Nonadiabatic dynamics at surfaces

Experiments and theoretical approaches to nonadiabatic dynamics at surfaces have recently been reviewed.[9,14] The importance of nonadiabatic effects has been demonstrated for a variety of different systems. Especially, for dynamics at metal surfaces, it is obvious that the Born-Oppenheimer approximation might not lead to an accurate description. This is because there is a continuum of electronic states and thus the Massey criterion 2.38 that gives the condition under which a process can be described precisely in the adiabatic

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2.5. Nonreactive dynamics at surfaces picture is not fulfilled. In reference [9], the authors showed in general that the parameter Φ−E_ais a good descriptor for the nonadiabaticity of a surface process. Here,Φis the work function of the material andE_ais the electron affinity of a projectile. The smallerΦ−E_a, the more likely nonadiabatic effects are to play an important role. A nice example of the Born-Oppenheimer breakdown is given by experiments on H-atom scattering from the Au(111) surface. The breakdown of the Born-Oppenheimer approximation becomes clear by a comparison to the analogous experiment at the insulating Xe-surface.[83]Figure 2.10 shows the results of time-of-flight experiments on the scattered H-atoms for both surfaces and the derived translational energy loss distributions. Obviously, the translational energy loss is much larger at the Au(111) surface than at the Xe-surface. In a simple impulsive collision picture the energy loss is expected to be small since the H-atom mass is much lighter than the surface atom mass such that considering energy and momentum conservation nearly the complete collision energy is retained in the atom. This is the case for scattering from Xe. At the metallic Au(111) surface, however, the energy loss is very large and can only be described by taking nonadiabatic effects into account. In reference [83] the authors showed that this process can be understood treating the nonadiabatic interactions as a kind of friction experienced by the H-atom in an electron bath. This approach is known as molecular dynamics with electronic friction. In this method the dynamics can still be described by a single effective potential energy surface and nonadiabatic effects are treated implicitly as frictional and fluctuating forces.

In the following, the remarks will be focused on molecule/metal surface scattering that, in contrast to the H-atom scattering experiment, presumably cannot be understood in an electronic friction picture. In the scattering of highly vibrationally excited NO with an initial vibrational quantum number ofv_i= 15 from Au(111) the average vibrational energy loss is very large (1.4 eV) compared to similar experiments at the insulating LiF surface where almost no vibrational relaxation is observed.[11] The Debye frequency of Au is 115 cm⁻¹[84]and 448 cm⁻¹[85]for LiF. The fundamental frequency of NO is 1876 cm⁻¹. Based on these values and simple mechanic arguments the vibrational energy transfer should be less efficient at the Au surface than at the LiF surface. The efficient vibrational relaxation of the NO molecule can only be explained by taking the coupling between vibrational motion and electronic excitation into account. In addition to relaxation, the vibrational excitation has also been investigated on Ag(111)[86] and Au (111)[12]. Fig-ure 2.11 shows the dependence of the vibrational excitation on surface temperatFig-ure and incidence translational energy. The Arrhenius-like surface temperature dependence with the slope close to the vibrational spacing of the NO molecule (see Figure 2.11a)) as well

2. Scientific context

Figure 2.10.:Upper panel: Arrival time distribution of H-atom at the detector for scatter-ing from a Xe surface (filled squares) and a Au(111) surface (open circles). The incidence parameters are E_i = 2.76 eV and 45° incidence angle. Scattered H-atoms are detected at the specular angle. Lower panel: Derived translational energy loss in the collision of H-atom at the Xe-surface (filled squares) and at the Au(111) surface (open circles). Figure taken from reference [83]. Reprinted with permission from AAAS.

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2.5. Nonreactive dynamics at surfaces

(a) (b)

Figure 2.11.: a) Vibrational excitation probability of NO at Ag(111) as a function of the inverse surface temperature. b) Branching ratio between NO(v = 1) and NO(v = 0) as a function of the incidence translational energy. Figures taken from reference [86].

