Corannulene is an unsaturated hydrocarbon composed of fused rings, with one central five-membered ring and five peripheral six-membered rings. Its structure can be considered as a portion of C60. Corannulene is a curved π surface, but unlike C60, it has two accessible different faces: one concave (inside) and one convex (outside). In this work, computational modeling of the binding between alkali metal cations (Li(+), Na(+), and K(+)) and corannulene has been performed at the DFT and MP2 levels. Different corannulene···M(+) complexes have been studied and the transition states interconnecting local minima were located. The alkali cations can be bound to a five or six membered ring in both faces. At the DFT level, binding to the convex face (outside) is favored relative to the concave face for the three alkali cations studied, as it was previously published. This out preference was found to decrease as cation size increases. At the MP2 level, although a similar trend is found, some different conclusions related to the in/out preference were obtained. According to our results, migration of cations can take place on the convex or on the concave face. Also, there are two ways to transform a concave complex in a convex complex: migration across the edge of corannulene and bowl-to-bowl inversion.