Landau-Zener transmission coefficient

The transition described by (2.62) is classical and it is characterized by an activation energy equal to the potential at the crossing point. The prefactor is the attempt frequency co/27c times the Landau-Zener transmission coefficient B for nonadiabatic transition [Landau and Lifshitz 1981]... 

Marcus proposed that the analysis involving Eqs. (18 to 22) was also valid in the adiabatic limit. Smith and coworkers criticized this point on the basis of the fact that the transmission coefficient exhibits a complex dependent on the distance separating the redox species, and therefore should be considered in the integration step [36]. Let us consider the Landau-Zener transmission coefficient... 

The height of the potential barrier is lower than that for nonadiabatic reactions and depends on the interaction between the acceptor and the metal. However, at not too large values of the effective eiectrochemical Landau-Zener parameter the difference in the activation barriers is insignihcant. Taking into account the fact that the effective eiectron transmission coefficient is 1 here, one concludes that the rate of the adiabatic outer-sphere electron transfer reaction is practically independent of the electronic properties of the metal electrode. 

FIGURE 34.7 Dependence of the effective electron transmission coefficient on the electrochemical Landau-Zener parameter. 

The effect of the reaction adiabaticity on the electronic transmission coefficient can be estimated by making use of an extension of the Landau-Zener formalism [43—47] ... 

Relation (12) describes a thermally activated transition with activation energy = ( j — A) /4 j equal to the potential at the point of intersection. The preexponential factor in Eqn. (12) is equal to the vibration frequency co/2n multiplied by the transmission coefficient P representing the Landau-Zener factor [16] for the transition between the terms in the region of their... 

Newton determined the transmission coefficient, k, for the homogeneous electron transfer reaction between Fe " (H20)6 and Fe " (H20)6 redox couples in solution. The transmission coefficient was expressed in terms of the Landau-Zener " ° probability factor, P12, i.e.,... 

---