Correlation of Vibrational Excitations and Electronic Structure\\ with Submolecular Resolution
Daniela Rolf, Friedrich Maass, Christian Lotze, Constantin Czekelius, Benjamin W. Heinrich, Petra Tegeder, Katharina J. Franke
CCorrelation of Vibrational Excitations and Electronic Structurewith Submolecular Resolution
Daniela Rolf, Friedrich Maaß, Christian Lotze, Constantin Czekelius, Benjamin W. Heinrich, Petra Tegeder, and Katharina J. Franke Fachbereich Physik, Freie Universit¨at Berlin, 14195 Berlin, Germany Physikalisch-Chemisches Institut, Universit¨at Heidelberg, 69120 Heidelberg, Germany Institut f¨ur Organische Chemie und Makromolekulare Chemie,Heinrich-Heine-Universit¨at D¨usseldorf, 40225 D¨usseldorf, Germany
The detection of vibrational excitations of individual molecules on surfaces by scanning tunnelingspectroscopy does not obey strict selection rules but rather propensity rules. The experimental ver-ification of these is challenging because it requires the independent variation of specific parameters,such as the electronic structure, while keeping the vibrational modes the same. Here, we make use ofthe versatile self-assembled structures of Fe-tetra-pyridyl-porphyrin molecules on a Au(111) surface.These exhibit different energy-level alignments of the frontier molecular orbitals, thus allowing thecorrelation of electronic structure and detection of vibrations. We identify up to seven vibrationalmodes in the tunneling spectra of the molecules in some of the arrangements, whereas we observenone in other structures. We find that the presence of vibrational excitations and their distributionalong the molecule correlates with the observation of energetically low-lying molecular states. Thiscorrelation allows to explain the different numbers of vibrational signatures for molecules embeddedwithin different structures as well as the bias asymmetry of the vibrational intensities within anindividual molecule. Our observations are in agreement with a resonant enhancement of vibrationsby the virtual excitation of electronic states.
INTRODUCTION
Since the seminal discovery of molecular excitations insingle molecules on surfaces by inelastic electron tunnel-ing spectroscopy (IETS) in a scanning tunneling micro-scope (STM) [1], various studies reported on the obser-vation of vibrational excitations of chemisorbed as wellas physisorbed molecules [2–10]. For some molecules, alarge set of vibrational excitations was observed, whereasothers did not show a single vibrational mode. Moreover,the resolution of vibrational excitations depended on thespecific substrate underneath the molecules [9]. Whileselection rules exist that predict the intensity of vibra-tional modes for optical spectroscopic techniques, such asRaman and infrared spectroscopy, there are no such uni-versal criteria in scanning tunneling spectroscopy (STS).Instead, a set of propensity rules has been proposed [11–13].Theoretical models suggested different mechanismsleading to vibrational excitations within the neutralmolecule, i.e. , at energies below a molecular ion reso-nance. The common requirement is that the energy ofthe tunneling electron exceeds the excitation energy ofthe vibration [14]. The first mechanism is an excitationvia impact scattering of the tunneling electron, whichis independent of existing molecular resonances [15, 16].The corresponding change of the differential conductance(d I/ d V ) is positive but typically very small [15], suchthat excitations by impact scattering are rarely detectedin spectroscopy. The second mechanism depends on theelectronic structure. Even for the case that the electronenergy falls below a molecular resonance, virtual excita- tions to low-lying molecular states enhance the excitationcross section of vibrations [4–6, 16–18]. Note, that thisregime is distinctly different from the resonant regime,in which the vibrational excitation