High-level ab initio calculations have been carried out to reexamine relative stability of bowl, cage, and ring isomers of C 20 and C 20 − . The total electronic energies of the three isomers show different energy orderings, strongly depending on the hybrid functionals selected. It is found that among three popular hybrid density-functional ͑DF͒ methods B3LYP, B3PW91, PBE1PBE, and a new hybrid-meta-DF method TPSSKCIS, only the PBE1PBE method ͑with cc-pVTZ basis set͒ gives qualitatively correct energy ordering as that predicted from ab initio CCSD͑T͒/cc-pVDZ ͓CCSD͑T͒-coupled-cluster method including singles, doubles, and noniterative perturbative triples; cc-pVDZ-correlation consistent polarized valence double zeta͔ as well as from MP4͑SDQ͒/cc-pVTZ ͓MP4-fourth-order Moller-Plesset; cc-pVTZ-correlation consistent polarized valence triple zeta͔ calculations. Both CCSD͑T͒ and MP4 calculations indicate that the bowl is most likely the global minimum of neutral C 20 isomers, followed by the fullerene cage and ring. For the anionic counterparts, the PBE1PBE calculation also agrees with MP4/cc-pVTZ calculation, both predicting that the bowl is still the lowest-energy structure of C 20 − at T =0 K, followed by the ring and the cage. In contrast, both B3LYP/cc-pVTZ and B3PW91/cc-pVTZ calculations predict that the ring is the lowest-energy structure of C 20 − . Apparently, this good reliability in predicting the energy ordering renders the hybrid PBE method a leading choice for predicting relative stability among large-sized carbon clusters and other carbon nanostructures ͑e.g., finite-size carbon nanotubes, nano-onions, or nanohorns͒. The relative stabilities derived from total energy with Gibbs free-energy corrections demonstrate a changing ordering in which ring becomes more favorable for both C 20 and C 20 − at high temperatures. Finally, photoelectron spectra ͑PES͒ for the anionic C 20 − isomers have been computed. With binding energies up to 7 eV, the simulated PES show ample spectral features to distinguish the three competitive C 20 − isomers.