  Hydroxyapatite (HAp) is a widely used biomaterial for the preparation of bone
and dental implants. Despite the relevance of HAp in medicine, exciting
applications involving this material as a bio-compatible photocatalyst, depend
on how well we understand its fundamental properties. Experimental evidence
suggests that oxygen vacancies play a critical role in the production of
surface radicals upon exposure of HAp to ultra-violet (UV) light. However, very
little is known about the underlying physical and chemical details. We present
a hybrid density-functional study of the structural and electronic properties
of oxygen vacancies in large HAp supercells within the plane-wave formalism. We
find that under equilibrium conditions, vacancies occur either as a simple
vacant oxygen site (in the neutral charge state), or as extended structures
replacing several crystalline moieties (in the double plus charge state). Large
atomic relaxations upon ionization make the oxygen vacancy a negative-$U$
defect, where the single plus charge state is metastable, being only accessible
under UV excitation. From inspection of the transition levels, we find that
electron promotion from the valence band top to the donor state of the vacancy,
involves a zero-phonon transition of 3.6-3.9 eV. This mechanism is the most
likely explanation to the 3.4-4.0 eV absorption onset for the observation of
photocatalysis using HAp under persistent UV illumination.
