Optical line shape

Geva E and Skinner J L 1997 Theory of single-molecule optical line-shape distributions in low-temperature glasses J. Chem. Phys. B 101 8920-32... 

Geva E and Skinner J L 1998 Optical line shapes of single molecules in glasses temperature and scan-time dependence J. Phys. Chem 109 4920-6... 

Srajer, V., and Champion, P. M. 1991. Investigations of optical-line shapes and kinetic hole burning in myoglobin. Biochemistry 30 7390-7402. 

The coherent fs time-resolved CARS method is highly sensitive for the investigation of collision induced (or pressure dependent) changes in optical line shapes especially when line mixing occurs and frequency resolved measurements come to their limits [7]. The fs-CARS spectroscopy is applied to various collision systems (N2-N2, N2-rare gas, C2H2-C2H2, CO-CO)... 

Equation [134], given in the form of a weighted sum of individual solvent-induced line shapes, provides an important connection between optical band shapes and CT free energy surfaces. Before turning to specific models for the Franck-Condon factor in Eq. [134], we present some useful relations, following from integrated spectral intensities, that do not depend on specific features of a particular optical line shape. 

The use of the analogy between (42) and Boltzmann statistical mechanics leads to a simple semi-quantitative description of radiationless processes in aromatic hydrocarbons, but a more accurate approach to the calculation of nonradiative decay rates has also been investigated in other contexts. For the case in which the vibrational modes are harmonic, but need not be parallel or have the same frequencies in the two electronic manifolds s and l, Eq. (40) is mathematically similar to expressions considered by Kubo and Toyazawa in discussions of optical line shapes in solids s°). In particular, they showed how the double summation in (40) can be expressed as a single definite (Fourier) integral of the form... 

In Eq. (5.1) the integral presents the spectral overlap, gx(E) being the normalized optical line. shape function of centre X (see Fig. 5.1, where the spectral overlap has been hatched). Equation [5.1] shows that the transfer rate Pja vanishes for vanishing spectral overlap. The matrix element in Eq. (5.1) represents the interaction (Hsa being the interaction Hamiltonian) between the initial state S, A > and the final State S, A >. 

An experimental approach to measurement of the spatial coherence of excitons is offered by analysis of optical line shapes and hnewidths. However, a quantitative understanding of the exciton-phonon interaction is rendered difficult by the fact that the bandwidfhs of exciton bands are relatively small (in the singlet state lOOcm, in the triplet state 10cm ). The exciton-phonon interaction is not small in comparison to this. In the literature, one thus can find rather widely divergent numbers for coherence times which were measured by different methods. 

The recent theoretical approaches include a theory of barrierless electronic relaxation which draws on the model of nonradiative excited state decay, and a general treatment of the effect of solvent dielectric relaxation based on the theory of optical line shapes, as well as treatments based on classical and quantum rate theories. Equation(5) does not hold for all solvents and, more generally, may be frequency-dependent. Papers by Hynes, Rips and Jortner, Sumi and Marcus, and Warshel and Hwang " contain good overviews of the theoretical developments. 

Renger, T., Trostmann, 1., Theiss, C., Madjet, M.E., Richter, M., et al. Refinement of a structural model of a pigment-protein complex by accurate optical line shape theory and experiments. J. Phys. Chem. B 111, 10487-10501 (2007)... 

Friesner, R.A. Green functions and optical line shapes of a general 2-level system in the strong electronic coupling limit. J. Chem. Phys. 76, 2129-2135 (1982)... 

The experimental results of this Section show that optically generated phonons can be used to study the transient broadening of the optical line shape of a single absorber. In principle, the dependence on the phonon frequency can be studied in such an experiment. In the same experiment the time-resolved dynamics of phonon diffusion and phonon decay in polymeric systems can be investigated via the dephasing mechanism of the optical probe. 

It is known that the dipolar moment d(t) of a molecule osdllating with time is a source d electro-magnetic radiation. If this oscillation is of a harmonic type, so that d(t) = d exp( — io t), the dipolar moment al orl and radiates monochromatic light with a frequency Oq. This means that the optical line is described by a Lorentzian with a vanishing half-width i.e. by a 5-function. By using the integral representation for 5-fimction, we can write for the optical line shape function the following expression ... 

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