occurs in the chargedstate, such that vibronic peaks would appear on top ofthe molecular resonance in the d I/ d V spectra [19, 20].Due to the limited lifetime of the vibronic states inmolecules on metal substrates, the vibronic peaks wouldjust contribute to an overall broadening of the electronicresonances. In the resonant regime, the observation ofvibronic peaks has been improved by an increase of thelifetime of the excited states by either ultrathin insulatinglayers [21, 22], layers of organic molecules [18] or bulkymolecular groups attached to the molecule, which wereemployed to decouple the molecule from the substrate[23].Off-resonance inelastic vibrational excitations are typ-ically not observed when the molecules lie on decou-pling layers, because the probability of virtual excita-tions is suppressed due to the up-shift of the molecularion resonances. It is therefore difficult to achieve opti-mum conditions for the observation of strong inelasticsignals. One notable example of achieving these condi-tions was reported by Ohta et al. on Fe-phthalocyaninebilayers on Ag(111) [24]. The authors also noted a pecu-liar difference in the observation of different vibrationalmodes in different adsorption configurations, which couldnot be explained within the currently available modelsand underlines the quest for a microscopic understand-ing of propensity rules. However, propensity rules alsoinclude the electronic structure of the molecule and thetip [10, 11, 25, 26] and the dipole moment of the modes a r X i v : . [ c ond - m a t . m e s - h a ll ] M a r [25]. The experimental verification of propensity rules ischallenging, because the variation of one of these param-eters is typically achieved by exchanging the molecule,which often entails a variation in several properties. Toavoid these complexities, previous studies compared theIETS signal of the same molecule on different surfaces[9], with different orientations [10, 27], or at different ad-sorption sites [28]. Despite all those studies, there is stillno comprehensive picture to date that allows to predictthe intensity of molecular vibrations in IETS. Therefore,a more detailed understanding is necessary.Our approach is to use a molecule that exhibits dif-ferent conformations on a surface. Thereby, the elec-tronic structure undergoes some variations while localvibrational modes, such as C–H- and C–C-stretching andbending modes are not expected to change much. Such asystem allows for a direct correlation of electronic struc-ture and vibrational excitation intensity. We use theflexible molecule Fe-5,10,15,20-tetra-4-pyridyl-porphyrin(FeTPyP) (shown in Fig. 1a) as a model system to inves-tigate the role of the electronic structure for the detec-tion of vibrations in tunneling spectroscopy within thesame species. The FeTPyP molecules consist of an Fecenter embedded in a porphyrin core with four pyridylmoieties [29, 30]. This molecule adapts different struc-tures in molecular assemblies, concomitant with a changein the energy-level alignments. Using STS, we find up tonine inelastic steps in some of the molecular structureswhile others are featureless. We identify seven of thesesteps as molecular vibrations whereas the other two cor-respond to spin excitations. We show that the intensityof vibrational excitations can be correlated to the energyof the frontier molecular orbitals in the different struc-tures. We explicitly show that an asymmetric electronicstructure around the Fermi level leads to an asymmetryin the vibrational excitation intensity when comparingpeaks at positive and negative bias voltage. METHODS
