Electronically Non-Adiabatic Dynamics at Surfaces

As indicated by Equation 2.20, an electronically non-adiabatic event is likely to occur at nuclear configurations where the spacing between adjacent electronic states is small.

Due to the lack of a band gap, metal surfaces exhibit a large density of electronic states near the Fermi energy. A system in which a molecule resides in the vicinity of a metal surface has a large number of closely spaced electronic states.

A molecule may accept an electron from the surface forming an anionic species if the energy released by attaching an electron to the molecule exceeds the energy that is needed to elevate a surface electron above the vacuum level. Of course, the electron transfer (ET) can proceed in an electronically adiabatic manner. However, an elec-tronically non-adiabatic electron transfer from the surface to the molecule is likely to occur because of the continuum of occupied electronic states. See Panel (A) of Figure 2.2. Similarly, an anionic molecule that leaves the surface may transfer the electron back into one of the numerous unoccupied electronic states of the metal, as indicated in Panel (B). For systems in which the momentum and kinetic energy coupling terms, T_ij⁰ and T_ij⁰⁰, respectively, are significantly large, the Born-Oppenheimer approximation breaks down and electronically non-adiabatic dynamics dominate the molecule-surface interaction. This leads researchers to pose questions like, “Can we trust the Born-Oppenheimer approximation for surface chemistry?” [21] and “How non-adiabatic are surface dynamical processes?” [22] Consequently, electronically non-adiabatic surface dynamics has become an important field of research in surface science, which has been explored by both experimentalists [21–23, 45] and theorists [34, 46–48] for more than 30 years.

A large variety of approaches have been taken to study non-adiabatic surface dy-namics. Methods such as reflection absorption infrared spectroscopy (RAIRS), surface enhanced Raman spectroscopy (SERS), and sum frequency generation (SFG) are em-ployed to investigate the vibrational dynamics of adsorbates [49]. The lifetime of vibra-tionally excited adsorbates is much shorter on metal surfaces than on insulator surfaces because of the non-adiabatic coupling between molecular vibration and electron-hole pairs (EHPs) in the metal [50, 51]. In surface femtochemistry, the vibrational excita-tion as well as the desorpexcita-tion and chemical conversion of adsorbates are initiated by photo-excited electron-hole pairs that interact with vibrational degrees of freedom of the adsorbed molecule [52]. Conversely, products of highly exothermic gas-surface

reac-A A

A

A

(B) Scattered anion

Energy

Molecule-surface distance (A) Incoming molecule

A

A

A A

A

Molecule-surface distance

Figure 2.2: Adiabatic potential energy surfaces for a hypothetical molecule A in the vicinity of a metal surface. Panel (A): The approaching molecule may ac-cept an electron from a variety of different electronic states in the surface if electronically non-adiabatic transitions occur. Non-adiabatic transitions are indicated by the arrows. Panel (B): When the anion A⁻leaves the sur-face, the electron is transferred back to the surface and an excited electron-hole pair is generated if the system suffers non-adiabatic transitions. The figure is adapted from Figure 1 in Reference [21].

tions can relax in an electronically non-adiabatic way by transferring energy to surface electrons, which results in chemiluminescence at or exo-electron emission from surfaces [53, 54]. The detection of exo-electrons provides direct evidence for electronically non-adiabatic energy dissipation at surfaces. An alternative way to observe non-non-adiabatic dynamics directly is the measurement of chemicurrents induced by the adsorption or chemical reaction of gaseous molecules at the surface of metal-semiconductor [55] (Schot-tky diode) or metal-insulator-metal detector devices [56, 57]. With the advent of molec-ular beams in surface science, quantum-state resolved studies on energy transfer [58, 59]

and reaction dynamics [60] in single-bounce molecule-surface collisions has become feasi-ble. The remainder of this section briefly reviews electronically non-adiabatic dynamics in direct molecule-surface scattering events [21, 45, 61], providing background knowledge for experimental results presented and discussed in Chapter 5.

