Direct Observation of Translation-to-Vibration ... - ACS Publications

Jun 28, 2013 - Daniel J. Auerbach,. †,‡,∥. Alec M. Wodtke,. †,‡ and Christof Bartels*. ,†,‡. †. Institute for Physical Chemistry, Geor...
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State-to-State Time-of-Flight Measurements of NO Scattering from Au(111): Direct Observation of Translation-to-Vibration Coupling in Electronically Nonadiabatic Energy Transfer Kai Golibrzuch,†,‡ Pranav R. Shirhatti,†,‡ Jan Altschaff̈ el,† Igor Rahinov,§ Daniel J. Auerbach,†,‡,∥ Alec M. Wodtke,†,‡ and Christof Bartels*,†,‡ †

Institute for Physical Chemistry, Georg August University of Göttingen, Göttingen 37077, Germany Max Planck Institute for Biophysical Chemistry, Göttingen 37077, Germany § Department of Natural Sciences, The Open University of Israel, Ra’anana 4353701, Israel ∥ Department of Chemistry and Biochemistry, University of California Santa Barbara, Santa Barbara, California 93106, United States ‡

ABSTRACT: Translational motion is believed to be a spectator degree of freedom in electronically nonadiabatic vibrational energy transfer between molecules and metal surfaces, but the experimental evidence available to support this view is limited. In this work, we have experimentally determined the translational inelasticity in collisions of NO molecules with a single-crystal Au(111) surfacea system with strong electronic nonadiabaticity. State-tostate molecular beam surface scattering was combined with an IR-UV double resonance scheme to obtain high-resolution time-of-flight data. The measurements include vibrationally elastic collisions (v = 3→3, 2→2) as well as collisions where one or two quanta of molecular vibration are excited (2→3, 2→4) or de-excited (2→1, 3→2, 3→1). In addition, we have carried out comprehensive measurements of the effects of rotational excitation on the translational energy of the scattered molecules. We find that under all conditions of this work, the NO molecules lose a large fraction (∼0.45) of their incidence translational energy to the surface. Those molecules that undergo vibrational excitation (relaxation) during the collision recoil slightly slower (faster) than vibrationally elastically scattered molecules. The amount of translational energy change depends on the surface temperature. The translation-to-rotation coupling, which is well-known for v = 0→0 collisions, is found to be significantly weaker for vibrationally inelastic than elastic channels. Our results clearly show that the spectator view of the translational motion in electronically nonadiabatic vibrational energy transfer between NO and Au(111) is only approximately correct.

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INTRODUCTION

The NO/Au(111) system is by far the best characterized case of nonadiabatic vibrational energy exchange. Several experimental and theoretical investigations have revealed without doubt that excitation and relaxation of the NO vibration in collisions with a metal surface is due to nonadiabatic coupling of the molecular vibration to electron− hole pairs (EHPs) of the metal, implying a breakdown of the Born−Oppenheimer approximation (BOA).2 Therefore, NO/ Au(111) is ideal for studying the validity of various approximations, assumptions, and hypotheses that have been discussed previously in the literature. One of these is that in strongly nonadiabatic systems, translation behaves as a spectator degree of freedom with respect to the exchange of energy between vibration and solid (that is, electron−hole pair) excitations.

When a molecule collides with a metal surface, energy may be exchanged between several degrees of freedom. The molecule has translational, vibrational, and rotational motion, and the surface has electronic and phonon excitations. For chemical reactions at surfaces, molecular translation and vibration are of particular interest: the loss of molecular translational energy dictates sticking probability, and the molecular vibration is along the direction of the reaction coordinate for dissociation. From a fundamental point of view, it is desirable to understand such processes in as much detail as possible, especially for a few benchmark systems that might be compared to first principles theory. State-to-state molecular beam scattering is an appealing experimental approach. Molecules can be prepared in low energy quantum states and with narrow velocity distributions and can be optically pumped to specific ro-vibrational states with high efficiency. Well-defined singlecrystal surfaces can be used under UHV conditions. Finally, scattered molecules can be detected with quantum-state resolution using, for example, resonance-enhanced multiphoton ionization (REMPI) or laser-induced fluorescence (LIF).1 © 2013 American Chemical Society

