Exciton-vibration coupling

Figure 2.2. Scheme of nuclear potentials in the ground electronic state E°(Q) and the excited electronic state E (Q). In the excited state, the frequency changes (i20->S2r) and the equilibrium point is shifted. The classical relaxation energy to the new nuclear configuration in the excited state is the Franck-Condon energy Efc and characterizes the linear exciton-vibration coupling. 

This subsection summarizes what is known about exciton-vibration coupling in general. Thereafter, specific cases will be treated. We restrict our discussion to a minimal model of coupling characterized by the following approximations50 ... 

The exciton-vibration coupling is assumed to be linear, given by (2.26) or by (2.15), when the frequency change upon excitation is neglected. 

Figure 3.21. Scheme of the expected excitation profile due to the relaxation mechanisms illustrated in Fig. 3.22. We expect A) a Raman peak (quasi-resonant), (B) a dip where the intrasurface relaxation ris is quenched by the relaxation to the bulk rt, and (C) a bump / s competing with rB and overhelmed at higher energies f s. depending on the exact exciton vibration coupling, and different for the modes at 390 and 45 cm. ...

Vibrational mode wavenumbers for the ground (/) and excited (F) states and the parameters (z, D and d /dQ) describing the interaction between the 2.0 eV exciton and those modes are listed for each of the four strongly Raman-active modes. The reduced mass for all the vibrational modes has been taken as that for a carbon atom so that the displacement of the normal mode equilibrium position, D, is given in nm and the exciton-vibration coupling constant dE/dQ in eV/nm. 

Perturbation theory with respect to the chromophore vibrational coupling can be introduced if the excitonic coupling dominates. Now, it is advisable to change to an exciton representation and to introduce the (reduced) exciton density matrix... 

The mixed quantum classical description of EET can be achieved in using Eq. (49) together with the electronic ground-state classical path version of Eq. (50). As already indicated this approach is valid for any ratio between the excitonic coupling and the exciton vibrational interaction. If an ensemble average has been taken appropriately we may also expect the manifestation of electronic excitation energy dissipation and coherence decay, however, always in the limit of an infinite temperature approach. 

During this study, we found that the exciton model underestimates the splitting between the coupled states by about a factor of four, indicating that interactions other than dipole-dipole coupling act between adjacent carbonyl groups. These interactions are most likely straightforward vibrational coupling terms, as discussed at the end of Section 3. 

The B(b) are operators of excitons (vibrations) the Vnm are intermolecular interactions a dimensionless parameter, characterizes the linear coupling. H is qualitatively characterized by the following parameters ... 

First, we envisage the weak exciton-photon coupling (which allows an intuitive description of the phonon effects on the nature of the secondary emissions). Therefore we write the hamiltonian of the total system as sums of free photons (Hy), free excitons (He), and free phonons (Hp), with the appropriate interactions Hey (Section I) and Hep (see Sections II, A, B, C.), including intramolecular vibrations too. 

In resonant infrared multidimensional spectroscopies the excitation pulses couple directly to the transition dipoles. The lowest order possible technique in noncentrosymmetrical media involves three-pulses, and is, in general, three dimensional (Fig. 1A). Simulating the signal requires calculation of the third-order response function. In a small molecule this can be done by applying the sum-over-states expressions (see Appendix A), taking into account all possible Liouville space pathways described by the Feynman diagrams shown in Fig. IB. The third-order response of coupled anharmonic vibrations depends on the complete set of one- and two-exciton states coupled to thermal bath (18), and the sum-over-states approach rapidly becomes computationally more expensive as the molecule size is increased. 

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