Transition polarizabilities, vibrational line

We have described our most recent efforts to calculate vibrational line shapes for liquid water and its isotopic variants under ambient conditions, as well as to calculate ultrafast observables capable of shedding light on spectral diffusion dynamics, and we have endeavored to interpret line shapes and spectral diffusion in terms of hydrogen bonding in the liquid. Our approach uses conventional classical effective two-body simulation potentials, coupled with more sophisticated quantum chemistry-based techniques for obtaining transition frequencies, transition dipoles and polarizabilities, and intramolecular and intermolecular couplings. In addition, we have used the recently developed time-averaging approximation to calculate Raman and IR line shapes for H20 (which involves... 

FIGURE 2.1 Energy of the 0-0 vibrational transition in the principal electronic absorption spectrum of violaxanthin (l Ag-—>1 BU+), recorded in different organic solvents, versus the polarizability term, dependent on the refraction index of the solvent (n). The dashed line corresponds to the position of the absorption band for violaxanthin embedded into the liposomes formed with DMPC (Gruszecki and Sielewiesiuk, 1990) and the arrow corresponds to the polarizability term of the hydrophobic core of the membrane (n = 1.44). 

While for an accurate (+1%) treatment of the rototranslational spectra (v = v = 0) the matrix elements (vj (9 v f) of the lower rotational states do not much depend on the rotational transitions (j,f), for the vibrational bands (v > 0), for v f v, relatively strong j,f dependences are usually observed (9 designates the multipole and polarizability operator. Similar j dependences are also obtained for the dipole components Bc that are significant for line shape computations [63]. The accounting for the j dependences is relatively easy because the main effect of the j dependence is on the integrated intensity, but not so much on the shape of the profile. The main effect of neglecting the j dependence in the low-temperature spectra is an excess intensity of the Sj(l) lines. 

As already pointed out, this description of the Raman effect is based on the polarizability theory (Placzek, 1934) which is valid in a good approximation if the exciting frequency is much higher than the frequency of the vibrational transition // , but lower than the frequency of the transition to the electronic excited state If, on the other hand, is approaching then resonances occur which considerably enhance the intensities of the Raman lines, i.e., the resonance Raman effect. This effect and its applications are described in Sec. 6.1 and also in Secs. 4.2 and 4.8. 

The changes in molecular polarizability during vibrational transitions determine the intensities of Raman lines. The aj polarizability matrix element for a transition from a vibronic state m to a vibronic state n can be presented as follows [4,254-256]... 

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