Electron-transfer . nonadiabatic solvent electronic coupling

In the nonadiabatic case, electron transfer is a rare event. Therefore, the equilibrium distribution in the initial well is undisturbed, and the preexponential factor is determined by the electronic coupling between the reactants. In adiabatic reactions, the electronic system is in equilibrium at all points of the trajectory therefore, the rate is not limited by electron transfer but by solvent dynamics. 

We have presented several approaches to calculate the rate constants of electron transfer occurring in solvent from the weak to strong electronic couplings. In the fast solvent relaxation limit, the approach based on the nonadiabatic transition state theory can be adopted. It is related to the Marcus formula by a prefactor and referred as a modified Marcus formula. When the solvent dynamics begin to play a role, the quantum Kramers-like theory is applicable. For the case where the intramoleeular vibrational motions are much faster than the solvent motion, the extended Sumi-Mareus theory is a better ehoice. As the coherent motion of eleetron is ineorporated, such as in the organic semiconductors, the time-dependent wavepaeket diffusion approach is proposed. Several applications show that the proposed approaches, together with electronic structure calculations for the faetors eontrolling eleetron transfer, can be used to theoretically predict electron transfer rates correctly. 

In this section, we switch gears slightly to address another contemporary topic, solvation dynamics coupled into the ESPT reaction. One relevant, important issue of current interest is the ESPT coupled excited-state charge transfer (ESCT) reaction. Seminal theoretical approaches applied by Hynes and coworkers revealed the key features, with descriptions of dynamics and electronic structures of non-adiabatic [119, 120] and adiabatic [121-123] proton transfer reactions. The most recent theoretical advancement has incorporated both solvent reorganization and proton tunneling and made the framework similar to electron transfer reaction, [119-126] such that the proton transfer rate kpt can be categorized into two regimes (a) For nonadiabatic limit [120] ... 

In the simplest case, the R mode is characterized by a low frequency and is not dynamically coupled to the fluctuations of the solvent. The system is assumed to maintain an equilibrium distribution along the R coordinate. In this case, ve can exclude the R mode from the dynamical description and consider an equilibrium ensemble of PCET systems with fixed proton donor-acceptor distances. The electrons and transferring proton are assumed to be adiabatic with respect to the R coordinate and solvent coordinates within the reactant and product states. Thus, the reaction is described in terms of nonadiabatic transitions between two sets of intersecting free energy surfaces ( R, and ej, Zp, corresponding to... 

Figure 9.6 Pressure-effect on rates of some self-exchange electron-transfer reactions between metal ions comparison of observed volumes of activation with values calculated from classical Marcus theory for adiabatic reactions. The plot shows calculated and observed AP values (cm mol ) at mid-range of pressure (100 MPa, except 70 MPa for Fe(H20)g ) for adiabatic (filled symbols) and nonadiabatic (open circles) self-exchange in couples with rigid ligands. Solvents (o, ) water ( ) CD3CN (A) (CD3)2CO (V) CD3OD. Key (A,B) (C,D) Cu(dmp)2 (E-G) Ru(hfac)j (H) Fe(C5H5)2 (I-K) Mn(CN-t-Bu)g ...

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