Vibronic transitions oscillator strength

A detailed study of the electronic structure and optical properties was published for the spiro derivative of f-Bu-PBD, Spiro-PBD (40) [108]. The vibronic structure of the lowest energy absorption band is well resolved, in solution as well as in the amorphous him. The 0-0 transition is at 351 nm (3.53 eV), the 0-1 and 0-2 vibronic bands that have a higher oscillator strength, are at 336 nm (3.69 eV) and 318 nm (3.90 eV), respectively. The fluorescence spectrum of this compound is symmetrical to the absorption spectrum with a Stokes shift of 43 nm. 

X being a 4/ wave function. From this expression, one estimates that the oscillator strengths should be about the same as for an ion situated in a noncentrosymmetric field (P 10 6). A rigorous formal treatment for the vibronically induced electric-dipole transitions has been developed by Satten (32-34),... 

The extent to which the IC process is blocked by vibrational deficiency can be ascertained by the quantum yield for fluorescence, <1>F. Such information can be extracted from the measured fluorescence lifetimes, X[, of the vibronic levels of the Sj state, providing the oscillator strength of the S i < S0 transition is known. The radiative lifetime, based on the transition strength, rr, can calculated from the oscillator strength through the expression, xr 1.5//V2. With a measured oscillator strength of / 1.2 x 10 4 and an average transition frequency of... 

In the crude Born-Oppenheimer approximations, the oscillator strength of the 0-n vibronic transition is proportional to (FJ)2. Furthermore, the Franck-Condon factor is analytically calculated in the harmonic approximation. From the hamiltonian (2.15), it is clear that the exciton coupling to the field of vibrations finds its origin in the fact that we use the same vibration operators in the ground and the excited electronic states. By a new definition of the operators, it becomes possible to eliminate the terms B B(b + b ), BfB(b + hf)2. For that, we apply to the operators the following canonical transformation ... 

Figure 2.4. Variation vs Jk of the solutions zk of (2.54) for the eigenenergies of the system of coupled vibrons. The curve labeled 0-n represents the nth vibronic transition. The oscillator strengths of each state are given by the slopes of the curves. In particular, for Jk negative and strong, only the 0-0 vibron (purely electronic) is optically accessible.

The vibrations at 392, 390 cm"1 in the excited state, strong, whose molecular spectrum shows the first and the second harmonics.58 From the oscillator strength of the vibronic 0-392-cm"1 transition, we may roughly derive a purely linear coupling with c,2 0.14. Each one of the principal 1400-cm-1 vibronic transitions is flanked with a vibration at 390cm", building the sequence 1400 + 392, 2 x 1400 + 392,...cm". ... 

Here v is the frequency under consideration, Vij the absorption frequency and fij the oscillator strength of the electronic transition between the states i and j. From the diffuse reflection spectrum discussed above it is clear that a(OH ) at the frequency of the vibronic transition involved will be large, since i, / - is relatively small. 

According to the MIM calculations, the Si state is mainly express ed as the LE function of B2u transition of benzene.(Table 3) The B2u transition of benzene(250 nm) is a forbidden transition and its oscillator strength vanishes in the calculations althou the experimental value is f=0.002. The transition is considered to be a vibronic one having intervals of 925 cm-T of the aig vibration of benzene ring with... 

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