Vibronic exciton states, excitation

Weak coupling (U AE, Aw U As) The interaction energy is much lower than the absorption bandwidth but larger than the width of an isolated vibronic level. The electronic excitation in this case is more localized than under strong coupling. Nevertheless, the vibronic excitation is still to be considered as delocalized so that the system can be described in terms of stationary vibronic exciton states. 

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... 

In the case of the coherent vibronic state excitations, we shall take into account a change of the frequency of the collective vibrations in the polyene chain caused by the exciton excitation ... 

In triplet transitions, the resonance interaction and thus the Davydov splitting can, as mentioned, no longer be understood in terms of a dipole interaction, but rather as an exchange betv een orbitals which overlap. Measured values are available only for Ti states. Figure 6.10 shows as an example, similar to Fig. 6.1, the two 0,0 components of the excitation spectrum Ti So, of the triplet exciton Ti in an anthracene crystal here, however, the spectrum was taken at 1.8 K. 0,0 transition means that the excitation affects only excitons and that no additional phonons or vibrons are excited. In anthracene, the Davydov splitting of the Ti excitonic state is 21.5 cm" (cf Fig. 6.10). In naphthalene, it is 9.8 cm [34]. 

Fluorescence-sensitization experiments have been made with molecular crystals containing a small amount of an impurity with lower excitation energy. The best known example is that of anthracene crystals with traces of naphthacene . These crystals emit the naphthacene fluorescence even at an impurity mole ratio of 10 with exclusive excitation of the host molecules. Here the multi-step nature of the transfer process is evident because of the weak coupling properties of the host material. It is further substantiated by the low concentration of the acceptor required and by the decrease in transfer efficiency at low temperature . The transfer is expected here to occur by the migration of vibronic excitons, which, after more or less efficient scattering, are finally trapped by an impurity molecule with its lower energy state. 

The enhancement of the total S value by the CT state coupling can be understood using the simplest possible model of the system two excited electronic states and a single vibrational mode. The first state [Qy exciton state) is assumed to carry all the oscillator strength while the second state,(CT state) is dark. In the diabatic representation, the effective Hamiltonian in the linear vibronic coupling model of the excited state surface can be written as " " ... 

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. 

Thus the hamiltonian (2.15) couples the electronic excitations to the vibrations by linear terms in and by quadratic terms in A. The molecular eigenstates of (2.15) are the vibronic states they are different from tensorial products of electronic excitations and undressed vibrations. Even for this simple intramolecular effect, we cannot, when moving to the crystal, consider excitonic and vibrational motions as independent. 

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 ... 

---