Special Issue: Structure and Dynamics: ESDMC, IACS-2013 Received: April 5, 2013 Revised: June 6, 2013 Published: June 28, 2013 8750

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Figure 1. Schematic view of the IR system used for vibrational overtone pumping. We use pulse amplification of a cw ring dye laser (line width si, especially for the measurements taken at higher surface temperature. We find that the distributions are significantly different for the vibrationally elastic and inelastic channels. On average, molecules that lose one or two quanta of vibrational energy arrive earlier by approximately 0.6 and 1.2 μs, respectively, compared to vibrationally elastically scattered molecules. The opposite effect is observed for the v = 2→3, 4 channels, where molecules that are vibrationally excited tend to arrive later than in the vibrationally elastic case. However, this effect is smaller in magnitude for vibrational excitation than for relaxation. In fact, it is clearly observable only for v = 2→3 scattering, which is carried out at a surface temperature of TS = 570 K but is less obvious for the v = 2→3,4 channels observed at higher temperatures. Furthermore, we observe a significant broadening in the time-of-flight distributions with increasing surface temperature. The incident molecules time-of-flight data were analyzed by the following procedure. We assume that the speed-dependent flux of the incident molecules, φi(s), can be described by the distribution function φi(s) = A·s3 exp[−(s − s0)2/α02], where s0 and α0 are parameters.13 Because the angular divergence of the incident beam is small (1.2°), we can assume that the velocity component along the laser beam direction is negligible. In this case, the speed-dependent flux is directly converted to density, ρ(t) = φi(d/t)/t, which is fitted to the experimental data.10a For the scattered molecules, the velocity component along the laser beam can no longer be neglected. We assume that the angular distribution of scattered molecules is proportional to cosm θ, where θ is the scattering angle from the surface normal. The m values, which are weakly dependent on surface temperature, were determined by a fit to previously recorded angular distributions.12 For each incidence velocity si, the velocity distribution of the scattered molecules is modeled as a flowing Maxwell−Boltzmann distribution, φf(s,si) = A·s3exp[−(s − γsi)2/α2], where α and γ are parameters.14 Integration over the incident-beam velocity distribution yields the velocity distribution of the scattered molecules: φf(s) = ∫ Φf(s,si) × φi(si) dsi. We assume that we ionize all molecules in the laser beam with similar efficiency. In this case, the measured signal is expected to be given by S(t) = ∫ ρ(x,dy,dz,t) dx, where ρ(x,dy,dz,t) = [φf(r/t)/r2t] × cosm θ is the time-dependent Cartesian density of molecules, x is the coordinate along the laser propagation direction, and dy, dz are the y, z components of the total flight distance d. The resulting function S(t) was fitted to the experimental data points by varying (A,γ,α) as fit parameters. Energy distributions P(E), deconvoluted from the incident-beam velocity distribution, were then calculated from the velocity distribution according to P(E) = Φf((2E/ m)1/2,⟨si⟩)/(2mE)1/2. Figure 4 presents a few of the derived translational energy distributions P(E)’s. These are obtained from the time-of-flight data shown in Figure 3 and show vibrationally elastic as well as inelastic channels, where −2 ≤ Δv ≤ 2. The corresponding fits

Figure 4. Same fit functions as shown in Figure 3 converted to energy space for incident NO(v=3) at TS = 320 K (top panel), and incident NO(v=2) at TS = 570 K (middle panel) and TS = 970 K (bottom panel). The translational energy of the incident molecules is approximately 0.6 eV. The vertical dashed line is drawn through the peak of the 3→3 channel at TS = 320 K to guide the eye. For the energy distributions of the scattered molecules, we clearly observe an energy loss and significant broadening, which depend on the vibrational channel and on the surface temperature. The average translational energy loss to the surface is 45% for vibrationally elastic scattering. The amount of broadening in the energy distribution increases with the surface temperature for all channels.

