Role of valence states of adsorbates in inelastic electron tunneling spectroscopy: A study of nitric oxide on Cu(110) and Cu(001)

We studied nitric oxide (NO) molecules on Cu(110) and Cu(001) surfaces with low-temperature scanning tunneling microscopy (STM) and density functional theory (DFT). NO monomers on the surfaces are characterized by STM images reﬂecting 2 π ∗ resonance states located at the Fermi level. NO is bonded vertically to the twofold short-bridge site on Cu(110) and to the fourfold hollow site on Cu(001). When NO molecules form dimers on the surfaces, the valence orbitals are modiﬁed due to the covalent bonding. We measured inelastic electron tunneling spectroscopy (IETS) for both NO monomers and dimers on the two surfaces, and detected characteristic structures assigned to frustrated rotation and translation modes by density functional theory simulations. Considering symmetries of valence orbitals and vibrational modes, we explain the intensity of the observed IETS signals in a qualitative manner.


I. INTRODUCTION
Chemical identification of individual molecules adsorbed onto surfaces is one of the most significant challenges for nanoscale investigations using scanning probe microscopes (SPM) such as scanning tunneling microscopy (STM) and atomic force microscopy (AFM).Although SPM gives realspace images with atomic resolution, the topographic images alone usually provide insufficient information to characterize the chemical components of the adsorbates.In order to identify chemical species on surfaces at the single-molecule level, several techniques have been reported: bottom-up fabrication of molecular complexes with manipulation [1], vibrational spectroscopy with tip-enhanced Raman scattering [2], and measuring short-range force curves with AFM [3].Inelastic electron tunneling spectroscopy (IETS) is also a powerful tool for chemical characterization in the tunneling junction [4].Characteristic signatures in d 2 I /dV 2 spectra on metal-insulator-metal systems, originating from the excitation of vibrational modes of molecules in the insulating layer by the tunneling electrons, were first reported in 1966 [5].Three decades later, Stipe et al. [6,7] measured vibrational IET spectra of individual molecules on metal surfaces with the STM.Subsequently, STM-IETS has been appreciated as a detection method not only for molecular vibrations but also for surface phonon modes [8] and spin flips of magnetic atoms and molecules [9,10].
In contrast to intuitive selection rules of infrared and Raman spectroscopy, a definitive selection rule of IETS has not been established.Nonetheless, recent theoretical studies have demonstrated valid models for elastic and inelastic tunneling processes, and have successfully reproduced experimental STM-IET spectra [11][12][13][14][15][16][17][18][19][20].IETS for CO on metal surfaces have been thoroughly investigated as a typical model of a simple * shiotari@k.u-tokyo.ac.jp molecule-metal substrate system [12,15,[21][22][23][24][25][26][27][28][29][30].O 2 /Ag(110) is also an interesting subject of study [15][16][17] because on-resonant IETS signals, i.e., dips (peaks) in d 2 I /dV 2 at positive (negative) sample biases, are detected [31].Alducin et al. [16,17] reproduced the IET spectrum theoretically and elucidated that elastic components of the tunneling current become predominant if a resonance state of the adsorbate located just at the Fermi level couples conveniently with vibrational modes.According to the theoretical model, the symmetric property of the molecular orbitals near the Fermi level plays an important role in electron-vibration coupling owing to the inelastic and elastic tunneling processes.Very recently, characteristic on-resonant features were also observed in IETS of H 2 O bonded onto a NaCl ultrathin film on Au(111) [32]; the IETS intensities were enhanced by bringing the STM tip closer to the adsorbate, and the lineshapes changed from symmetric dips to asymmetric features in d 2 I /dV 2 .Based on theoretical modeling, these modifications of the IETS were argued to result from the energy shift of the highest occupied molecular orbital states toward the Fermi level (E F ) [32].However, an experimental insight into a correlation between vibrational modes and electronic states of adsorbates still remains insufficient; only few IETS studies in combination with scanning tunneling spectroscopy (STS) have been reported hitherto [33,34].
Nitric oxide (NO) molecules on Cu surfaces have been prominent systems to monitor the local electronic states with STM images and STS measurements [35][36][37].For an isolated NO molecule adsorbed onto Cu(110) at ∼15 K, the resonance state of its valence orbital (2π * ) remains at E F , and therefore, the orbital is visible in the STM image at low bias voltage [36].Moreover, the electronic states can be modified by formation of covalent bonding to yield a dimer [(NO) 2 ] on the surface [35].Therefore NO on Cu surfaces seem to be an ideal model system to investigate a correlation between IETS signals and resonance states.
In this study, we observed isolated NO monomers on Cu(110) and Cu(001), which are vertically bonded onto the short-bridge site and the hollow site, respectively.On Cu(110) the doubly degenerate 2π * orbital of NO is lifted upon adsorption onto the anisotropic substrate.Conversely, on Cu(001), the 2π * orbital remains degenerate and is located at E F .We also observed NO dimers [(NO) 2 ] on these surfaces, fabricated by approaching two NO monomers to each other with STM manipulation.STS measurements clarify their resonance states near E F , which characterize the STM images.We measured IETS for both NO monomers and dimers on the two Cu surfaces.The experimental observations were also studied theoretically by electronic structure calculations for the role of vibrational excitations in the tunneling process.This enabled us to assign the characteristic peaks in IETS to specific adsorbate vibrational modes and to discuss "propensity rules" based on symmetry considerations of the electron-vibration coupling matrix elements.