In 1985, Rettner et al. reported the direct vibrational excitation of ground-state NO in collisions with a Ag(111) surface [62, 63]. The excitation probability of the NO(v= 0)→NO(v= 1) process increases with incidence translational energy and

de-pends strongly on surface temperature. These findings provide evidence for an electroni-cally non-adiabatic energy transfer in which the nuclear motion of the diatomic molecule couples to excited electron-hole pairs in the surface. An electron transfer mechanism, in which an electron jumps from the surface to the molecule forming a short-lived anionic species, has been proposed in order to explain the experimental observations [64, 65].

See Section 5.3.2 for detailed information about the mechanism. In contrast to non-adiabatic energy transfer [66], electronically non-adiabatic vibrational excitation at surfaces depends only weakly on the surface temperature. The electronically adiabatic energy transfer—also referred to asmechanical energy transfer—is characterized by a threshold behavior observed in the translational energy dependence of the vibrational excitation probability, which strongly suggests direct conversion of translational to vibrational energy, as reported for the scattering of ammonia at Au(111) [67].

To date, vibrational excitation via coupling to electron-hole pairs has been reported for a variety of molecule-surface systems, including NO/Cu(110) [68], NO/Au(111) [69–

72], HCl/Au(111) [73, 74], CO/Au(111) [75–77], and N2/Pt(111) [78]. The NO/Au(111) system is the most thoroughly studied system and serves as a model system for the de-termination of absolute vibrational excitation probabilities in single- and multi-quantum vibrational excitation [70]. The Arrhenius-like surface temperature dependence with ac-tivation energies similar to the energy spacing between vibrational levels indicates that the excitation energy stems from thermally excited electron-hole pairs [66, 70].

Further insights into non-adiabatic surface dynamics are gained by studies on the vi-brational relaxation of excited molecules (v >0) [79–82]. In these studies, the molecule loses vibrational energy during the collision event by exciting electron-hole pairs in the metal. In particular, the scattering of highly vibrationally excited molecules (v0) at-tracted special attention because the observed surface dynamics are strongly dominated by electronic non-adiabaticity [25]. NO(v = 15) scattered from Au(111) undergoes multi-quantum vibrational relaxation, giving rise to a distribution of vibrational energy loss that peaks at ∆v = −7,−8. The vibrational energy loss is inhibited when high-v NO is scattered from LiF(001) [83], supporting the hypothesis that vibrational energy is gained or lost through non-adiabatic coupling to surface electrons. Further studies investigating the dependence of molecular orientation on the scattering dynamics of highly vibrationally excited NO are consistent with the non-adiabatic picture [84–87].

Perhaps the most compelling evidence for electronic excitation induced by the nu-clear motion of a vibrating molecule is the vibrationally promoted emission of electrons observed when highly vibrationally excited NO is scattered from a low-work function surface [88–91]. As the vibrational energy of NO(v = 15) exceeds the work function of a cesium covered Au(111) surface, multi-quantum vibrational relaxation excites a

surface electron above the vacuum level. Electron emission is observed as soon as the incident molecule is prepared in a vibrational state that carries along sufficient energy to overcome the work function. Kinetic energy distributions of the ejected electrons are consistent with the vibrational energy loss [92, 93].

In order to elucidate the nature and the underlying mechanism of electronically non-adiabatic dynamics in molecule-surface scattering, it is worth extending the aforemen-tioned experimental findings withab initio theoretical investigations. The NO/Au(111) system serves as a benchmark system for theory because the system exhibits strong non-adiabaticity and has been extensively studied by experimentalists. Two conceptu-ally different approaches have been developed by theorists to explain and predict the scattering outcome. For systems with weak non-adiabatic couplings, electronic fric-tion based models [26, 27, 94] are commonly used to go beyond the Born-Oppenheimer approximation [95–97]. The coupling of low-energy electron-hole pair excitations to the nuclear motion of molecules at surfaces are treated by introducing a friction force to the classical equations of motion. For systems with strong non-adiabatic interac-tions, independent-electron surface hopping (IESH) based approaches are used, which explicitly include transitions between adiabatic electronic states [28, 29]. Combined theoretical and experimental studies [30, 34, 71, 72, 82] show that, for the scattering of highly vibrationally excited NO from Au(111), neither the vibrational energy loss nor the incidence translational energy dependence of the relaxation probability is predicted correctly [30]. However, the trend in the velocity dependence is accurately described by a semi-empirical approach assuming anion-mediated vibrational relaxation [98].