Excitons transition dipole moments

This dependence of the dressed exciton dispersion ( k) for angle 9 = 0 when the transition dipole moment is perpendicular to chain is displayed in Fig. 4.4. For another orientation of the exciton transition dipole moment the dependence of k) can be very different. For excitons with small transition dipole moment the renormalization of the exciton dispersion due to account of retardation is usually small and can be important only at low temperature of order of 1-2 K or less because of the smallness of the parameter A/Efx. In the same situation the radiative width of exciton states with small wavevectors determined by the same parameter A/EM can be a hundred-fold larger than the radiative width of a molecule in solution. Very interesting is the problem of the temperature dependence of the radiative lifetime and we come back to the discussion of this problem later. 

We have tried to express the results of Weigang s treatment in pictorial form (Scheme 6), applying the language of the exciton chirality rulesld to the coupling of the chromophore transition dipole moments with those induced in the nearby bonds. These are regarded... 

For non-coplanar electric transition dipole moments pi0a and pj0a of the two chromophores at Rjj interchromophoric distance the exciton chirality is nonzero and defined by ... 

In the case of flexible molecules all chiral conformers contribute to the observed CD spectrum. This usually leads to substantial reduction of the magnitude of the exciton Cotton effect. Nevertheless, if the conformation of the main contributor is established independently (e.g.. by molecular mechanics or NMR spectroscopy), its absolute configuration can be deduced from the exciton Cotton effect. Thus, for 3-(l-naphthalenyl)phthalide 5, the preferred conformation is 5 a. The negative couplet is in accordance with the left-handed screw between the phthalide 1 Ld and the naphthalene lBb transition dipole moment vectors, when the absolute configuration is R121. 

Movement of an electron from the ground electronic state of a molecule to an excited state creates a momentary dipole, called an electric transition dipole. Thus, associated with each electric transition is a polarization (electric transition dipole moment) that has both direction and intensity which vary according to the nature of the chromophore and the particular excitation. When two or more chromophores lie sufficiently close together, their electric transition dipoles may interact through dipole-dipole (or exciton) coupling. Exciton coupling arises from the interaction of two (or more) chromophores through... 

In the Forster mechanism, the energy transfer upon excitation may take place between excited molecular entities separated by distances R, which are considered as spatially fixed Frenkel excitons. It is described in terms of resonant interaction between their transition dipole moments, which decreases as Rr6. 

The calculated frequency separation of the amide I exciton components are much larger for the NMR structure than for the X-ray structure, although in both cases identical values for the unperturbed amide I frequency (1665 cm 1), and for the transition dipole moment were used. Further, and it was assumed for computational simplici-... 

Figure 38. (a) Absolute configuration of (55,125)-(+)-dimethyl-5,12-dihydro-5,12[l, 2 ]-benzonaphthacene-l,15-dicarboxylate (b), (c) and (d) orientations of pairs of electric transition dipole moments from the chromophores 1 and 3 from the methylbenzoate chromophores 2 from the naphthalene. The helicities are shown to the right. The 1,3 couplet is predicted to be zero since the dipoles are parallel. The 1,2 and 2,3 couplets have (+) chirality. The net chirality is predicted to be (+). (e) CD Cotton effects for the intense 233 nm transition of the benzotriptycene showing a (+) exciton chirality. 

Figure 4.5. Wave vectors around the center of the excitonic Brillouin zone for which coherent emission [solution of equations 4.10 and 4.25] is possible according to the disorder critical value Ac. We notice that r0 is the imaginary eigenvalue for K = 0 (emission normal to the lattice plane) and that K" and K1 indicate, respectively, components of K parallel and perpendicular to the transition dipole moment, assumed here to lie in the 2D lattice. The various curves for constant disorder parameter Ac determine areas around the Brillouin-zone center with (1) subradiant states (left of the curve) and (2) superradiant states (right of the curve). We indicate with hatching, for a large disorder (A,. r ), a region of grazing emission angles and superradiant states for a particular value of A.

