Time-Domain Theoretical Analysis of the Noncoincidence Effect, Diagonal Frequency Shift, and the Extent of Delocalization of the C=O Stretching Mode of Acetone/Dimethyl Sulfoxide Binary Liquid Mixtures

A time domain method for simulating vibrational band profiles that simultaneously takes into account both the diagonal and off-diagonal effects is developed and applied to the C=O stretching bands of neat liquid acetone and the acetone/dimethyl sulfoxide (DMSO) binary liquid mixtures. By using this method, it is possible to examine the influence of liquid dynamics on the noncoincidence effect (NCE), which arises from the off-diagonal vibrational interactions, as well as the frequency shifts and band broadening, which are related to both the diagonal and off-diagonal effects. It is shown that the simulations for the C=O stretching bands of acetone in acetone/DMSO binary liquid mixtures on the basis of this method can reproduce the experimentally observed concave curvature of the concentration dependence of the NCE and the unusually large frequency shift of the anisotropic Raman band. The widths of the infrared, isotropic Raman, and anisotropic Raman bands calculated for neat liquid acetone are also in good agreement with those observed. Based on these calculations, the extent of delocalization of the C=O stretching vibrational motions is examined by referring to two quantitative measures of this property, one calculated in the frequency domain and the other in the time domain. It is shown that the extent of delocalization gets larger as the mole fraction of acetone increases, the C=O stretching vibrations being delocalized over a few tens of molecules in neat liquid acetone. It is also shown that the extent of delocalization is related to the quantity called NCE detectability, which is the ratio between the magnitude of NCE and the band width. It is therefore suggested that the extent of delocalization of vibrational motions may be estimated from observable features of Raman band profiles.