ofPt n and Pd n with 1 ≤ n ≤
15 on Ag(110) were investi-gated using photoelectron spectroscopy. The authors ob-served size-dependent d states at binding energies around2 eV below the Fermi energy. The line widths were ob-served to be size-dependent as well. From a comparisonwith total-energy calculations a chainlike shape of theclusters was inferred.An ideal experiment enables the control of cluster sizeand shape at the atomic scale. Therefore, atom manip-ulation with the tip of a scanning tunneling microscopewas applied in a variety of investigations, for instance,gold, manganese, iron, and cobalt dimers on NiAl(100), nickel dimers and chromium trimers on Au(111), cop-per chains on Cu(111), and manganese monomers totetramers on Ag(111). Quantum confinement of elec-tronic states to chains and islands was also revealed forhomogeneous metallic systems.
Here we report on studies of electronic properties ofsilver assemblies fabricated by single-atom manipulationon Ag(111) using the tip of a low-temperature scan-ning tunneling microscope. As key results we obtainthat unoccupied resonances exhibit energies whose ac-tual values depend on the size and the shape of theadatom clusters. In particular, linear and monatomicallywide chains exhibit higher resonance energies than theirequally sized compact counterparts. Moreover, confine-ment of the unoccupied resonance states to the linearassemblies is found. The energies of unoccupied reso-
FIG. 1: (Color online) STM images of silver monomer, dimer, trimer, tetramer, and pentamer (from left to right) together withsketches of the proposed atomic arrangements (dark and bright circles depict substrate atoms and adsorbed atoms, respectively).Sample voltage and tunneling current were V = 100 mV and I = 0 . . × . ,. . . ,Ag and3 nm × nances of monomers, dimers, and a long silver chain arein agreement with density functional theory calculations. II. EXPERIMENT
Measurements were performed with a custom-builtscanning tunneling microscope operated in ultrahigh vac-uum at a base pressure of 10 − Pa and at 7 K. TheAg(111) surface and chemically etched tungsten tips werecleaned by argon ion bombardment and annealing. Indi-vidual silver atoms were deposited onto the sample sur-face by controlled tip-surface contacts as previously de-scribed in Ref. 38. Clusters with sizes ranging from one toeight atoms were fabricated by tip-induced movements.For tunneling resistances of ≈ Ω, dragging of sin-gle silver atoms was feasible. Coalescence of adsorbedatoms (adatoms) to dimers up to octamers was accom-plished by moving single adatoms close enough to thecoalescence partner ( ≈ one nearest-neighbor distance).We notice a propensity of silver adatoms to coalesce into compact assemblies rather than into linear clusters. Forinstance, adding an adatom to an already existing dimerin most of the cases resulted in a compact trimer ratherthan in a three-adatom chain. Silver chains containingmore than 100 atoms were prepared by moving the tiptoward the surface by 3 to 5 nm. Various surface dislo-cations were observed to result from this procedure. Inparticular, extraordinarily long and monatomically widechains were found several hundreds of nanometers apartfrom the indentation area. Spectra of the differentialconductance (d I/ d V ) were acquired by superimposinga sinusoidal voltage signal (root-mean-square amplitude1 mV, frequency 10 kHz) onto the tunneling voltage andby measuring the current response with a lock-in ampli-fier. Prior to and in between spectroscopy of the clustersthe tip status was monitored by giving a sharp onset ofthe Ag(111) surface state band edge in spectra of d I/ d V .To obtain sharp onsets of the d I/ d V signal for the sur-face state and to image single adatoms with nearly circu-lar circumference the tip was controllably indented intothe substrate. Due to this in vacuo treatment of the tipwe expect the tip apex to be covered with substrate ma-terial. All STM images were acquired in the constantcurrent mode with the voltage applied to the sample. III. THEORY
The total energy of the electronic groundstate andthe Kohn-Sham eigenenergies have been calculatedfor the silver monomer and dimer configurations onAg(111) using the Vienna ab initio simulation pack-age (VASP).
