Vibrational modes, spectral activities

The principal modes of vibration of the anthracene molecule, active in absorption and in fluorescence, have been given in ref. 58. This subsection is intended to provide a consistent analysis of the whole structure of the crystal absorption (reflectivity) and to discuss its shape in terms of vibron-two-particle states and collective couplings and of the spectral and dynamical (relaxation) effects to which they give rise. These active vibration modes are here summarized in decreased order of strength ... 

The two main nuclear modes affecting electronic energies of the donor and acceptor are intramolecular vibrations of the molecular skeleton of the donor-acceptor complex and molecular motions of the solvent. If these two nuclear modes are uncoupled, one can arrive at a set of simple relations between the two spectral moments of absorption and/or emission transitions and the activation parameters of ET. The most transparent representation is achieved when the quantum intramolecular vibrations are represented by a single, effective vibrational mode with the frequency Vy (Einstein model). 

To clarify the correspondence between spectral peaks and vibrational modes obtained by FTs of TSVAFs, we also performed an INM analysis for the active center (see Section 8.3.1.1.1). It was found that the frequencies of V7, V32, Vg, and V5 are 616, 772, 800, and 1070 cm , respectively. These are quite similar to experimental values of MbCO [9a] and/or those of NiOEP [58]. The relatively small differences, therefore, would come almost certainly from whether or not the active center is buried in the globin. 

An important achievement of the early theories was the derivation of the exact quantum mechanical expression for the ET rate in the Fermi Golden Rule limit in the linear response regime by Kubo and Toyozawa [4b], Levich and co-workers [20a] and by Ovchinnikov and Ovchinnikova [21], in terms of the dielectric spectral density of the solvent and intramolecular vibrational modes of donor and acceptor complexes. The solvent model was improved to take into account time and space correlation of the polarization fluctuations [20,21]. The importance of high-frequency intramolecular vibrations was fully recognized by Dogonadze and Kuznetsov [22], Efrima and Bixon [23], and by Jortner and co-workers [24,25] and Ulstrup [26]. It was shown that the main role of quantum modes is to effectively reduce the activation energy and thus to increase the reaction rate in the inverted... 

Nevertheless, even for polyacetylene, the electronic structure is not that of a simple metal in which the bond-alternation and the tc-tc gap have gone to zero there are infrared active vibrational modes (IRAV) and a pseudo-gap. This is indicated by the spectra in Figure 2 which demonstrate the remarkable similarity between the doping-induced absorption found with heavily doped trans-(CH)x, and the photoinduced absorption spectrum observed in the pristine semiconductor containing a very few photoexcitations. Not only are the same IRAV mode spectral features observed, they have almost identical frequencies. 

As an example, let us briefly consider the case of benzene, a Dgj molecule. By reference to the character table, one sees that the eleven spectrally active different vibrational modes of the molecule (eight doubly degenerate, three non-degenerate) have rotational side-bands whose width and shape are governed by the following time-dependent functions ... 

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