Vibrational equilibration

Grabiner F R, Flynn G W and Ronn A M 1973 Vibration-vibration equilibration in laser excited CH3F and CH3F-X mixtures J. Chem. Phys. 59 2330-4... 

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. 

The derivation of equations like (29) and (30) for ktt relies on the use of equilibrium statistical mechanics to calculate statistical populations amongst various vibrational distributions. Electron transfer is assumed to be a slow process on the timescale for vibrational equilibration. In that limit, electron transfer occurs occasionally from a vibrational distribution of the reactants to a vibrational distribution of the products and the population of the initial distribution is rapidly reestablished. However, for vibrational levels near the intersection region, this assumption may not be valid and, in general, it may not be valid for any case where electronic coupling is significant. 

Vibrationally equilibrated electronic excited states in molecules are unique chemical species. These are metastable species with unusual electronic configurations, and on this basis alone they might be expected to exhibit unusual patterns of reactivity. However, it is probably a more striking feature... 

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). 

In Figure 2(a), step 22, the internal conversion of state A2 to the ground state, is reproduced from Figure 1 as a single step including vibrational equilibration, as is appropriate for a photochemical system in a condensed medium. Figure 2(b) is more appropriate for a gas-phase system the internal conversion is shown as an iso-... 

In the same sense, in condensed media, it is often assumed that upper excited electronic states relax rapidly by internal conversion and vibrational equilibration to the lowest excited electronic state of the same multiplicity. Thus, referring to Figure 3, which extends the mechanism of Figure 1, if two excited states, A2 and A, have the same multiplicity, it is likely that the upper state, A, would undergo rapid internal conversion to A2 in solution. The sequence 03-32 could then be considered as the equivalent of step 02, provided that neither of steps 34 or 35 could compete, under these conditions, with step 32. A common diagnostic test (but not proof) of this situation is independence of the quantum yield on wavelength. 

However, especially for the nonradiative transitions to the ground state, steps 22 and 13, and especially in the gas phase, vibrational equilibration might have to be considered to represent the true final photophysical primary steps, as in Figure 2(b). 

The electronic-transition dipole moment for the G E transition is defined by Mge = ( g A/ ge1 e> where the are the state wave functions and A/ ge is the dilference in dipole moment of the ground and excited states [22]. The intensity of the transition is proportional to Mge - The broad absorption bands usually observed in transition metal systems are composed of progressions in the vibrational modes that correlate with the differences in nuclear coordinates between the vibrationally equilibrated ground and excited state. Since the energy difference between the donor and acceptor is generally solvent-dependent, the distribution of solvent environments that is characteristic of solutions may also contribute to the bandwidth (see further discussion of this point in the sections below). If the validity of the Born Oppenheimer approximation is assumed, the intensity of each of these vibronic components is given by Eq. 11,... 

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... 

If we assume vibrational equilibration as before, then this model used in... 

The fluorescent rise times were also measured for a variety of states in the system. As in previous studies of other molecules, a number of states that are close in energy to each other and for which fluorescence from an individual state could not be resolved were considered to be a single tightly coupled state. The rate of rise of the Vg,v, v2, v ), and ( ], J e) states have been measured. With the rise signals analyzed as single exponentials, the reported rates are 263 12, 212 21, 291 29, and 130 13 ms torr, respectively. In the original study there was some speculation as to the likely paths for vibrational equilibration of these states however, much more specific and detailed information is now available with regard to vibrational equilibration pathways. ... 

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