II. METHODS
The STM experiments were carried out in an ultrahighvacuum chamber at 6 K (USM-1200, Unisoku).An electrochemically etched tungsten tip was used as an STM probe.Single-crystalline Cu(110) and Cu(001) surfaces were cleaned by repeated cycles of Ar + sputtering and annealing.The surfaces were exposed to NO gas via a tube doser positioned ∼1 cm from the surface at up to 15 K, through a variable-leak valve.For STS, dI /dV curves were obtained by using a lock-in amplifier with modulation voltage V (rms) mod = 1-4 mV at 590 Hz with the feedback loop open.Unless otherwise stated, each presented STS spectrum is displayed after subtraction of dI /dV obtained over the bare surface at the same tip height (see Appendix for a discussion of the background subtraction).For IETS, d 2 I /dV 2 curves were obtained by using a lock-in amplifier with V (rms) mod = 6-10 mV at 590 Hz with the feedback loop open.Each IETS spectrum is displayed after subtraction of d 2 I /dV 2 obtained over the bare surface at the same set point (see Appendix).
Electronic structure calculations were performed with density functional theory (DFT) and the GGA-PBE exchangecorrelation functional [38] as implemented in the VASP code [39].The projected-augmented-wave (PAW) method was used to describe the atomic cores [40,41].One or two NO molecules were placed on a five-layer Cu slab exposing either the (110) or the (001) surface, using a lattice constant of a = 3.64 Å.Each slab was separated by about 11 Å of vacuum along the surface normal to reduce the interaction between periodic cells.Similarly, the single-adsorbate(s) limit was modeled with 4 × 5 surface cells, except for NO/Cu(001) for which a 4 × 4 cell was used to improve the symmetry of the low-frequency vibrational modes.We used an energy cutoff of 515 eV in the plane-wave basis set, a 4 × 4 × 1 Monkhorst-Pack sampling of the Brillouin zone, and a firstorder Methfessel-Paxton scheme [42] with a smearing of 50 meV for the orbital occupancies.Forces on the molecule(s) and on the two topmost layers were relaxed to 0.02 eV/ Å. Vibrational frequencies and modes were computed using finite displacements of 0.02 Å and a stringent electronic convergence criterion for accurate forces (total energies were converged to 10 −6 eV).
Spin-resolved projected density of states (PDOS) were computed using the implementation of Ref. [43] ) for positive (negative) W values. IETS maps were computed using the methodology developed by Lorente and coworkers, which is based on the many-body extension of the Tersoff-Hamann theory for the STM [11][12][13][14].Here we used the expressions that take into account finite values of the vibrational quanta and voltage in evaluating the DOS [16,17].Specifically, the relative change in conductance σ /σ is evaluated as the sum of the inelastic σ ine and elastic σ ela components normalized to the conductance σ , which are given for positive sample bias (V > 0) by and respectively, where σ denotes the differential conductance, ρ(r 0 ,E F + eV ) is the local DOS at the position r 0 of the tip apex, and υ is the local electron-vibration potential for a vibrational mode with energy ω.Note that within the Tersoff-Hamann approximation the change in conductance is interpreted as the change in the sample DOS at the tip apex caused by the vibration [11][12][13][14].Equations

