Vibronic band shapes

Of these four properties, spectral shifts are the most sensitive to environmental changes and also the most readily measured. As a result the majority of investigations into electronic absorption spectral changes resulting from surface adsorption have been confined to measurements of spectral shifts. While the shift of the 0-0 bands is the most meaningful measurement to make, these 0-0 bands are not always discernible, especially when the molecules are adsorbed on polar surfaces, so it has become common practice simply to measure the shift of the absorption maximum. In most cases this measurement would correspond to the shift of the 0-0 band, in others, however, adsorption processes can produce unequal displacement of the ground and excited state potential curves, resulting in a different vibronic band shape. 

It is possible to model the vibronic bands in some detail. This has been done, for example, by Liu et al. (2004) forthe 6d-5f emission spectrum of Pa4+ in Cs2ZrCl6, which is analogous to the emission spectrum of Ce3+. However, most of the simulations discussed in this chapter approximate the vibronic band shape with Gaussian bands. The energy level calculations yield zero-phonon line positions, and Gaussian bands are superimposed on the zero-phonon fines in order to reproduce the observed spectra. Peaks of the Gaussian band are offset from the zero phonon fine by a constant. Peak offset and band widths, which are mostly host-dependent, may be determined from examination of the lowest 5d level of the Ce3+ spectrum, as they will not vary much for different ions in the same host. It is also common to make the standard... 

If the experunental technique has sufficient resolution, and if the molecule is fairly light, the vibronic bands discussed above will be found to have a fine structure due to transitions among rotational levels in the two states. Even when the individual rotational lines caimot be resolved, the overall shape of the vibronic band will be related to the rotational structure and its analysis may help in identifying the vibronic symmetry. The analysis of the band appearance depends on calculation of the rotational energy levels and on the selection rules and relative intensity of different rotational transitions. These both come from the fonn of the rotational wavefunctions and are treated by angnlar momentum theory. It is not possible to do more than mention a simple example here. 

Similarly, parallel or perpendicular elecfronic or vibronic bands of a symmefric rotor (see Section 6.2.4.2) show widely varying shapes, unlike fhe parallel or perpendicular vibrational bands illusfrafed in Figure 6.28 and 6.29, respectively. 

Emission spectra at these points are shown in Figure 8.2d. The band shapes were independent of the excitation intensity from 0.1 to 2.0 nJ pulse . The spectrum of the anthracene crystal with vibronic structures is ascribed to the fluorescence originating from the free exdton in the crystalline phase [1, 2], while the broad emission spectra of the pyrene microcrystal centered at 470 nm and that of the perylene microcrystal centered at 605 nm are, respectively, ascribed to the self-trapped exciton in the crystalline phase of pyrene and that of the a-type perylene crystal. These spectra clearly show that the femtosecond NIR pulse can produce excited singlet states in these microcrystals. 

Piepho has responded to the criticisms of the PKS model by developing an improved version, the MO vibronic coupling model for mixed-valence complexes (32). Multicenter vibrations are now considered and a molecular orbital basis set (as with the three-site model) is used. This model was used to calculate band shape and g values for the Cretuz-Taube ion (33). The MO vibronic coupling model is admittedly more empirical than the three-site model but it has the advantage in being applicable to all mixed-valence complexes. 

The spectroscopic behavior of a JT system is to a large extent governed by the quenching of electronic operators (Ham effect), which causes a shift of the absorption (or emission) bands and a modification of their shapes. Moreover the vibronic mixing of different electronic states can strongly affect relaxation processes, which also modify spectral band shapes. 

Ai,Ai-Dipropyl-4-nitroaniline and Ai,A-dibutyl-4-nitroaniline (49) were prepared by Helburn and coworkers54 in order to have more lipophilic probes of the polarity of aqueous-organic interface systems. These probes also exhibit the solvent-dependent vibronic structure of the band shapes such as observed for 5. The value of s in equation 9 decreased in the series 7 > 5 > 49. 

The quantum mechanical formulation of this principle was given in Section 2.1.5 the intensity of a vibronic transition is proportional to the square of the Franck Condon integrals between the vibrational wavefunctions of the two states that are involved in the transition. Thus, the band shape of an electronic transition depends on the displacement of the excited electronic state relative to that of the ground state. This is illustrated for one vibrational degree of freedom of a given molecule in the schematic diagram in Figure 2.10. 

Figure 7 also compares the lattice phonons of the C-O2 products with those of NO NOs" and shows striking similarities in the number of bands, band shapes, widths and intensities. Differences in the peak positions can be attributed to different pressures, force constants, and reduced masses. Similarities of vibrons and lattice phonons between NO Os and the C-O2 reaction products imply that they have similar molecular configurations, CO CO, and similar crystal structures. The crystal structure of CO COs has not been determined as yet that of NC Os has been determined to be aragonite-like structure (see below). 

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