The Electronic Coupling Element

Fig. 1.18 Variation of the standard heterogeneous rate constant, k°, with the electronic coupling element for different vn and X values. The effect of the electronic interaction on the activation energy has been ignored [2, 49]. / r = 108cm I, pM = 0.3 eV4, T = 298 K...

Most importantly, the spectral characteristics of the charge-transfer (CT) absorption band also provide a quantitative measure of the electronic coupling element in the intermolecular complex, i.e. [14-16] ... 

As is apparent from Eq. (7), the energy of the electronic transition in CT complexes is determined as the sum of the two terms, the difference in the energy of the diabatic states (Ada) and the electronic coupling element (HDa). Depending on their relative values, there can be two limiting cases represented by weak complexes with Hda Ada and strong complexes with Ada HDA. 

Fig. 8. Typical profiles of the potential-energy surfaces for electron-transfer in the isergonic region (for 2 = 1.8 eV). The dotted lines represent the diabatic (non-interacting) states (HDa = 0). Adiabatic states (solid lines) are presented with the values of the electronic coupling element Hda...

As mentioned earlier, KT/3-21G calculations offer a simple computational method for reliably estimating both the distance dependence and the strength of the electronic coupling element for ET in a variety of systems.39,83 In this context, one also requires a method for analysing and dissecting intra-bridge orbital interactions, and several elegant treatments are available.39,42-45,84,85,89,125-140... 

Figure 3. Plot of the diabatic (Ga, Gb) and adiabatic (G, G2) free-energies of the reactants and products against the reaction coordinate for an electron transfer reaction with AG° = 0. i/ab is the electronic coupling element between the diabatic states of the reactants and products and X is the reorganization energy for the reaction.

Using the Mulliken formalism, Hush [29] showed that the electronic coupling element is related to the intensity of the charge transfer transition by ... 

For most charge transfer reactions the electronic coupling element is simply given by the coulomb matrix element defined by Eq. 61a. 

The electronic coupling element for a charge transfer reaction 7/ab is equal to... 

Figure 12. The relationship between the n ionization potential splitting energy in a diene and the electronic coupling element for hole transfer in the corresponding radical cation.

This study, together with other experiments on 23(n) (vide infra) provided the first definitive experimental evidence for the exponential distance dependence of long-range ET processes which was predicted on the basis of an exponential decay behavior of the electronic coupling element, V i, with increasing donor-acceptor separation (Eq. 3). 

It is interesting to note that the electronic coupling elements, Vei are much larger for the charge shift ET reactions in the anion radicals of 23(n) (Figure 24c) than for CR in the CS states in the respective systems (Figure 23), notwithstanding the comparable p i values for the two reactions. For example, for 23(8), Vei is six times... 

Figure 23. Values of the electronic coupling elements, V i, calculated from charge transfer fluorescence data for 23(n) in n-butylether 75],...

The mixed-valence complexes 33(n) displayed intervalence absorption bands from which the electronic coupling elements, Vet were calculated using Hush theory [77, 78], The distance dependence of Vei was found to be [85] ... 

The electronic coupling elements between the lowest excited CT state and the ground state (Fq) or the locally excited state lying most closely in energy V ) can be estimated from the CT absorption and fluorescence investigations [14, 54, 57], Applying a simple kinetic model of an irreversible excited CT state formation (with 100 % efficiency) the radiationless (k r) and radiative (kf) rate constants can be determined from the CT fluorescence quantum yields Of and lifetimes r ... 

In the theoretical description of the overall reaction rate the modified Eq. (1) may be applied (with the assumption that the electronic coupling element does not depend on the quantum number, j, of the excited vibrational mode) ... 

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