to the time-of-flight data are also shown in Figure 3 as solid lines. We note that they fit the experimental data well. The resulting fit parameters obtained in this way are compiled in Table 1. Table 1. Observed Values for Mean Final Translational Energy ⟨Ef⟩ and the Fit Parameters γ and α for Various Scattering Channels and Surface Temperatures scattering channel (v (v (v (v (v (v (v (v (v

= = = = = = = = =

3, 3, 3, 2, 2, 2, 2, 2, 2,

J J J J J J J J J

= = = = = = = = =

1.5) 1.5) 1.5) 1.5) 1.5) 1.5) 1.5) 1.5) 1.5)

→ → → → → → → → →

(v (v (v (v (v (v (v (v (v

= = = = = = = = =

3, 2, 1, 2, 3, 1, 2, 3, 4,

J J J J J J J J J

= = = = = = = = =

5.5) 5.5) 5.5) 5.5) 5.5) 5.5) 5.5) 5.5) 5.5)

TS/K

⟨Ef⟩/eV

γ

α/m s−1

320 320 320 570 570 570 970 970 970

0.366 0.401 0.432 0.354 0.320 0.395 0.401 0.387 0.383

0.744 0.775 0.818 0.688 0.610 0.717 0.686 0.657 0.667

285 309 278 328 407 372 452 474 448

We also obtained data like those presented in Figure 3 for a variety of final rotational states with rotational energies up to 0.23 eV (J = 32.5) for vibrationally elastic and inelastic scattering. The mean translational energies were calculated from the fitted energy distributions using the relation ⟨E⟩ = ∫∞ 0 E P(E) dE. They are shown in Figure 5. We find an approximately linear decrease in translational energy with increasing rotational excitation (T−R coupling). For the 8754

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surface, M ≫ m, the loss of translational energy is negligible. The loss of molecular translational energy is maximal when the effective collision partner has the mass of a single gold atom and the collision occurs at zero impact parameter. This upper limit to the translational energy transferred in a single electronically adiabatic collision with the surface is often referred to as the Baule limit.15 For masses m = 30 amu for NO and M = 197 amu for one Au atom, this limit is ⟨Ef⟩/⟨Ei⟩ = (M − m)2/(M + m)2 ≈ 0.54, corresponding to ⟨Ef⟩ ≈ 0.34 eV for ⟨Ef⟩ = 0.63 eV used in our experiments. Although this agrees remarkably well with the observed mean scattered-molecule energies, the observed distributions are rather broad with significant fractions corresponding to energy transfer to the surface beyond the Baule limit. This cannot be explained within this simple model. In a previous study, Rahinov et al.10a showed that for HCl/ Au(111) collisions, the mean scattered energies of vibrationally elastically scattered HCl molecules are close to the Baule limit (for HCl, ⟨Ef⟩/⟨Ei⟩ = 0.475) over a wide range of incidence energies. In analogy with our results for NO/Au(111), broad energy distributions with significant fractions of translational energies below (i.e., beyond) the Baule limit were observed. The authors introduced a modified “attractive” Baule limit, which shifts the mechanically possible ⟨Ef⟩/⟨Ei⟩ to lower values, but their experimental data clearly exhibit scattering events even beyond this attractive Baule limit. Our data can also be compared with experimental results for NO(v=0→0) scattering from Ag(111), where the translational inelasticity was measured for several incidence energies and angles.16 Interpolating the results from that paper to estimate how NO scattering on Ag would appear at the incidence energy of this work, Ei = 0.63 eV, we find the mean recoil energy of the scattered molecules to be 0.28 eV, which is significantly lower than the value obtained in this work (Ef = 0.35−0.40 eV) for NO scattering from Au(111). Obviously, silver has a considerably smaller atomic mass than gold (108 amu vs 197 amu), and in a binary collision model, NO may transfer more energy to Ag than to Au. The Baule limit for NO/Ag scattering yields ⟨Ef⟩/⟨Ei⟩ = 0.32, corresponding to Ef = 0.20 eV when Ef = 0.63 eV. It appears that for NO scattering from Ag(111), the observed mean energy transfer is clearly below the Baule limit. Thermal Broadening and Energies Exceeding Ei. We observe a significant broadening of the Ef distributions when increasing the surface temperature from 320 to 970 K, which includes an increasing fraction of molecules with translational energies in excess of the incidence kinetic energy. It is conceivable that both the broadening and the appearance of energies higher than Ei originate from the thermal motion of the surface atoms. In a simple hard cube model,17 the NO molecule collides with a cube with the mass of a Au atom, whose velocity component perpendicular to the surface follows a Maxwell−Boltzmann distribution. Depending on its direction at the instant of the collision, the thermal motion of the cube can increase or decrease the final velocity of the NO molecule. Furthermore, probabilities for collisions while the surface atom is moving into the surface are lower than for an atom moving out of the surface, and given by Pcoll = (sNo − sAu)/2sNo.17a The resulting predictions from this simple model are shown in Figure 6 together with previously described fits to temperaturedependent time-of-flight data for (v = 2, J = 1.5)→(v = 2, J = 5.5) scattering. Comparing the simulation to the experimental data, we find that the simple model describes the broadening effect as well as