A. STM observations of NO monomers
Figures 1(a) and 1(b) show typical STM images of Cu(110) and Cu(001), respectively, exposed to NO at ∼12 K.Each image was obtained at 6 K. STM images of NO/Cu(110) have been reported previously [35]; dumbbell-shaped protrusions with an apparent height of ∼0. ) is located around E F + 0.5 eV [36].Therefore the intrinsic double degeneracy of the 2π * orbital is lifted upon adsorption onto the anisotropic substrate.
Conversely, STM images of NO/Cu(001) reveal a ringshaped protrusion with an apparent height of ∼0.1 Å [Fig.1(b)].The image is centered at the hollow site, which is determined by coadsorbed CO molecules bonded on top of Cu atoms [21] (not shown).Note that this adsorption site is in contradiction with a previous report based on infrared spectroscopy [44].The dI /dV curve recorded over the protrusion [blue cross in Fig. 1 We note that it cannot simply be ascribed to the derivative of the comparably smooth 2π * resonance itself.The width of the vibrational fingerprint is relatively broad (full width at half maximum of ∼30 meV), suggesting that a few vibrational modes contribute to the structure.The assignment of the peaks will be described later.
We also acquired simultaneous topography and spatial maps of the d 2 I /dV 2

B. DFT calculations of NO monomers
We conducted spin-polarized DFT calculations for both NO/Cu(110) and NO/Cu(001).The energetic and geometric properties of the systems, listed in Table I, are basically in agreement with very recent DFT studies [45,46].On Cu(110), we find that a single NO molecule preferentially adsorbs on the short-bridge site in an upright configuration.Note, however, that we are unable to explain the relative stabilities of the upright and bent ("flat-lying") structures reported in Ref. [47] (the bent configuration is computed to be metastable).While the intrinsic spin polarization of NO is generally reported to be lost upon adsorption on Cu surfaces [48,49], we found magnetic solutions for upright NO/Cu(110) using different k meshes, smearing values, and surface coverages, albeit the energy difference to the corresponding spin-degenerate calculation was at most a few meV/cell.With the tetrahedron method on a very dense 12 × 12 -centered k grid the spin polarization eventually disappeared (Table I).The PDOS of NO/Cu(110) is shown in Fig. 3(a).The resonance states of 2π * [1 10] and 2π * [001] orbitals are nondegenerate and located near E F , compatible with STS data (Fig. 1(c) and Ref. [36]).
Figures 3(b) and 3(c) show simulated topographies of NO/Cu(110) for negative and positive W , respectively.The former reflects the shape of 2π * [1 10] , whereas the latter corresponds to the sum of the 2π * [1 10] and 2π * [001] features, in qualitative agreement with STM images acquired at different bias voltages [36].However, the computed splitting between 2π * [001] and 2π * [1 10] is relatively weaker than experimentally observed.More precisely, the maxima of the corresponding PDOS are separated by less than 300 meV and the resonances, which are rather broad, overlap at both sides of E F within a large energy interval ([E F − 1 eV, E F + 1 eV]).Consequently, the simulated topography for a sampling of the density of states in the energy interval [E F , E F + 0.2 eV] exhibits a ring-shaped protrusion [Fig.3(c)], another manifestation of the strongly overlapping resonances above E F in the DFT electronic structure.However, the experimentally observed 2π * [1 