Reorganizational energy

Here we mention as an example that in the coordination-chemistry field optical MMCT transitions between weakly coupled species are usually evaluated using the Hush theory [10,11]. The energy of the MMCT transition is given by = AE + x- Here AE is the difference between the potentials of both redox couples involved in the CT process. The reorganizational energy x is the sum of inner-sphere and outer-sphere contributions. The former depends on structural changes after the MMCT excitation transition, the latter depends on solvent polarity and the distance between the redox centres. However, similar approaches are also known in the solid state field since long [12]. 

In addition, the determination of metal-ligand bond distances in solution and their oxidation state dependence is critical to the application of electron transfer theories since such changes can contribute significantly to the energy of activation through the so-called inner-sphere reorganizational energy term. 

Nuclear frequency factors are calculated directly from the calculated molecular vibrational frequencies and the reorganizational energies, and these, in conjunction with the calculated Hab values lead to values for the electronic transmission coefficient, Kep... 

This energy formula [234,235] is general and suffers from no approximations in that all the appropriate bonded and nonbonded contributions are formally accommodated and because the electroneutrality requirements are met in the definition of reorganizational energy. Only dissociations yielding electroneutral products need be considered as the formation of ions, KL + L, require no more than... 

TABLE 12.3. Radical Atomization and Reorganizational Energies (kcal/mol)... 

The approximate validity of Eq. (12.9) highhghts the leading role played by the reorganizational energies but also vividly demonstrates the importance of using the correct intrinsic bond energies, whose values range from 69.63 to 89.1 kcal/mol... 

This brings us to examine the formal resemblance and the conceptual difference between Eq. (12.9) and Sanderson s approximation [244,245]. The latter can be deduced from Eqs. (12.1) and (12.3) by redefining the reorganizational energies as A (K) — A (K )—an approach oblivious of the fact that K and K are not isoelec-tronic in most cases, but approximately valid as long as the CNE terms remain sufficiently small. The point is that Sanderson s formula, Dec = ecc + RE(K) - - RE(L), treats 8cc as a constant, which is not true. This simplifying hypothesis did not appear... 

The approximate linear decrease of reorganizational energies with increasingly larger 8ch energies (Eig. 12.2) and Eq. (12.11) explain the existence of a correlation between Dch and sch-... 

The approximations (12.10) and (12.11) can be used to obtain information about reorganizational energies, as shown in the following two examples. 

Figure 12.2. A comparison between reorganizational energies and theoretical bond energies of alkane CH bonds (kcal/mol). The numbering refers to that shown in Table 12.3 [233].

The first step regards the reorganizational energy of the NH2 CH2 radical—it is known (Table 12.3). 

This reorganizational energy, the A energies deduced from experimental enthalpies [248], and the energies of the alkyl radicals (Table 12.3) now give the following... 

A few typical nitrogen-nitrogen bonds are briefly examined. The key is in the result obtained from dimethylamine, leading to RECCHsNH ) = 9.19 kcal/mol. With AHf° (CHsNH ) = 43.6 3 kcal/mol [246] and ZPE + Hr Hq = 31.7S, kcal/mol [139], we get AE/= 471.54 kcal/mol for this radical hence Dcn = 89.27 kcal/ mol for dimethylamine, and thereby the reorganizational energy indicated above. 

Electron transfer is often associated with the conformation changes. For organic ion radicals the inner reorganizational energies remain modest, allowing a fast passage between the different conformations during the electron transfer (for example, see Bellec and others 2000). 

For real systems, the distance dependence of the FCWDel term cannot be completely neglected due to the presence of reorganizational energy and the driving force. Thus, a correction for these influences should be done to Eq. 3.3 before applying to experimental results. 

Let us now take a closer examination of the expressions used to estimate the total reorganizational energy. 

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