Relaxation spectral band intensities

Note that there is a constant t in the expression for polarized band intensity this yields a delta function when the Fourier transform is taken. The resulting spectral feature is the narrow peak often observed in polarized Raman spectra and has a finite width due to vibrational relaxation function Vjt,(t). In experimental studies, this peak shape is often analyzed to obtain V (t), which is then used to extract the rotational contributions from the shapes of the other bands, While the transfer of V (t) from one band to another is by no means rigorously correct, it is perhaps the best available approach to the difficult problem of separating vibrational relaxation from the rotational contribution to the band shape. 

Figure 2.21. Scheme of the various distributions D, and D2 of the polaritons leading to the observed bulk fluorescence. The model of two main distributions accounts for the narrow lines, the satellite broad bands, and their relative intensities. The energy of the main fluorescence lines is given in reciprocal centimeters. The bold arrow represents the relaxation in the excitonic band to states above 0. The primary distribution of excitons ( >,) relaxes by the creation of acoustical phonons (wavy arrow) to the secondary distribution of polaritons (D2) below E0 as well as to other vibrations in the ground state as given by the spectral model85 or the dynamical model (second ref. 87). 

Estimates of IVR rates have also been inferred from spectral studies. The principal spectral approach, the measurement of the emission spectra of isolated molecules (for a review, see, for example, Ref. 3), relies on the fact that the spectral characteristics of emission from a molecule will depend intimately on the vibrational character of the excited molecular state. If one prepares a gaseous molecule in a well-defined vibrational state and subsequently observes emission bands that would not be expected to arise from this initially prepared state, then some IVR process can be inferred. Moreover, a rate can be calculated for the process by comparing the intensities of expected emission bands (vibrationally unredistributed emission) and unexpected emission bands (vibrationally redistributed emission). Redistributed and unredistributed emission often are loosely termed relaxed and unrelaxed. Since energy is conserved in isolated molecules, there is no real energy relaxation, as occurs in solution or in solids. 

The general experimental approach in 2D-spectroscopy involves the application of an external perturbation that can selectively excite various chemical components of a given system. The excitation and subsequent relaxation processes, which are manifested by changes in peak intensities, shifts in spectral frequencies and variations in band shape, are monitored by a given spectroscopic probe. 

All NMR experiments were performed on a Varian XL-200 spectrometer at 50.31 MHZ. Relevant instrument settings include 90 degree pulse angle, 1.0 second acquisition time, 0.5 second pulse delay, 238.5 ppm spectral width, and broad band proton decoupling. About 40,000 transients were collected for each spectrum. Temperature was maintained at 40 C. Spin-lattice relaxation time (Tl) and Nuclear Overhauser Enhancement (NOE) values for all C-13 NMR resonances were carefully measured to determine the optimum NMR experimental conditions. The spectral intensity data thus obtained were assured of having quantitative validity. 

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