| Endohedral metallofullerenes (EMFs) are fullerene-based derivatives that have a metal atom or metal-containing cluster inside hollow fullerene cages. Due to their unique electronic structures, EMFs have attracted wide interests in the past two decades. However, structural determinations of EMFs are still quite a challenge because of low yields in Kr(?)tschmer-Huffman arc-discharge reactions, difficulties in separations and purifications, complicated and low signal-to-noise 13C NMR spectra and lacks of suitable single crystals for X-ray diffraction analyses et al.It's an essential issue of determining the structures of EMFs in order to understand their optical, magnetic and chemical properties for the potential applications.Based on the fullerene topology, we carried out systematic investigations on structures and electronic properties of EMFs by means of quantum chemical computations. The results are summarized as follows:1. Sc2C70:SC2C70 takes the form of Sc2C2@C68,but not Sc2@C70.Its formal charge state can be described as (Sc3+)2(C2)2-@C684-.2. M2C2@C78 (M=Ti, Zr, Hf): Structures of the M2C80 (M=Ti, Zr, Hf) series are M2C2@C78 instead of previous assigned M2@C80.The formal charge states of these dimetallic carbide endofullerenes are (M4+)2(C2)2-@C786-.3. U2@C60:The ground state of U2@C60 is U2@C60 (D3d,7A2u).The encapsulated U2 cluster has a sixfold ferromagnetically coupled one-electron-two-center U-U bond with the electronic configuration of (5fπu)2(5fσg)1(5fδg)2(5fφu)1.4. Structural rules of Sc2C2n (30≤n≤43): i) formal charge states for the most stable Sc2C2@C2n-2 and Sc2@C2n are (Sc3+)2(C2)2-@C2n-24- and (Sc3+)2@C2n6-, respectively; ii) Sc2C2n with small fullerenes (2n=60, 62, 64, 68) are unstable in experiments; iii) except for Sc2C70,Sc2C2n with medium (2n=66,72-82) and large (2n≥84) cages prefer Sc2@C2n and Sc2C2@C2n-2 structures, respectively.
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