Figure 5. Mean recoil energies of vibrationally elastically and inelastically scattering molecules, recorded for various final rotational states ranging from J = 3.5 to J = 33.5. The data indicate translation-torotation coupling for vibrationally elastic as well as inelastic scattering. The color scheme is identical to the one used in Figures 3 and 4. The loss of translational energy does not correspond to the rotational energy uptake. These observations have been shown previously for NO(v=0→0) scattering and explained by an anticorrelation of the translational energy transfer to molecular rotation and to the surface (phonons).16,18 However, our results show that this anticorrelation is different for vibrationally inelastic scattering.

vibrationally elastic channels, the slopes are −0.50 ± 0.04; they differ from −1, which would be expected for complete conversion of translational to rotational energy with no participation of other degrees of freedom. Furthermore, we observe that for the vibrationally inelastic channels, the final translational energy has a weaker dependence on the final rotational energy, with slopes ranging from −0.50 to −0.22.

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DISCUSSION Magnitude of the Translational Energy Loss Is Described by the Baule Limit. The most obvious feature of our results is that, on average, the NO molecules lose a large fraction of translational energy during the collision. Despite small quantitative differences, this statement is a good description of our observations under all scattering conditions of this work, that is, for changes of vibrational energy in the range −0.47 eV ≤ ΔEvib ≤ +0.47 eV, and for changes of rotational energy in the range 0 ≤ ΔErot ≤ 0.23. For vibrationally elastic and rotationally quasi-elastic collisions (that is, ΔEvib = 0 for v = 2→2, 3→ 3; ΔErot ≤ 0.002 eV for J = 1.5→5.5), we find mean scattered-molecule translational energies between 0.35 and 0.40 eV (Table 1 and Figure 4). The corresponding loss of translational energy, ⟨Ei⟩ − ⟨Ef⟩, is between 0.23 and 0.28 eV, which represents between 37% and 44% of the mean initial translational energy, 0.63 eV. Conservation of energy requires that Ei = Ef + ΔEvib + ΔErot + ΔEs, where ΔEs describes the excitation of the surface. For vibrationally and rotationally elastic collisions (ΔEvib = ΔErot = 0), the translational energy lost in the collision can only be transferred to the surface, Ei − Ef = ΔEs. It is remarkable that NO molecules lose such a large fraction of their energy when colliding with a bulk gold crystal. In a binary collision model, NO molecules (mass m) collide with a collision partner of mass M, and the final velocity of the NO molecule is dictated by the conservation laws for energy and linear momentum. For a collision with an effective collision partner that describes a stiff 8755

