Ab initio calculations were performed for neutral corannulene (1) and its dianion and tetraanion. The minimum energy conformations, as well as the transition states for bowl-to-bowl inversion, were located and characterized by calculation of vibrational frequencies. For some charged species, the Hartree-Fock method predicts critical point symmetries that are lower than those deduced from Huckel theory. However, inclusion of electron correlation effects shows this to be an artifact of the HF method. Consideration of electron correlation is also crucial for the estimation of the inversion barriers, while the quality of the basis set has only moderate impact on these results. The ''best theoretical estimate'' of the barriers decreases from 14.2 kcal mol(-1) for neutral 1, to 7.9-9.2 kcal mol(-1) for the dianions, and to 3.2 kcal mol(-1) for the tetraanion. While the introduction of negative charges into corannulene causes overall flattening of its curvature, even in the most extreme case - the tetraanion - preference for a bowl-shaped geometry remains. Within C-5v symmetry, the (3)A(2) triplet state is clearly favored over the (1)A(1) and (1)E(2) Singlet states of the isolated dianion. However, no significant preference of the triplet vs. singlet electronic state emerges if the symmetry of the molecular framework of the dianion is allowed to distort. Finally, analysis of the charge distribution in the tetraanion 5 does not support the ''anion within a trianion'' model for the tetraanion of corannulene.