Electronic Transitions The Franck-Condon Principle

Vibrational and rotational spectra arise from the movements of the atomic nuclei of the molecule. In transitions between different electronic configu- 

Molecular spectra have been discussed in more detail in the molecular-physics books referred to in Chap.3. 

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In the case of non-equilibrium conditions, the crossing point is located for a frozen solvent structure. During an electron transition the Franck-Condon principle is applicable and the solvent nuclei remain fixed during the transition. Consequently, the solvent structure is in equilibrium with the charge distribution of the solute in its ground state. The crossing point search procedure is performed in presence of this solvent structure. 

The phenomenological theory has been applied by Skwierczynski to the Et values of the Dimroth-Reichardt betaine, a quantity sensitive to the polarity of the medium. The approach is analogous to the earher development. We need only consider the solvation effect. The solute is already in solution at extremely low concentration, so solute-solute interactions need not be accoxmted for. The solvent cavity does not alter its size or shape dining an electronic transition (the Franck-Condon principle), so the general medium effect does not come into play. We write Ej. of the mixed solvent as a weighted average of contributions from the three states ... 

As with diatomic molecules, vibrational and rotational transitions in polyatomic molecules take place along with electronic transitions. The Franck-Condon principle applies, so that the final state will usually be an excited vibrational state as well as an excited electronic state. Since there are several normal modes in any polyatomic molecule the simultaneous electronic, vibrational, and rotational transitions can give very complicated spectra. The most important selection rule is the same for all molecules and atoms The total spin quantum number is the same for the final as for the initial state ... 

The Franck-Condon principle says that the intensities of die various vibrational bands of an electronic transition are proportional to these Franck-Condon factors. (Of course, the frequency factor must be included for accurate treatments.) The idea was first derived qualitatively by Franck through the picture that the rearrangement of the light electrons in die electronic transition would occur quickly relative to the period of motion of the heavy nuclei, so die position and iiioiiientiim of the nuclei would not change much during the transition [9]. The quaiitum mechanical picture was given shortly afterwards by Condon, more or less as outlined above [10]. 

In electronic spectra there is no restriction on the values that Au can take but, as we shall see in Section 1.2.53, the Franck-Condon principle imposes limitations on the intensities of the transitions. 

Section 6.13.2 and illustrated in Figure 6.5. The possible inaccuracies of the method were made clear and it was stressed that these are reduced by obtaining term values near to the dissociation limit. Whether this can be done depends very much on the relative dispositions of the various potential curves in a particular molecule and whether electronic transitions between them are allowed. How many ground state vibrational term values can be obtained from an emission spectrum is determined by the Franck-Condon principle. If r c r" then progressions in emission are very short and few term values result but if r is very different from r", as in the A U — system of carbon monoxide discussed in Section 7.2.5.4, long progressions are observed in emission and a more accurate value of Dq can be obtained. 

Solvatochromic shifts are rationalized with the aid of the Franck-Condon principle, which states that during the electronic transition the nuclei are essentially immobile because of their relatively great masses. The solvation shell about the solute molecule minimizes the total energy of the ground state by means of dipole-dipole, dipole-induced dipole, and dispersion forces. Upon transition to the excited state, the solute has a different electronic configuration, yet it is still surrounded by a solvation shell optimized for the ground state. There are two possibilities to consider ... 

The elementary act of an electrochemical redox reaction is the transition of an electron from the electrode to the electrolyte or conversely. Snch transitions obey the Franck-Condon principle, which says that the electron transition probability is highest when the energies of the electron in the initial and final states are identical. 

These selection rules are affected by molecular vibrations, since vibrations distort the symmetry of a molecule in both electronic states. Therefore, an otherwise forbidden transition may be (weakly) allowed. An example is found in the lowest singlet-singlet absorption in benzene at 260 nm. Finally, the Franck-Condon principle restricts the nature of allowed transitions. A large number of calculated Franck-Condon factors are now available for diatomic molecules. 

The optical absorption of the solvated electron, in the continuum and semicontinuum models, is interpreted as a Is—-2p transition. Because of the Franck-Condon principle, the orientational polarization in the 2p state is given... 

Fig. 21. Top The general Jablonski diagram for the flavin chromophore. The given wavelengths for absorption and luminescence represent crude average values derived from the actual spectra shown below. Due to the Franck-Condon principle the maxima of the peak positions generally do not represent so-called 0 — 0 transitions, but transitions between vibrational sublevels of the different electronically excited states (drawn schematically). Bottom Synopsis of spectra representing the different electronic transitions of the flavin nucleus. Differently substituted flavins show slightly modified spectra. Absorption (So- - S2, 345 nm S0 -> Si,450nm 1561) fluorescence (Sj — S0) 530 nm 156)) phosphorescence (Ty Sq, 605 nm 1051) triplet absorption (Tj ->Tn,...

FIGURE 17.13 An illustration of the Franck-Condon principle. In this case, the transition is from v = 0 in the electronic ground state to the state with id = 3 in the excited electronic state. 

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),... 

