Abstract
We use first-principles many-body theories to investigate the low energy excitations of the carbon fullerenes C_20, C_24, C_50, C_60, C_70, and C_80. Properties are calculated via the GW-Bethe-Salpeter Equation (GW-BSE) and diffusion Quantum Monte Carlo (QMC) methods. At a lower level of theoretical complexity, we also calculate these properties using static and time-dependent density-functional theory. We critically compare these theories and assess their accuracy against available experimental data. The first ionization potentials are consistently well reproduced and are similar for all the fullerenes and methods studied. The electron affinities and first triplet excitation energies show substantial method and geometry dependence. Compared to available experiment, GW-BSE underestimates excitation energies by approximately 0.3 eV while QMC overestimates them by approximately 0.5 eV. We show the GW-BSE errors result primarily from a systematic overestimation of the electron affinities, while the QMC errors likely result from nodal error in both ground and excited state calculations.