Moreover, the Ag chain on Ag(111)has been calculated using the total energy packageFHI96MD. Both program packages are based on den-sity functional theory with the generalized gradient ap-proximation (GGA) (monomer, dimer: PW91 ; chain:PBE ) applied to the exchange correlation functional.These GGAs are expected to yield comparable results.For the monomer and dimer configuration the electron-ion interaction is treated within the framework ofBloechl’s projector augmented wave method (PAW). For the calculation of the Ag chain a Troullier-Martinspseudopotential has been generated with the FHI98PP program. The monomer and dimer configurations havebeen modeled in a slab geometry comprising 14 layers ofsilver and a (4 ×
4) or (5 ×
4) surface unit cell, respectively.For the chain configuration the slab geometry consistedof 14 silver layers and a (9 ×
1) surface unit cell. Per-pendicular to the surface the periodically repeated silverslabs are separated by a vacuum region of approximately1 . k points using meshes consisting of 16, 9 and 6 k points in thecomplete first Brillouin zone for the monomer, dimer andchain, respectively. The local density of states (LDOS)has been calculated using the latter k point meshes incase of the monomer and dimer. Additionally, to ac-curately sample the dispersion of the unoccupied stateclose to the lower one-dimensional band edge, a meshof 144 special k points in the first Brillouin zone hasbeen used for the Ag chain. The Kohn-Sham wave func-tions at these additional k points have been calculated viaso-called bandstructure runs, which are carried out at afrozen electron density from a previous self-consistent re-laxation. The densities of states have been convolutedwith a Lorentzian with a full width at half maximum of150 meV. Convergence tests for the silver monomer us-ing an 8 layer slab show that upon increasing the cutoffenergy to 300 eV the calculated Kohn-Sham eigenener-gies change by less than 15 meV. Increasing the number TABLE I: Apparent heights and full widths at half maximum(FWHM) of silver clusters extracted from cross-sectional pro-files of STM images. The FWHM refers to the longest lateraldimension of linear assemblies.cluster height (nm) FWHM (nm)Ag .
06 1 . .
08 1 . .
10 1 . .
10 1 . .
10 2 . .
10 2 . .
10 2 . .
10 3 . of k points for the dimer calculation to 16 leads to achange in the Kohn-Sham eigenenergies at ¯Γ of less than10 meV (in a test calculation for an 8 layer slab). Usingthe normconserving pseudopotential and the PBE-GGAfor exchange and correlation, the equilibrium lattice con-stant of silver is calculated to be 0 .
419 nm. The resultis very similar (0 .
417 nm) when the PAW pseudopoten-tial is used together with the PW91-GGA for exchangeand correlation. These values are slightly larger thanthe experimental lattice constant of 0 .
409 nm, but theslight overestimate is consistent with other density func-tional calculations, e. g. , for noble metals using GGAfunctionals. The slabs were set up using the respec-tive theoretical lattice constants. The silver atoms ofthe outermost three layers on both sides of the slab aswell as the adatoms were allowed to relax without con-straints until the residual forces per atom were smallerthan 7 × − Hartree/Bohr. The remaining layers of theslab were kept fixed at their ideal bulk positions. Forthe calculation of the monomer, one silver adatom is re-laxed above the face-centered cubic (fcc) hollow site onboth sides of the slab, corresponding to a coverage of oneadatom per 16 surface atoms. For the dimer calculationtwo silver adatoms are relaxed above adjacent fcc hollowsites on both sides of the slab, corresponding to a cover-age of one dimer per 20 surface atoms. The chain geom-etry consists of silver atoms adsorbed at next-neighborfcc hollow sites in the direction of the chain.
IV. RESULTS AND DISCUSSIONA. Compact and linear silver clusters: frommonomer to octamer
Individual clusters with an exactly known number ofatoms were fabricated by single atom manipulation. Theresults are presented in Fig. 1. Compact as well as linearassemblies were produced up to sizes of five and eight,respectively (Fig. 1 shows clusters containing five atomsat maximum). We assume that individual silver adatoms d I/ d V / I/ V Sample Voltage (V) Ag n Ag Ag Ag Ag Ag Ag(111)
FIG. 2: Normalized spectra of d I/ d V acquired on cleanAg(111), monomers (Ag ), dimers (Ag ), trimers (Ag ),tetramers (Ag ), and pentamers (Ag ). A compact silver as-sembly (Ag n ) with probably n ≈
10 was also analysed. Thetunneling gap for the spectra was set at 1 nA and 3 . ,Ag ), 3 . ), 2 . , Ag , Ag n ). Spectra of Ag n ( n ≥
1) are vertically offset for clarity. The dashed lines in-dicate the respective zero of the spectra. occupy the threefold coordinated fcc hollow sites of theAg(111) lattice. Table I compares apparent heights andfull widths at half maximum (FWHM) of linear assem-blies with sizes ranging from a monomer to an octamer.Cross-sectional profiles of STM images were evaluatedto this end. Per additional silver atom the length ofthe chains increases by 0 .
