Quantum chemical calculations of the structures, stabilities, and interactions of the title series at the CCSD(T) theoretical level are performed. The analysis of binding energies, average binding energies, and fragmentation energies indicate that the n = 2 system is more stable than its neighbors. Topological analysis of the natural bond orbital, electron density deformation, integrated charge transfer, bond critical point properties, reduced density gradient analysis are performed to explore the nature of the interaction. The results show that the present Rn–Cu2+ interactions fall into intermediate interaction type with a pronounced covalent character.