10] orbital can be reasonably reproduced by simulations involving only the occupied states [E F − 0.2 eV, E F ], see Fig. 3(b).We note that we explored two mechanisms that could potentially increase the orbital splitting on Cu(110) in the calculations: (i) NO was forced closer to the substrate by 0.4 Å, representing a possible underestimate of the binding distance to the substrate and therefore of the crystal field splitting and (ii) we performed DFT+U calculations with U = 1-4 eV to favor spin splitting.However, while the quantitative details changed, the relative separation between 2π * [001] and 2π * was not significantly altered.The symmetry dependence of the IETS maps can be explained in terms of "propensity rules" proposed by Lorente et al. [11,13,[15][16][17].Equations ( 2) and (3) show that an IET signal requires ψ m,k |υ|ψ n,k to be nonzero, i.e., that an IETS feature is "allowed" if the following equation holds [50]: where Γ n(m) denotes the symmetry representation of the ψ n,k(m,k) states involved in the electron-vibration coupling induced during the tunneling process, Γ vib denotes the symmetry , where E NO is the energy of a single gas-phase NO, E surf is the energy of the clean surface, and E system the energy of the combined system with n NO molecules.b Numbers in parentheses were obtained using the tetrahedron method on a very dense 12 × 12 -centered k grid.
representation of the corresponding vibrational mode, and Γ sym denotes the totally symmetry representation (e.g., A 1 for the C nv point group).
As an example, Fig. 5 shows simulated maps of the separate inelastic and elastic tunneling components for the FT [1 10] mode.The inelastic map shows a positive intensity on top of NO [Fig.5(a)], which dominates the total IETS map of Fig. 4(e).This can be explained by "propensity rules" [Eq.( 4)] as follows.The δ function in Eq. ( 2) determines that the ψ n,k state during the tunneling process is the 2π * orbital below E F .Actually, we have verified that FT(R) [001] and not FT(R) [1 10] dominate the IETS maps for positive W (not shown).Remarkably, both the experimental and theoretical results discussed so far show that the presence of a resonance at E F does not necessarily imply a dip in the IETS spectra at V > 0, as it is the case for O 2 on Ag(110) [15][16][17]31].Possible "allowed" combinations for the elastic tunneling of NO/Cu(110) correspond to Γ n = Γ m = B 2 and Γ vib = A 1 , which would lead to a negative IETS map with a dumbbell shape along the [1 10] direction.However, neither the ν nor CM modes show any noticeable IETS intensity [Figs.4(a) and 4(c)], probably because of weak couplings υ between the resonance states via these A 1 modes.This is analogous with IETS for CO on Cu(111) with a metal tip, where the 2π * orbital of the adsorbate couples predominantly with the FR mode, while coupling between 2π * and the C-O stretch mode is quite weak [15,27,28].
We next turn to a similar analysis for NO/Cu(001).The NO molecule is found to preferentially adsorb upright on the hollow site.An upright configuration bonded to the bridge site is found to be meta-stable (about 170 meV higher in energy).The molecule is practically unpolarized (Table I) as well as NO/Cu(111) [48,49].The calculated PDOS shows that the doubly degenerate 2π * [110] and 2π * in the IETS maps from these modes [Figs.7(a) and 7(d)], probably resulting from weak couplings υ via these modes, as speculated above also for the case of NO/Cu(110).