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deviation than the corresponding one-quantum processes but additional experiments are necessary to more fully explore these phenomena. The origin of this behavior is the subject of ongoing research; it will be addressed in a forthcoming publication. Dependence of Outgoing Translational Energy on Vibrational Channel. From the energy distributions in Figure 4, we see that there is a clear shift to higher translational energies for scattered molecules that undergo vibrational relaxation, whereas for molecules undergoing vibrational excitation a small shift to lower energies shows up at TS = 570 K. We assign both effects as a T−V coupling. Note that the T−V coupling effect is clearly visible in the raw time-of-flight data in Figure 3. For v = 3→3, 2, 1 scattering data recorded at TS = 320 K, the energy distributions are shifted by about 0.03 eV per vibrational quantum released, which corresponds to 13% of the liberated vibrational energy. For scattering of v = 2→1, 2, 3 at TS = 570 K surface temperature, we find a similar trend. Specifically for the v = 2→1 relaxation channel, the mean kinetic energy is somewhat higher than for the elastic 2→2 channel. In addition, we observe vibrational excitation to v = 3, which shows the opposite tendency: the mean outgoing translational energy for v = 2→3 is shifted toward lower values. When the surface temperature is increased even further to 970 K, the effects for vibrational excitation on the translational energy are nearly impossible to see for scattering into J = 5.5. The detailed measurement of vibrationally and rotationally inelastic translational energy distributions provides the possibility to extrapolate the observed T−V coupling to ΔErot = 0 (Figure 5). Here, we find an increase of ⟨Ef⟩ of approximately 0.03 eV for per vibrational quantum released out of v = 3 at 320 K surface temperature. At TS = 570 K we obtain approximately 0.05 eV translational energy gain for vibrational relaxation and approximately 0.04 eV translational energy loss for vibrational excitation. This effect is not as easily seen for scattering of NO(v=2→2,3,4) at TS = 970 K. Here, the reduction of final translational energy is between 0.02 and 0.03 eV for both NO(v=2→3) and NO(v=2→4) scattering. Deriving the T−V Coupling in the Presence of Temperature Effects. To investigate more carefully the apparent decrease of the T−V coupling at high surface temperature, we measured translational energy distributions for vibrationally elastic and inelastic scattering of NO(v=2→ 2,1,3) at a series of surface temperatures. The mean kinetic energies are shown in Figure 7 for scattering of (v = 2, J = 1.5) into (v = 2, J = 5.5), (v = 2, J = 28.5), (v = 1, J = 5.5) and (v = 3, J = 5.5). For vibrationally elastic and rotationally quasi-elastic scattering (black solid points), the mean recoil energy increases slightly with increasing surface temperature. The values agree reasonably well with the prediction of the hard-cube model (dashed line) presented above. For vibrationally elastic but rotationally inelastic scattering (black open circles), the slope of the temperature dependence Δ⟨Ef⟩/ΔTS is not affected by the rotational excitation; the curve is only shifted toward lower energies due to translation-to-rotation energy transfer. Interestingly, we find that the temperature dependence for vibrationally inelastic scattering is different from the elastic case. The mean recoil energy for vibrational relaxation (green) and vibrational excitation (orange) increases more rapidly with increasing surface temperature. Assuming a linear behavior of the surface temperature dependence of ⟨Ef⟩ we find slopes of Δ⟨Ef⟩/ΔTS = 0.07 meV/K for the 2→2 channel, Δ⟨Ef⟩/ΔTS =

Figure 6. Comparison of the surface-temperature-dependent energy profiles for NO(v=2,J=1.5) scattering into NO(v=2,J=3.5) (black dots) and a hard cube model where the cube (Au atom) movement follows a one-dimensional Maxwell−Boltzmann distribution (red lines). The translation-to-rotation coupling can be neglected because the rotational energy uptake is only 0.002 eV. In the fit and the simulation the temperature-dependent broadening is clearly visible. The gray dashed line is again drawn through the peak of the distribution at TS = 320 K to guide the eye.

