Rate of PIET

We need the free energy of the reaction -AG, the total reorganization energy A, the coupling A/2, and the vibrational frequencies of the modes coupled to ET 

K is the electronic (transmission) factor equal to the probability to pass the avoided crossing region on the lower PES. 

FIGURE 13.5 The Marcus model with the important parameters reorganization energy X, coupling H[2 = A/2, free energy of reaction AG , and activation energy AG.  

It is thus possible to use Equation 13.11 and determine the free energy AG of the reaction experimentally by measuring reduction potentials for the acceptor and donor in a solvent. If we assume AS = 0, we have ordinary PES based on AH . PES may be assumed to be parabolic. It is also possible to define an effective force 

Equation 13.12 with K = 1 is a typical expression for a rate constant if it is assumed that the nuclei are moving by classical mechanics with the ground state PES as potential. This is the simplest approximation for the rate. However, in ET reactions, we have to remember that the barrier is associated with an avoided crossing between two different PES, and that there is a probability that the system jumps to the upper surface. In that case, k 1 in Equation 13.12. Thus, the system is in a formally different electronic state, but the character of the wave function does not 

---