Dispersed polaron

Warshel, A. Chu, Z.T. Parson, W.W., Dispersed polaron simulations of electron transfer in photosynthetic reaction centers, Science 1989, 246, 112-116. 

Warshel, A. and Hwang, J.-K. (1986). Simulation of the dynamics of electron transfer reactions in polar solvents semiclassical trajectories and dispersed polaron approaches. 

This relationship is only applicable if the system can be described by the linear response approximation (see Ref. [46]), but this does not require that the system will be harmonic. The above vibronic treatment is similar to the expression developed by Kuznetsov and Ulstrup [47]. However, the treatment that leads to Eq. (8.21), which was developed by Warshel and coworkers [1, 42, 46], is based on a more microscopic approach and leads to much more consistent treatment of Ag (see also below) where we can use rigorously AG rather than AE. Furthermore, our dispersed polaron (spin boson) treatment [46] of Eq. (8.18) and if needed Eq. (8.21) gives a clear connection between the spectral distribution of the solvent fluctuations and the low temperature limit of Eq. (8.18). It is also useful to note that Bor-gis and Hynes [48] and Antoniou and Schwartz [49] have used a similar treatment but considered only the lowest vibrational levels of the proton. 

Simulation of the Dynamics of Electron Transfer Reactions in Polar Solvents Semidassical Trajectories and Dispersed Polaron Approaches,... 

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)],... 

To apply Redfield theory to these real-world condensed-phase problems, it will clearly be essential to construct appropriate reduced models from classical simulations, as in the dispersed polaron method of Warshel [67,68]. Carrying this process out for a general multilevel, as opposed to a two-level, system will necessitate considerable study as to the most... 

We have used the dispersed-polaron theory to examine the reaction in which an electron moves from Hl" to the first quinone (Qa) and also the much slower back-reaction between Qa and P+ (26,27). The rate of electron transfer from Hl to Qa is predicted to be essentially independent of temperature, which agrees well with the experimental observations on Rps. viridis (31). 

Hl (18) shows a similiar insensitivity to AG°. Application of the dispersed-polaron theory to these initial steps is currently underway. 

However, one should be cautious about overinterpreting the field and temperature dependence of the mobility obtained from ToF measurements. For instance, in the analyses of the data in [86, 87], ToF signals have been considered that are dispersive. It is well known that data collected under dispersive transport conditions carry a weaker temperature dependence because the charge carriers have not yet reached quasi-equilibrium. This contributes to an apparent Arrhenius-type temperature dependence of p that might erroneously be accounted for by polaron effects. 

In fact, in their recent work, Mensfoort et al. [90] conclude that in polyfluorene copolymers hole transport is entirely dominated by disorder. This is supported by a strictly linear In p cx dependence covering a dynamic range of 15 decades with a temperature range from 150 to 315 K (Fig. 8). Based upon stationary space-charge-limited current measurement, where the charge carriers are in quasi equilibrium so that dispersion effects are absent, the authors determine a width a of the DOS for holes as large as 130 meV with negligible polaron contribution. 

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