Vibrationally equilibrated excited states

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... 

For thiones the processes of intramolecular (subpicosecond) and intermolecular (a few ps) vibrational relaxation occur on a time scale that is rather shorter than in at least some solvents (water [84] is exceptional). Thus the relaxation dynamics of the vibrationally equilibrated excited state can be observed in different solvents [54,58,59,63,67,85-87]. 

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. 

The techniques outlined above provide information on the structure and accessibility of the photochemical reaction paths. As mentioned, this information is structural (i.e., nondynamical) and provides insight into the mechanism of photoproduct formation from vibrationally cold excited state reactants such as those encountered in many experiments where slow excited state motion or/and thermal equilibration is possible (in cool jets, in cold matrices, and in solution). 

FIGURE 1. A schematic photochemical mechanism, showing some of the possible elementary transformations. For the purpose of illustration, it is assumed that the states A and A2 have the same multiplicity, and correspond to the ground and lowest excited singlet states of most organic molecules. The state A] would then represent the lowest triplet state. Thus 21 and 11 are radiative transitions, fluorescence and phosphorescence, respectively, and 23 and 13 (intersystem crossing) and 22 (internal conversion) are nonradiative. All of 8, C, D, and F are chemical species distinct from A. Only vibrationally equilibrated electronic states are included in this mechanism (see discussion in Section III.A.l). 

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. 

A common situation found in condensed phases under illumination is for all levels, except electronic levels, to be thermally equilibrated. Thus, under constant illumination, the sample is a mixture of thermally/vibrationally-equilibrated ground-state(s) with a very small, non-Boltzmann population of the excited electronic state, but which is itself thermally and vibrationally Boltzmann distributed. So the situation is similar to two non-equilibrated chemical species each of which is thermally equilibrated a thermally equilibrated ground-state, and a thermally equilibrated high energy excited-state. 

These complexes also demonstrate a change in the excited state character between a Frank-Condon (vibrationally hot ) electronically excited state and the vibrationally relaxed, lowest excited state. Resonance Raman (rR) spectra show that the vibrationally hot Franck-Condon states of [RuI(Me)(CO)2(iPr-DAB)] have virtually pure XLCT character [55]. However, the TRIR data indicate that thermally equilibrated, vibrationally-relaxed excited state has a mixed MLCT-XLCT character [6]. Hence, combining the results from resonance Raman and TRIR data allows one to obtain insight into charge redistribution processes in the excited state on a very short timescale. 

For most practical systems (solid, liquid, and atmospheric pressure gaseous phase) vibrational relaxation occurs in the picosecond time scale. Since most of the interesting chemistry and physics that takes place in electronically excited states occurs on a much longer timescale (see below), thermally equilibrated excited states should he considered as the only relevant intermediates in photochemistry, regardless of the initial amount of vibrational excitation with which they may have been created. 

In these processes, return to So from the minimum in Si or Ti originally reached by the molecule is slow enough that vibrational equilibration in the minimum occurs first and the reaction can be said to have an excited state intermediate. Sum of the quantum yields of all processes which proceed from a given minimum (intermediate) then cannot exceed one. 

SM = iAM2 a measure of the distortion of the acceptor vibration in the excited state. A is the dimensionless, fractional displacement in normal vibration M between the thermally equilibrated excited and ground states. It is related to AQeq by A AQe ( )l/2, where M is the reduced mass for the vibration. 

Eq 7 calculates the energy difference arising from the medium between the thermally equilibrated mixed-valence ground state and a vibrationally nonequilibrium, mixed-valence excited state. The value of Ae depends on the nonequilibrium state 1) For optical charge transfer, Ae = e, the unit electron charge. 2) For thermal electron transfer between chemically symmetrical sites, Ae = e/4. 3) For a chemically unsymmetrical electron transfer... 

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