Marcus theory semiclassical approaches

The last three years have seen considerable interest in the development of semiclassical methods for treating complex molecular collisions, i.e. those which involve inelastic or reactive processes. One of the reasons for this activity is that the recent work, primarily that of Miller and that of Marcus,2 has shown how numerically computed classical trajectories can be used as input to the semiclassical theory, so that it is not necessary to make any dynamical approximations when applying these semiclassical approaches... 

An alternative approach to polaron transport in organic solids is in terms of electron transfer (ET). The process can be viewed as a special case of the non-radiative decay of an electronic state. The derivation of the theory is developed in various books or review papers [13-15]. The parameter of importance here is the transition probability per unit time (or transition rate) kif between an initial and a final state. The rate is estimated within the Franck-Condon approximation. In the high-temperature regime ( cOif < kT) the Franck-Condon-weighted density (FCWD) reduces to a standard Arrhenius equation, so the rate takes its semiclassical Marcus theory expression [16] ... 

Two different theoretical approaches have been used to relate the ET rate constant (k ) to the thermodynamic driving force (AG ) and parameters related to molecular structure. The first approach is the semiclassical treatment derived from the early work by Marcus on ET theory [2-4,45],... 

The theoretical description of the kinetics of electron transfer reactions starts fi om the pioneering work of Marcus [1] in his work the convenient expression for the free energy of activation was defined. However, the pre-exponential factor in the expression for the reaction rate constant was left undetermined in the framework of that classical (activate-complex formalism) and macroscopic theory. The more sophisticated, semiclassical or quantum-mechanical, approaches [37-41] avoid this inadequacy. Typically, they are based on the Franck-Condon principle, i.e., assuming the separation of the electronic and nuclear motions. The Franck-Condon principle... 

In recent years the semiclassical "statistical theory of RICE, RAMSPERGER, KASSEL, and MARCUS /136/ has made great progress in its development. The computational techniques of this theory provide the possibility of calculating the velocities of unimolecular reactions using suitable, models for the activated complex. This approach is certainly very useful for a correlation of the experimental facts and a description of various aspects of the observed phenomena. The success of such applications of the RRKM-theory does not at all preclude an alternative treatment based on the collision theory of... 

---