the peak of the distribution reasonably well at the lowest temperature, which indicates that the observed broadening can be related to the increased movement of the surface atoms at this temperature. However, it seems the model overestimates the effect at higher surface temperatures, which might be related to other degrees of freedom and the rather simplistic description of the Au atom movement by a simple 1D Maxwell−Boltzmann distribution. For a better comparison it might be necessary to apply more advanced models to take the roughness of the surface into account17d or to use more realistic potentials. Translation−Rotation Coupling. We obtain a linear decrease in final translational energy with increasing rotational excitation. For vibrationally elastic scattering we observe on average a slope of Δ⟨Ef⟩/ΔErot = −0.50 ± 0.04. This is clearly different from −1, which would be expected if rotational excitation were exclusively caused by complete energy transfer from translation. Kimman et al. found similar behavior for NO(v=0→0) scattering from Ag(111).18 They showed that this deviation can be explained in a purely mechanical picture and that it is due to an anticorrelation between translational energy transfer to rotation and to phonons. In addition to what was possible in that work, we can also measure the T−R coupling for vibrationally inelastic collisions. We find even stronger deviation of the slopes from −1 for vibrational relaxation as well as for vibrational excitation; the effect is much more pronounced in the excitation process. Furthermore, it seems that the loss/gain of two vibrational quanta shows a stronger 8756

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cover a range of only 0.15 eV whereas the range of vibrational energy change studied in this work is 0.94 eV.

Figure 7. Mean final translational energy as a function of surface temperature, TS, for vibrationally elastic and inelastic channels. Shown are data for (v = 2, J = 1.5) → (v = 2, J = 5.5) (black solid circles), (v = 2, J = 1.5) → (v = 2, J = 28.5) (black open circles), (v = 2, J = 1.5) → (v = 1, J = 5.5) (green solid circles), and (v = 2, J = 1.5) → (v = 3, J = 5.5) (orange solid circles) scattering as well as the prediction of the hard cube model (dashed line). We observe a stronger dependence of ⟨Ef⟩ on TS for the vibrationally inelastic channels.

Figure 8. Temperature-scaled mean recoil energies for different final rotational energies. Shown are the data points of Figure 5 but corrected according to the observed surface temperature dependence of ⟨Ef⟩ shown in Figure 7 (here all values are shifted to TS = 570 K). The dotted line indicates the incidence energy of 0.63 eV. Note that the range of vibrational energy change covers −0.47 eV ≤ ΔEvib ≤ 0.47 eV whereas the variation in the translational energy only varies over 0.15 eV, as indicated by the dashed lines. The inset shows the TScorrected recoil energies extrapolated to zero rotational energy as a function of the change in vibrational quantum number, Δv. A linear fit yields a slope of −0.049 eV per vibrational quantum. (The value for Δv = +2 was excluded from this fit.)

0.12 meV/K for the 2→1 channel, and Δ⟨Ef⟩/ΔTS = 0.14 meV/K for the 2→3 channel. We conclude that in nonadiabatic vibrational excitation of NO molecules scattered from a Au(111) surface, the vibrational energy can be partially released into translation for NO(v=3→ 2,1) and NO(v=2→1) scattering. The amount of vibration-totranslation coupling depends on the surface temperature, ranging from 11% of the vibrational energy release (26 meV) at TS = 470 K to about 20% (47 meV) at TS = 970 K. In addition, we find the opposite trend for molecules undergoing vibrational excitation, where we observe translation-to-vibration coupling values between 8% (18 meV) at TS = 970 K and 23% (53 meV) at TS = 470 K. The opposite tendencies in the T−V couplings for vibrational relaxation and excitation are contrasted by similar dependencies of the scattered translational energy on the surface temperature. For both vibrational excitation and relaxation, the mean recoil energy increases about twice as fast with increasing surface temperature as for vibrationally elastically scattered molecules in the range of temperatures studied in this work. It turns out that the comparison of recoil energy distributions between the different vibrational channels is complicated by the additional dependence on TS. To remove TS effects from this comparison, we employ the measured TS dependence on the v = 2→1, 2, 3 channels. Using linear extrapolation with different Δ⟨Ef⟩/ΔTS slopes for vibrationally elastic, excitation and relaxation channels, all data were referenced to the same temperature. The TS-corrected data, all shifted to TS = 570 K, are shown in Figure 8. We find that the resulting recoil energies

