We present results of a systematic study of the theoretical determination of equilibrium geometries, harmonic frequencies, total atomization energies, and dipole moments using Hartree-Fock, a hybrid Hartree-Fock density-functional-theory, and coupled-cluster methods in conjunction with a triple zeta basis set for a large set of molecules. This allows a direct comparison of the three theoretical methods applied to a range of chemical systems. The average errors (experimental value-theoretical value) for the Hartree-Fock, hybrid Hartree-Fock density-functional-theory, and coupled-cluster methods, respectively, are bond length (Angstrom) 0.022, 0.005, 0.005; bond angle (degrees) 2.7, 1.7, 1.9; harmonic frequencies (cm(-1)) 144, 40, 30; atomization energies (kcal/mol) 81.9, 3.6, 11.5; and dipole moments (debye) 0.29, 0.14, 0.10. This clearly demonstrates that the relatively inexpensive hybrid Hartree-Fock density-functional-theory method yields results which represent a reliable, significant improvement over those obtained with the Hartree-Fock method. The results obtained using the hybrid Hartree-Fock density-functional-theory method are, in fact, quite comparable with the corresponding results obtained using the high level, ab initio coupled-cluster method. For certain difficult open shell examples, the hybrid Hartree-Fock density-functional theory using a spin restricted open shell Hartree-Fock density is much improved over the corresponding hybrid Hartree-Fock density-functional-theory results obtained using a spin unrestricted Hartree-Fock density.