  We study the modifications on the ground and excited state properties of
polycyclic aromatic hydrocarbons (PAHs), induced by the variation of concavity
and $\pi$-connectivity. Inspired by experimentally feasible systems, we study
three series of PAHs, from H-saturated graphene flakes to geodesic buckybowls,
related to the formation of fullerene C60 and C50-carbon nanotube caps. Working
within the framework of quantum chemistry semi-empirical methods AM1 and
ZINDO/S, we find that the interplay between concavity and \pi-connectivity
shifts the bright optical lines to higher energies, and introduces
symmetry-forbidden dark excitations at low energy. A generally good agreement
with the available experimental data supports our results, which can be viewed
as the basis for designing optical properties of novel curved aromatic
molecules.
