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. Th2C8 was identified as being a ThC4-Th(C2)2 structure, U2C8 has been found to favor the U-U(C8) structure, and both Th3C8 and U3C8 adopt the (AnC3)2-(AnC2) structure. Then, the wave function analyses reveal that the interactions between the Th 7s-based orbital and the σg molecular orbital of the C2 unit compensate for the excitation energy of 7s16d1 → 6d2 and lead to the stabilization of two Th(IV)s in the ThC4-Th(C2)2 structure. It also reveals that the U species exhibit magnetic exchange coupling behavior in UxC8, for instance, as seen in the direct interaction of U2C8 and the superexchange pathway of U3C8, which effectively stabilizes their low-spin states. This interpretation indicates that the geometric and electronic structures of AnxC8 species are largely influenced by the local magnetic moment and spin correlation.