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We investigate the accuracy of first-principles many-body theories at thenanoscale by comparing the low energy excitations of the carbon fullerenesC_20, C_24, C_50, C_60, C_70, and C_80 with experiment. Properties arecalculated via the GW-Bethe-Salpeter Equation (GW-BSE) and diffusion QuantumMonte Carlo (QMC) methods. We critically compare these theories and assesstheir accuracy against available photoabsorption and photoelectron spectroscopydata. The first ionization potentials are consistently well reproduced and aresimilar for all the fullerenes and methods studied. The electron affinities andfirst triplet excitation energies show substantial method and geometrydependence. These results establish the validity of many-body theories asviable alternative to density-functional theory in describing electronicproperties of confined carbon nanostructures. We find a correlation betweenenergy gap and stability of fullerenes. We also find that the electron affinityof fullerenes is very high and size-independent, which explains their tendencyto form compounds with electron-donor cations.

Neutral and charged excitations in carbon fullerenes from first-principles many-body theories