Electronic coupling strength

Figure 23. Arrhenius plot of the electron transfer rate. The electronic coupling strength is TIad = 0.0001 a.u. Solid line-Bixon-Jortner perturbation theory Ref. [109]. FuU-circle present results of Eq. (26 ). Dashed line-results of Marcus s high temperature theory [Eq.(129)]. Taken from Ref. [28].

Figure 25. Electron-transfer rate the electronic coupling strength at T = 500 K for the asymmetric reaction (AG = —3ffl2, oh = 749 cm ). Solid line-present full dimensional results with use of the ZN formulas. Dotted line-full dimensional results obtained from the Bixon-Jortner formula. Filled dotts-effective ID results of the quantum mechanical flux-flux correlation function. Dashed line-effective ID results with use of the ZN formulas. Taken from Ref. [28].

Such exponential decays of Hi/2 with distance are characteristic of the electronic coupling strengths in all electron-transfer studies [8-11], not just those... 

As already mentioned, the electronic interactions involved at the metal oxide-adsorbate interface have not been studied nearly as extensively as, for example, metal surfaces. Some notable experimental progress has, however, taken place in the last few years, see e.g. [101, 102], and some relevant theoretical models have recently been proposed [103, 104, 105, 106, 107, 108]. However, little is known about the perhaps single most important factor determining the interaction the electronic coupling strength between the excited adsorbate levels and the metal oxide conduction band. 

Both the cluster and the periodic calculations indicate a similarity to the Newns-Anderson model for metal adsorbates, in that both energy shifts, and broadenings need to be included in models of electron transfer, as shown schematically in Fig. 13. It will be a challenge in the near future to incorporate the increasingly accurate calculations of the crucial electronic coupling-strength parameter in existing dynamical models of the surface electron transfer processes. 

Fig. 15.8. Schematic one-dimensional illustration of electronic predissociation. The photon is assumed to excite simultaneously both excited states, leading to a structureless absorption spectrum for state 1 and a discrete spectrum for state 2, provided there is no coupling between these states. The resultant is a broad spectrum with sharp superimposed spikes. However, if state 2 is coupled to the dissociative state, the discrete absorption lines turn into resonances with lineshapes that depend on the strength of the coupling between the two excited electronic states. Two examples are schematically drawn on the right-hand side (weak and strong coupling). Due to interference between the non-resonant and the resonant contributions to the spectrum the resonance lineshapes can have a more complicated appearance than shown here (Lefebvre-Brion and Field 1986 ch.6). In the first case, the autocorrelation function S(t) shows a long sequence of recurrences, while in the second case only a single recurrence with small amplitude is developed. The diffuseness of the resonances or vibrational structures is a direct measure of the electronic coupling strength.

In the nonadiabatic limit, the probability is quite low that reactants will cross over to products at the transition-state configuration. This probability depends upon the electronic hopping frequency (determined by Hab) and upon the frequency of motion along the reaction coordinate. In simple models, the electronic-coupling strength is predicted to decay exponentially with increasing donor-acceptor separation (Equation 6.28) ... 

Here r is the separation distance, ro the sum of the van der Waals radii of the donor and acceptor sites. Ho the electronic coupling strength at van der Waals contact, and P the distance attenuation factor, which can be used to parameterize the efficiency of the donor-acceptor coupling. Thus, under conditions of activationless electron transfer (-AG = A,), the maximum ET rate constant, is expected to obey Eq. (4) ... 

Note that the sink function represents the local reaction rate along the intramolecular vibrational coordinate g at a given solvent coordinate x. It can be obtained from eqn (12.4) or eqn (12.19) together with the ZN formula or R-matrix approach for wide electronic coupling strengths. 

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