Radiationless electron transfer

This lineshape analysis also implies tliat electron-transfer rates should be vibrational-state dependent, which has been observed experimentally [44]- Spin-orbit relaxation has also been identified as an important factor in controlling tire identity of botli electron and vibrational-state distributions in radiationless ET reactions. 

Knowledge of photoiaduced electroa-transfer dyaamics is important to technological appUcations. The quantum efficiency, ( ), ie, the number of chemical events per number of photons absorbed of the desired electron-transfer photoreaction, reflects the competition between rate of the electron-transfer process, eg, from Z7, and the radiative and radiationless decay of the excited state, reflected ia the lifetime, T, of ZA ia abseace ofM. Thus,... 

Instead of the quantity given by Eq. (15), the quantity given by Eq. (10) was treated as the activation energy of the process in the earlier papers on the quantum mechanical theory of electron transfer reactions. This difference between the results of the quantum mechanical theory of radiationless transitions and those obtained by the methods of nonequilibrium thermodynamics has also been noted in Ref. 9. The results of the quantum mechanical theory were obtained in the harmonic oscillator model, and Eqs. (9) and (10) are valid only if the vibrations of the oscillators are classical and their frequencies are unchanged in the course of the electron transition (i.e., (o k = w[). It might seem that, in this case, the energy of the transition and the free energy of the transition are equal to each other. However, we have to remember that for the solvent, the oscillators are the effective ones and the parameters of the system Hamiltonian related to the dielectric properties of the medium depend on the temperature. Therefore, the problem of the relationship between the results obtained by the two methods mentioned above deserves to be discussed. 

In the quantum mechanical formulation of electron transfer (Atkins, 1984 Closs et al, 1986) as a radiationless transition, the rate of ET is described as the product of the electronic coupling term J2 and the Frank-Condon factor FC, which is weighted with the Boltzmann population of the vibrational energy levels. But Marcus and Sutin (1985) have pointed out that, in the high-temperature limit, this treatment yields the semiclassical expression (9). 

This case is shown in Fig. 10.6c and d where through absorption of light a photohole in the vb and a photoelectron in the cb are formed. The probability that interfacial electron transfer takes place, i.e. that a thermodynamically suitable electron donor is oxidized by the photohole of the vb depends (i) on the rate constant of the interfacial electron transfer, kET, (ii) on the concentration of the adsorbed electron donor, [Rads]. and (iii) on the rate constants of recombination of the electron-hole pair via radiative and radiationless transitions,Ykj. At steady-state of the electronically excited state, the quantum yield, Ox, ofinterfacial electron-transfer can be expressed in terms of rate constants ... 

When molecules absorb a photon and produce an electronic excited state, the energy can be dissipated in several ways luminescence, radiationless decay to the ground state, and photochemistry. Luminescence dominated the older literature because it was easy to observe. A good review of luminescence is in Volume 3 of David Dolphin s seven-volume series The Porphyrins. Picosecond laser spectroscopy allowed for exploration of the radiationless decay pathways, particularly the initial steps that compete with luminescence and lead to photochemistry. Two principal forms of radiationless decay lead to long-term metastables ligand ejection and electron transfer. 

Kuzmin MG, Soboleva IV, Dolotova EV (2007) The behavior of exciplex decay processes and interplay of radiationless transition and preliminary reorganization mechanisms of electron transfer in loose and tight pairs of reactants. J Phys Chem A 111 206... 

Electron transfer reactions have also been treated from the quantum mechanical point of view in formal analogy to radiationless transitions, considering the weakly interacting states of a supermolecule AB the probability (rate constant) of the electron transfer is given by a golden rule expression of the type17... 

Next, let the focus be on one of the chosen ions, say, Fe3, and its hydration sheath (somewhat distorted by adsorption in the double layer). The energy levels in this ion at 300 K are predominantly in the ground state. Because the tunneling of the electron to the ion is taken to occur from the Fermi level of the metal and to be radiationless, the energy states in the ion are the ones of interest for electron transfer. This means that the electrons will be likely to find a home only in electronic states of the hydrated Fe3 ion, well above the ground state. 

The first quantum mechanical treatment for the radiationless electron transfer was developed by Gurney [68] for hydrogen evolution on mercury. In his model, Gurney assumed that the intermediate H " is not... 

Electron transfer from the excited states of Fe(II) to the H30 f cation in aqueous solutions of H2S04 which results in the formation of Fe(III) and of H atoms has been studied by Korolev and Bazhin [36, 37]. The quantum yield of the formation of Fe(III) in 5.5 M H2S04 at 77 K has been found to be only two times smaller than at room temperature. Photo-oxidation of Fe(II) is also observed at 4.2 K. The actual very weak dependence of the efficiency of Fe(II) photo-oxidation on temperature points to the tunneling mechanism of this process [36, 37]. Bazhin and Korolev [38], have made a detailed theoretical analysis in terms of the theory of radiationless transitions of the mechanism of electron transfer from the excited ions Fe(II) to H30 1 in solutions. In this work a simple way is suggested for an a priori estimation of the maximum possible distance, RmSiX, of tunneling between a donor and an acceptor in solid matrices. This method is based on taking into account the dependence... 