After the TS correction, we find a systematic dependence of the mean recoil energy ⟨Ef⟩ on the vibrational energy change. Extrapolating the ⟨Ef⟩ values to zero rotational energy, we find a linear dependence of the mean recoil energy on Δv (Figure 8, inset diagram). A linear fit yields a slope of d⟨Ef⟩/dv = −0.049 ± 0.005 eV, showing that for each vibrational quantum exchanged with the surface a 49 meV change in translational energy is seen. We emphasize that ⟨Ef⟩ is increased for vibrational relaxation and decreased for vibrational excitation. (The data point for Δv = +2 was excluded from the fit. Its uncertainty is largest because of small S/N in the measurement.) Origin of the T−V Coupling. The main question arising from this work is the origin of the T−V coupling. Before we list the possible explanations, let us summarize the two key experimental observations against which hypotheses can be tested: (1) The mean translational energy ⟨Ef⟩ of scattered molecules is smaller (larger) for vibrational excitation (relaxation) than for elastic scattering. (2) For both excitation and relaxation, the ⟨Ef⟩ vs TS dependence exhibits a steeper slope d⟨Ef⟩/dTS than for elastic scattering. 8757

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One last mechanism for T−V coupling has been suggested by Rahinov et al.10a for vibrationally inelastic scattering of HCl(v=2) from Au(111). Here it is supposed that the translation directly couples to EHPs, which are known to couple to vibration. Although such a T-EHP coupling has been observed earlier for incidence energies of 3−10 eV,20 the T−V coupling seen for HCl/Au(111) suggested that it could also be important at much lower incidence translational energies. In this mechanism, T→EHP conversion would lead to a reduction of the final translational energies independent of surface temperature and vibrational-state change. The opposite process, EHP→T conversion, could be based on thermally excited EHPs, leading to a broadening of the final translational energy distribution on the high energy side, which increases with surface temperature. If vibrational excitation (EHP→V) occurs in the collision, one could argue that less energy is available for EHP→T conversion, and the final translational energy is reduced. For vibrational relaxation (V→EHP), one can imagine that the produced transient EHP could (partially) decay into translation (EHP→T), increasing the final translational energy. Note that the dependence on vibrational-state change arises only through these secondary effects, which we expect to be small at least at high temperatures, where EHPs are sufficiently available. But the predicted behavior is not in contradiction with observation 1. None of the discussed mechanisms makes predictions that agree with observation 2. The hard cube model predicts, although not quantitatively, that the mean final translational energy increases with surface temperature (Figure 7, dashed line) but it does not explain the observation that the slope d⟨Ef⟩/dTS is higher for vibrationally inelastic than for elastic scattering. We speculate that this observation could be qualitatively explained by the following argument. The probabilities for collision-induced vibrational excitation of NO(0→1,2) and relaxation of NO(3→2,1) are known to increase with incidence energy.8,21 Within the hard cube model, if the Au atom is moving into (out of) the surface at the instant of the collision, the collision happens at a lower (higher) effective velocity and thus a reduced (enhanced) nonadiabatic coupling, but at the same time the recoiling molecule will have less (more) translational energy. The vibrationally elastically scattered molecules sample all relative velocities evenly whereas vibrationally inelastically scattered molecules preferentially sample higher relative velocities. The mean recoil energies of excited or de-excited molecules will thus have a stronger dependence on surface temperature. Their offset with respect to vibrationally elastically scattered molecules cannot be explained with this approach. We conclude that our experimental observations can partially be explained by two different mechanisms: by a direct mechanical coupling between translation and vibration and also by an EHP-mediated coupling where both translation and vibration couple to EHPs but not to one another. The more subtle dependence on surface temperature cannot be explained by either of these models. Clearly more experimental work and careful simulations are necessary for a complete understanding.

