Vibronic bandwidth

Pinan J P, Ouillon R, Ranson P, Becucci M and Califano S 1998 High resolution Raman study of phonon and vibron bandwidths in isotropically pure and natural benzene crystal J. Chem. Phys. 109 1-12... 

Thus, the level of the aggregate electronic excitation becomes split for N levels, N being the number of the molecules in an aggregate. The energy of the aggregate excitation AEj k) is thus varied between Asf + Df— 2Mj and Asf + Df + 2Mj (Fig. 1). Consider the case when 2MJ AEv, where AEv is the vibronic bandwidth... 

The magnitude of the interaction is even more important than its nature, and it is thus convenient to make a distinction, as proposed by Forster, between three main classes of coupling (strong, weak and very weak), depending on the relative values of the interaction energy (U), the electronic energy difference between D and A (AE), the absorption bandwidth (Aw) and the vibronic bandwidth (As) (Figure 4.15). 

Fig. 3. Resonance Raman spectra and excitation profiles for a displaced (B = 2) harmonic oscillator (totally symmetric normal mode). The spectra plotted as line spectra perpendicular to the plane of the paper include the Rayleigh line u = 0, the Raman fundamental = 1, and the first two overtones u = 2 and u = 3. The panels parallel to the plane of the paper represent the corresponding excitation profile. The front (i.e., Rayleigh) excitation profile resembles the squared absorption spectrum. Unless otherwise stated, all figures are based on unit vibrational frequencies and transition moments, and values , = 15 for the energy of the excited state considered and F = 0.2 for its vibronic bandwidth.

Another effect that may complicate the simple structure of Fig. 6 is a variable vibronic bandwidth. The d = 0 band in an absorption spectrum is sometimes narrower than the other bands since it is not subject to vibrational relaxation. This produces an asymmetry in the Mortensen doublet as illustrated in Fig. 8, where we show results for the system of Fig. 6 but with all bandwidths doubled except that for v = 0. 

The anthracene sym-trinitrobenzene complex was studied as a dilute solute in glasses and host crystals. The CT absorption and fluorescence spectra in both types of media were found to be essentially identical (e.g., vibronic bandwidths 1000 cm ). Furthermore, the CT fluorescence origin band in the glass was invariant to the location of the laser excitation frequency within the origin band of the CT absorption spectrum. The results of ref. 21 lead to Ft 300 cm" for this 100% CT transition. It is, therefore, germane to... 

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. 

Martin s group has also performed the same type of measurements to wild-type RCs of Rh. sphaeroides [77], A rapid ET takes place upon an excitation of the special pair in this system. Since the bandwidth of the pumping pulse can only cover one electronic state (special pair), quantum beats result from a generation of the vibrational coherence. However, the system also exhibits single-vibronic ET. In this case, the coupled-master equations can be written as... 

The measurement of fluorescence decay times can provide information on a number of fundamental processes. Consider the following kinetic scheme. The molecule AB in its electronic ground state (X) is irradiated by a short, narrow bandwidth pulse of light at a wavelength which corresponds to the transition to the vibronic level (F) t j-, viz. 

For some reactions, it is possible to infer the energy change for the electron-transfer step, from the energy and bandwidth of the ftmdamental vibronic component of the CT absorption or emission band see the discussion below,... 

The electronic-transition dipole moment for the G E transition is defined by Mge = ( g A/ ge1 e> where the are the state wave functions and A/ ge is the dilference in dipole moment of the ground and excited states [22]. The intensity of the transition is proportional to Mge - The broad absorption bands usually observed in transition metal systems are composed of progressions in the vibrational modes that correlate with the differences in nuclear coordinates between the vibrationally equilibrated ground and excited state. Since the energy difference between the donor and acceptor is generally solvent-dependent, the distribution of solvent environments that is characteristic of solutions may also contribute to the bandwidth (see further discussion of this point in the sections below). If the validity of the Born Oppenheimer approximation is assumed, the intensity of each of these vibronic components is given by Eq. 11,... 

The time-dependent oscillations in absorption or other observables can be thought of as quantum beats resulting from coherent excitation of several vibronic levels contained within the bandwidth of the ultrashort excitation pulse. In a formal sense, the experiment is the same as other quantum beat experiments carried out on femtosecond or longer time scales. However, in most such experiments different molecular vibrational degrees of freedom that... 

Since the development of ultrashort lasers, nudear wavepacket dynamics of various matters have attracted continuing attention [1,2]. The research targets extend from gas phase molecules [3, 4] to molecules in solution [5, 6], and solids [7]. In general, an excitation of matter by an ultrashort pulse with sufficient bandwidth leads to the creation of coherence between vibrational (or vibronic) eigenstates [1]. The induced nuclear wavepacket then starts to evolve on a certain potential energy surface and the dynamics is probed by a suitable pump-probe spectroscopy. The direct time-domain observation of the nudear motion provides us with valuable information on photochemical reaction dynamics, vibrational excitation/relaxation mechanisms, electron-vibration (phonon) coupling, and so on. 

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