Vibron dispersion

The vibronic exciton is a collective oscillation of the crystal where vibronic molecular states (e.g. electronic and molecular excitations) stay on the same site. To the first order of the perturbations Jnm the vibron dispersion is given by... 

Fig. 12. Phonon-vibron dispersion curves in solid TCNE from inelastic neutron scattering [103] (1 THz = 33.36 cm ). The modes below 5 THz are strongly mixed [58, 103]...

Single vibronic level, or dispersed, fluorescence spectroscopy... 

The photoconductivity and absorption spectra of the multilayer polydiacetylene are shown in Fig. 22 [150]. The continuous and dotted line relate to the blue and red polymer forms respectively. Interpretation is given in terms of a valence to conduction band transition which is buried under the vibronic sidebands of the dominant exciton transition. The associated absorption coefficient follows a law which indicates either an indirect transition or a direct transition between non-parabolic bands. The gap energies are 2.5 eV and 2.6 eV for the two different forms. The transition is three dimensional indicating finite valence and conduction band dispersion in the direction perpendicular to the polymer chain. 

Now we can discuss the influence of the collective coupling. For Jk hQ0, the crystal vibrons are deduced from the molecular states by means of the dispersion (Fg)2 Jk, as in Section II.B.l.b above, with the molecular oscillator... 

Figure 2.5. Dispersion diagram of the system of vibron-multiparticle states. The vibrons coupled to two-particle states become unstable (broken curves).

Figure 2.7. The various responses of the 0-1 vibron-two-particle states described by the hamiltonian (2.65H2.69) vs the two parameters EFC and AO, for a 2D lattice with two molecules per cell. The scheme of the absorption is given in each delimited area. Apart from the well-known case FC = hO0 ( 2 = 1), the boundaries of the areas depend on the excitonic dispersion of the lattice. Rigorously speaking, this scheme is valid only for a 3D lattice.

Overall, the band shifts experimentally observed for all kinds of absorptions are the net results of three, partly counteracting contributions electrostatic (dipole/dipole dipole/induced dipole blue shift), dispersion ( red shift), and specific hydrogen-bonding blue shift). Which of these solute/solvent interactions are dominant for the solute under study depends on the solvents used. For example, the results obtained for pyridazine, as shown in Fig. 6-5, clearly implicate hydrogen-bonding as the principle cause of the observed hypsochromic band shift that occurs when the HBD solvent ethanol is added to solutions of pyridazine in nonpolar -hexane [98]. The intensity of n n absorption bands is usually very low because they correspond to symmetry-forbidden transitions, which are made weakly allowed by vibronic interactions cf. Fig. 6-5). 

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