Marcus charge-transfer theory

Theoretical analysis of (2.5.1) based on the Marcus-Levich charge-transfer theory can be found in [34]. 

For route 2, charge transport mechanism is similar to the hopping mechanism of small molecules. According to the charge transport theory developed hy Bredas et al. [22], the charge carrier transport in organic materials can be described by Marcus electron transfer theory (Eq. 1.3). In organic ciystals, the AG is 0 because the electron transfer happens in a same kind of molecules. Thus the Eq. 1.3 formula can be simplified into Eq. 1.4 as follows ... 

A unified view has been published of the Marcus electron transfer and Mullikan charge transfer theories as applied in organometallic chemistry.In... 

Figure 42. Scheme comparing expected potential-independent charge-transfer rates from Marcus-Gerischer theory of interfacia) electron transfer (left) with possible mechanisms for explaining the experimental observation of potential-dependent electron-transfer rates (right) a potential-dependent concentration of surface states, or a charge-transfer rate that depends on the thermodynamic force (electric potential difference) in the interface. 

According to the Marcus theory [9], the electron transfer rate depends upon the reaction enthalpy (AG), the electronic coupling (V) and the reorganization energy (A). By changing the electron donor and the bridge we measured the influence of these parameters on the charge transfer rate. The re-... 

The extent to which steric effects adversely affect the attainment of such intimate ion-pair structures would be reflected in an increase in the work term and concomitant diminution of the inner-sphere rate. This qualitative conclusion accords with the reactivity trend in Figure 16. However, Marcus theory does not provide a quantitative basis for evaluating the variation in the work term of such ion pairs. To obtain the latter we now turn to the Mulliken theory of charge transfer in which the energetics of ion-pair formation evolve directly, and provide quantitative informa-... 

Po is a prefactor mobility (zero held, inhnite temperature), C is an empirical constant of 2.9 X 10 (cm/V), a and S express the energetic (diagonal) and positional disorder (off-diagonal), respectively. Other approaches also exist, one of them being based on the Marcus theory of charge transfer [247, 248]. 

An analytical theory based upon the effective medium approach (EMA) has been developed by Fishchuk et al. [70]. They consider the superposition of disorder and polaron effects and treat the elementary charge transfer process at moderate to high temperatures in terms of symmetric Marcus rates instead of Miller-Abrahams rates (see below). The predicted temperature and field dependence of the mobility is... 

Excited State Charge Transfer. Our goal here is to discuss aspects of ET theory that are most relevant to the charge transfer processes of excited molecules. One important point is that often the solvent relaxation is not well modeled with a single t, but rather a distribution of times apply. This subject has been treated by Hynes [63], Nadler and Marcus [65], Rips and Jortner [66], Mukamel [67], Newton and Friedman [68], Zusman [62], Warshel [71], and Fonseca [139], We also would like to study ET in the strongly adiabatic regime since experimental results on BA indicate this is the correct limit. Finally, we would like to treat the special case of three-well ET, which is the case for BA. 

One of the most important new areas of theory of charge transfer reactions is direct molecular simulations, which allows for an unprecedented, molecular level view of solvent motion during reactions in this class. One of the important themes for research of this type is to ascertain the validity at a molecular level of the linear response theory estimates of solvent interactions that are inherent in Marcus theory and related approaches. In addition, the importance of dynamic solvent effects on charge transfer kinetics is being examined. Recent papers on this subject have been published by Warshel [71], Hynes [141] and Bader and Chandler [137, 138],... 

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