Electron transfer energy surfaces

In classical kinetic theory the activity of a catalyst is explained by the reduction in the energy barrier of the intermediate, formed on the surface of the catalyst. The rate constant of the formation of that complex is written as k = k0 cxp(-AG/RT). Photocatalysts can also be used in order to selectively promote one of many possible parallel reactions. One example of photocatalysis is the photochemical synthesis in which a semiconductor surface mediates the photoinduced electron transfer. The surface of the semiconductor is restored to the initial state, provided it resists decomposition. Nanoparticles have been successfully used as photocatalysts, and the selectivity of these reactions can be further influenced by the applied electrical potential. Absorption chemistry and the current flow play an important role as well. The kinetics of photocatalysis are dominated by the Langmuir-Hinshelwood adsorption curve [4], where the surface coverage PHY = KC/( 1 + PC) (K is the adsorption coefficient and C the initial reactant concentration). Diffusion and mass transfer to and from the photocatalyst are important and are influenced by the substrate surface preparation. 

Fig. 5. Potential energy surfaces for different states involved in the interpretation of the primary electron transfer. Energies relative to the ground state PBH are reported from Ref [119]. The arrows indicate electron transfers whose rate have been experimentally measured...

For electrochemists whose principal objective is analysis of constituents in solution, the path is straighter and the hill less steep. The reaction model often used is a redox reaction in which the interfacial reaction is simply electron transfer, and surface chemical reactions among radicals can be neglected. The electrode is regarded as stable during the reaction and is not intended to take any chemical part in it. The function of the surface is not electrocatalytic, it is simply to be a source and sink of electrons, the energy of which may be controlled by variation of the electrode potential. 

Surface atoms, crystal imperfections and adsorbed molecules can give rise to localized energy levels located in the band gap. These so-called surface states play an important role as mediators of interfacial electron transfer. The surface states may or may not be occupied by an electron the surface-localized electrons give a contribution, as, to the surface charge ... 

It is a point peculiar to electrochemical reaction kinetics (77), however, that the rates of charge-transfer processes at electrodes measured, as they have to be, at some well-defined potential relative to that of a reference electrode, are independent of the work function of the electrocatalyst metal surface. This is due to cancellation of electron-transfer energies, O, at interfaces around the measuring circuit. In electrochemistry, this is a well-understood matter, and its detailed origin and a description of the effect may be found, among other places, in the monograph by Conway (77). 

FIGURE 1.16. Circumstances in which electron transfer does not oecur between the energy levels at the band edge on the surface and those in the electrolyte, (a) Electron transfer via surface states (b) electron tunneling through the potential barrier in the space charge layer. 

As already mentioned in the previous section, any electron transfer across the semiconductor-liquid interface occurs via the energy bands. There may also be an electron transfer via surface states at the interface the electrons or holes, however, must finally be transported via one of the energy bands. This is possible by capturing an electron from the conduction band or a hole from the valence band in the surface states. In the present section the basic rules for the charge transfer will be given, in particular, physical factors which determine whether an electron transfer occurs via the conduction or the valence band, will be derived. For illustration, the Gerischer model will be used here because it best shows the energetic conditions. 

The efficiency of collision-induced intramolecular energy transfer on an excited electronic state energy surface is very much higher than on the ground-state energy surface. 

Conical intersections (CIs) between electronic potential energy surfaces play a key mechanistic role in nonadiabatic molecular processes [1 ]. In this case the nuclear and electronic motions can couple and the energy exchange between the electrons and nuclei may become significant. In several important cases like dissociation, proton transfer, isomerization processes of polyatomic molecules or radiationless deactivation of the excited state systems [5,6] the CIs can provide very efficient channels for ultrafast interstate crossing on the femtosecond time scale. 

The dynamics of fast processes such as electron and energy transfers and vibrational and electronic deexcitations can be probed by using short-pulsed lasers. The experimental developments that have made possible the direct probing of molecular dissociation steps and other ultrafast processes in real time (in the femtosecond time range) have, in a few cases, been extended to the study of surface phenomena. For instance, two-photon photoemission has been used to study the dynamics of electrons at interfaces [ ]. Vibrational relaxation times have also been measured for a number of modes such as the 0-Fl stretching m silica and the C-0 stretching in carbon monoxide adsorbed on transition metals [ ]. Pump-probe laser experiments such as these are difficult, but the field is still in its infancy, and much is expected in this direction m the near fiitiire. 

In many instances tire adiabatic ET rate expression overestimates tire rate by a considerable amount. In some circumstances simply fonning tire tire activated state geometry in tire encounter complex does not lead to ET. This situation arises when tire donor and acceptor groups are very weakly coupled electronically, and tire reaction is said to be nonadiabatic. As tire geometry of tire system fluctuates, tire species do not move on tire lowest potential energy surface from reactants to products. That is, fluctuations into activated complex geometries can occur millions of times prior to a productive electron transfer event. 

This difference is a measure of the free-energy driving force for the development reaction. If the development mechanism is treated as an electrode reaction such that the developing silver center functions as an electrode, then the electron-transfer step is first order in the concentration of D and first order in the surface area of the developing silver center (280) (Fig. 13). Phenomenologically, the rate of formation of metallic silver is given in equation 17,... 

The detailed mechanism of battery electrode reactions often involves a series of chemical and electrochemical or charge-transfer steps. Electrode reaction sequences can also include diffusion steps on the electrode surface. Because of the high activation energy required to transfer two electrons at one time, the charge-transfer reactions are beheved to occur by a series of one electron-transfer steps illustrated by the reactions of the 2inc electrode in strongly alkaline medium (41). 

This section contains a brief review of the molecular version of Marcus theory, as developed by Warshel [81]. The free energy surface for an electron transfer reaction is shown schematically in Eigure 1, where R represents the reactants and A, P represents the products D and A , and the reaction coordinate X is the degree of polarization of the solvent. The subscript o for R and P denotes the equilibrium values of R and P, while P is the Eranck-Condon state on the P-surface. The activation free energy, AG, can be calculated from Marcus theory by Eq. (4). This relation is based on the assumption that the free energy is a parabolic function of the polarization coordinate. Eor self-exchange transfer reactions, we need only X to calculate AG, because AG° = 0. Moreover, we can write... 

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