Electron transfer processes nonadiabatic coupling

The Fermi Golden rule describes the first-order rate constant for the electron transfer process, according to equation (11), where the summation is over all the vibrational substates of the initial state i, weighted according to their probability Pi, times the square of the electron transfer matrix element in brackets. The delta function ensures conservation of energy, in that only initial and final states of the same energy contribute to the observed rate. This treatment assumes a weak coupling between D and A, also known as the nonadiabatic limit. 

From the standard quantum mechanical expression for the rate of nonadiabatic electron-transfer, it is apparent that the pure electronic coupling matrix element (V) and adiabatic electronic energy gap (O) are important factors for consideration of dispersive kinetics of the DA —> D A electron-transfer process, where D s donor and A s acceptor. By necessity, we assume that these two variables are uncorrelated. We begin by considering dispersive kinetics from a distribution of Q-values. Next we present some of our experimental data that speak to the question of dispersive kinetics from a distribution of V-values. 

If the system under consideration possesses non-adiabatic electronic couplings within the excited-state vibronic manifold, the latter approach no longer is applicable. Recently, we have developed a simple model which allows for the explicit calculation of RF s for electronically nonadiabatic systems coupled to a heat bath [2]. The model is based on a phenomenological dissipation ansatz which describes the major bath-induced relaxation processes excited-state population decay, optical dephasing, and vibrational relaxation. The model has been applied for the calculation of the time and frequency gated spontaneous emission spectra for model nonadiabatic electron-transfer systems. The predictions of the model have been tested against more accurate calculations performed within the Redfield formalism [2]. It is natural, therefore, to extend this... 

An important factor is the electron coupling between the electrode metal and the redox species or between the two members of the redox couple. If this coupling is strong the reaction is called adiabatic, i.e., no thermal activation is involved. For instance, electrons are already delocalized between the metal and the redox molecule before the electron transfer therefore, in this case no discrete electron transfer occurs [see also -> adiabatic process (quantum mechanics), - nonadiabatic (diabatic) process]. 

Electron transfer in proteins generally involves redox centers separated by long distances. The electronic interaction between redox sites is relatively weak and the transition state for the ET reaction must be formed many times before there is a successhil conversion from reactants to products the process is electronically nonadiabatic. A Eandau-Zener treatment of the reactant-product transition probability produces the familiar semiclassical expression for the rate of nonadiabatic electron transfer between a donor (D) and acceptor (A) held at fixed distance (equation 1). Biological electron flow over long distances with a relatively small release of free energy is possible because the protein fold creates a suitable balance between AG° and k as well as adequate electronic coupling between distant redox centers. 

Most LRET processes in biological systems are nonadiabatic. In quantum-mechanical electron-transfer theory, the rate constant for nonadiabatic ET from a donor to acceptor can be expressed as the product of the square of an electronic coupling matrix element (Hp ) and a nuclear Franck-Condon factor (FC) kpy = (27t/h)[Hpj2(FC).The [HpJ is a measure ofthe... 

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