Structures, harmonic vibrational frequencies, and mode assignments for p-benzoquinone, p-fluoranil, and p-chloranil were calculated by using unrestricted Hartree-Fock (UHF), density-functional (DF), and hybrid Hartree-Fock/density-functional (HF/DF) methods with a 6-31G(d) basis set. For p-benzoquinone, the three-parameter, hybrid HF/DF methods (B3P86 and B3LYP) yield bond distances and angles within experimental error of structures determined by electron diffraction. The second-order Moller-Plesset perturbation method (UMP2) and the local density-functional method combining Slater's exchange functional with the correlation functional of Vosko, Wilk, and Nusair (SVWN) give excellent bond distances and angles, whereas the UHF method gives the poorest structure for p-benzoquinone. All methods tested indicate that the three molecules are planar and display D-2h symmetry. Calculated C=O distances depend on substituent pi-donor ability and decrease in the order p-benzoquinone > p-fluoranil > p-chloranil, whereas C-C single-bond distances decrease in the opposite order, p-chloranil > p-fluoranil > p-benzoquinone. A qualitative, frontier orbital rationale is given for the calculated trend in C=O and C-C single-bond distances, and the trend is predicted to continue for p-bromanil and p-iodanil. Unscaled, harmonic vibrational frequencies calculated by using the B3P86 hybrid HF/DF method are in very good agreement with experiment and differ from experimental frequencies by an average of only 46 cm(-1) for p-benzoquinone, 34 cm(-1) for p-fluoranil, and 27 cm(-1) for p-chloranil. For p-benzoquinone, calculated mode assignments agree with those inferred from experiment. For p-fluoranil and p-chloranil, several modes whose frequencies were not experimentally measured were calculated and the b(1u) symmetry C=O stretching frequency is correlated with substituent pi-donor ability. The C=O stretching mode of b(1u) symmetry is also identified as a particularly faithful indicator of bond strengths and bond lengths because the b(1u) C=O mode of all three molecules is composed of 84-93% C=O stretching motion for all methods tested.