28 nm on an average, which isin good agreement with the nearest-neighbor distance ofAg(111). Starting from the trimer the apparent height is0 .
10 nm for all subsequent silver assemblies.In Ref. 50 copper clusters on Cu(111) were investigatedat 5 K and the Cu assembly exhibited a nearly circularshape in STM images. This observation was attributedto intracell diffusion, i. e. , the dimer diffuses within a cellof adjacent hexagonal close-packed and fcc sites centeredaround an on-top site. In our case, however, the silver FIG. 3: (Color online) Contour plots of the absolute squareof the Kohn-Sham wave function at ¯Γ for the silver monomer(a) and the silver chain (b). The corresponding Kohn-Shameigenenergies relative to the Fermi level are 2 .
66 eV for theAg monomer and 1 .
37 eV for the Ag chain. dimer on Ag(111) exhibits different dimensions along aclose-packed direction ( ≈ .
28 nm) and perpendicular toit ( ≈ .
06 nm). We therefore conclude that intracell diffu-sion of a silver dimer adsorbed on Ag(111) plays a minorrole.Next we focus on unoccupied electronic states of thesilver assemblies. Figure 2 shows a series of normalizedd I/ d V spectra acquired with the tip positioned abovethe center of compact clusters. The tunneling gap forspectroscopy was stabilized at 1 nA and 3 . ,Ag , 3 . , and 2 . , Ag , Ag n . Dueto different tip-cluster distances for the various spectrawe normalized the d I/ d V data sets by the conductance I/V according to Refs. 51,52,53. The spectrum of cleanAg(111) is featureless up to ≈ . Thus, Ag(111) is a suitable substrate forobserving unoccupied electronic states of clusters in therange of 0 to ≈ . I/ d V spectrum of a sin-gle Ag adatom exhibits a pronounced peak slightly below3 eV. By performing spectroscopy in the vicinity of andon the single atom we found that the monomer resonanceshows a spatial extension comparable to the size of theatom in STM images. These results suggest that thesilver monomer exhibits a quasiatomic resonance. Thisinterpretation is in accordance with observations for sin-gle Au atoms on NiAl(110) and for Pd monomers onAl O layers. Thus, the enhanced normalized differen-tial conductance can be attributed to resonant tunnelinginto an empty state of the Ag atom. Indeed, our calcula-tions reveal that this state is of sp character arising fromthe hybridizaton of atomic Ag 5 p z orbitals with 5 s ad-mixtures localized at the adsorbate and silver substratestates. A typical wave function is shown in Fig. 3a.Spectra acquired on compact as well as linear clusterscontaining a higher number of atoms likewise exhibit aresonance whose energy shifts to lower values with in-creasing cluster size. Figure 4a summarizes the resonanceenergies for compact (triangles) and linear (circles) silver E ne r g y ( e V ) E ne r g y ( e V ) Number of Atoms linear compact ab FIG. 4: Energies of unoccupied resonances as a function ofcluster size. Resonance energies for compact (triangles) andlinear (circles) assemblies are presented. (a) Experimentalvalues. Error margins for the energies ( ≈ ± .