All experiments were performed under ultra-high vac-uum conditions with in-situ sample preparation in dif-ferent chambers. The clean Au(111) samples were pre-pared by subsequent cycles of sputtering and anneal-ing. The FeTPyP-Cl molecules were deposited from aKnudsen cell evaporator at 410 ◦ C onto a Au(111) sam-ple held at room temperature. During the deposition,the molecules are dechlorinated, such that the Fe-centerchanges its oxidation state from +3 to +2 [31–34]. TheSTM measurements were performed in two different low-temperature STMs, working at 1 . . I/ d V spec-tra were recorded in open feedback-loop conditions witha lock-in amplifier. HREELS measurements were per- d)c) top view pyridylgrouppyrrolegroup a) b) Figure 1. a) Schematic structure of the FeTPyP molecule,with the pyrrole groups marked in blue and the freely rotat-able pyridyl groups indicated in orange. Due to its flexibility,the molecules adapt a saddle-shape configuration upon ad-sorption. b-d) Different arrangements of FeTPyP on Au(111):b) Disordered structure of FeTPyP; c) Densely-packed struc-ture of FeTPyP; d) Staggered arrangement of FeTPyP withan alternating orientation of the molecules. In this arrange-ment, two types of molecules can be identified by their spec-tral properties. In all STM topographies, the saddle-shape de-formation of the molecules is apparent, as two pyrrole groupsof the molecules appear higher than the other two. The colorof the boxes around the images indicates the colors of thespectra in Fig. 2). Topographies recorded at 440 mV, 93 pA(b), 200 mV, 200 pA (c) and 230 mV, 160 pA (d). formed at 90 K at an incident electron energy of 3 . RESULTS AND DISCUSSION
Using scanning tunneling microscopy, we observe threedifferent structures of FeTPyP on Au(111). An STM to-pography of the first observed molecular arrangement atsub-monolayer coverage is shown in Fig. 1b. It reveals adisordered arrangement of the FeTPyP molecules withthe pyridyl moieties of neighboring molecules facing eachother. We speculate that atoms that were unintendedlyco-deposited during the evaporation act as bonding nodesto the electron-rich pyridyl endgroups. These appear flat-ter than typically observed in pure molecular structures.The rather flat pyridyl groups lead to an enhancementof the screening and hybridization of the molecule withthe substrate’s electronic states [36]. This is reflected inlow-lying molecular states (see below).In a different preparation, we find two densely-packedarrangements without any adatoms. In the first, themolecules are aligned in two alternating rows of paral-lel molecules (Fig. 1c). In the second structure (Fig. 1d),the molecules are ordered in a staggered arrangement,with their saddle orientation rotated by 90 ° with respectto the neighboring molecules. This structure containstwo different types of FeTPyP molecules, which exhibitdistinct spectroscopic properties. The saddle deforma-tion, which is observable in all structures, is a resultof molecule–substrate interactions [37]. These force thepyridyl groups from the perpendicular orientation withrespect to the porpyhrin plane into an inclined orienta-tion. As a consequence of steric hindrance between adja-cent hydrogen atoms in the pyrrole and pyridyl groups,two pyrrole groups bend up while the other pair is bentdown.To compare the properties of the FeTPyP moleculesin the different arrangements, d I/ d V spectra in the en-ergy range of ±
150 meV are shown in Fig. 2, which wererecorded both in the center and on the upper pyrrolegroup of the molecules. The color of the spectra corre-sponds to the color of the boxes around the respectivemolecular structures in Fig. 1. For comparison, a spec-trum of one of the metal-free TPyP molecules, which areoccasionally found on the surface, is shown as well. Itneither exhibits peaks nor steps. In the center of all Fe-containing molecules (Fig. 2a), an almost bias-symmetricshape on the scale of ±
150 meV can be observed. How-ever, upon closer inspection there are some differences.The red and green spectra exhibit a strong increase inconductance at ±
