Energetics of carboxyl groups at the periphery of a graphene sheet are studied using density functional theory (B3LYP) with a 6-31G* basis set, augmented with diffuse functions on O. Corner sites are energetically preferred followed by zigzag edges, and armchair edges are least stable. The energy and geometry of each is attributed to a competition between π-conjugation and steric repulsion factors. Vibrational analyses reveal certain features that are characteristic of each site location, which may help in the assignment of experimental spectra of graphene and other polycyclic aromatic hydrocarbons. For example, zigzag sites typically lead to an intense C═O stretching band that occurs below 1700 cm–1, quite uncommon for the carboxyl group.