Kohn-Sham density functional theory calculations are presented for CH4, C6H6, and O-3 using popular exchange-correlation functionals based on the adiabatic connection method (ACM). The structure and harmonic vibrational frequencies of CH4 and C6H6 are described very well with the ACM functional. In particular, a very accurate description of CH vibrations is obtained, suggesting a possible resolution of this well-known deficiency of conventional functionals. In contrast, the application of ACM functionals to the energetics, structure, and harmonic frequencies of O-3 yields results which are rather poor compared to conventional functionals. These observations appear to be closely related to the performance of Hartree-Fock theory for these systems.