Internal conversion (IC) is a competing process to 7-ray decay and occurs when an excited nucleus interacts electromagnetically with an orbital electron and ejects it. This transfer of the nuclear excitation energy to the electron occurs radiationlessly (without the emission of a photon). The energy of the internal conversion electron, Eic, is given by... 

A + RCH2OH - AH. + RCHOH At low concentrations of photoexcited dye and in competition with radiationless deactivation processes the radicals can react with oxygen to form additional radicals and/or hydrogen peroxide. At higher concentrations electron transfer reactions to semi-reduced (A ) and semi-oxidized (A +) anthraquinone compounds can occur which in turn undergo secondary reactions. 

The Marcus Inverted Region (MIR) is that part of the function of rate constant versus free energy where a chemical reaction becomes slower as it becomes more exothermic. It has been observed in many thermal electron transfer processes such as neutralization of ion pairs, but not for photoinduced charge separation between neutral molecules. The reasons for this discrepancy have been the object of much controversy in recent years, and the present article gives a critical summary of the theoretical basis of the MIR as well as of the explanations proposed for its absence in photoinduced electron transfer. The role of the solvent receives special attention, notably in view of the possible effects of dielectric saturation in the field of ions. The relationship between the MIR and the theories of radiationless transitions is a topic of current development, although in the Marcus-Hush Model electron transfer is treated as a thermally activated process. 

Chapter 3 describes radiationless transitions in the tunneling electron transfers in multi-electron systems. The following are examined within the framework of electron Green s function approach the dependence on distance, the influence of crystalline media, and the effect of intermediate particles on the tunneling transfer. It is demonstrated that the Born-Oppenheimer approximation for the wave function is invalid for longdistance tunneling. 

The next two chapters are devoted to ultrafast radiationless transitions. In Chapter 5, the generalized linear response theory is used to treat the non-equilibrium dynamics of molecular systems. This method, based on the density matrix method, can also be used to calculate the transient spectroscopic signals that are often monitored experimentally. As an application of the method, the authors present the study of the interfadal photo-induced electron transfer in dye-sensitized solar cell as observed by transient absorption spectroscopy. Chapter 6 uses the density matrix method to discuss important processes that occur in the bacterial photosynthetic reaction center, which has congested electronic structure within 200-1500cm 1 and weak interactions between these electronic states. Therefore, this biological system is an ideal system to examine theoretical models (memory effect, coherence effect, vibrational relaxation, etc.) and techniques (generalized linear response theory, Forster-Dexter theory, Marcus theory, internal conversion theory, etc.) for treating ultrafast radiationless transition phenomena. 

The theory of the multi-vibrational electron transitions based on the adiabatic representation for the wave functions of the initial and final states is the subject of this chapter. Then, the matrix element for radiationless multi-vibrational electron transition is the product of the electron matrix element and the nuclear element. The presented theory is devoted to the calculation of the nuclear component of the transition probability. The different calculation methods developed in the pioneer works of S.I. Pekar, Huang Kun and A. Rhys, M. Lax, R. Kubo and Y. Toyozawa will be described including the operator method, the method of the moments, and density matrix method. In the description of the high-temperature limit of the general formula for the rate constant, specifically Marcus s formula, the concept of reorganization energy is introduced. The application of the theory to electron transfer reactions in polar media is described. Finally, the adiabatic transitions are discussed. 

A microscopic theory for describing ultrafast radiationless transitions in particular for, photo-induced ultrafast radiationless transitions is presented. For this purpose, one example system that well represents the ultrafast radiationless transaction problem is considered. More specifically, bacterial photosynthetic reaction centers (RCs) are investigated for their ultrafast electronic-excitation energy transfer (EET) processes and ultrafast electron transfer (ET) processes. Several applications of the density matrix method are presented for emphasizing that the density matrix method can not only treat the dynamics due to the radiationless transitions but also deal with the population and coherence dynamics. Several rate constants of the radiationless transitions and the analytic estimation methods of those rate... 

Deactivation of an excited species can proceed through radiation or radiationless decays, energy transfer quenching, or electron transfer routes. The operation of artificial photosynthetic devices relies mainly on electron-transfer (ET) processes induced by an excited species [16, 17]. Two general mechanisms can be involved in the ET process of an excited species Reductive ET quenching of an excited species, S, by an electron donor D, results in the redox products S- and D+ (Fig. 4 a). Alternatively, oxidative quenching of the excited species by an electron acceptor, A, can occur (Fig. 4b), resulting in the electron transfer products S+ and A-. 

In a supramolecular system, electronic energy transfer, as depicted in Fig. 3.1, can be viewed as a radiationless transition between two locally, electronically excited states. Similarly to the electron transfer described above, we deal with two different states. Nevertheless, these states are local excitations lacking any charge transfer. 

Fig. 4. Electron transfer quenching via exciplex formation, a exciplex emission b exciplex radiationless deactivation c geminate ion recombination. For sake of simplicity, processes such as exciplex dissociation into A + B, exciplex reactions other than the electron transfer one and direct formation of a solvated ion pair from the encounter complex have been omitted...

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