C. NO dimers on Cu(110) and Cu(001)
We also studied on NO dimers [(NO) 2 ] on Cu(110) and Cu(001).Figures 8(a (NO) 2 /Cu(110) and (NO) 2 /Cu(001), respectively, together with a NO monomer.Two NO molecules on each surface [Cu(110) in Fig. 1(a) and Cu(001) in Fig. 1(b)] were approached to each other with STM manipulation [35] to yield the dimer.Figure 8(c) [8(d)] shows a dI /dV curve for (NO) 2 /Cu(110) [(NO) 2 /Cu(001)] recorded over the cross marker in Fig. 8(a) [8(b)].The spectrum in Fig. 8(c) shows a shoulder of a peak at V > 200 mV, suggesting the resonance state is located around E F + 0.5 eV.The resonance state in Fig. 8(d) is observed at ∼50 meV above E F .Insets of Figs.8(c) and 8(d) show dI /dV spatial maps of (NO) 2 /Cu(110) and (NO) 2 /Cu(001) recorded at V = 300 and 150 mV, respectively.These intensity maps show an elongated dumbbell shape along a direction perpendicular to the molecular plane.The structure probably reflects the shape of the 2b 1 and/or the 2a 2 orbitals (discussed below).The different resonance position between the two substrates originates from the energetic variation between 2π * [001] for NO/Cu(110) [Fig. 3 A d 2 I /dV 2 curve for (NO) 2 /Cu(110) was measured over the center of the dimer [Fig.9(a)], showing vibrational features at ±9 and ±27 mV.The latter signal is localized at the center of the dimer, as shown by an IETS spatial map at the corresponding bias [Fig.9(d)].An IETS curve and a map for (NO) 2 /Cu(001) were also measured in the similar way, revealing vibrational features at ±11 and ±41 meV [Fig.9(b)].The latter signal is also localized at the center of the dimer [Fig.9(f)], while the simultaneously-measured topography shows the feature of 2b 1 and/or 2a 2 orbitals [Fig.9(e)].
We also calculated the optimized structures of (NO) 2 on the Cu surfaces (see Table I), which are quite similar to those reported in Ref. [46].We find that the dimers on both surfaces are practically unpolarized.According to the calculated adsorption energies, dimer formation from two monomers on the surfaces is energetically  3] eV resembles more or less the 2b 1 and/or the 2a 2 orbitals, and therefore, it is meaningful to compare the simulated IETS for this W with the experimental results.Figures 11 and 13 show the simulated IETS maps for the normal modes for (NO) 2 /Cu(110) and (NO) 2 /Cu(001), respectively, along with the schematic illustrations of the corresponding vibrations.Since the dimer on both surfaces belong to C 2v point group, we can consider "propensity rules" [Eq.( 4)] for the dimers on the same symmetry conditions.Note that four FT modes of (NO) 2 /Cu(001) are degraded from C 2v due to the (numerically) slightly asymmetric adsorption structure.
First, we find that all of A 1 modes, e.  with A 2 symmetry; Fig. 11(g)] has strong intensity whereas FT a [001] [A 2 symmetry; Fig. 11(k)] has no signal.The strength of electron-vibration coupling depends on the vibrational energies and vibrational-displacement distributions [17,50], suggesting that the former mode couples with the resonance state more strongly than the latter.
Finally, the experimental IETS peaks of the dimers can be assigned to the "active" vibrational modes in Figs.[Figs. 11(g) and 11(h)] appear as an oval protrusion localized between the NO molecules, whereas the corresponding experimental IETS map [Fig.9(d)] shows an almost round distribution.We assume that the experimental distribution is broadened by the measurement with a relatively blunt tip apex [29], and that a burred intensity distribution around the dimer in the simulated maps is also reflected by the experimental map.For (NO) 2 /Cu(001), the 41 meV signal is assigned to FR a mode is active.This variation results from the switching of the electronic states from B 2 to B 1 upon the formation of the dimer.Therefore, the IETS measurement for NO and (NO) 2 clearly demonstrates a crucial role of symmetry of both electronic and vibrational states involved in the tunneling process.

IV. CONCLUSIONS
We studied nitric oxide molecules on Cu(110) and Cu(001) surfaces by a combination of STM experiments and DFT calculations.We observed isolated NO monomers on Cu(001) for the first time, and found that they are bonded to the hollow site in an upright configuration.The 2π * state of NO/Cu(001) remains doubly degenerate and located at the Fermi level.We also fabricated NO dimers on the surfaces by STM manipulation.The resonance states of the dimers are modified due to the covalent bonding between the involved NO molecules.Vibrational fingerprints were experimentally detected in IETS of NO monomers and dimers on Cu(110) and Cu(001).The simulated IETS successfully reproduce the experimental threshold energies and spatial distributions, and the active modes are concluded to be the FR and FT modes along the specific Cu surface directions.On the basis of "propensity rules", the inelastic signals can be explained in a qualitative manner.

