Polarizable chromophores

The model of polarizable dipolar chromophores suggests that the 3D nuclear reaction field of the solvent serves as a driving force for electronic transitions. Even in the case of an isotropic solute polarizability, two projections of the reaction field should be included the longitudinal (parallel to the difference solute dipole) component and the transverse (perpendicular to the difference dipole) component. The 8 function in Eq. [18] eliminates integration over only one of these two field component. The integral still can be taken analytically resulting in a closed-form solution for the Franck-Condon factor 

The Franck-Condon factors of polarizable chromophores in Eq. [153] can be used to generate the complete vibrational/solvent optical envelopes according to Eqs. [132] and [134]. The solvent-induced line shapes as given by Eq. [153] are close to Gaussian functions in the vicinity of the band maximum and switch to a Lorentzian form on their wings. A finite parameter ai leads to asymmetric bands with differing absorption and emission widths. The functions in Eq. [153] can thus be used either for a band shape analysis of polarizable optical chromophores or as probe functions for a general band shape analysis of asymmetric optical lines. 

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Of course, for chromophores with dipole moments less than 6 Debye and corresponding small polarizability, chromophore-chromophore intermolecular electrostatic interactions are unimportant and independent particle analysis is completely appropriate. However, it is unlikely that such chromophores will ever have commercial relevance. 

The reorganization energies follow from Eq. [71] and take the following form for polarizable chromophores ... 

The challenges outlined above still await a solution. In this section, we show how some of the theoretical limitations employed in traditional formulations of the band shape analysis can be lifted. We discuss two extensions of the present-day band shape analysis. First, the two-state model of CT transitions is applied to build the Franck-Condon optical envelopes. Second, the restriction of only two electronic states is lifted within the band shape analysis of polarizable chromophores that takes higher lying excited states into account through the solute dipolar polarizability. Finally, we show how a hybrid model incorporating the electronic delocalization and chromophore s polarizability effects can be successfully applied to the calculation of steady-state optical band shapes of the optical dye coumarin 153 (C153). We first start with a general theory and outline the connection between optical intensities and the ET matrix element and transition dipole. 

F. Steybe, F. Effenberger, U. Gubler, C. Bosshard and P. Gunter, Highly polarizable chromophores for nonlinear optics syntheses, structures and properties of donor-acceptor substituted thiophenes and oligothiophenes. 

Studies of the high-ju,j8 chromophores of Table 2 have shown the problem to be more severe than suggested by early work on less polarizable chromophores and argue for a reexamination of the approximations that lead to Eqs. 16 and 17. Neglect of the (1/2)q F F term of t/, can be ruled out, as its incorporation [76] leads to only an insignificant modification of Eq 16. 

It can be seen from Figures 3.7 and 3.8 that the calculations reproduce very well not only the experimental spectra but also the experimentally observed isotopic shifts indicating a high reliability of the computational method. According to this comparison, definite attribution can be made for even the difficult Raman bands that cannot be assigned based solely on the experimental results. It is, however, necessary to mention at this point that the calculated Raman spectrum provided directly by the ab initio computations correspond to the normal Raman spectrum with the band intensity determined by the polarizability of the correlating vibration. Since the intensity pattern exhibited by the experimentally recorded resonance Raman spectrum is due to the resonance enhancement effect of a particular chromophore, with no consideration of this effect, the calculated intensity pattern may, in many... 

We shall consider here in more detail two models first a dynamic coupling approach, due to Weigang33, who considered optical activity deriving from the coupling of electric dipoles (the diene chromophore and the polarizable bonds around it) and second, a localized orbital investigation, which permits one to separate the contributions from the intrinsic diene optical activity and from the axial substituents. 

A few examples will illustrate the case. The parent trans-diene derivatives 31a and 3235 have nearly planar chromophores, but the Cotton effects are quite strong and opposite in sign (+15 and —27.9, respectively). This can be attributed mainly to the allylic axial C—CH3 bonds, which provide a positive contribution for compounds 31 and a negative for 32. Furthermore, the As values of P-chiral s-trans-31 are strongly dependent on the polarizability of the allylic C—X bond. 

From a theoretical perspective, since the designation of the lab-fixed axes is arbitrary, what is relevant is the relative orientation of the polarizations of the excitation and scattered light. Thus the line shape for excitation light polarized along axis p, and scattered light polarized along axis q (p or q denote X, Y, or Z axes in the lab frame) is called Ipq(co). When p = q this is lyy, and when p q this is IVH. Mixed quantum/classical formulae for Ipq(co) are identical to those for the IR spectmm, except mPi is replaced by apqP which is the pq tensor element of the transition polarizability for chromophore i. Thus we have, for example [6],... 

Within the mixed quantum/classical approach, at each time step in a classical molecular dynamics simulation (that is, for each configuration of the bath coordinates), for each chromophore one needs the transition frequency and the transition dipole or polarizability, and if there are multiple chromophores, one needs the coupling frequencies between each pair. For water a number of different possible approaches have been used to obtain these quantities in this section we begin with brief discussions of each approach to determine transition frequencies. For definiteness we consider the case of a single OH stretch chromophore on an HOD molecule in liquid D2O. 

To obtain Raman spectra one needs the trajectories of the pq tensor elements of the chromophore s transition polarizability. Actually, for the isotropic Raman spectrum one needs only the average transition polarizability. This depends weakly on bath coordinates and this, together with the weak frequency dependence of the position matrix element, was included in our previous calculations [13, 98, 121]. For the VV and VH spectra, others have implemented... 

For olefins, the first term has been studied in terms of the symmetry D2 independently by two groups913. The second term, which was also called the one-electron term, is usually neglected in cases of electronically allowed transitions because it is small compared with the other two terms. It is even smaller in the olefinic case, where the molecules contain mainly nonpolar bonds. Scott and Yeh73 have therefore concentrated on the third term, which arises from the coupling of a considered transition a with all the transitions of different chromophores within the molecule. If transition a falls energetically below all the transitions of the other chromophores, the latter can be viewed as polarizable groups and their anisotropies fi determine the dynamic coupling74. The final expression obtained was... 

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