A simple application of Kubo’s line shape theory to the domain of vibrational frequencies is presented, compared with the experiment, and used for predictions. In vibrational modes where vibrational dephasing processes are predominant in determining the shape of the condensed phase band contour, the formalism shows that the vibrational correlation obeys a fast modulation mechanism (’’motional narrowing’’), e.g., in quinoline, tetravinyl tin, and isopropyl alcohol. However, even smaller molecules such as chloroform and methyl iodide show similar characteristics and only in exceptional cases (the uncoupled O–D stretch of D2O in H2O) is the modulation slow. This behavior is a consequence of the short modulation times (order of fractions of a picosecond) in the liquid which determine the phase loss of the vibrational amplitude after a brief period of a quasistatic distribution of molecular environments (’’rigid lattice’’) —times which can be approximately identified with the inverse average collision frequency. In order to compare theory and experiment quantitatively, the model requires that the vibrational second spectral moment must be measured in addition to the vibrational correlation function. Comparisons with vibrational memory functions, obtained from the correlation functions via the modified Langevin equation, corroborate the usefulness of the model.

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The stretched (‘‘extended’’ or ‘‘fractional’’) exponential, exp{−(t/T)α}, where 0<α≤1 and T (ps) a time constant, is introduced as a modulation function for a vibrational T2 process in order to describe the non-Markovian dynamics of the bath of amorphous systems in the picosecond domain. The theory simulates well published dephasing data of probe oscillators in concentrated aqueous solutions of KSCN, molten mixtures of Li and Rb nitrates, and of polycrystalline and smectic phases of the liquid crystal 4-n-octyloxy-4′-cyanobiphenyl. The temperature and phase dependence of dispersion parameter α follows an accepted model of constrained-sequential relaxation with a scale-invariant (‘‘fractal’’) distribution of relaxation times.

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