Ab initio Study of Oxygen Vacancies Across Structural Phases of La₃Ni₂O₇

La₃Ni₂O₇ has recently attracted significant attention as a strongly correlated nickelate that exhibits superconductivity and multiple pressure-induced structural phases. Oxygen vacancies strongly influence its electronic structure and lattice stability; however, their precise role in the properties of La₃Ni₂O₇ diversity remains unclear. In this work, we systematically investigate oxygen vacancies at all symmetry-inequivalent oxygen sites across the experimentally reported low- (Amam) and high-pressure (Cmmm, F mmm, I4/mmm) phases of La₃Ni₂O₇. We first perform DFT+U analyses to examine the magnetic ordering of these phases, followed by many-body Quantum Monte Carlo (QMC) calculations to quantify correlation-driven contributions to vacancy formation energies and their impact on the local electronic environment. Our initial DFT results indicate that La₃Ni₂O₇ favors distinct antiferromagnetic orderings. The impact of Oxygen vacancies in the properties of La₃Ni₂O₇ will be discussed.