H–atoms are scattered back with only little loss of translational energy. For H–atoms scattered from the clean Au(111) surface, energy can also be non–adiabatically trans-ferred to electron–hole pairs. This coupling seems to be very strong, and the scattered H–atoms loose a lot of their translational energy to the surface.(35) This experiment might also explain the high sticking probability of H–atoms on many metal surfaces.
The two experiments discussed up to this point show, that the generation of electron–
hole pairs for reactions at metal surfaces are the rule rather than the exception and that non–adiabatic effects can play an important role for chemical reactivity.
2.2 Electron transfer energetics at metal surfaces
The result that electron–hole pairs are important in surface dynamics and are generated by non–adiabatic transitions poses the question: What is the nature of these non–
adiabatic transitions? In other words: Between which potentials do the non–adiabatic transitions occur?
I have already discussed the gas–phase example of the avoided curve–crossing in the NaI molecule (Fig. 2.2). In this example, the non–adiabatic transitions were due to electron transfer. Upon vibration of the molecule, the adiabatic potentials rapidly change from a covalent (NaI) character to an ionic character. The inability of the electronic structure to adapt to the change of internuclear separation induced non–adiabatic transitions.
Indeed, it is believed that electron transfer also plays an important role for many non–
adiabatic effects in gas–metal surface interactions.(29, 32) A characteristic feature of metal surfaces is that they can be directly involved in electron transfer reactions and that they stabilize ions in their vicinity due to the image–charge effect (28). This stabilization of ionic species can lead to additional curve crossings to the potential energy landscape.
In order to obtain an estimate in which systems of gas–metal surface dynamics electron transfer might be important, it is useful to study some theory on the energetics of electron transfer at metal surfaces. A positive point chargeqat a distancezin front of a metal surface induces a polarization cloud of opposite charge on the surface (Fig. 2.5A).
According to the method of image charges in electrostatics, the field lines outside the metal can be described as if the positive charge was interacting with its negative image charge−q at distance −z inside the surface (Fig. 2.5B).
2. Theory and previous results
Figure 2.5: Electron transfer energetics at metal surfaces– (A) A positive charge (blue) at a distancezfrom a metal surface induces negative (red) surface charge. (B) The electric field lines outside the metal are as if a negative charge was placed at position−z.
(C) For a molecule far from a metal surface, the energy required to transfer an electron from the metal to the molecule (the formation of an anion) is given by the difference of the surface work functionφS and the electron affinity of the molecule EA. This difference has to be overcome by image charge stabilization to make electron transfer (ET) feasible. As the affinity level is stabilized upon approach of the molecule to the surface, the affinity level broadens as the lifetime decreases. The blue function indicates the density of states in the metal. (D) The energetics for possible ET reactions are compared for different systems. The smaller the valueφS−EAthe more likely is the anion formation. In a similar way, one can argue that cation formation is energetically feasible for small values of a difference between the first ionization potential IP and the surface work function φ . The NO/Au(111)
2.2 Electron transfer energetics at metal surfaces
To a fist approximation the interaction between the charge and its image charge can be described by a Coulomb interaction. In a more detailed study(39), Appelbaum and Hamann showed that the energy of a point charge q at a distancez greater than 2 ˚A from a surface (more exactly the distance from the jellium edge) is given by
E(z) =− 1 4π0
q2
4 (z−d), (2.12)
where0 is the vacuum permittivity, anddis an origin shift, which is a function of the electron density at the metal surface.
The image charge effect promotes electron transfer between a metal surface and an approaching atom or molecule (Fig. 2.5C). The energy released when an electron from the vacuum is added to a neutral atom or molecule is the electron affinityEA.
X+e− →X−+EA (2.13)
The energy that is required to remove an electron from the Fermi level at the Fermi energy (F ermi) is the surface work function φS. This means, that the energy required to transfer an electron from the surface to an atom/molecule far from the surface is given by the difference φS −EA. However, the electron affinity level is energetically stabilized upon approach of the molecule. Eventually, the affinity level might cross the Fermi energy at a certain critical distancez∗ and electron transfer from the metal to the molecule becomes energetically possible. The stabilization due to image charge effect is limited due to quantum effects (formula 2.12 is only a good approximation for z > 2 ˚A), and the electron transfer energetics are more complex than the pure image charge effect. Nevertheless, values of φS −EA can be used as a predictor whether electron transfer (anion formation) is likely to be involved in a particular gas–surface interaction (Fig. 2.5D).(40) The NO/Au(111) system studied in this work has favorable energetics for anion formation due to the large electron affinity of NO (+0.03 eV) compared to other diatomic molecules, the work function of Au(111) is 5.31 eV1. The image charge effect does also stabilize cations in front of a surface. In this case, the relevant measure for the energetics is the difference of the first ionization potential (IP)
1Values for the electron affinity are typically negative for diatomic molecules, e.g. -3.155 eV for H2-, -1.967 eV for N2 or -0.531 eV for HCl. The values φS of the surface work function are relatively similar for the different metals, ranging from 4.24 eV for Al(111) to 5.7 eV for Pt(111). See the caption of Fig. 2.5 for references.
2. Theory and previous results
and the surface work function φS. Although the energetics would seem not to rule it out, to my knowledge, there are no known examples of ET at surfaces involving cation formation. With respect to this work, it should be noted, that the stretched bonds of highly vibrationally excited NO molecules favor anion formation. I will return to this point in section 2.4.2.