The use of state diagrams allowed incorporation of previous conclusions about transitions between electronic states. At the 1926 Oxford meeting, it was agreed that the primary process to which the Einstein law applies was the formation of excited states. The conditions required in order that this led to a photochemical reaction was considered in the important contribution by Franck (Sect. 3.4). A necessary condition was that the molecule acquired vibrational energy exceeding the dissociation limit, that is, the energy to break a chemical bond in that state. The likelihood that excitation led to a chemical reaction could be assessed only if the properties of the excited state were known, since the fact that the photon energy exceeded that of fragmentation was not per se sufficient. In solution excited molecules lost excess energy by collision with other molecules, but even in gas phase at low pressure a molecule may take up many times its dissociation energy without dissociating. As mentioned, this point was stressed by Franck, who quoted the example of iodine molecules that absorbed and reemitted as a resonance spectrum an amount of energy five times the work of dissociation when illuminated in the far UV and did not undergo cleavage with unitary quantum yield (see Fig.3.11) [49].
Fig. 3.10 Polarization-sensitive Jabłon´ski diagram for a spherical rotor: the three sublevels of each electronic states are connected by “rotational” transitions (only the singlet system is shown).
By permission from [48]
58 3 The Framework of Photochemistry: State Diagram
Thus, according to Franck, the question whether a molecule would dissociate was “reduced to a consideration of the magnitude of the oscillation and rotation energy changes, which are coupled with the changes which the electron system undergoes upon absorption of light. Only when this amount equaled or exceeded the dissociation energy for the state considered could dissociation take place.” Since it was assumed that electron transitions affected only the binding of the atoms, leaving unaltered the relative nuclear separation and the potential well in the excited state had a different shape with respect to the ground state, a nuclei position different from the minimum could be reached. Franck [49] found a correlation between a large change in the oscillation quantum number and a large alteration of the bonding in the excited state. He based a classification of photochemical mechanisms on these characteristics. Thus, promotion from ground state n to excited states a and a0included a vibrational component (the equilibrium distance is longer in both excited states than in the ground state, r0, r00>r), and this may lead to overcome the barrier to dissociation. This was no necessary consequence, however, as it depended on the specific case and might still require an energetic contribution (D0<D; see Fig.3.12, left side).
Fig. 3.11 Fluorescence from iodine vapor excited by the Al lines at 185.4 and 186.2 nm. By permission from [50]
Fig. 3.12 Energy involved in the (photo)fragmentations of the excited state of biatomic mole- cules. By permission from [49]
3.6 Moving Along the States 59
This was the case of halogens. On the other hand, in molecules such as oxygen and nitrogen, the equilibrium distance r did not change, and the dissociation energy was essentially independent on excitation (D0¼D; Fig. 3.12, center). Finally, the equilibrium distance r0 may be smaller in the excited state, as in “molecules”
(or rather complexes) that were stable only in the excited state, as it was the case for Na2and Hg2(D0>D; Fig.3.12, right side).
Franck also recognized that upon direct dissociation, the amount of energy (hvD) translated into kinetic energy of the fragments [51]. The communication by Franck at the Oxford meeting spurred the interest by Condon, who developed quantitatively the theory for calculating the amplitude in spectra applied to transi- tions where the molecule was vibrating in the initial state and assumed further that the nuclear velocities were not changed by the electron transition. In this way, the major aspects of the observed intensity distributions in band systems in emission and absorption were explained. “It is at the two extreme positions that the vibrator spends most of the time, i.e., the electronic transition is most likely to occur when the vibrator is in one of these” positions [52–54]. The equations for the extrema thus give the bands which one expects to be strongest in a band system. This is the basis of the “Franck–Condon principle,” asserting that a vibrational transition accompa- nying an electronic transition is more likely when the starting and final vibrational wave functions overlap to a larger degree. This rationalizes the shape of the absorption bands, the fact that fluorescence is to the red of the absorption spectrum (Stokes’ shift), as well as, as seen above, the likelihood that a photochemical cleavage occurs.
In terms of classical mechanics, the Franck–Condon principle “is the approxi- mation that an electronic transition is most likely to occur without changes in the positions of the nuclei in the molecular entity and its environment. The resulting state is called a Franck–Condon state, and the transition involved, a vertical transition. The quantum mechanical formulation of this principle is that the inten- sity of a vibronic transition is proportional to the square of the overlap integral between the vibrational wavefunctions of the two states that are involved in the transition” [55]. This principle was readily accepted and from the beginning quoted with the names of the two scientists [56–58].
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