Electron transfer nonadiabatic

Adiabatic Versus Nonadiabatic Electron Transfer Across Linear Fused... 

Fig. 2 The molecular structure of I—III and the representation of the potential energy surfaces for adiabatic to nonadiabatic electron transfer reactions...

Samanta, A. A., and S. K. Gosh. 1995. Density functional approach to the solvent effects on the dynamics of nonadiabatic electron transfer reactions. J. Chem. Phys. 102, 3172. 

Let us summarize the results obtained. The theory is restricted to nonadiabatic electron-transfer reactions. If only classical modes are reorganized during the transition, the rate constant for the oxidation is ... 

Following earlier workby Warshel, Halley and Hautman"" and Curtiss etal presented an approximate numerical scheme to calculate the nonadiabatic electron transfer rate under the above conditions. The method is based on solving Eq. (18) to the lowest order in the coupling F by treating the elements Hj and as known functions of time obtained from the molecular dynamics trajectories. The result for the probability of the system making a transition to the final state at time t, given that it was in the initial state at time fo. is given by... 

By measuring the temperature dependence of kex, activation parameters (Aff and AS ) could be calculated and were reported. However, I am not sure how to physically interpret these numbers. The temperature dependence of rate can be fit to other expressions, and here it is fit to the Marcus equation for nonadiabatic electron transfer in the case of degenerate electron transfer (e.g., AG° = 0)... 

Let the Fe2+ ion be abandoned for the moment to describe the somewhat different events with H30+ a femtosecond after electric transfer. For transfer to Fe3+ when the electron leaves the metal and in an interval of 10-15 s transfers to the hydrated ion awaiting it, the decisive quantity is 12 in Fig. 9.22. It is liable to be very small, for Fe3+ and similar redox species, less than 0.1 eV and so the probability of the useless nonadiabatic electron transfer will be large and the successful rate of formation of Fe2+ relatively small. 

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... 

Nonadiabatic Electron Transfer in Oxidation-Reduction Reactions... 

In the case of adiabatic electron transfer reactions, it is found that the potential energy profiles of the reactant and product sub-systems merge smoothly in the vicinity of the activated complex, due to the resonance stabilization of electrons in the activated complex. Resonance stabilization occurs because the electrons have sufficient time to explore all the available superposed states. The net result is the attainment of a steady, high, probability of electron transfer. By contrast, in the case of -> nonadiabatic (diabatic) electron transfer reactions, resonance stabilization of the activated complex does not occur to any great extent. The result is a transient, low, probability of electron transfer. Compared with the adiabatic case, the visualization of nonadiabatic electron transfer in terms of potential energy profiles is more complex, and may be achieved in several different ways. However, in the most widely used conceptualization, potential energy profiles of the reactant and product states... 

The nonadiabatic electron transfer between donor (D) and acceptor (A) centers is treated by the Fermi Golden Rule... 

Emission and Nonadiabatic Electron Transfer Rates In Gondensed Phases. 

When the appropriate equilibrium constants are not extremely small, direct electron (or hole) transfer to bridge units may occur and the electron (or hole) may then hop from moiety-to-moiety (randomly) along the bridge. When this happens, the electron-transfer rate will decrease only slowly with bridge length. This behavior has been treated in terms of standard nonadiabatic electron-transfer theory. ... 

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. 

The redox potentials of organic cofactors are directly responsible for controlling the equilibrium behavior of the corresponding cofactor-mediated electron transfer processes. The relative redox potentials of the cofactor and its redox partner are also intimately related to the rate of adiabatic electron transfer Ret through the classical Marcus equation [13, 14], and nonadiabatic electron transfer through the semi-classical Marcus equation [15, 16]. The direct dependence of both the kinetics and thermodynamics of electron transfer processes on the cofactor redox potential makes the control of these potentials a key determinant of the activity of redox proteins. 

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