Figure 14. Schematic diagram of the stabilization of the CDMA excimer due to exciton resonance interaction. An ideal sandwich-like conformation with opposite orientation of the two monomers is assumed for the excimer. The values of the excited-state energies and the corresponding transition dipole moments were taken from Ref [33cj. The exciton splitting of the Lb state is only 39 cm owing to the low transition dipole moment corresponding to the Lb <— So emission. The much larger A/nu value for the La — So fluorescence makes the exciton splitting of the La state the dominant stabilization. The in-phase and the out-of-phase combinations of the exciton resonance states are labeled L and L, respectively. The unknown contributions of the charge resonance interaction are indicated by a question mark. Reproduced with permission from Ref [92a].

The excimer fluorescence (with respect to the excited vdW dimer emission) is red shifted and structureless because the emission is terminated in a repulsive ground-state potential energy surface (Figure 15). For parallel transition moments, emission from the out-of-phase exciton state to the ground state is forbidden and for the in-phase exciton state emission is allowed [28a]. It should be noted, however, that the forbidden emission from the out-of-phase exciton state is expected to have a similar transition dipole moment as the Lb So emission. The actual dynamics of the initially excited vdW dimer depend on the energy gap and the coupling strength between the primary excited (LE) state and the excimer state. 

Fig. 26.9. Comparison of the energetic separation and the relative orientation of the transition-dipole moments of the k = 1 and k = 2 exciton states from individual RC-LHl complexes with results from numerical simulations for three different arrangements of the BChl a molecules in the pigment-protein complex. The top row shows the model structures A-C that have been used for the numerical simulations. Details are given in the text. The second row compares the experimental ensemble absorption spectrum (black line) with the ensemble spectrum that results from numerical simulation (gray line) for the three model structures. The third row compares the experimentally obtained energetic separations between the k = 1 and k = 2 exciton states (gray columns) with numerical simulations (black squares) for the three model structures. The fourth row compares the experimentally obtained relative orientations of the transition-dipole of the A = 1 and k = 2 exciton states (gray columns) with numerical simulations (black squares) for the three model structures. Adapted from [62]...

The exciton model of linear aggregates was used to explain the evolution of the electronic state parameters with stepwise incorporation of additional monomer units [64,408,409]. In this model, the transition dipole moments have only one component directed along the main molecular axis. Thus, the amplitude of the transition dipole moment is expressed by Eq. (47) for nc< 12. 

Whereas the distinction between collective and cooperative effects can appear artificial, it is obvious that, since optical responses are gs properties, their nonadditivity cannot be ascribed to the delocalized nature of excited states. On the other hand, static responses can be calculated from sum-over-state (SOS) expressions involving excited state energies and transition dipole moments [35]. And in fact tlie exciton model has been recently used by several authors to calculate and/or discuss linear and non-linear optical responses of mm [36, 37, 38, 39, 40, 41, 42]. But tlie excitonic model hardly accounts for cooperativity and one may ask if there is any link between collective effects related to the delocalized nature of exciton states and cooperative effects in the gs, related to the self-consistent dependence of tlie local molecular gs on the surrounding molecules. 

This term breaks down tire excitonic approximation mixing up states whose exciton number differs by two units. This so called non-Heitler-London term has negligible effects for systems with J 2wo [47]. So the excitonic approximation is expected to work well for clusters of molecules with large excitation energies and not too large transition dipole moments, i.e. for hardly polarizable molecules. 

The tlrlrd portion of the total Hamiltonian, in (14), collects all terms beyond the excitonic approximation, being responsible for the mixing of states with different number of excitons. The first term in this ultraexcltonic Hamiltonian corresponds to the non-Heitler London term in Eq. (2), as originating from the interaction between transition dipole moments. The second term describes the interaction between transition and mesomeric dipole moments and corresponds to the term in Eq. (4) wiflr = V (l -2p)yp(l -p) (cf. Eqs. (8)-(7)). 

Figure 6. Excitation energy calculated in the excitonic approximation against the number of excitons n, for A (left panels), B (middle panels) and C clusters (right panels) with N = 6. v=l, for two different w. The z parameter is fixed to — 1 for the A cluster, to 1 for the B and C clusters. States on the zero energy axis correspond to the gs. Error bars measure the squared transition dipole moment from the gs to the relevant states. Insets show the p(w) mf curve for the relevant parameters, with the dotted vertical line marking the w value for which results are reported in the parent panel...

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