Symmetry of the benzene ring and its normal vibrations: The “breathing” mode is not always a normal vibration of a benzene ring
Vibrational analysis based on density-functional theory calculations at the B3LYP/6-311+G(d,p) level has been performed for benzene and its 10 deuterated analogs. The results show that the “breathing” mode, which is usually regarded as a normal vibration intrinsic to a benzene ring, is present for the d0, p-d2, 1,2,3,4-d4, 1,2,4,5-d4, and d6 species (group A), but absent for the d1, m-d2, 1,2,3-d3, 1,3,5-d3, 1,2,3,5-d4, and d5 species (group B). It is noted that the species in group A have a two-fold symmetry axis passing through the middle points of the two CC bonds in the opposite position, but the species in group B do not. The Raman spectra of the benzene species in groups A and B have been observed. In the 1010–940 cm−1 region of the spectra observed for the species in group A, only one very strong band arising from the breathing mode exists. In the same region of the spectra observed for the species in group B, two bands, one strong and the other less strong or weak, are observed. The two bands observed for the species in group B are assigned to the two trigonal ring deformation modes in which primarily the three carbon atoms at either the 1,3,5-positions or the 2,4,6-positions move in phase toward and away from the center of the ring. The Raman intensities of these two modes and the separation between them are discussed.
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