05 eV) arethe standard deviation resulting from a statistical analysisof spectra of a variety of clusters. (b) Theoretical values fromthe tight-binding model described in the text (open circlesand triangles), compared to ab inito
Kohn-Sham eigenener-gies (filled circles). The dashed line denotes the lower bandedge of the dispersion of the chain states as obtained fromdensity functional calculations. For each geometry the lowesttight-binding eigenenergy is given. The island configurationsrefer to those displayed in Fig. 1. The compact islands enfoldthe trimer, the tetramer, and the pentamer. clusters of different sizes. The spectra were acquired atopthe center of the assemblies. The resonance energies forcompact clusters are lower than those for their equallysized linear counterparts. This observation is in agree-ment with our experience that in the course of atomicmanipulation the silver adatoms exhibited the propen-sity to form compact rather than linear clusters. There-fore, compact clusters seem to be more stable reflectingthe lower energy of their resonance. From Fig. 4a we fur-ther infer that for both cluster types the change of theresonance energy becomes less pronounced with increas-ing cluster size. For instance, the energy of the compactpentamer resonance is at ≈ . n ( n ≈
10) inFig. 2. Lagoute et al. showed for Cu adatom islandson Cu(111) an evolution of quasiatomic resonances to FIG. 5: (Color online) d I/ d V spectra acquired at indicated(1, 2,. . . ,8) positions of a linear pentamer. Inset: STM imageof linear pentamer showing the positions at which spectrawere taken. the two-dimensional Shockley-type surface state. In thisstudy triangular Cu adatoms islands containing up to 15atoms were investigated. In our case, an extrapolation ofthe energy data does not give the binding energy of theAg(111) surface state which is at ≈ −
70 meV. We pro-pose that this result is due to the shape of our clusterswhich is triangular only for the compact trimer. We willsee in the following paragraph that a long silver chainexhibits an unoccupied resonance whose energy is wellabove the Fermi level.
B. Monatomically wide silver chains
One-dimensional metal chains may exhibit interestingproperties among which the Peierls distortion is proba-bly most famous.
This effect describes a modificationof the spatial periodicity of the chain upon forming anenergy gap around the Fermi level. In other words, theone-dimensional system gains energy by performing me-chanical work for lattice deformation and by lowering its d I/ d V / I/ V Sample Voltage (V)
FIG. 6: Normalized spectrum of d I/ d V at the center of a ≈
45 nm long and monatomically wide silver chain. electronic energy. For one-dimensional silver chains dis-cussed here, however, no changes in the geometric struc-ture were observed. The adsorption of silver atoms onAg(111) leads to a hybridization of adatom orbitals withsubstrate electronic states and to resonances whose ener-gies are far from the Fermi level (see Figs. 4 – 6). Conse-quently, small deviations in the chain geometric structureare not likely to modify the electron occupation of theresonance and therefore are ineffective in reducing thetotal energy of the silver chain. Nevertheless, a differentcombination of substrate and adatom material may leadto resonances close to the Fermi level and therefore mayfavor a Peierls transition.Below we focus on electronic properties of monatomi-cally wide silver chains. Figure 5 shows spatially resolvedd I/ d V spectra acquired at different sites on a linear pen-tamer (see inset of Fig. 5). The d I/ d V spectrum takenatop the center of the assembly exhibits a single peak at ≈ . ≈ . ≈ . ≈ . ≈ . and for Cu chains on Cu(111). How does the confinement evolve for chains containingan extremely high number of atoms? Starting from thelinear octamer it became difficult to resolve confinement-related peaks in d I/ d V spectra, which may be related tooverlap of neighboring peaks. Nevertheless, confinementwas evidenced by localization of density of states at theends of an extremely long chain, to be discussed next. d I / d V ( a r b . un i t s ) Lateral Distance (nm) A ppa r en t H e i gh t ( n m ) Sample Voltage (V) F W H M ( n m ) Sample Voltage (V) abc
FIG. 7: (Color online) (a) Cross-sectional profile in a map ofd I/ d V along the middle axis of the chain showing the increaseof the signal at the end of the chain at a lateral displacementof ≈ . The length of the chain is ≈
45 nm and follows a close-packed direction of the hosting Ag(111) lattice. Con-sequently, the number of silver atoms is approximately160. Figure 6 shows a normalized d I/ d V spectrum ofthe resonance in the middle of the chain. We extract anenergy of ≈ . ≈ . L D O S ( e V - Å - ) E - E F (eV) monomerdimerchain FIG. 8: (Color online) Calculated local density of states(LDOS) for (a) a silver monomer, (b) a silver dimer, and(c) an infinitely long silver chain on Ag(111). The LDOS hasbeen computed atop a silver adatom in case of the monomerand the chain, and atop the center of the silver dimer. Thepeaks are located at 2 . . . . compare Figs. 6 and 8).In addition to the unoccupied resonance, STM imagesand spatial maps of d I/ d V acquired at different volt-ages evidence confinement of the resonance within thechain. In Fig. 7a spatially resolved d I/ d V data acquiredalong the long symmetry axis of the chain at the indi-cated voltages are presented. Starting from a voltagewhich corresponds approximately to the resonance en-ergy the d I/ d V signal is piled up at the end of the chainwhose position is indicated by a dashed line in Fig. 7a).In Figs. 7b and 7c we show the evolution of the apparentheight and the width (FWHM) of the chain as a func-tion of the applied voltage. Both properties exhibit anincrease with increasing voltage. At sample voltages be-tween ≈ . ≈ . ≈ . TABLE II: Comparison of experimental (exp) and calculated(cal) energies ( E ) of unoccupied resonances.cluster E exp (eV) E cal (eV)monomer 2 . . . . . . . C. Theoretical results
To compare experimental resonance energies with cal-culated results, we evaluated the LDOS at a position of ≈ .
