Franck-Condon considerations

This represents a useful, but extreme simplification and, not surprisingly ( ), a model based on Franck-Condon considerations alone sometimes proves inadequate. For example, in a discussion of vibrational en gy disposal in photo-eliminations of the type... 

Another conventional simplification is replacing the whole vibration spectrum by a single harmonic vibration with an effective frequency co. In doing so one has to leave the reversibility problem out of consideration. It is again the model of an active oscillator mentioned in section 2.2 and, in fact, it is friction in the active mode that renders the transition irreversible. Such an approach leads to the well known Kubo-Toyozawa problem [Kubo and Toyozava 1955], in which the Franck-Condon factor FC depends on two parameters, the order of multiphonon process N and the coupling parameter S... 

As shown in Fig. 6, there is a correlation between absorption spectrum and emission spectrum. Taking into consideration the Franck-Condon principle, which states that there is no motion of the atoms during an electronic transition, one has to differentiate between the two following possibilities in the one the geometry of the excited state is similar to the one of the ground state (same interatomic distances),... 

Another consequence of the stronger interactions upon ionization is that the equilibrium geometry of the ionized complex may differ signihcantly from that of the neutral states. Broadened ionization onsets are frequently attributed to the spectral superposition of ionization into several vibrational levels for which Franck-Condon factors are more favorable. As a result, the adiabatic ionization potential may be considerably lower than the vertical potential, and the observed ionization onsets may occur above the adiabatic potential. Another factor to be considered is the conformation-dependent efifect, due to the different conformations of the solvent molecules. The most populated form of a complex may involve a less stable form of the solvent. After photoionisation, the lowest-energy dissociation channel in the complex ion leads to the most stable form of isolated solvent, which has to be taken into account for the estimate of the binding energy. 

The high laser intensity enables molecular transitions to be measured even when their Franck-Condon factors are small, so that the fluorescence progression can be followed up to high vibrational levels, thus considerably increasing the accuracy of the molecular constant determination. It furthermore permits fluorescence measurements at low pressures. 

Figure 14.2 Schematic relationship between vertical absorption and emission energies and the adiabatic energy difference between the ground and excited states. [Note that a more rigorous treatment requires inclusion of ZPVE and thermal contiibutions in the adiabatic energy difference, and consideration of Franck-Condon overlap between quantized vibrational states for the vertical processes some of these points are discussed in Section 14.5.]...

The temperature sensitivity arises due to disposition of T2 state with respect to S, state. If T2 is considerably above S, transfer to T, is less probable because of unfavourable Franck-Condon factor. As a consequence, fluorescence is the easiest way for deactivation and fluorescence yield is nearly unity. No dependence on temperature is expected. On the other hand, if T2 is sufficiently below S so that the density of state is high at the crossing point, fluorescence quantum yield should be less than unity as triplet transfer is fecilitated. Again no temperature dependence is observed. But if T2 is nearly at the same energy as S, a barrier to inter-system crossing is expected and fluorescence yield will show temperature dependence. 

Another way of calculating the distribution of product states would be to apply an extension of RRKM that Wardlaw, Klippenstein, and I developed. However, judging from your observations, the reaction is highly vibrationally nonadiabatic, considering, for example, the considerable difference in vibrational quantum number vco in HCO and CO and the major change in bending — rotational state. In that case a Franck-Condon approach would seem to be much more appropriate than any adiabatic or near-adiabatic or statistically adiabatic model. 

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