  Defects in the rutile TiO${}_2$ structures have been extensively studied, but
the intrinsic defects of the oxygen deficient Ti${}_n$O${}_{2n-1}$ phases have
not been given the same amount of consideration. Those structures, known as
Magn\'eli phases, are characterized by the presence of ordered planes of oxygen
vacancies, also known as shear-planes, and it has been shown that they form
conducting channels inside TiO-based memristor devices. Memristors are
excellent candidates for a new generation of memory devices in the electronics
industry. In this paper we present DFT-based electronic structure calculations
for Ti${}_n$O${}_{2n-1}$ Magn\'eli structures using PBESol+U ($0 \leq U \leq 5$
eV) and HSE functionals, showing that intrinsic defects present in these
structures are responsible for the appearance of states inside the bandgap,
which can act as intrinsic dopants for the enhanced conductivity of TiO${}_2$
memristive devices.
