Franck-Condon principle approximation

The difference in the time-scales for electronic and nuclear motions is, of course, the basis of the Bom-Oppenheimer approximation (and the Franck-Condon principle). This... 

When PRODAN is excited to its lowest singlet state, it undergoes a change in dipole moment of approximately 20 Debye units (38). According to the Franck-Condon principle, absorption of a photon occurs faster than nuclei can move (31,40). Therefore, immediately following optical excitation, there will be an excited-state dipole moment produced, but this dipole is essentially surrounded by a ground-state solvent cage. That is, the system is not in equilibrium. With time, the solvent... 

The solvent effects on spectroscopic properties i.e., electronic excitation, leading to absorption spectra in the ultraviolet and/or visible range, of solutes in solution are due to differences in the solvation of the ground and the 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 profound change in the dipole moments. The excited state, in distinction 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 re-adjustment 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. The consideration of the solvation of the excited state as if it were an equilibrium state of the system is therefore an approximation, which, however, is commonly implicitly made. 

The rate constant of an electrode reaction does not measure the rate of electron transfer itself, as this is an adiabatic process, following the Franck-Condon principle, and occurs in approximately 10 16s. What it does measure is the time needed for the species, once they have reached the interfacial region, to arrange themselves and their ionic atmospheres into position for electron transfer to be able to occur. 

Only if there were a transfer of, say, an H+, H, or H in a reaction, AH + B - A + HB (charges not indicated), at a fairly large AB separation distance, would the situation be rather analogous to that of ETs. The H transfer would occur at an approximately fixed position of A and B, fixed because of the substantially larger masses of A and B compared with that of H. That is, an approximate version of the Franck-Condon principle would apply. Under such conditions of an H transfer, the description of the reaction via two intersecting approximate parabolas would be a reasonable first approximation. 

Franck-condon principle Classically, the Franck-Condon principle is the approximation that an electronic transition is most hkely 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. 

FIGURE 6.8 The Franck-Condon principle is shown by the vertical dotted line. The clear rectangle shows schematically the broader possibilities of transitions when the Herzberg-TeUer approximation is used. 

The optical transitions between the two states are described by the adiabatic approximation, in which the electronic and vibrational components of the wavefunction are treated separately. According to the Franck-Condon principle, absorption and emission take place without change in the configuration, as illustrated in Fig. 8.3. The energy of the emission is... 

The early discussion of the role of nuclear reorganization in energy transfer, especially among classical photochemists, centered on the concept of nonvertical excitation transfer . While many of the conclusions fully agree with the spirit of the Marcus-Jortner approach, the term itself is rather unfortunate as it suggests that the process may be violating the Franck-Condon principle and the Bom-Oppenheimer approximation. 

The time-dependent perturbation theory of the rates of radiative ET is based on the Born-Oppenheimer approximation [59] and the Franck Condon principle (i.e. on the separation of electronic and nuclear motions). The theory predicts that the ET rate constant, k i, is given by a golden rule -type equation, i.e., it is proportional to the product of the square of the donor-acceptor electronic coupling (V) and a Franck Condon weighted density of states FC) ... 

Figure 1.13. Schematic representation of the band shape to be expected from the Franck-Condon principle as a function of geometry changes on excitation a) approximately equal equilibrium intemuclear distances in the ground and excited state b) intemuclear distance in the excited state larger than in the ground state.

It should be emphasized here that the electron transfer in the activated state is a very fast process which occurs within a time interval of about 10" s. The relaxation times for the solvent and the reacting nuclei are much longer, typically 10"" to 10" - s for vibrational motion and 10" to 10"" s for rotational motion. Accordingly, it is a reasonable approximation that the positions of the nuclei are unchanged in the course of the electron transfer. This condition is called the Franck-Condon principle. It is well known from studies of absorption and emission of light by molecules. 

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... 

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