  We provide a systematic study on the electronic structure of a series of
Ta$_2$O$_5$ polymorphs using standard density functional theory (DFT)
calculations as well as the more accurate many-body perturbation theory within
the GW approximation. For the defect-free polymorphs, the variation trend of
band gap can be microscopically related to the strength of orbital
hybridization, and to the macroscopic bulk formation energy. The presence of
oxygen vacancies is found to have profound effects on the electronic properties
near the Fermi level, notably the reduction of band gap and gap closure
(insulator-to-metal transition). Furthermore, depending on the vacancy sites,
the band gap of some defective system may be enlarged with comparison to its
defect-free counterpart. Such an anomalous behavior originates from the
unexpected formation of Ta-Ta bonds.
