Quantum Reorganization energy

Figure 1. Activation energy of electron-transfer process as a function of electronic energy gap of a reaction. Er = Eg + Ec is the total reorganization energy where Es is the classical solvent reorganization energy and Ec is the reorganization energy of an intramolecular mode, l

The essentials of quantum kinetics were in place by 1954, Weiss having added to the Gurney theory a comprehensive theory of redox reactions. By this date, tunneling, adiabatic and non-adiabatic electron transfer, the simplicity introduced by considering redox reactions between isotopes, the separate contribution from outer sphere and inner sphere, and in particular the equation for the reorganization energy involving and stat had all been published. 

The role of the quantum number nf is different depending upon the relationship between the exothermicity and the reorganization energy. If Er > J, then the growth of n results in that of the activation energy for the transition (0 -> n ). In this case the most essential is the transition (0 - 0) and the probability of tunneling has the form... 

Let us now consider the system with an arbitrary spectrum of normal vibrations. In this case normal vibrations should be first divided into classical < T) and quantum (cok > T) vibrations. If the reorganization energy of the classical vibrations exceeds the reaction exothermicity then, neglecting the excitation and absorption of phonons with the frequencies k > T, in the same way as when deriving eqn. (41), i.e. taking into account, for the quantum degrees of freedom, only the transitions (0 - 0), we obtain for the probability of tunneling the expression... 

Figure 3.54. The quantum yield of excited states as a function of the ionization free energy at the large (a) and small (b) reorganization energy of electron transfer. The numerically calculated curves for remote transfer are shown by solid lines for slow diffusion (D = 1CT7 cm2/s) and by the long dashed lines for the faster one (D = 10 6cm2/s). Contact calculations (CAs) of the same curves are made with (dotted lines) and without taking into account the reverse electron transfer to the ionized state (dashed-dotted line). (From Ref. 189.)...

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