  Mn is used as a dopant to improve the electromechanical properties of
perovskite oxides. We elucidate the role of Mn defects and associated vacancies
on the electronic, atomic and ferroelectric properties of BaTiO$_3$. Using
density functional theory (DFT) and DFT+U we investigate the equilibrium
geometry and electronic properties of Mn ion on A or B sites and with
compensating oxygen vacancies. We study the change in the oxidation state of Mn
in response to local environment changes, such as the presence of oxygen
vacancies.
