Franck Condon principle

Electron-transfer reactions, which occur either by the inner-sphere or by the outer-sphere mechanism, are subject to restrictions defined by the Franck-Condon principle. The principle explains the distribution of relative intensities of the vibrational structure of an electronic transition. Namely, since the nuclei have a much larger mass than the electrons, electron transition takes place much faster than the nuclei can respond. Thus, the electron transition takes place in about 10 to 10 s, while the nuclei need about 10 s to respond (which is approximately the time of one vibration). This is the reason why electron density is rapidly built up in the new molecular region. The new electron density distribution acts upon the nuclei, which become subject to a new force field, causing them to vibrate. Since the nuclear framework remains unchanged with respect to its geometry during a very fast electronic transition, the expression vertical transition is used to describe this situation. 

The reaction is very slow because it requires a spin change (from the high spin [ Co (NH3)6]2+ to the low spin [ Co (NH3)g]3+). 

On the other hand, reaction (5.2.3) is fast because the electron transfer proceeds from the Cg orbital of one cobalt atom to the eg orbital of the other cobalt atom thus, the outer-sphere electron-transfer mechanism appears very probable  

The spectral distribution of fluorescence usually exhibits an approximate mirror-image relationship to the first absorption band when the spectra are plotted on a frequency or wavenumber scale. This is expected from the Franck Condon principle, when the 

The spectral positions of the 0 O bands of absorption and fluorescence usually do not coincide exactly. The difference is called the Stokes shift. The excited state is generally more polarizable and often more polar than the ground state. Solvent relaxation then stabilizes the excited state following Franck Condon excitation, so that the 0 0 band of absorption is usually at higher frequency than that of emission. When the excited state is much less polar than the ground state, the 0 0 band of fluorescence may appear at higher frequency than that of absorption anti-Stokes shift). Unfortunately, the term Stokes shift is also used to refer to the gap between the band maxima of absorption and emission (see the footnote to fluorescence in Section 2.1.1), which may be much larger than the shift between the 0 0 bands. 

A recent development is the use of quantum dots (see Special Topic 6.30) as optical brighteners in fibres. 

Figu re 2.17 Potential energy curves for ground (So) and excited (Si) states. Reprinted from ref [11], with permission from Elsevier. 

Phosphorescence can be observed only by populating the Ti electronic state, which occurs when the Si potential energy curve that has been populated by 

Finally, we note that radiative decay transitions have the same nature as absorption ones and consequently they obey the same selection rules (see Sections 2.1 and 2.2). 

In order to evaluate the contribution from the nuclear component it is necessary to know the vibrational wavefunctions. For a simple harmonic oscillator, the potential energy well for intemuclear distances is given by a parabolic curve where the vibrational energy levels are quantized (Fig. 1.4). The curves for v = 0,1,2, and 3 represent the wavefunctions for each vibrational level. When a transition occurs from the ground to an excited state, it is necessary to consider the potential energy wells of both states. Since the electronic structure of the excited state is different from that of the ground state, the vibrational energy profiles will be different. In 

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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]. 

The synnnetry selection rules discussed above tell us whether a particular vibronic transition is allowed or forbidden, but they give no mfonnation about the intensity of allowed bands. That is detennined by equation (Bl.1.9) for absorption or (Bl.1.13) for emission. That usually means by the Franck-Condon principle if only the zero-order tenn in equation (B 1.1.7) is needed. So we take note of some general principles for Franck-Condon factors (FCFs). 

Condon E U 1947 The Franck-Condon principle and related topics Am. J. Phys. 15 365-79... 

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

The Franck-Condon principle reflected in tire connection between optical and tliennal ET also relates to tire participation of high-frequency vibrational degrees of freedom. Charge transfer and resonance Raman intensity bandshape analysis has been used to detennine effective vibrational and solvation parameters [42,43]. 

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. 

Figure 7.21 Franck-Condon principle applied to a case in which > r" and the 4-0 transition is the most probable...

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. 

Figure 8.8 The Franck-Condon principle applied to the ionization of Fl2...

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... 

The state may decay by radiative (r) or non-radiative (nr) processes, labelled 5 and 7, respectively, in Figure 9.18. Process 5 is the fluorescence, which forms the laser radiation and the figure shows it terminating in a vibrationally excited level of Sq. The fact that it does so is vital to the dye being usable as an active medium and is a consequence of the Franck-Condon principle (see Section 7.2.5.3). 

INFRARED TECHNOLOGY AND RAMAN SPECTROSCOPY - RAMAN SPECTROSCOPY] (Vol 14) Franck-Condon principle... 

Excited-State Relaxation. A further photophysical topic of intense interest is pathways for thermal relaxation of excited states in condensed phases. According to the Franck-Condon principle, photoexcitation occurs with no concurrent relaxation of atomic positions in space, either of the photoexcited chromophore or of the solvating medium. Subsequent to excitation, but typically on the picosecond time scale, atomic positions change to a new equihbrium position, sometimes termed the (28)- Relaxation of the solvating medium is often more dramatic than that of the chromophore... 

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 ... 

Fock-Dirac density matrix, 225-Framework, 379 Franck-Condon principle, 199 Free volume, 26, 27, 33... 

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. 

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