A molecule exhibits a great difference in the speeds of electronic transitions and vibrational atomic motions. The absorbtion of photon and a change in the electronic state of a molecule occurs in 10 15—10—18 s. The vibrational motion of atoms in a molecule takes place in 10 1 s. Therefore, an electronically excited molecule has the interatomic configuration of the nonexited state during some period of time. Different situations for the exited molecule can exist. Each situation is governed by the Franck-Condon principle [203,204],... 

In spectroscopy we may distinguish two types of process, adiabatic and vertical. Adiabatic excitation energies are by definition thermodynamic ones, and they are usually further defined to refer to at 0° K. In practice, at least for electronic spectroscopy, one is more likely to observe vertical processes, because of the Franck-Condon principle. The simplest principle for understandings solvation effects on vertical electronic transitions is the two-response-time model in which the solvent is assumed to have a fast response time associated with electronic polarization and a slow response time associated with translational, librational, and vibrational motions of the nuclei.92 One assumes that electronic excitation is slow compared with electronic response but fast compared with nuclear response. The latter assumption is quite reasonable, but the former is questionable since the time scale of electronic excitation is quite comparable to solvent electronic polarization (consider, e.g., the excitation of a 4.5 eV n — n carbonyl transition in a solvent whose frequency response is centered at 10 eV the corresponding time scales are 10 15 s and 2 x 10 15 s respectively). A theory that takes account of the similarity of these time scales would be very difficult, involving explicit electron correlation between the solute and the macroscopic solvent. One can, however, treat the limit where the solvent electronic response is fast compared to solute electronic transitions this is called the direct reaction field (DRF). 49,93 The accurate answer must lie somewhere between the SCRF and DRF limits 94 nevertheless one can obtain very useful results with a two-time-scale version of the more manageable SCRF limit, as illustrated by a very successful recent treatment... 

The simplest electron transfer reactions are outer sphere. The Franck-Condon principle states that during an electronic transition, electronic motion is so rapid that the metal nuclei, the metal ligands, and solvent molecules do not have time to move. In a self-exchange example,... 

The Franck-Condon principle states that there must be no movement of nuclei during an electronic transition therefore, the geometry of the species before and after electron transfer must be unchanged. Consequently, the active site geometry of a redox metalloenzyme must approach that of the appropriate transition state for the electronic transfer. Every known copper enzyme has multiple possible copper oxidation states at its active site, and these are necessary for the enzyme s function. 

This idea may be summarized from within the Franck-Condon principle. Because the atomic nuclei are relatively massive and effectively immobile, the transition is from the ground state to the excited state lying vertically above it. We say that the electronic excitation is vertical, which explains why the arrow drawn on Figure 9.13 is vertical. 

Nuclei move much more slowly than the much-lighter electrons, so when a transition occurs from one electronic state to another, it takes place so rapidly that the nuclei of the vibrating molecule can be assumed to be fixed during the transition. This is called the Franck-Condon principle, and a consequence of it is that an electronic transition is represented by a vertical arrow such as that shown in Figure 2.5 that is, an electronic transition occurs within a stationary nuclear framework. Thus the electronic transition accompanying the absorption of a photon is often referred to as a vertical transition or Franck-Condon transition. 

Radiative transitions may be considered as vertical transitions and may therefore be explained in terms of the Franck-Condon principle. The intensity of any vibrational fine structure associated with such transitions will, therefore, be related to the overlap between the square of the wavefunctions of the vibronic levels of the excited state and ground state. This overlap is maximised for the most probable electronic transition (the most intense band in the fluorescence spectrum). Figure... 

G. C. Pimentel, Hydrogen bonding and electronic transitions The role of the Franck-Condon principle,. 1. Am. Chem. Soc. 79, 3323-3326 (1957). 

Spectroscopy provides a window to explain solvent effects. The solvent effects on spectroscopic properties, that is, electronic excitation, leading to absorption spectra in the nltraviolet and/or visible range, of solutes in solution are due to differences in the solvation of the gronnd and excited states of the solute. Such differences take place when there is an appreciable difference in the charge distribution in the two states, often accompanied by a profonnd change in the dipole moments. The excited state, in contrast with the transition state discussed above, is not in equilibrium with the surrounding solvent, since the time-scale for electronic excitation is too short for the readjustment of the positions of the atoms of the solute (the Franck-Condon principle) or of the orientation and position of the solvent shell around it. 

We have seen how the position and intensity of is affected by the energy difference between the electronic energy levels. The Franck-Condon principle states that electronic transitions involve the movement of electrons, including those of the solvent, but not the movement of atoms. When the solvent electrons can rearrange to stabilize the excited state of a molecule, the energy difference between the electronic levels of the molecule is lowered and the absorption moves to higher wavelength. 

The most probable transitions, according to the Franck-Condon principle are the vertical ones. They correspond to the maxima of electron groups in the kinetic spectrum. The upper limits in the kinetic energies for each group correspond to the adiabatic ionization potentials. Thus from the difference of these energy values one can get the difference Ip between the vertical and adiabatic potentials (Table IV). 

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