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The ground state of the magnetic rare earth pyrochlore Yb₂Ti₂O₇ is on the boundary between competing states. We have carried out ab initio density functional calculations of pure and "stuffed" systems (with an Yb replacement on a Ti site) to determine the most stable chemical formula and structure as a function of the oxygen chemical potential. In the "stuffed" crystal, we studied the effect of oxygen vacancies on the electronic properties of the system. In addition, with the inclusion of the contribution of spin-orbit-coupling (SOC) on top of the GGA+U approach, we investigated the electronic structure and the magnetic moments of the most stable "stuffed" system. Our first-principle findings should form a foundation for effective models describing the low-temperature properties of this material whose true ground state remains controversial.