Donor electron-vibration coupling

The full quantum-mechanical treatment of the vibrations coupled to the changes of the electronic state is rather sophisticated. A convenient simplification is to consider only one vibrational mode for the donor, cop, and another one for the acceptor, This is a dramatic simplification, but the result can be generalised to multi-mode processes using a suitable procedure. Another simplification is the classical treatment of the low-frequency modes, attributed to the medium and to low vibrational frequencies of the reactants and products. This is a good approximation if o k T. For example, v < 100 cm corresponds to a spacing of <1 kJ mol" between the vibrational levels, which is less than the thermal energy at room temperature, RT = 2.5 kJ mol f A difference of 200 cm between the simulation of the anthracene absorption and emission was found in Figure 15.11. 

In this formula, V is the electron coupling energy, R is the distance between the centres of the D and A particles, a is the width of the charge transfer band, and Emax = Ed — Ea + Av, where (ED — EA) is the difference of the redox potentials of the donor and the acceptor and Av is the energy spent on the excitation of the vibrational degrees of freedom. 

---