A benchmark study of DFT methods on the electronic properties of lanthanofullerenes: a case study of Ce@C2v(9)-C82 anion†
Density functional theory (DFT) methods, including PW91PW91, BP86, TPSSTPSS, B3LYP, B3PW91, PBE1PBE, BHandHLYP, CAM-B3LYP, and M06 were employed to study the NMR properties of [Ce@C2v(9)-C82]− and [La@C2v(9)-C82]−, representing open-shell and closed-shell lanthanofullerene molecular systems respectively. Among the methods employed, results from calculations with BHandHLYP show better agreement with experimental data to predict the NMR spectra of [Ce@C2v(9)-C82]− than those using the other DFT methods, while B3LYP wins in treating [La@C2v(9)-C82]−. Frontier molecular orbitals are analyzed to explain the calculated NMR data. According to the calculations, the BHandHLYP method gives the reasonable explanation that [Ce@C2v(9)-C82]− keeps closed shell electronic configurations near the Fermi level, and the HOMO and HOMO−1 orbitals of [Ce@C2v(9)-C82]− are composed of the 2π orbitals of the C82 cage filled with 5d16s2 electrons of Ce and the extraneous electron, while the unpaired 4f1 electron of Ce is localized at Ce and there is a large energy gap between the singly occupied molecular orbital (SOMO) and the HOMO. The LUMO of [Ce@C2v(9)-C82]− is the π* orbital of the C82 cage, and the LUMO+1, LUMO+2, LUMO+3 of [Ce@C2v(9)-C82]− are composed of the ds hybrid orbitals of Ce and the 2π* orbitals of C82 cage.