The title compounds, the uranium (VI) fluoride chlorides (UF6-nCln, n = 0-6) and methoxyuranium (VI) fluorides [UF6-n(OCH3)(n), n = 0-5], have been studied using relativistic density functional theory. Applying the B3LYP hybrid functional and an effective core potential on uranium, equilibrium geometries have been calculated for these molecules. In addition, harmonic vibrational frequencies have been computed for the chloride fluorides. Calculated frequencies have been compared to experiment where possible. All experimentally observed bands have been assigned, based on these calculations. The average deviation between theoretical and experimental frequencies is 15.6 cm(-1) for 23 experimental modes. Theory always underestimates the experimental frequencies. This can be explained by the calculated bond lengths that are somewhat too long. The electronic structure of the uranium (VI) chloride fluorides has been investigated using scalar relativistic calculations and the PW91 functional. Periodic trends in the role and bonding contribution of the uranium 5f orbitals are discussed.