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The molecular structures and vibrational spectra of Dewar benzene, benzvalene, trimethylenecyclopropane, prismane and 3,4-dimethylenecyclobutene have been investigated by density functional theory using Becke's exchange with Lee-Yang-Parr's correlation functional and the 6-31G* basis set. Both the calculated structural parameters and vibrational frequencies are in good agreement with available experimental data. On the basis of the agreement between the calculated and experimental results, assignments of fundamental vibrational frequencies of Dewar benzene, benzvalene, and trimethylenecyclopropane were examined and some reassignments are proposed. The calculations also predict prominent IR and Raman spectral features of prismane and 3,4-dimethylenecyclobutene, which can assist experimental identification of these compounds and the assignment of observed spectral features when they are available.