Search for suitable approximation methods for fullerene structure and relative stability studies: Case study with C₅₀

Local density approximation (LDA), several popular general gradient approximation (GGA), hybrid module based density functional theoretical methods: SVWN, BLYP, PBE, HCTH, B3LYP, PBE1PBE, B1LYP, and BHandHLYP, and some nonstandard hybrid methods are applied in geometry prediction for C₆₀ and C₇₀. HCTH with 3-21G basis set is found to be one of the best methods for fullerene structural prediction. In the predictions of relative stability of C₅₀ isomers, PM3 is an efficient method in the first step for sorting out the most stable isomers. HCTH with 3-21G predicts very good geometries for C₅₀, similar to the performance of B3LYP/6-31G(d). The gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital from the predictions of all the density functional theory methods has the following descending order: E_gap(half-and-half hybrid) > E_gap(B3LYP) > E_gap(HCTH)(GGA) > E _gap(SVWN)(LDA).