Molecular-dynamics simulations are used to elucidate the molecular basis for the solvent effects on the isolated C-H stretching bands observed in the Raman spectrum of cyclohexane-d(11). The main focus is on modeling the density dependence of the spectrum in supercritical CO2 recently reported by Pan, McDonald, and MacPhail [J. Chem. Phys. 110, 1677 (1999)], but several liquid solvents (CCl4, CS2, and CH3CN) have also been examined. The frequency shifts and line shapes of the Raman spectrum are simulated using a rigid solute and standard line shape theory in the limit of pure dephasing. Three models for the vibration-solvent coupling are considered. The simplest model, which is based on ground-state forces alone, provides a surprisingly good representation of the density dependence of the linewidths-line shapes but predicts the wrong sign for the gas-to-solution frequency shifts. This failure is due to the neglect of changes in bond polarizability upon vibrational excitation. Allowing for this polarizability difference via a semiempirical approach provides an accurate description of both the linewidths and frequency shifts with a physically reasonable vibrational difference potential. Interpretation of the instantaneous frequency shifts simulated with this model leads to the following general conclusions concerning the solvent effect on these spectra: (i) The relatively small gas-to-solution frequency shifts observed in experiment are the result of the near cancellation of much larger positive and negative contributions from repulsive and attractive interactions. (ii) Fluctuations in the instantaneous frequency are sufficiently fast (correlation times similar to 100 fs) that the spectra are homogeneously broadened in all solvents examined. (iii) The dynamics of the solvent-solute interactions that determine the Raman line shapes are quite well described by an isolated binary collision ("IBC") type picture. (iv) The simplicity of the dynamics, and the success of this IBC description, is due at least in part to the special, localized character of these isolated C-H stretching modes. (v) The linear density dependence of the linewidths observed in supercritical CO2 reflects the modest extent of local density augmentation in the cyclohexane-CO2 system.