80 meV. At similar energies, the con-ductance increase in the black spectrum seems broader.The blue spectrum is almost featureless at negative biasvoltages and exhibits a shoulder at about 70 meV at pos-itive bias voltage. Additionally, all of these spectra showone or two steps at low bias voltages (see grey shadedarea), which are attributed to inelastic spin excitations[34]. Moreover, the green and red curve show a variety ofsteps at higher energies, whose position and relative in-tensities are independent of the employed Au tip. Thesehigher-lying steps are assigned to vibrational excitations.In Fig. 2b, we probe the presence/absence of steps onthe upper pyrrole groups of the molecules. While thelow-energy spin excitations are present in all moleculesalso on the ligand, the overall lineshapes of the d I/ d V spectra differ quite drastically between the molecules inthe different structures. The blue and the black spectrashow a rather flat d I/ d V curve at negative bias volt-ages, whereas the green and red spectra exhibit a broadshoulder at around −
84 mV. Moreover, only the red andgreen spectra exhibit some additional steps at positive bias voltages. These steps are followed by double-peakstructures at about 35 mV and 90 mV. In the black spec-trum these peaks appear shifted to higher energies, i.e. ,to 70 mV and 115 mV (see grey dashed line as guide tothe eye of the shift). The blue spectrum exhibits a singlepeak at 72 mV.To confirm the assignment of the higher-lying steps asvibrational excitations, we performed HREELS measure-ments. HREELS is a complementary method to iden-tify molecular vibrations by inelastic electron scattering[38, 39]. The incident electron energy (here 3 . . . I/ d V spectra as spin excitations.For better comparison of vibrational energies detectedby HREELS and IETS, we plot the d I/ d V spectra ofthe molecules in the green and red structure (Fig. 3b).The steps in the d I/ d V spectra correspond to peaks anddips in the d I/ d V signals at positive and negative biasvoltage, respectively. The dashed lines indicate the peakpositions of the vibrational modes as deduced from theHREEL spectrum. Besides the two lowest-energy peaksin the d I/ d V signal, which have been discussed above,we find similarities between the vibrational modes fromthe IETS and from the HREELS measurements.A more detailed comparison of the vibrational ener-gies is compiled in Tab. I. We note that there are differ-ences in the mode energies of a few meV between theHREELS data as well as between the staggered and dis-ordered structure probed by IETS. We suggest that thedifferent mode energies in IETS can be qualitatively un-derstood by the different molecular conformations. Thedeviation from the HREELS data is roughly of the samesize. However, HREELS is an ensemble method, suchthat an average energy both of several molecules and ofdifferent structures is determined, whereas d I/ d V spec- a) b) Figure 2. Comparison of the vibrational signatures a) in the center and b) on the ligand of FeTPyP molecules in the differentarrangements (compare to color of the boxes in Fig. 1). Overall, all FeTPyP molecules show bias-symmetric lineshapes in thecenter, and more asymmetric lineshapes on the ligand. The featureless gray spectrum corresponds to a non-metallated TPyPmolecule. Different numbers of steps can be observed in the spectra. The gray-shaded area indicates those steps that originatefrom spin excitations. Feedback opened at green: 150 mV, 3 nA with V mod = 1 mV, T = 4 . mod = 0 . B = 0 . T = 1 . mod = 1 mV, T = 4 . I/ d V signal of the staggered and the disorderedarrangements of FeTPyP, together with a general assignment of the modes by comparison to DFT calculations (b3pw91/genecp).All energies are given in meV. HREELS IETS (stagg.) IETS (disord.) Mode
16 24.4 21 (cid:27) buckling/breathing modes, Fe-tapping32 33.9 30.545 - -
