Structures and Electronic Properties of M₂C₂ @C₇₈(M = Ti, Zr, Hf): A Density Functional Theory Study

A systematic DFT investigation has been conducted to explore the structures and electronic properties of the metal-carbide endofullerenes M₂C₂ @ C₇₈ (M = Ti, Zr, Hf) at the PBE/DNP level of theory. The theoretical calculations predicted the following: (i) this series of endofullerenes have the valence states [M⁴⁺]₂C²⁻ ₂@C⁶⁻ ₇₈; (ii) the structure of the [M₂C₂]⁶⁺ cluster encapsulated in the C⁶⁻ ₇₈(D_3h) cage varies with the increasing of the ionic radius of M⁴⁺, i.e., from a linear M-C ≡ C-M geometry for M = Ti, through a zigzag geometry for M = Hf to a side-on binding mode for M = Zr; (iii) M₂C₂ @ C₇₈ (M = Zr, Hf) should display interesting intramolecular dynamic behavior at room temperature, i.e., the encapsulated C²⁻ ₂ moiety can rotate freely around the C₃-axis of the C⁶⁻ ₇₈(D_3h) cage; (iv) the [Ti₂C₂]⁶⁺ in the lightest Ti₂C₂ @C₇₈ is far more fixed by adopting the linear Ti-C ≡ C-Ti geometry; (v) the order for their ionization potentials is Ti₂C₂ @ C₇₈ < Hf₂C₂ @C₇₈ ≪Zr₂C₂ @C₇₈, whereas their EAs follow the order: Ti₂C₂ @C₇₈ < Hf₂C₂ @C₇₈ ≈ Zr₂C₂ @C₇₈. The predicted redox properties of these endofullerenes suggest that Zr₂C₂ @C₇₈ is synthetically as approachable as Hf₂C₂ @C₇₈.