Hydroxyapatite (Ca-10(PO4)(6)(OH)(2), HAp) is a calcium phosphate employed both in biomedicine and for environmental remediation. It is known that HAp can also be photocatalytic under UV light, probably due to oxygen deficiencies, but the mechanism is unclear, and reported optical band gap energies vary greatly. For the first time we propose the mechanisms and precise kinds of vacancies which may cause the photocatalytic activity of HAp, and compare these theoretical data with our measured data on both samples of marine origin and commercial HAp powders. Density functional theory (DFT) (from first principles calculations and Density of States (DOS) modelling) was used to calculate the optical band gap energy (E-g) created by various possible oxygen vacancies in the HAp lattice: O from PO4, O from OH, the loss of an entire OH group, or the simultaneous loss of O from PO4 and an entire OH group. The modelled values match the measured values very closely, suggesting that in non-photocatalytic HAp, if any vacancies exist, they are O atoms from the OH group, resulting in a band gap of similar to 5 eV in the UVC region (not present in solar light at the Earth's surface). However, in photocatalytic HAp, reduction from the combustion of an organic component at 1000 degrees C led to oxygen deficiency in the phosphate groups, probably in the O15 position, giving an E-g of similar to 3.45 eV, in the UVA region (present in sunlight). Heating HAp with no organic component to 1200 degrees C also led to vacancies, of both an entire OH group and oxygen from PO4 groups, which led to an intermediate Eg value of similar to 4 eV, on the boundary of the UVA-UVB regions. Absorption peaks were also predicted in the visible-light region with some types of vacancy. (C) 2016 Elsevier B.V. All rights reserved.