25 nm atop the adsorbed Ag atom for the monomerand the chain. For the dimer configuration the LDOSwas computed at approximately the same height atopthe center of the dimer. The results are presented inFig. 8. A similar LDOS for Cu chains on Cu(111) hasbeen calculated by Stepanyuk et al. In case of the monomer, a resonance predominantly de-rived from Ag sp z orbitals occurs at ≈ . p z bonding resonance at ≈ . p z antibonding resonance. The LDOS of the Ag chainis characterized by a one-dimensional band formed froman uncoccupied p z -like resonance as shown in Fig. 3b.The lower band edge of this one-dimensional band is lo-cated at ≈ . E F (as de-rived from the electronic eigenenergies at ¯Γ). A peakarises at around 1.5 – 1.6 eV. No upper band edge of theone-dimensional band was observed for energies belowthe work function of silver. Table II summarizes experi-mental and calculated resonance energies. Owing to theagreement between experiment and theory we interpretpeaks in the d I/ d V spectra as the signature of sp z - or p z -like Ag adsorbate resonances and their electronic in-teraction with silver substrate states.We did not perform ab initio calculations for silverclusters of sizes larger than two atoms due to the largecomputational costs arising from the increasing size of thesurface unit cell. However, we provide estimates for theelectronic eigenenergies of larger clusters by means of asimple tight-binding model. The purpose of this estimateis to explain the energy shifts observed by tunneling spec-troscopy semi-quantitatively. In our tight-binding ap-proach the substrate is not considered explicitly, i. e. , theislands are represented by free-standing two-dimensionalclusters. We include one Ag sp z orbital per atom. Thereare only two free tight-binding parameters: the orbitalenergy ε and the next-neighbor transfer matrix-element t , which accounts for the direct interaction between near-est neighbor Ag atoms and, implicitly, part of the interac-tion via the Ag substrate. All further interactions withrespect to more distant atoms are neglected, as is thevariation of the crystal-field energy shift of the orbitalenergy for different geometrical environments. As usual,orbital overlaps are not accounted for explicitly.The tight-binding parameters are consistently derivedfrom our DFT results, i. e. , the resonance energy of themonomer ε = 2 . . ε + 6 t = +0 .
05 eV (experimental value − .
07 eV) arereproduced by the tight-binding model. The quality ofthe tight-binding results can be estimated from compari-son with the DFT Kohn-Sham eigenenergies of the dimerand the chain shown in Fig. 4b. The lowest energy eigen-value is given for each configuration. For further evalua-tion of the quality of the tight-binding model we noticethat for the effective mass m ∗ of the surface state weobtain 0 . e (m e is the free electron mass) from tight-binding calculations to be compared with a DFT value of0 .
39 m e and an experimental value of (0 . ± .
