System-bath coupling electron transfer

This spectral density has a characteristic low-frequency behavior J((o) — rjo), where rj is the usual ohmic viscosity. The system-bath coupling strength can then be measured in terms of the dimensionless Kondo parameter K, and time scale of bath motions is described by a cutoff frequency (o. For many problems in low-temperature physics, this cutoff frequency is taken to be the largest frequency scale in the problem. In the case of electron transfer, the same spectral density with some intermediate value for is most appropriate for a realistic description of... 

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... 

The third alternative is to use the classical correlation functions to define an equivalent quantum mechanical harmonic bath. This approach was pioneered by Warshel as the dispersed polaron method [67, 68]. More recently, this idea has been used in studies of electron transfer systems in solution [64] and in the photosynthetic reaction center [65,69] (see also Ref. 70). This approach is based on the realization that the spectral density describing a linearly coupled harmonic bath [Eq. (29)] can be obtained by cosine transformation of the classical time-correlation function of the bath operator [Eq. (28)]. Comparing the classical correlation function for the linearly coupled harmonic bath [Eqs. (25) and (26)],... 

The model is based on the standard tight-binding Hamiltonian consisting of a donor, a number of bridge sites, and an acceptor, all coupled to form a linear chain. In addition, a single linearly coupled oscillator is included, representing a high-frequency vibrational coordinate coupled to the electron transfer. The lack of detailed information about this system makes it appropriate to treat the bath stochastically. Thus... 

The first quantum-mechanical consideration of ET is due to Levich and Dogonadze [7]. According to their theory, the ET system consists of two electronic states, that is, electron donor and acceptor, and the two states are coupled by the electron exchange matrix element, V, determined in the simplest case by the overlap between the electronic wave functions localized on different redox sites. Electron transfer occurs by quantum mechanical tunneling but this tunneling requires suitable bath fluctuations that bring reactant and product energy levels into resonance. In other words, ET has... 

Fig.1 Schematic views of typical electron transmission systems, (a) A standard electron transfer system containing a donor, an acceptor, and a molecular bridge connecting them (not shown are nuclear motion baths that must be coupled to the donor and acceptor species), (b) A molecular bridge connecting two electronic continua, L and R, representing, e.g., two metal electrodes (c) same as (b) with the bridge replaced by a molecular layer.

We present a derivation of the broadening due to the solvent according to a system/ bath quantum approach, originally worked out in the field of solid-state physics to treat the effect of electron/phonon couplings in the electronic transitions of electron traps in crystals [67, 68]. This approach has the advantage to treat all the nuclear degrees of freedom of the system solute/medium on the same foot, namely as coupled oscillators. The same type of approach has been adopted by Jortner and co-workers [69] to derive a quantum theory of thermal electron transfer in polar solvents. In that case, the solvent outside the first solvation shell was treated as a dielectric continuum and, in the frame of the polaron theory, the vibrational modes of the outer medium, that is, the polar modes, play the same role as the lattice optical modes of the crystal investigated elsewhere [67,68]. The total Hamiltonian of the solute (5) and the medium (m) can be formally written as... 

The Zusman equation (ZE)/ due mainly to its physically insightful picture on solvation dynamics, is (at least used to be) one of the most commonly used approaches in the study of quantum transfer processes. In this approach, the electronic system degrees of freedom are coupled to a collective bath coordinate that is assumed to be diffusive. The only approximation involved is the classical high temperature treatment of bath. To account for the dynamic Stokes shift, the standard ZE includes also the imaginary part of bath correlation function. This part does not depend on temperature and is therefore exact in the diffusion regime. 

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