The study of the bulk and surface properties of cubic (fluorite structure) HfO2 and UO2 was performed using the hybrid Hartree–Fock density functional theory linear combination of atomic orbitals simulations via the CRYSTAL06 computer code. The Stuttgart small-core pseudopotentials and corresponding basis sets were used for the core–valence interactions. The influence of relativistic effects on the structure and properties of the systems was studied. It was found that surface properties of Mott–Hubbard dielectric UO2 differ from those found for other metal oxides with the closed-shell configuration of d-electrons.