We have studied surface hydroxyls adsorbed onto (001), (011), and (111) gamma alumina surfaces using a quantum-chemistry approach in order to compare with empirical models proposed in the literature. Local electronic structures and geometries in the low OH coverage limit have been evaluated for both ideal and relaxed surfaces with the help of a large scale periodic quantum-chemical code. Hydroxyl groups are adsorbed onto surfaces, and a study of their local electronic structure, vibrational frequencies, charges, and adsorption energies is performed and analyzed as a function of their adsorption site geometry. Our results show that, even on ideal (nonrelaxed) surfaces, OH local environments are more complicated than those stated by empirical models and strongly influence the hydroxyl stretching vibrational mode. Large scale simulation shows that disorder takes place even at 0 K, and the analysis of the vibrational frequencies leads to a revision of Knozinger's empirical model. Cationic vacancies in the first surface layers have also been taken into account; they have a significant influence on the surface atomic and electronic structures, modifying the physical properties of adsorbed OH entities. This work emphasizes the necessity to perform an electronic structure calculation to better understand adsorbed OH properties on gamma alumina surfaces and reveals the difficulty to make a one-to-one correspondence between OH stretching frequencies and their other physical properties. Finally, we show that these results agree with some available experimental studies.