Franck-Condon principle electronic

The vibrational overlap factor (6t 6t) is also known as the Franck-Condon factor and represents the probability of finding a common nuclear geometry in the initial and final states. If the nuclei do not move during the electronic transition, such a transition can take place only in such a common nuclear geometry. Figure 3.12, p. 39, provides an illustration of this Franck-Condon principle electronic radiative transitions are vertical, non-radiative transitions are horizontal but they are followed by vertical vibrational deactivation. 

With reference to absorption spectroscopy, we deal here with photon absorption by electrons distributed within specific orbitals in a population of molecules. Upon absorption, one electron reaches an upper vacant orbital of higher energy. Thus, light absorption would induce the molecule excitation. Transition from ground to excited state is accompanied by a redistribution of an electronic cloud within the molecular orbitals. This condition is implicit for transitions to occur. According to the Franck-Condon principle, electronic transitions are so fast that they occur without any change in nuclei position, that is, nuclei have no time to move during electronic transition. For this reason, electronic transitions are always drawn as vertical lines. 

According to the Franck-Condon principle, electron transition from donor to acceptor takes place while the atomic positions can be regarded as fixed on the reaction coordinate Q. This means that it takes place at the crossing point between the diabatic potentials KiQ) and Fp(0 for the reactant and product states, respectively, because energy conservation is satisfied only at that point under this principle. This situation can be formulated by... 

According to the Franck-Condon principle electronic transitions are so fast that they occur without change in the position of the nuclei, i.e. the nuclei have no time to move during the electronic transition. In fact, the lifetime of an electronic transition is about 1.4 X 10 s, while the lifetime of a nuclei vibration is 22 x 10" s. Thus, the lifetime of the nuclei vibration is approximately 16 times longer the lifetime of an electronic transition. This is why the electronic transitions are showed always as vertical lines. 

According to the Franck-Condon principle, electronic excitation is much faster s) than solvent reorganization around the molecule ( 10 2-10 s). 

While the occurrence of a photochemical excitation is fundamentally governed by electronic considerations, the shape of the absorption band and the nature of the primary photoproduct is determined by the vibrational part of the wave functions.According to the Franck-Condon principle electronic transitions take place without significant changes in nuclear structure. A semiclassical justification follows from the fact that electrons are very light compared with nuclei. The electron distribution may thus be altered in an interval that is short compared to the time required for significant vibrational motion. ... 

Figure 6.4 illustrates for a diatomic molecule, the possible excited-state potential energy curves that permit dissociation. As mentioned previously (the Franck-Condon principle) electronic transitions occur so rapidly that the nuclei are, in effect, clamped during transition. Quantum mechanics requires that the transition occur between states which have large probability amplitudes at the same internuclear separation. The vibrational wave function of the ground state is maximum at the center of the well those of excited states have major maxima near the classical... 

Franck-Condon principle According to this principle the time required for an electronic transition in a molecule is very much less than the period of vibration of the constituent nuclei of the molecule. Consequently, it may be assumed that during the electronic transition the nuclei do not change their positions or momenta. This principle is of great importance in discussing the energy changes and spectra of molecules. 

Section BT1.2 provides a brief summary of experimental methods and instmmentation, including definitions of some of the standard measured spectroscopic quantities. Section BT1.3 reviews some of the theory of spectroscopic transitions, especially the relationships between transition moments calculated from wavefiinctions and integrated absorption intensities or radiative rate constants. Because units can be so confusing, numerical factors with their units are included in some of the equations to make them easier to use. Vibrational effects, die Franck-Condon principle and selection mles are also discussed briefly. In the final section, BT1.4. a few applications are mentioned to particular aspects of electronic spectroscopy. 

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]. 

Duschinsky F 1937 On the interpretation of electronic spectra of polyatomic molecules. I. Concerning the Franck-Condon Principle Acta Physicochimica URSS 7 551... 

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. 

Using the Franck-Condon principle in this way we can see that the band system associated with the second lowest ionization energy, showing a long progression, is consistent with the removal of an electron from a bonding n 2p MO. The progressions... 

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 ... 

Even where the promotion is to a lower vibrational level, one that lies wholly within the 2 curve (such as Vi or V2), the molecule may still cleave. As Figure 7.2 shows, equilibrium distances are greater in excited states than in the ground state. The Franck-Condon principle states that promotion of an electron takes place much faster than a single vibration (the promotion takes... 

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. 

It follows from the Franck-Condon principle that in electrochemical redox reactions at metal electrodes, practically only the electrons residing at the highest occupied level of the metal s valence band are involved (i.e., the electrons at the Fermi level). At semiconductor electrodes, the electrons from the bottom of the condnc-tion band or holes from the top of the valence band are involved in the reactions. Under equilibrium conditions, the electrochemical potential of these carriers is eqnal to the electrochemical potential of the electrons in the solution. Hence, mntnal exchange of electrons (an exchange cnrrent) is realized between levels having the same energies. 

Effect of diagonal dynamic disorder (DDD). Fluctuations of the polarization and the local vibrations produce the variation of the positions of the electron energy levels eA(Q) and eB(C ) to meet the requirements of the Franck-Condon principle. 

Electronic transitions in a solute take place very fast, i.e., almost immediately in comparison with the movement of the molecules as a whole and vibrations of atoms in organic molecules. Hence, absorption and fluorescence can be denoted in Fig. 5 by vertical arrows, in accordance with Franck-Condon principle. Both these processes are separated by relaxations, which are intermolecular rearrangements of the solute-solvent system after the excitation. 

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. 

Certain features of light emission processes have been alluded to in Sect. 4.4.1. Fluorescence is light emission between states of the same multiplicity, whereas phosphorescence refers to emission between states of different multiplicities. The Franck-Condon principle governs the emission processes, as it does the absorption process. Vibrational overlap determines the relative intensities of different subbands. In the upper electronic state, one expects a quick relaxation and, therefore, a thermal population distribution, in the liquid phase and in gases at not too low a pressure. Because of the combination of the Franck-Condon principle and fast vibrational relaxation, the emission spectrum is always red-shifted. Therefore, oscillator strengths obtained from absorption are not too useful in determining the emission intensity. The theoretical radiative lifetime in terms of the Einstein coefficient, r = A-1, or (EA,)-1 if several lower states are involved,... 

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... 

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