Spectra, molecular collisional broadening

In Eq. (10), E nt s(u) and Es(in) are the s=x,y,z components of the internal electric field and the field in the dielectric, respectively, and p u is the Boltzmann density matrix for the set of initial states m. The parameter tmn is a measure of the line-width. While small molecules, N<pure solid show well-defined lattice-vibrational spectra, arising from intermolecular vibrations in the crystal, overlap among the vastly larger number of normal modes for large, polymeric systems, produces broad bands, even in the crystalline state. When the polymeric molecule experiences the molecular interactions operative in aqueous solution, a second feature further broadens the vibrational bands, since the line-width parameters, xmn, Eq. (10), reflect the increased molecular collisional effects in solution, as compared to those in the solid. These general considerations are borne out by experiment. The low-frequency Raman spectrum of the amino acid cystine (94) shows a line at 8.7 cm- -, in the crystalline solid, with a half-width of several cm-- -. In contrast, a careful study of the low frequency Raman spectra of lysozyme (92) shows a broad band (half-width 10 cm- -) at 25 cm- -,... 

So far, this discussion of selection rules has considered only the electronic component of the transition. For molecular species, vibrational and rotational structure is possible in the spectrum, although for complex molecules, especially in condensed phases where collisional line broadening is important, the rotational lines, and sometimes the vibrational bands, may be too close to be resolved. Where the structure exists, however, certain transitions may be allowed or forbidden by vibrational or rotational selection rules. Such rules once again use the Born-Oppenheimer approximation, and assume that the wavefunctions for the individual modes may be separated. Quite apart from the symmetry-related selection rules, there is one further very important factor that determines the intensity of individual vibrational bands in electronic transitions, and that is the geometries of the two electronic states concerned. Relative intensities of different vibrational components of an electronic transition are of importance in connection with both absorption and emission processes. The populations of the vibrational levels obviously affect the relative intensities. In addition, electronic transitions between given vibrational levels in upper and lower states have a specific probability, determined in part... 

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