Reprinted with permission. Copyright (1985) by the American Physical Society.

as the zero incidence translational energy threshold (see Figure 2.11b)) have been inter-preted in terms of electron-hole pairs providing the energy for vibrational excitation.[24]

Furthermore, electron emission has been observed for scattering experiments with highly vibrationally excited NO at low work function caesiated surfaces.[13] Interestingly, the electron emission increases approximately linearly with incidence vibrational energy of the NO molecule starting at a threshold corresponding to the work function of the caesiated surface. This observation was interpreted such that during certain scattering events the complete vibrational energy of the molecule can be transferred to a single electron.

There have been several theoretical approaches for understanding vibrational energy transfer in the NO/Au(111) surface system, which employ Monte Carlo wave packet dynamics[87], molecular dynamics with electronic friction[15]on model potentials, or in-dependent electron surface hopping (IESH) on a DFT-derived potential.[8]Little attention has been paid to the Monte Carlo wave packet study. Those three approaches were used to calculate the final vibrational state distribution after vibrational relaxation at the surface.

Thus, the predictions can be directly compared to the outcome of the experiment. All three studies almost quantitatively reproduced the final vibrational state distribution for NO(v_i = 15) scattered from Au(111) at a low incidence translational energy. Further-more, the predictions of molecular dynamics with electronic friction theory as well as the

2. Scientific context

IESH program were directly compared to experimentally determined excitation probabil-ities.[88]Whereas electronic friction theory fails in explaining the vibrational excitation probabilities, the experiment is more accurately reproduced by IESH. Recently, an almost complete experimental data set for the scattering of NO at Au (111) has been obtained:

The translational inelasticity in low-v NO/Au(111) surface scattering has been analyzed by quantum-state-resolved time-of-flight techniques resulting in a detailed picture of the coupling between the different molecular degrees of freedom.[17,89] In addition, the im-portant role of molecular orientation has been investigated in the vibrational relaxation of NO(v_i = 3). Here, a dramatic enhancement of vibrational relaxation is found if the molecule is oriented with the N-atom towards the surface.[90,91]The dependence of the vibrational relaxation probability on incident vibrational and translational energy has been examined in reference [6]. Figure 2.12 shows the central findings of this work. As can be seen in Figure 2.12a), the vibrational relaxation is promoted by both incidence transla-tional as well as vibratransla-tional energy. Furthermore, N-atom down orientation is favorable for vibrational relaxation as long as the relaxation probability does not approach unity.

See Figure 2.12b).

Following ideas developed earlier, the multi-quantum vibrational relaxation is explained as proceeding via the transient formation of the anion and subsequent excitation of an elec-tron in the metal, thus involving two elecelec-tron transfers in the mechanism.[11]Figure 2.12c) shows that this is possible because the anionic species becomes stabilized at the surface due to image charge stabilization. Figure 2.12d) shows that the anion can serve as a mediator between neutral potential energy surfaces, allowing the conversion of vibrational energy into electronic excitation. As the dynamics evolve on the anionic diabat the system can undergo several nonadiabatic transitions. That means that the molecule/surface system stays on the anionic diabat such that finally the transition back to a neutral potential en-ergy surface corresponding to less vibrational enen-ergy and higher electronic excitation can occur. More incidence translational energy allows the molecule to approach closer to the surface such that the formation of the anion and thus vibrational relaxation becomes more likely. However, both IESH theory and MDEF fail to reproduce the incidence translational energy dependence of the relaxation process.[7]Moreover, a detailed comparison between the predictions of the IESH theory and the experimental observations revealed severe problems with the adiabatic potential energy surface used as the basis for the description of nonadiabatic dynamics in the IESH program.[16]Here, I would like to point out that the Monte Carlo wave packet study[87]deserves more recognition since it successfully predicts the promoting role of incidence translational energy on vibrational relaxation. It would

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2.5. Nonreactive dynamics at surfaces be interesting to test the prediction of this method for the available experimental data on excitation.

In the study presented here, remaining gaps in the available dataset for the NO/nobel metal surface scattering system are filled. The following question are addressed: First, do the rotational state distributions in multi-quantum relaxation of initially highly vi-brationally excited NO contain valuable information on the nonadiabatic interactions?

Second, can we understand the coupling between the different molecular degrees of free-dom in collisions of highly vibrationally excited NO? And last, how do surface properties influence the scattering process?