C-C/C-H stretching and bending modes60 61.0 5470 - 6978 80.4 -88 - 90100 - -109 107 104122 - 115135 - -151 - - troscopy determines the vibrational energies of a specificmolecule. Moreover, the excitation mechanism of the twospectroscopic methods is different, which might accountfor further discrepancies in the spectra.To gain qualitative insights into the origin of the modesand of the deviations, we performed DFT calculations(see Methods) of isolated FeTPyP molecules with twodifferent dihedral angles (25 ° and 60 ° ), which mimic dif-ferent degrees of the saddle-shape distortion. Indeed, theenergies of the modes of these molecules differ. However,it is difficult to draw a one-to-one correspondence be-tween these modes and the experimentally observed ones. The calculations reveal more than 100 different modes inthe considered energy window. Therefore, we only cat-egorize the modes at low and high energies. The low-energy modes correspond to symmetric and asymmetricbuckling and stretching modes of the pyrrole groups, aswell as Fe tapping modes. Since these modes involve adeformation of the pyrrole groups and the Fe–N distancewithin the molecule, their energies are expected to de-pend on the exact conformation of the molecule on thesurface. At higher energies, the vibrational modes con-stitute in-plane and out-of-plane stretching and bend-ing modes of the C–H and C–C bonds. Similar vi- b)a) Electron Energy Loss [meV] I n t en s i t y [ - s - ] - no annealingannealed to 400 K x 200 I n t en s i t y [ s - ] Electron Energy Loss [meV]
16 32 45324560707888100 122135151 175 193 246 380109
Figure 3. Identification of molecular vibrations: a) HREELspectrum recorded with a primary electron energy of 3 . . . I/ d V spectra (greenand red) corresponding to the d I/ d V spectra of Fig. 2a andthe HREEL spectrum of the annealed sample (black). Thedashed lines indicate the positions of the vibrational modes asdetermined from the HREEL spectrum. The two lowest-lyingpeaks in the d I/ d V spectra, are assigned to spin excitations. brational modes at comparable energies were also ob-served on double-layer FePc molecules on Ag(111) [24],in agreement with similar intramolecular bonds in thesemolecules.In Fig. 2 we saw that the vibrational excitations wereonly resolved in the d I/ d V spectra of some of the molec-ular structures and with strong bias asymmetries. Tounderstand these variations, we first consider possibleeffects of the tunneling barrier and the tip’s electronicstructure. Small asymmetries of the signal intensities atopposite bias voltages might be explained by an asym-metry of the tunneling barrier [40]. However, barrier-induced differences in the signal intensity should occursimilarly at all positions across the molecule, which is incontrast to our experimental findings of almost symmet-ric intensities in the center. Moreover, the symmetry andelectronic structure of the tip was shown to affect the in-tensity of the vibrational fingerprints [25, 26]. However, as the measurements in the center of the molecule andon the ligand were all performed using the same tip, thiscannot explain the different inelastic signals.Instead, by comparison to the position of close-lyingresonances in the d I/ d V spectra, we find that the in-tensity of the vibrational modes across the molecules fol-lows the localization of the molecular electronic states.The overall symmetric shape of the d I/ d V spectra in thecenter of the molecules (Fig. 2a) suggests the presenceof occupied and unoccupied molecular states symmetri-cally around the Fermi level. In contrast, the energiesof molecular states on the ligand are asymmetric withbias polarity, as the spectra in Fig. 2b only reveal statesat positive bias voltages. The absence of features in thed I/ d V spectra around E F on the metal-free porphyrin(gray curve in Fig. 2a) indicates that the conductance inthe FeTPyP molecules mainly stems from Fe d states.This interpretation is supported by recent studies on Fe-tetra-phenyl-porphyrin (FeTPP) on Au(111) [41], whichshowed similar lineshapes. In that case, the density ofstates (DoS) around the Fermi level in the center of themolecule was assigned to the half-occupied d z orbital,which mostly interacts with the substrate. The resonanceat positive bias voltages on the upper pyrrole groups wasassigned to an empty hybrid state between the Fe d yz orbital and ligand states. Given the structural and spec-troscopic similarities between FeTPyP and FeTPP, thisassignment is probably also valid for our case.This electronic structure allows us to correlate the elec-tronic structure with the vibrational sensitivity. We firstanalyze the observations in the center of the molecules.In the absence of any molecular states close to E F , the ex-citation cross section of molecular vibrations is negligible.This is the case for the metal-free molecule. In contrast,the red and green spectrum show the largest increaseof conductance at ±
80 meV. The energetic proximity ofoccupied and unoccupied d states thus enhances the ex-citation cross section of the molecular vibrations at bothbias polarities. A broadening of these states as in theblack and blue spectrum largely suppresses the inelasticexcitation probability. On the ligand, the situation be-comes even more interesting. In this case, there are onlyunoccupied states close to E F , which stem from a differ-ent orbital than in the center. The presence of this stateenhances the vibrational excitations for the red and greenmolecule at positive bias voltages. This hybrid state isshifted away from E F in the blue and black spectra, suchthat the IETS intensity is below our experimental reso-lution. At negative bias voltages, none of the molecularspecies exhibits occupied states sufficiently close to E F .All observations thus agree with the picture of an en-hancement of the IETS signal by the presence of a low-energy molecular resonance. The lower the energy of thevirtual excitation of this resonance, the more probable isthis excitation. Therefore, also the cross section of theinelastic excitations increases. CONCLUSIONS
We resolved several molecular vibrations of FeTPyPon a Au(111) substrate by a combination of HREEL andd I/ d V spectroscopy. A comparison of different struc-tures of FeTPyP on a Au(111) substrate showed a varyingnumber of inelastic steps between 20 meV and 120 meVin the corresponding d I/ d V spectra, which were asso-ciated with excitations of molecular vibrations. Inter-estingly, the intensity of the inelastic steps varied be-tween the molecular structures and within the individ-ual molecules. The simultaneous resolution of molecularorbital energies suggests a correlation of the vibrationintensity with the proximity of the molecular orbital tothe Fermi level. This correlation immediately reflectsthe applicability of the resonant-enhancement model [17],which describes the vibrational excitation via virtual ex-citations of molecular resonances.Funding by the ERC Consolidator grant ”NanoSpin”(K. J. F.) and by the International Max Planck ResearchSchool ”Functional Interfaces in Physics and Chemistry”(D. R.) is gratefully acknowledged. F. M. and P. T. ac-knowledge funding by the German Research Foundation(DFG) through collaborative research center SFB1249”N-Heteropolycylces as Functional Materials” (projectB06). [1] B. C. Stipe, M. A. Rezaei, and W. Ho, Science , 1732(1998).[2] W. Ho, J. Chem. Phys. , 11033 (2002).[3] T. Komeda, Progr. Surf. Sci. , 41 (2005).[4] L. J. Lauhon and W. Ho, J. Phys. Chem. A , 2463(2000).[5] J. I. Pascual, J. J. Jackiw, Z. Song, P. S. Weiss, H. Con-rad, and H.-P. Rust, Phys. Rev. Lett. , 1050 (2001).[6] Y. Kim, T. Komeda, and M. Kawai, Phys. Rev. Lett. , 126104 (2002).[7] A. J. Heinrich, J. A. Gupta, C. P. Lutz, and D. M. Eigler,Science , 466 (2004).[8] N. Okabayashi, Y. Konda, and T. Komeda, Phys. Rev.Lett. , 217801 (2008).