A benchmark study of DFT methods on the electronic properties of lanthanofullerenes: a case study of Ce@C2v(9)-C82 anion

Abstract

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@C_2v(9)-C₈₂]⁻ and [La@C_2v(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@C_2v(9)-C₈₂]⁻ than those using the other DFT methods, while B3LYP wins in treating [La@C_2v(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@C_2v(9)-C₈₂]⁻ keeps closed shell electronic configurations near the Fermi level, and the HOMO and HOMO−1 orbitals of [Ce@C_2v(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@C_2v(9)-C₈₂]⁻ is the π* orbital of the C₈₂ cage, and the LUMO+1, LUMO+2, LUMO+3 of [Ce@C_2v(9)-C₈₂]⁻ are composed of the ds hybrid orbitals of Ce and the 2π* orbitals of C₈₂ cage.