Is this a chemical bond? A theoretical study of Ng₂@C ₆₀ (Ng = He, Ne, Ar, Kr, Xe)

Quantum-chemical calculations using DFT (BP86) and ab initio methods (MP2, SCS-MP2) have been carried out for the endohedral fullerenes Ng ₂@C₆₀ (Ng = He-Xe). The nature of the interactions has been analyzed with charge- and energy-partitioning methods and with the topological analysis of the electron density (Atoms-in-Molecules (AIM)). The calculations predict that the equilibrium geometries of Ng₂@C ₆₀ have D_3d symmetry when Ng = Ne, Ar, Kr, while the energy-minimum structure of Xe₂@C₆₀ has D_5d symmetry. The precession movement of He₂ in He₂@C ₆₀, has practically no barrier. The Ng-Ng distances in Ng ₂@C₆₀ are much shorter than in free Ng₂. All compounds Ng₂@C₆₀ are thermodynamically unstable towards loss of the noble gas atoms. The heavier species Ar₂OC₆₀, Kr₂@C₆₀, and Xe₂@ C₆₀ are high energy compounds which are at the BSSE corrected SCS-MP2/ TZVPP level in the range 96.7-305.5 kcal mol^-1 less stable than free C₆₀,+ 2Ng. The AIM method reveals that there is always an Ng-Ng bond path in Ng ₂@C₆₀. There are six Ng-C bond paths in (D_3d) Ar₂@C₆₀, Kr₂@C₆₀, and Xe ₂@C₆₀, whereas the lighter D_3d homologues He₂@C₆₀ and Ne₂@C₆₀ have only three Ng-C₂ paths. The calculated charge distribution and the orbital analysis clearly show that the bonding situation in Xe₂@C ₆₀ significantly differs from those of the lighter homologues. The atomic partial charge of the [Xe₂] moiety is +1.06, whereas the charges of the lighter dimers [Ng₂] are close to zero. The a _2u HOMO of (D_3d) Xe₂@C₆₀ in the ¹A_1g state shows a large mixing of the highest lying occupied σ* orbital of [Xe₂] and the orbitais of the C₆₀ cage. There is only a small gap between the a_2u HOMO of Xe₂@ C₆₀ and the e_u LUMO and the a _2u LUMO+ 1. The calculations show that there are several triplet states which are close in energy to each other and to the ¹A _1g state. The bonding analysis suggests that the interacting species in Xe₂@C₆₀ are the charged species Xe₂ ^q+ and Q₆₀^q-, where 1 < q < 2. The calculated Xe-Xe distance in the endohedral fullerene (2.494 Å) is even shorter than the calculated value for free Xe₂²⁺ (2.746 Å). Thus, the Xe-C and Xe-Xe interactions in Xe₂@C₆₀ should be considered as genuine chemical bonds which are enforced by the compression energy. The Ng-Ng and Ng-C interactions in the lighter homologues Ar₂@ C₆₀ and Kr₂@C₆₀ may also be considered as chemical bonds because the theoretically predicted properties of the endohedral fullerenes are significantly different from the free C ₆₀ and noble gas atoms. According to the bonding analysis, He ₂@C₆₀ and Ne₂@ C₆₀ are weakly bonded van der Waals complexes.