Global-minimum optimizations combined with relativistic quantum chemistry calculations have been performed to characterize the ground-state stable structures of four titled compounds and to analyze the bonding properties. Th 2 C 8 was identified as being a ThC 4 −Th(C 2 ) 2 structure, U 2 C 8 has been found to favor the U− U(C 8 ) structure, and both Th 3 C 8 and U 3 C 8 adopt the (AnC 3 ) 2 −(AnC 2 ) structure. Then, the wave function analyses reveal that the interactions between the Th 7s-based orbital and the σ g molecular orbital of the C 2 unit compensate for the excitation energy of 7s 1 6d 1 → 6d 2 and lead to the stabilization of two Th(IV)s in the ThC 4 −Th(C 2 ) 2 structure. It also reveals that the U species exhibit magnetic exchange coupling behavior in U x C 8 , for instance, as seen in the direct interaction of U 2 C 8 and the superexchange pathway of U 3 C 8 , which effectively stabilizes their low-spin states. This interpretation indicates that the geometric and electronic structures of An x C 8 species are largely influenced by the local magnetic moment and spin correlation.