Let us turn now to some hypotheses concerning the mechanism for T−V coupling. It is well established that the nonadiabatic coupling of the NO vibration to EHPs of the metal occurs via formation of a transient NO anion.7,8,19 In this picture an electron hops onto the molecule, forms an NO− ion, and leaves a positive image charge at the surface. It is reasonable that the Coulomb interaction between the transient anion and its image charge leads to an acceleration of the molecule, resulting in higher final translational energy for those molecules that experience stronger nonadiabatic coupling. Assuming that strong nonadiabatic coupling is required for vibrational excitation and relaxation, this picture predicts the same effect for both vibrational excitation and relaxation. This prediction does not agree with our observations (1), and hence we rule out this mechanism. Of course, this does not mean that electron transfer is unimportant in this system. Rather it is likely that the lifetime of the transient negative ion is so short that the influence of image charge acceleration is too small to be seen in this work. Alternatively, it may be that image charge acceleration of NO approaching the surface is compensated by image charge deceleration occurring while NO is leaving the surface. A second possible mechanism was proposed earlier for HCl/ Au(111).10a It is based on the hypothesis that nonadiabatic coupling is enhanced at specific surface sites. For example, vibrational relaxation and excitation might predominantly occur at certain surface sites, where the effective mass needed for the binary collision model is more than the mass of one Au atom. This would result in less energy transferred to the surface for collisions at sites that are hypothetically more efficient for vibrational energy exchange, and consequently in higher translational energy of scattered molecules. Again, this mechanism predicts the same sign of T−V coupling for vibrational excitation and relaxation, inconsistent with observation. Similarly, specific orientations of the NO molecule at the instant of closest approach could enhance or reduce the transfer of translational energy to the surface. It has been suggested that nonadiabatic coupling is orientation-dependent19 and could thus lead to higher or lower final translational energies for molecules that are vibrationally inelastically scattered. Once again, this hypothesis cannot explain the observations of this work that the T−V coupling depends on the sign of Δv. A fourth possible mechanism is a direct adiabatic (mechanical) coupling between translation and vibration. Strong adiabatic T→V coupling was for example observed for NH3 scattering from Au(111), where up to three quanta of the “umbrella inversion” vibrational mode can be excited when the initial translational energy exceeds the vibrational excitation energy.3a,b For NO/Au(111), a system with strong electronically nonadiabatic character, the adiabatic T→V coupling is known to be insufficient to excite a single vibrational quantum even at the highest incidence energies investigated,8 but there may still be a (small) T→V coupling contributing to the (dominant) EHP→V mechanism. In this picture, we would expect the recoil energy of vibrationally excited molecules to be reduced in comparison to elastically scattered molecules. Assuming the same coupling for the opposite process, i.e., V→T conversion, we would expect the recoil energy of vibrationally de-excited molecules to be increased as compared to elastically scattered molecules. These expectations agree with observation 1.

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CONCLUSIONS In summary, we have presented experimental results on the translational inelasticity of NO(v=2,3) scattered from a Au(111) surface, comparing vibrationally elastic channels (2→2, 3→3) to inelastic channels where the NO molecules absorb (2→3,4) or release (3→2,1 and 2→1) one or two 8758

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quanta of vibrational energy. For all channels, the molecules lose a large fraction of translational energy to the solid. Both the mean recoil energy and the observed broadening of the distributions are consistent with a binary collision hard cube model. The coupling between translation and rotation is observed to be strong and dependent on vibrational channel. In addition, our observations show that there is, albeit weak, coupling between translation and vibration. After correcting the data for the dependence on surface temperature, we find that for each vibrational quantum that is consumed (released) in the collision, the mean recoil energy is decreased (increased) by approximately 49 meV, corresponding to 21% of the vibrational energy change. The observation that vibrational excitation and relaxation have opposite effects on the final translation energy allows us to conclude that the T−V coupling is not due to a correlation between the strengths of nonadiabatic interaction and translational inelasticity, e.g., a surface site specificity. Two different T−V coupling mechanisms, direct mechanical coupling and EHP-mediated coupling, are at least partially consistent with our observations. Neither mechanism can explain the observation that the increase of the mean recoil energy with surface temperature is stronger for both excitation and relaxation than for the vibrationally elastic channel.

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AUTHOR INFORMATION

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS D.J.A. and A.M.W. acknowledge the support from the Alexander von Humboldt foundation.

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REFERENCES

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