Prediction of vibrational frequencies of polyatomic molecules using density-functional theory (DFT) methods has become common because of its accuracy and therefore consistency with experimental data. However, the utility of DFT methods in predicting vibrational frequencies and normal mode descriptions of excited state intermediates has not been addressed so far. In this paper we have evaluated the performance of Hartree-Fock (HF) and various density-functional (DF) and hybrid Hartree-Fock/density-functional (HF/DF) methods in predicting the structure, vibrational frequencies, and normal mode descriptions of transient intermediates, taking p-benzoquinone (BQ) as an example. The structures, bond orders, harmonic vibrational frequencies, and isotopic shifts for BQ and its lowest triplet state, semiquinone radical, and semiquinone radical anion have been calculated using all of these methods employing 6-31G(d) and 6-31G(d,p) basis sets. Assignments of the calculated vibrational frequencies were made with the help of normal mode analysis. The calculated structural parameters and bond orders indicate that the structure of the triplet state is intermediate between those of the ground state and radical anion. The semiquinone radical shows a mixed aromatic and quinonoid structure. Geometrical changes involved in the triplet excited state and semiquinone radical anion with respect to ground state structure are explained on the basis of the calculated electronic structures. Of all the methods tested, the three parameter hybrid HF/DF methods (B3LYP, B3P86, and B3PW91) were found to give the most accurate geometries. These methods are also found to reproduce the experimental frequencies of the ground state as well as transient species within 2-4% error, whereas the isotopic shifts calculated for the deuterated species using the BP86 method are superior and show excellent agreement with experiment. Calculations using all of the methods show that both 6-31G(d) and 6-31G(d,p) basis sets yield very similar results.