Electron transfer, vibronic relaxation

Kr. In the B-emitting states, a slower stepwise relaxation was observed. Figure C3.5.5 shows the possible modes of relaxation for B-emitting XeF and some experimentally detennined time constants. Although a diatomic in an atomic lattice seems to be a simple system, these vibronic relaxation experiments are rather complicated to interiDret, because of multiple electronic states which are involved due to energy transfer between B and C sites. 

Figure C3.5.5. Vibronic relaxation time constants for B- and C-state emitting sites of XeF in solid Ar for different vibrational quantum numbers v, from [25]. Vibronic energy relaxation is complicated by electronic crossings caused by energy transfer between sites.

The first type of interaction, associated with the overlap of wavefunctions localized at different centers in the initial and final states, determines the electron-transfer rate constant. The other two are crucial for vibronic relaxation of excited electronic states. The rate constant in the first order of the perturbation theory in the unaccounted interaction is described by the statistically averaged Fermi golden-rule formula... 

The reactions of electron transfer and vibronic relaxation are ubiquitous in chemistry and many review papers have dealt with them in detail (see, e.g., Ovchinnikov and Ovchinnikova [1982], Ulstrup [1979]), so we discuss them to the extent that the nuclear tunneling is involved. 

If the system under consideration possesses non-adiabatic electronic couplings within the excited-state vibronic manifold, the latter approach no longer is applicable. Recently, we have developed a simple model which allows for the explicit calculation of RF s for electronically nonadiabatic systems coupled to a heat bath [2]. The model is based on a phenomenological dissipation ansatz which describes the major bath-induced relaxation processes excited-state population decay, optical dephasing, and vibrational relaxation. The model has been applied for the calculation of the time and frequency gated spontaneous emission spectra for model nonadiabatic electron-transfer systems. The predictions of the model have been tested against more accurate calculations performed within the Redfield formalism [2]. It is natural, therefore, to extend this... 

Processes associated with electron transfer and/or vibronic relaxation are ubiquitous in chemistry, and many review papers have discussed them... 

Charge injection is fast compared with nuclear relaxation of the excited state (k k,). In this case, interfacial charge transfer would take place from the prepared hot vibronic level (Eq. (34)) and the quantum yield for the primary injection process would be close to unity = 1). For both limiting cases, k[ kr and k[ kr, relation (30) would be relevant, provided electron transfer is nonadiabatic. 

Fig. 1. a The process of fluorescence i Incoming radiation excites an electron from the HOMO of a fluorophore to a high vibrational state of the LUMO, which ii relaxes to the lowest LUMO vibronic level, in Decay of the excited electron from the LUMO back to the HOMO occurs radiatively, with the emission of a photon, i.e., fluorescence, b In a PET-quenched system, iv excitation and v vibronic relaxation occur as before, vi With an electron-donor present in the system, an electron can be transferred from S0 of the quencher to S0 of the fluorophore, preventing fluorescence, vii Finally, the excited electron in the fluorophore LUMO decays nonradiatively to the S0 of the quencher... 

Doom and Hupp have used preresonance Raman spectra in an analysis of the vibronic components which contribute to the intervalence absorption maximum of [(CN)5Ru -CN-Ru (NH3)5] and to the MLCT absorption maximum of [(bpy)Ru(NH3)4] ". These authors employ the time-dependent scattering approach of Heller to obtain the nuclear displacements of several vibrational modes coupled to the electronic transitions. They find in each case that several vibrational modes, spanning a wide range of frequencies, do contribute significantly to the photoinduced electron transfer processes. Hopkins and co-workers have used a two-color, ps Raman technique to investigate interligand electron transfer in Ru(II)-tn5-polypyridyl complexes, and they find vibrational relaxation of the electronically excited mole ule occurs within about 30 ps of excitation, after which interligand equilibration occurs more slowly than 5 x 10 s. 

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