Reorganization energies

Within this framework, by considering the physical situation of the electrode double layer, the free energy of activation of an electron transfer reaction can be identified with the reorganization energy of the solvation sheath around the ion. This idea will be carried through in detail for the simple case of the strongly solvated... 

Imahori H, Hagiwara K, Akiyama T, Aoki M, Taniguchi S, Okada T, Shirakawa M and Sakata Y 1996 The small reorganization energy of Cgg in electron transfer Chem. Phys. Lett. 263 545-50... 

Here X is tire reorganization energy associated witli the curvature of tire reactant and product free energy wells and tlieir displacement witli respect to one another. Assuming a stmctureless polarizable medium, Marcus computed the solvent or outer-sphere component of tire reorganization energy to be... 

Figure 1 Temperature dependence of the reorganization energy and effective charges on...

This model permits one to immediately relate the bath frequency spectrum to the rate-constant temperature dependence. For the classical bath (PhoOc < 1) the Franck-Condon factor is proportional to exp( —with the reorganization energy equal to... 

Thus far we have discussed the direct mechanism of dissipation, when the reaction coordinate is coupled directly to the continuous spectrum of the bath degrees of freedom. For chemical reactions this situation is rather rare, since low-frequency acoustic phonon modes have much larger wavelengths than the size of the reaction complex, and so they cannot cause a considerable relative displacement of the reactants. The direct mechanism may play an essential role in long-distance electron transfer in dielectric media, when the reorganization energy is created by displacement of equilibrium positions of low-frequency polarization phonons. Another cause of friction may be anharmonicity of solids which leads to multiphonon processes. In particular, the Raman processes may provide small energy losses. 

Fig. 11. (a) Diagram of energy levels for a polyatomic molecule. Optical transition occurs from the ground state Ag to the excited electronic state Ai. Aj, are the vibrational sublevels of the optically forbidden electronic state A2. Arrows indicate vibrational relaxation (VR) in the states Ai and Aj, and radiationless transition (RLT). (b) Crossing of the terms Ai and Aj. Reorganization energy E, is indicated. 

Fig. 12. Marcus model of two harmonic terms in the limit of strong coupling. Reorganization energy E, is shown.

Note that only Er, which is actually the sum of the reorganization energies for all degrees of freedom, enters into the high-temperature rate constant formula (2.62). At low temperature, however, in order to preserve E, one has to fit an additional parameter co, which has no direct physical sense for a real multiphonon problem. 

Analyses of MEP have shown that the displacement of the center-of-mass of the reactant is much smaller than the tunneling length, and the environment reorganization energy is just 0.12-0.17 kcal/mol, being considerably smaller than F 2kcal/mol. This permits reduction of... 

Marcus theory. Consider that the reorganization energy for the ET reaction, AAb, can be approximated as the mean of the reorganization energies for the EE reactions Aab = (Aaa + ABb)/2. Show that substitution of this expression into Eq. (10-63) gives the usual form of the Marcus cross relation. 

Reaction scheme, defined, 9 Reactions back, 26 branching, 189 chain, 181-182, 187-189 competition, 105. 106 concurrent, 58-64 consecutive, 70, 130 diffusion-controlled, 199-202 elementary, 2, 4, 5, 12, 55 exchange, kinetics of, 55-58, 176 induced, 102 opposing, 49-55 oscillating, 190-192 parallel, 58-64, 129 product-catalyzed, 36-37 reversible, 46-55 termination, 182 trapping, 2, 102, 126 Reactivity, 112 Reactivity pattern, 106 Reactivity-selectivity principle, 238 Relaxation kinetics, 52, 257 -260 Relaxation time, 257 Reorganization energy, 241 Reversible reactions, 46-55 concentration-jump technique for, 52-55... 

Reactive trajectories, 43-44,45, 88,90-92,215 downhill trajectories, 90,91 velocity of, 90 Relaxation processes, 122 Relaxation times, 122 Reorganization energy, 92,227 Resonance integral, 10 Resonance structures, 58,143 for amide hydrolysis, 174,175 covalent bonding arrangement for, 84 for Cys-His proton transfer in papain, 141 for general acid catalysis, 160,161 for phosphodiester hydrolysis, 191-195,... 

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