( 2 )FIG. 1 .
FIG. 1. STM images of (a) NO/Cu(110) and (b) NO/Cu(001) acquired in the constant-current mode with a sample bias V = 30 mV and tunneling current I = 0.5 for (a) and 5 nA for (b).Meshes represent the lattice of surface Cu atoms and the black dots represent the position of NO.Recorded dI /dV curves of (c) NO/Cu(110) and (d) NO/Cu(001).The solid and dashed curves in (c) were recorded over the cross and the empty circle, respectively, in (a).The spectra in (c) [(d)] were acquired by lock-in detection with the bias modulation of V (rms) mod = 4 [1] mV with the feedback disabled at the tip height to give 30 mV and 0.5 [5] nA over the cross in (a) [(b)].The inset of (d) shows a dI /dV spatial map of the NO monomer on Cu(001).The map was acquired at V = 30 mV with V (rms) mod = 12 mV with the feedback disabled to give 30 mV and 5 nA over the cross in (b).The image sizes are 38 Å × 22 Å for (a), 30 Å × 20 Å for (b), and 13 Å × 11 Å for the inset of (d).
2 Å are assigned to NO monomers bonded onto the short-bridge sites (C 2v point group).The image shape of the monomer reflects the 2π * orbital along the [1 10] direction (2π * [1 10] ) of the molecule bonded vertically to the short-bridge site.The red solid curve in Fig. 1(c) shows a dI /dV spectrum recorded over the protrusion [red cross in Fig. 1(a)].The resonance state of 2π * [1 10] is located at E F and contributes predominantly to the STM images at low bias voltage.The resonance state of 2π * along the [001] direction (2π * [001] (b)] displays a resonance located at E F [Fig. 1(d)].The inset of Fig. 1(d) shows a dI /dV map at 30 mV, indicating that the resonance state originates from the isotropic 2π * orbital.Therefore the NO monomer is bonded vertically to the hollow site (C 4v point group) with a doubly degenerate 2π * orbital.Figures 2(a) and 2(b) show d 2 I /dV 2 curves for NO/Cu(110) and NO/Cu(001) with a characteristic feature around V = ±19 and ±25 mV, respectively.Each spectrum was measured over the center of the image (i.e., on top of the molecule).The structure in d 2 I /dV 2 , also directly observable in dI /dV over NO [dashed curve in Fig. 1(c)], corresponds to the increase of inelastic tunneling conductance due to vibrational excitation.
intensities at the corresponding bias voltages [Figs.2(c) and 2(d) for NO/Cu(110) and 2(e) and 2(f) for NO/Cu(001)].Despite different topographic appearances of NO on the two surfaces, the IETS intensity is in both cases centered on the molecule.

25 FIG. 2 .
FIG. 2. d 2 I /dV 2 curves of (a) NO/Cu(110) and (b) NO/Cu(001) recorded over on top of the molecule.The spectrum in (a) [(b)] was acquired by lock-in detection with the bias modulation of V (rms) mod = 6 [10] mV with the feedback disabled at the tip height to give 30 mV and 0.5 [5] nA.(c) [(e)] Topographic image and (d) [(f)] d 2 I /dV 2 spatial map of the monomer on Cu(110) [Cu(001)].The topographic image in (c) [(e)] was acquired with V = 30 mV and I = 0.5 [5] nA to give the tip height for measuring d 2 I /dV 2 signal at each point.The map in (d) [(f)] was subsequently acquired at V = 16 [20] mV with V (rms) mod = 12 [10] mV with the feedback disabled.The image sizes are 16 Å ×11 Å for (c) and (d) and 11 Å × 11 Å for (e) and (f).

Figure 4
shows simulated IETS maps for each of the normal modes for NO/Cu(110).The energy window W = −0.2eV and constant density contour of ρ = 5 × 10 −9 e/ Å3 were used to maximize features of the experimental 2π * [1 10] resonance.Schematic illustrations of the corresponding vibrations are shown as insets.It is noteworthy that the simulated IETS intensities and shapes strictly depend on the symmetry of the vibrational modes.The maps of the N-O stretch (ν) and center-of-mass stretch (CM) modes [Figs.4(a) and 4(c), respectively; A 1 symmetry] have no intensity, whereas those of the frustrated rotation and translation modes along the [1 10] direction [FR [1 10] and FT [1 10] modes shown in Figs.4(b) and 4(e), respectively; B 2 symmetry] have intensities on top of NO.The maps of FR [001] and FT [001] modes [Figs.4(d) and 4(f), respectively; B 1 symmetry] also have intensities on top of the molecule but they are comparatively weaker than those of the B 2 modes.The calculated vibrational energies (Fig. 4) indicate that the measured d 2 I /dV 2 structure around ±19 mV [Fig.2(a)] should be assigned mainly to the FT [1 10] mode (18 meV).The simulated IETS distribution of the FT [1 10] mode is in good agreement with the measured map [Fig.2(d)].The exceptionally broad peak width in Fig. 2(a) further suggests that the observed spectrum could include masked contributions as shoulders from FR [001] (20 meV) and FR [1 10] (42 meV).

