Franck point

To simulate the vibrational progression, we obtain the Franck—Condon factors using the two-dimensional array method in ref 64. We consider 1 vibrational quantum v = 0) from the EC stationary point and 21 vibrational quanta (z/ = 0, 1,. .., 20) from the GC stationary point. The Franck— Condon factors are then calculated for every permutation up to 21 quanta over the vibrational modes. It is necessary in order to get all Franck—Condon factors of the EC stationary point with respect to each three alg vibrational state (Figure 6) of the GC to sum to one. One obtains a qualitative agreement between the calculated and the experimental emission profiles (Figure... 

From a molecular structure point of view, for diCN-HBO, the lone pair electrons of the benzo-nitrogen atom are intrinsically involved in the Ji-electron resonance to establish the aromaticity, such that its electron donating strength, compared with those of alkyl and aryl amines, is negligibly weak. Thus, upon Franck-Condon... 

Since 1973, progress has been made in all the fields reviewed and a more complete review of Franck s work has appeared (29). For the present purposes it is necessary to concentrate on the two areas which are least well studied simple electrolytes between 300 C and the critical point and the chemistry of aqueous transition metal cations. A number of studies which do not fall into these categories must, however, be mentioned because of their direct relevance to boiler water chemistry. These are studies of sodium phosphate phase equilibria (30), ammonia dissociation (31) and isopiestic studies of calcium and magnesium chlorides (32). 

Fig. 12.2 Left The ground (X, solid line), excited (6, dashed line) and dissociative [a1g(3II), dotted line] electronic state potentials of the iodine molecule. The arrow indicates the electronic excitation. The initial excited wave packet is located in the Franck-Condon region near to the inner classical turning point of the B state. The transition from the B to the a state is forbidden by symmetry in the isolated molecule but becomes allowed when the molecule is placed in a solvent.

A most comprehensive discussion of the effect of solvent on spectra has been given by Bayliss and McRae.21 They point out that polarization or dispersion forces are the most general interactions involved in solution and that all solution spectra are subject to a generalized polarization red shift, relative to vapor spectra, due to solvent polarization by the transition dipole. However, these dispersion forces are relatively weak and are easily obscured by the effect of dipole-dipole and dipole-static charge forces in polar, but not highly polarizable, solvents. By applying the Franck-Condon principle, they showed... 

The wavelength of the probe pulse is tuned around 400 nm. This pulse resonantly excites the WP in the B state to the upper E state. Subsequent laser-induced fluorescence (LIT) from the E state is detected with a photomultiplier. We have utilized two kinds of probe lasers an fs laser and a nanosecond (ns) laser. If we use an fs probe pulse, the overall WP is resonantly excited from B io E states. The excitation predominantly occurs around a specific internuclear distance called a Franck-Condon point [37]. The Franck-Condon point r c is defined as... 

Figure 7.5 Relation between the probe wavelength and the Franck—Condon point Taken from Ref. [37]. Reprinted with permission from American Association for the Advancement of Science.

In line with the Franck-Condon principle, the electron transfer occurs at the seam of the crossing between diabatic (localized) states of donor and acceptor. The electronic coupHng is the off-diagonal matrix element of the Hamiltonian defined at the crossing point. 

Figure 14.2 Schematic relationship between vertical absorption and emission energies and the adiabatic energy difference between the ground and excited states. [Note that a more rigorous treatment requires inclusion of ZPVE and thermal contiibutions in the adiabatic energy difference, and consideration of Franck-Condon overlap between quantized vibrational states for the vertical processes some of these points are discussed in Section 14.5.]...

The temperature sensitivity arises due to disposition of T2 state with respect to S, state. If T2 is considerably above S, transfer to T, is less probable because of unfavourable Franck-Condon factor. As a consequence, fluorescence is the easiest way for deactivation and fluorescence yield is nearly unity. No dependence on temperature is expected. On the other hand, if T2 is sufficiently below S so that the density of state is high at the crossing point, fluorescence quantum yield should be less than unity as triplet transfer is fecilitated. Again no temperature dependence is observed. But if T2 is nearly at the same energy as S, a barrier to inter-system crossing is expected and fluorescence yield will show temperature dependence. 

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