Benchmark spinor-based relativistic coupled-cluster calculations for the ionization energies of the uranium atom, the uranium monoxide molecule (UO), and the uranium dioxide molecule (UO2) and for the bond dissociation energies of UO and UO2 are reported. The accuracy of these calculations in the treatments of relativistic, electron-correlation, and basis-set effects is analyzed. The intrinsic convergence of the computed results and the favorable comparison with the experimental values demonstrate the unique applicability of the spinor representation of quantum-chemical methods to open-shell uranium-containing atomic and molecular species with uranium oxidation states ranging from U(0) to U(V).