Electronic transmission factor

A quantitative determination of such matrix elements (to be elaborated below) is of crucial importance because it not only allows an absolute evaluation of the desired rate constants but also helps to reveal the qualitative aspects of the mechanism. In particular, questions regarding the magnitude of electronic transmission factors and the relative importance of ligands and metal ions in facilitating electron exchange between transition metal complexes can be assessed from a knowledge of... 

Figure 4. Calculated HAB values as a function of Fe -Fe separation, based on the structural model given in Figure 1 and the diabatic wavefunctions I/a and f/B. Curves 1 and 2 are based on separate models in which the inner-shell ligands are represented, respectively, by a point charge crystal field model [Fe(H20)62 -Fe(HsO)63 ] and by explicit quantum mechanical inclusion of their valence electrons [Fe(HgO)s2 -Fe(H20)s3+] (as defined by the dashed rectangle in Figure 1). The corresponding values of Kei, the electronic transmission factor, are displayed for various Fe-Fe separations of interest.

Figure 2.1(a) above illustrates the potential energy surface for a diabatic electron transfer process. In a diabatic (or non-adiabatic) reaction, the electronic coupling between donor and acceptor is weak and, consequently, the probability of crossover between the product and reactant surfaces will be small, i.e. for diabatic electron transfer /cei, the electronic transmission factor, is transition state appears as a sharp cusp and the system must cross over the transition state onto a new potential energy surface in order for electron transfer to occur. Longdistance electron transfers tend to be diabatic because of the reduced coupling between donor and acceptor components this is discussed in more detail below in Section 2.2.2. 

Adiabatic electron transfer Electron transfer process in which the reacting system remains on a single electronic surface in passing from reactants to products. For adiabatic electron transfer the electronic transmission factor is close to unity (see Marcus equation). 

Ab initio SCF and Mbller Flesset calculations with flexible valence basis sets including 4f orbitals are carried out for the ground and first excited spin states of the Co(NH3)52 and Co(NH3)5 complexes. The results of the calculations in conjunction with a first-order spin-orbit coupling model yield an estimate of 10" for the electronic transmission factor in the Co(NH3)5 exchange reaction using an apex-to-apex approach of reactants, thus providing a mechanism characterized by only a modest degree of non-adiabaticity, consistent with the experimental kinetic data. 

For cases of electron transfer between relatively weakly coupled reactants, the 2-state Landau-Zener model leads to the following expression for the electronic transmission factor, (as in... 

Thus, the electronic transmission factor /Cei (Eq. 52) will increase monotonically... 

The calculation of the electronic-transmission factor currently involves three different methods, viz. the Landau-Zener formula, Fermi s golden mle [35], and electron tunneling formalism such as the Wentzel-Kramer-Brillouin method [36]. We used the Landau-Zener formula [37,38] to calculate it ... 

For a nonadiabatic reaction eq(l) must be multiplied by an electronic transmission factor k<1. 

K is the electronic (transmission) factor, equal to the probability to pass the avoided crossing region on the lower PES. We will first assume that k is equal to unity. This is called adiabatic ET and physically means that the system moves exclusively on the lower PES. After the barrier has been passed, the electronic state corresponds to a state where the electron has moved to the other site. 

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

Expressions (1) and (2) are the basis for the Hush-Marcus model. They allow the construction of potential energy curves of parabolic shapes, when the energy is plotted as a function of a composite reaction coordinate. These curves in turn are the basis for an elementary description of the thermal and optical processes in mixed valences complexes. In principle, it is possible to compute a rate constant from this model, using the total reorganization energy as an activation energy and introducing an electronic transmission factor calculated by the Landau-Zener formula. However this procedure is now supplanted by the quantum models. 

---