Vibronic shift

Another difference regarding the comparison between Eqs. (10) and (16) is that this second approximation for the overlap function gives us a direct way to determine the parameters and e . Although we wiU not investigate state-specific line widths and vibronic shifts in the simulations discussed in this work, for completeness of the derivation, it is worth showing how these parameters can be computed. If A o,n(R) is approximately constant over R, then and in Eq. (15) can be obtained by comparison with Eq. (14) and be defined in terms of and of co, A , and dEo n = AEo,n AEq as ... 

Furan absorption cross section is shown in Fig. 2. Absorption was computed with Eq. (23), and the parameters employed in the simulations are given in Table 4. Vibronic shifts were set to zero, and all lines were assumed to have the same width <5 . Eight excited states for each one of the 350 ensemble points were computed. The gray area indicates the error in the numerical integration computed with Eq. (25). 

Other source of band shift is vibronic corrections, but they are much smaller than the shift caused by the electronic structure method. In the case of the first energy band of benzene (Fig. 3-left), we can employ Eq. (20) to estimate the vibronic shift. At TD-CAM-B3LYP/TZVP-mod level, AEo.i = 5.548 eV and AEg, = 5.421 eV, and therefore 8i = -0.06 eV, which is much smaller than the shift observed between theory and experiment in Fig. 3-left, about —0.6 eV from maximum to maximum. 

Figure 16-36 shows the absorption spectra of thin films of four differently substituted five-ring OPVs. in contrast to the solution spectra, which show structureless low-energy absorption bands, the absorption bands of the films are structured. In the solid slate, the molecules are spatially constrained, whereas in solution different conformers exist, resulting in a distribution of accessible levels. As a consequence, some details appear in the absorption spectrum of the films which can be attributed to vibronic coupling, while, in dilute solution, the spectrum is a broad featureless band. For oct-OPV5 and Ooci-OPV5 films, the absorption maxima are red-shifted over approximately 0.1 eV relative to the solution (see Fig. 16-12). The low-energy absorption band of a thin film of Ooct-OPV5-CN" displays an appreciably larger...

Techniques other than UV-visible spectroscopy have been used in matrix-isolation studies of Ag see, for example, some early ESR studies by Kasai and McLeod 56). The fluorescence spectra of Ag atoms isolated in noble-gas matrices have been recorded (76,147), and found to show large Stokes shifts when optically excited via a Si j — atomic transition which is threefold split in the matrix by spin-orbit and vibronic interactions. The large Stokes shifts may be explained in terms of an excited state silver atom-matrix cage complex in this... 

Different aromatic hydrocarbons (naphthalene, pyrene and some others) can form excimers, and these reactions are accompanying by an appearance of the second emission band shifted to the red-edge of the spectrum. Pyrene in cyclohexane (CH) at small concentrations 10-5-10-4 M has structured vibronic emission band near 430 nm. With the growth of concentration, the second smooth fluorescence band appears near 480 nm, and the intensity of this band increases with the pyrene concentration. At high pyrene concentration of 10 2 M, this band belonging to excimers dominates in the spectrum. After the act of emission, excimers disintegrate into two molecules as the ground state of such complex is unstable. 

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. 

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