The vibrational self-consistent field method is used to analyze the inhomogeneous spectral distribution of transitions caused by vacancies and thermally populated phonons, specializing to molecular iodine isolated in an Ar matrix. At experimentally relevant temperatures, for a vacancy concentration of 1.4%, both defect-induced and phonon-induced spectral shifts contribute to the spectral distribution. Both contributions scale linearly with vibrational overtone number. The predicted widths are consistent with reported resonant Raman spectra. In time-resolved coherent anti-Stokes Raman scattering (TRCARS) measurements, spectral indistinguishability implies that all members of the inhomogeneous ensemble contribute coherently to the detectable homodyne signal. The connection between spectral distribution and the observable in TRCARS is derived. The predicted polarization beats and free induction decay due to the inhomogeneous ensemble are in qualitative agreement with experiments.

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