Molecular and electronic structures of endohedral fullerenes, Sc₂C₂@C_3v-C₈₂ and Sc₂@C_3v-C₈₂: Benchmark for SCC-DFTB and proposal of new inner cluster structures

The molecular and electronic structures of Sc₂C₂@C_3v-C₈₂ and Sc₂@C_3v-C₈₂ were investigated by means of conventional density functional theory (DFT) and the self-consistent-charge density-functional tight-binding (SCC-DFTB, short: "DFTB") method. In the DFT calculations, three functionals were adopted: BP86, B3LYP, and PBE. We find that it is necessary to employ tight geometry convergence criteria, which will lead to a reduction of the number of unique isomers. Generally, the DFTB method shows good agreement on relative energies, inner cluster binding energies (BE), and geometries with those predicted by the DFT calculations. In optimized structures, we found that some fullerene cages contain a more linear Sc-CC-Sc inner cluster that are more stable than those containing the butterfly-shaped cluster that was reported before. We found that DFTB overestimates Sc-Sc binding in the case of Sc₂@C₈₂ isomers, which became also evident in a comparison of molecular orbital (MO) correlation diagrams between PBE and DFTB methods. It is concluded that DFTB with the present parameters can be reliably employed for fullerene systems consisting of C and Sc atoms without direct Sc-Sc bonding.