02) m e . The effective mass of the sp z resonance at the one-dimensional Ag chain is 1 . e in our tight-binding ap-proach to be compared with a value of about 0 . e de-rived from the dispersion of the Kohn-Sham eigenenergiesclose to ¯Γ. Most probably, the overestimate of the effec-tive mass by a factor of two in both cases may be par-tially due to the fact that no parameter describing thecrystal-field energy shift is included in the tight-bindingHamilton operator giving rise to an inaccurate value ofthe transfer parameter.Nevertheless, the simple tight-binding approach pro-vides all qualitative trends for the cluster eigenenergies (see Fig. 4b). Compact clusters have lower eigenenergiesthan equally sized linear assemblies and the trimer ex-hibits a lowest electronic eigenenergy which is close tothe lower band-edge of the infinite chain. V. SUMMARY
Size-selected silver clusters were fabricated by tip-assisted single-atom manipulation on Ag(111). Unoc-cupied electronic resonances exhibit energies which arecharacteristic of size and shape of the silver assemblies.In particular, the resonances of linear clusters have higherenergies than the resonances of equally sized compactclusters. For both types of clusters the resonance energyshifts toward the Fermi energy with increasing clustersize. These observations are qualitatively in agreementwith a tight-binding model of the clusters. Calculationsbased on density functional theory model the energiesof monomers, dimers, and monatomically wide infinitelylong chains. The resonances are of sp character and arisefrom Ag 5 p z orbitals (with 5 s admixtures) which are lo-calized at the adsorbate atom and hybridize with silversubstrate states.Funding of this work by the Deutsche Forschungsge-meinschaft through grant number SPP 1153 is gratefullyacknowledged. ∗ Electronic address: [email protected] N. Nilius, T. M. Wallis, and W. Ho, Science , 1853(2002). S. Abbet, A. Sanchez, U. Heiz, W.-D. Schneider, A. M.Ferrari, G. Pacchioni, and N. R¨osch, J. Am. Chem. Soc. , 3453 (2000). S. Abbet, A. Sanchez, U. Heiz, and W.-D. Schneider, J.Catal. , 122 (2001). J. Bansmann, S. H. Baker, C. Binns, J. A. Blackman, J.-P. Bucher, J. Dorantes-D´avila, V. Dupuis, L. Favre, D.Kechrakos, A. Kleibert, K.-H. Meiwes-Broer, G. M. Pastor,A. Perez, O. Toulemonde, K. N. Trohidou, J. Touaillon,and Y. Xie, Surf. Sci. Rep. , 189 (2005). A. S. W¨orz, K. Judai, S. Abbet, J.-M. Antonietti, U. Heiz,A. Del Vitto, L. Giordano, and G. Pacchioni, Chem. Phys.Lett. , 2666 (2004). R. M. Jaeger, H. Kuhlenbeck, H.-J. Freund, M. Wuttig,W. Hoffmann, R. Franchy, and H. Ibach, Surf. Sci. ,235 (1991). U. Bardi, A. Atrei, and G. Rovida, Surf. Sci. , 87(1992). C. Becker, J. Kandler, H. Raaf, R. Linke, T. Pelster, M.Dr¨ager, M. Tanemura, and K. Wandelt, J. Vac. Sci. Tech-nol. A , 1000 (1998). M. B¨aumer and H.-J. Freund, Prog. Surf. Sci. , 127(1999). K. Hojrup Hansen, T. Worren, E. Lægsgaard, F. Besen-bacher, and I. Stensgaard, Surf. Sci. , 96 (2001). D. C. Ralph, C. T. Black, and M. Tinkham, Phys. Rev. Lett. , 3241 (1995). J. von Delft and D. C. Ralph, Phys. Rep. , 6 (2001). J. A. Venables, G. D. T. Spiller, and M. Hanbucken, Rep.Prog. Phys. , 399 (1984). M. Copel, M. C. Reuter, E. Kaxiras, and R. M. Tromp,Phys. Rev. Lett. , 632 (1989). R. Kunkel, B. Poelsema, L. K. Verheij, and G. Comsa,Phys. Rev. Lett. , 733 (1990). H. Brune, Surf. Sci. Rep. , 121 (1998). P. Moriarty, Rep. Prog. Phys. , 297 (2001). L. Huang, S. J. Chey, and J. H. Weaver, Phys. Rev. Lett. , 4095 (1998). K.-H. Meiwes-Broer,
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