Equilibrated excited state

In solution, the excess vibrational energy following an FC transition is lost very quickly — there are indications that only a few picoseconds are needed for the complex to come to thermal equilibrium with the medium with respect to vibrational excitation.19 We speak of the thermally equilibrated excited state, or, as an abbreviation, of the thexi state. Photochemical and photophysical processes very often involve thexi states. 

A related view of the physical basis of the solvent coordinate is the well-known reaction field R, which is the field located on the solute dipole due to the dipole induced solvent polarization. For example, the reaction field for the equilibrated excited state dipole Rlq is given by... 

According to the Franck-Condon principle, the photoexcitation triggers a vertical transition to the excited state, which is followed by a rapid nuclear equilibration. Without donor excitation, the electron transfer process would be highly endothermic. However, after exciting the donor, electron transfer occurs at the crossing of the equilibrated excited state surface and the product state. 

The expression given in Eq. (10) for the work assumes that p = 0, where p is the ionic strength of the medium. AG is the free-energy of the equilibrated excited-state (AG AE00), rD and rA are the molecular radii of the donor and acceptor molecules, e5 is the static dielectric constant or permittivity of the solvent, and z is the charge on each ion. ss is related to the response of the permanent dipoles of the surrounding solvent molecules to an external electrical field. Equation (9), the Bom equation, measures the difference in solvation energy between radical ions in vacuo and solution. 

To a significant extent, the vibrationally equilibrated excited states (VEqES) can be treated as a well-defined thermodynamic system. The molecular geometry, the solvation environment, and so forth can, in principle, be inferred from the emission band shape (e. g., as in Eqs. 17 and 18) or they can be probed by the use of resonance Raman and time-resolved Raman and infrared techniques. Typically, the VEqES is a better oxidant and reductant than the ground state, and this is a very important aspect of the chemistry of charge-transfer excited states. 

Vibrationally Equilibrated Excited States Relaxation Processes... 

Figure 2. Generalized excited state diagram. M represents a ground-state molecule, M and M are the Franck-Condon and thermally equilibrated excited states, respectively, hv is the excitation energy, Eqq the excited state energy, and tq is the inherent excited state lifetime. Relevant ground-and excited state redox couples are shown.

In the light of the rapid excited-state relaxation dynamics and the observed <100 fs electron injection component, the fast injection component must occur from non-equilibrated excited states. Distinct singlet and triplet electron-injection pathways have been observed for Ru polypyridyl complexes on SnOa (Iwai et al, 2000) and TiOi (Benko et al, 2002 Kalloinen et al, 2002). In a detailed study of electron injection dynamics in N3/TiOi (Benko et al, 2002 Kalloinen et al, 2002), 55% of electron injection was shown to occur with 50 fs injection time from singlet MLCT... 

Because of the several qualitative diflFerences between the concepts of ligand field and thermally equilibrated excited states, it is useful to develop a distinguishing vocabulary. Conventional ligand field excited states will be called Franck-Condon states since the energies are those of band maxima and the transitions between them are essentially those vertical ones with maximum Franck-Condon overlap. The abbreviation thexi state has been proposed (12) for a thermally equilibrated excited state. The gist of the foregoing is that conventional ligand field theory treats hypothetical electronic excited states which are in reality Franck-Condon states, whereas it is thexi states that are important in photophysical and photochemical processes. New theory or new extensions of present theory are clearly needed to treat the latter type of state. 

Next, there are several indications that the photoreactive species is not in a Franck-Condon state, but rather it is in a thermally equilibrated excited state. One indication is that quantum yields as well as the nature of the photoreaction do not vary appreciably as the irradiating wavelength traverses the width of a ligand field band (although variations may occur on going from one band to another) (13, 14, 15). It appears that a common reactive state is reached, regardless of the degree of vibrational excitation of the initially produced Franck-Condon state. The simplest explanation is that this common state is a thexi state. 

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