Spectral function absorption spectrum analysis

A brief list of basic assumptions used in the ACF method precedes the detailed analysis of the results of calculations. The derivation of the formula for the spectral function is given at the end of the section. The calculations demonstrate a substantial progress as compared with the hat-flat model but also reveal two drawbacks related to disagreement with experiment of (i) the form of the FIR absorption spectrum and (ii) the complex-permittivity spectrum in the submillimeter wavelength region. We try to overcome these drawbacks in the next two sections, to which Fig. 2c refers. 

The analysis of the dynamics and dielectric relaxation is made by means of the collective dipole time-correlation function (t) = (M(/).M(0)> /( M(0) 2), from which one can obtain the far-infrared spectrum by a Fourier-Laplace transformation and the main dielectric relaxation time by fitting < >(/) by exponential or multi-exponentials in the long-time rotational-diffusion regime. Results for (t) and the corresponding frequency-dependent absorption coefficient, A" = ilf < >(/) cos (cot)dt are shown in Figure 16-6 for several simulated states. The main spectra capture essentially the microwave region whereas the insert shows the far-infrared spectral region. 

Qualitative analysis by Raman spectroscopy is very complementary to IR spectroscopy and in some cases has an advantage over IR spectroscopy. The Raman spectrum is more sensitive to the organic framework or backbone of a molecule than to the functional groups, in contrast to the IR spectrum. IR correlation tables are useful for Raman spectra, because the Raman shift in wavenumbers is equal to the IR absorption in wave-numbers for the same vibration. Raman spectral libraries are available from commercial and government sources, as noted in the bibliography. These are not as extensive as those available for IR, but are growing rapidly. 

Since the exponential factor of (FC) dominates Equation (5), several features are very easily discussed. First, this exponential function is in Gaussian form, and is the basis for a Gaussian analysis of absorption or emission spectra. A second point is that Equations (5)-(8) provide the basis for analyzing the absorption or emission spectral envelope by considering some range of values of light frequencies (i/obsd)> but the nonradiative rate constant corresponds to the zero-photon limit (a point, not a spectrum). 

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