FIG. 5 .
FIG. 5. Calculated intensity maps of (a) inelastic and (b) elastic tunneling components of the FT [1 10] mode for NO/Cu(110) with W = −0.2eV and ρ = 5 × 10 −9 e/ Å3 .The possible combination between ψ m,k , a vibrational mode, and ψ n,k is shown on the right side of each map.The image area is 12 Å × 12 Å.

FIG. 9 .
FIG. 9. d 2 I /dV 2 curves for the dimer on (a) Cu(110) and (b) Cu(001) recorded over on the molecular center (i.e., midpoint between NO and NO).The spectrum in (a) [(b)] was acquired by lock-in detection with the bias modulation of V (rms) mod = 6 [10] mV with the feedback disabled at the tip height to give 30 mV and 0.5 [5] nA.(c) [(e)] Topographic image and (d) [(f)] d 2 I /dV 2 spatial map of the dimer on Cu(110) [Cu(001)].The topographic image in (c) [(e)] was acquired with V = 30 mV and I = 0.5 [5] nA to give the tip height for measuring d 2 I /dV 2 signal at each point.The map in (d) [(f)] was subsequently acquired at V = 30 [40] mV with V (rms) mod = 12 mV with the feedback disabled.The approximate positions of NO molecules are shown by white dots in (c) and (e).The image sizes are 16 Å × 11 Å for (c) and (d) and 11 Å × 11 Å for (e) and (f).
g., the symmetric N-O stretching mode v s , are (almost) IETS inactive [Figs.11(a), 11(c), 11(f), 11(i), 13(a), 13(c), and 13(g)]similar to the A 1 modes of the NO monomers as described above.Next, some of the IETS maps for B 1 and A 2 modes have intensities located at the center of the dimer.This can be explained by Eq. (4); the coupling of B 1 (A 2 ) modes with the 2b 1 (2a 2 ) resonance state requires Γ m = A 1 .Thus the ψ m,k
[110] and FR s [110] [Figs.13(e) and 13(f)].On the other hand, the computed asymmetric maps of the FT modes complicate the assignment of the IETS signal at 11 meV.We tentatively assign the peak to FT 4 mode [Figs.13(l)] with reference to the vibrational energy.Comparing Figs. 4 with 11, FT along the [1 10] direction for the monomer on Cu(110) is IETS active, whereas for the dimer, FT s/a [1 10] modes are (almost) inactive while FT s [001]

Figure 14 (FIG. 14 .FIG. 15 .
Figure 14(a) shows a series of d 2 I/dV 2 spectra measured across a NO monomer on Cu(110) at intervals of 1.9 Å along the [1 10] direction.Spectrum i recorded over the bare Cu surface [inset of Fig. 14(b)] was used as the background the background subtraction [see Fig.1(c)].The background spectra for the NO monomer [red dotted curve in Fig.15(c)] and dimer (blue dotted) show a similar structure, while the curves recorded over the monomer (red solid) and dimer (blue solid) have different peaks.This indicates that the 2π * (derived) resonance states are located at different energy levels, as shown in Figs.1(d) and 8(d).Note that the background curves are not identical because of the different tip-sample heights.Figure15(d)shows the unsubtracted d 2 I/dV 2 curves for the NO monomer (red) and dimer (blue) on Cu(001), leading to Figs. 2(b) and 9(b), respectively.The background curves (dotted) are featureless as well as on Cu(110) (Spectra i in Fig.14), whereas IET signals are detected in the spectra recorded over the molecules (solid).

TABLE I .
Calculated GGA-PBE adsorption energies, geometric properties (atom-atom distances and angle of the NO axis with respect to the surface plane), and magnetization of NO molecules on Cu(110) and Cu(001).
a The adsorption energy per NO molecule is defined as