[9] K. J. Franke, G. Schulze, and J. I. Pascual, J. Phys.Chem. Lett. , 500 (2010).[10] S. Meierott, N. N´eel, and J. Kr¨oger, J. Phys. Chem. Lett. , 2388 (2016).[11] N. Lorente, M. Persson, L. J. Lauhon, and W. Ho, Phys.Rev. Lett. , 2593 (2001).[12] A. Troisi and M. A. Ratner, Nano Lett. , 1784 (2006).[13] M. Paulsson, T. Frederiksen, H. Ueba, N. Lorente, andM. Brandbyge, Phys. Rev. Lett. , 226604 (2008).[14] R. C. Jaklevic and J. Lambe, Phys. Rev. Lett. , 1139(1966).[15] N. Lorente and M. Persson, Phys. Rev. Lett. , 2997(2000).[16] N. Lorente, Appl. Phys. A , 799 (2004).[17] B. N. J. Persson and A. Baratoff, Phys. Rev. Lett. , 339 (1987).[18] K. J. Franke and J. I. Pascual, J. Phys.: Condens. Matter , 394002 (2012).[19] N. Liu, N. A. Pradhan, and W. Ho, J. Chem. Phys. ,11371 (2004).[20] T. Frederiksen, K. J. Franke, A. Arnau, G. Schulze,J. I. Pascual, and N. Lorente, Phys. Rev. B , 233401(2008).[21] X. H. Qiu, G. V. Nazin, and W. Ho, Phys. Rev. Lett. , 206102 (2004).[22] N. Krane, C. Lotze, G. Reecht, L. Zhang, A. L. Briseno,and K. J. Franke, ACS Nano , 11698 (2018).[23] F. Matino, G. Schull, F. Kohler, S. Gabutti, M. Mayor,and R. Berndt, Proc. Natl. Acad. Sci. , 961 (2011).[24] N. Ohta, R. Arafune, N. Tsukahara, M. Kawai, andN. Takagi, J. Phys. Chem. C , 21832 (2013).[25] A. Garcia-Lekue, D. Sanchez-Portal, A. Arnau, andT. Frederiksen, Phys. Rev. B , 155417 (2011).[26] N. Pavliˇcek, I. Swart, J. Niedenf¨uhr, G. Meyer, andJ. Repp, Phys. Rev. Lett. , 136101 (2013).[27] S. Meierott, N. N´eel, and J. Kr¨oger, Phys. Rev. B ,205437 (2017).[28] H. Gawronski and K. Morgenstern, Phys. Rev. B ,125420 (2014).[29] E. B. Fleischer, J. M. Palmer, T. S. Srivastava, andA. Chatterjee, J. Am. Chem. Soc. , 3162 (1971).[30] M. R. Nabid, Z. Zamiraei, R. Sedghi, and N. Safari,React. Funct. Polym. , 319 (2009).[31] B. W. Heinrich, G. Ahmadi, V. L. M¨uller, L. Braun, J. I.Pascual, and K. J. Franke, Nano Lett. , 4840 (2013).[32] B. W. Heinrich, L. Braun, J. I. Pascual, and K. J. Franke,Nano Lett. , 4024 (2015).[33] T. G. Gopakumar, H. Tang, J. Morillo, and R. Berndt,J. Am. Chem. Soc. , 11844 (2012).[34] D. Rolf, C. Lotze, C. Czekelius, B. W. Heinrich, andK. J. Franke, J. Phys. Chem. Lett. , 6563 (2018).[35] M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria,M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone,B. Mennucci, G. A. Petersson, H. Nakatsuji, M. Cari-cato, X. Li, H. P. Hratchian, A. F. Izmaylov, J. Bloino,G. Zheng, J. L. Sonnenberg, M. Hada, M. Ehara, K. Toy-ota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima,Y. Honda, O. Kitao, H. Nakai, T. Vreven, J. A. Mont-gomery, Jr., J. E. Peralta, F. Ogliaro, M. Bearpark,J. J. Heyd, E. Brothers, K. N. Kudin, V. N. Staroverov,R. Kobayashi, J. Normand, K. Raghavachari, A. Ren-dell, J. C. Burant, S. S. Iyengar, J. Tomasi, M. Cossi,N. Rega, J. M. Millam, M. Klene, J. E. Knox, J. B.Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts,R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi,C. Pomelli, J. W. Ochterski, R. L. Martin, K. Morokuma,V. G. Zakrzewski, G. A. Voth, P. Salvador, J. J. Dannen-berg, S. Dapprich, A. D. Daniels, . Farkas, J. B. Fores-man, J. V. Ortiz, J. Cioslowski, and D. J. Fox, GaussianInc. Wallingford CT 2009.[36] X. Chen, L. Shulai, C. Lotze, C. Czekelius, B. Paulus,and K. J. Franke, J. Chem. Phys. , 092316 (2017).[37] W. Auw¨arter, A. Weber-Bargioni, S. Brink, A. Riemann,A. Schiffrin, M. Ruben, and J. V. Barth, Chem. Phys.Chem. , 250 (2007).[38] H. Ibach and D. L. Mills,Electron Energy Loss Spectroscopy and Surface Vibrations(Academic Press, New York, 1982).[39] F. Maass, A. Stein, B. Kohl, L. Hahn, L. H. Gade, M. Mastalerz, and P. Tegeder, J. Phys. Chem. C ,2866 (2016).[40] L. J. Lauhon and W. Ho, Rev. Sci. Instrum. , 216(2001). [41] C. Rubio-Verd´u, A. Sarasola, D.-J. Choi, Z. Majzik,R. Ebeling, M. R. Calvo, M. M. Ugeda, A. Garcia-Lekue,D. S´anchez-Portal, and J. I. Pascual, Comms. Phys.1