  Stability of oxygen point defects in Ruddlesden-Popper oxides
(La$_{1-x}$Sr$_{x}$)$_{2}$MO$_{4{\pm}{\delta}}$ (M = Co, Ni, Cu) is studied
with density functional theory calculations to determine their stable sites,
charge states, and energetics as functions of Sr content ($x$), transition
metal (M) and defect concentration ({\delta}). We demonstrate that the dominant
O point defects can change between oxide interstitials, peroxide interstitials,
and vacancies. Generally, increasing $x$ and atomic number of M stabilizes
peroxide over oxide interstitials, as well as vacancies over both peroxide and
oxide interstitials; increasing {\delta} destabilizes both oxide interstitials
and vacancies, but affects little peroxide interstitials. We also demonstrate
that the O 2$p$-band center is a powerful descriptor for these materials and
correlates linearly with the formation energy of all the defects. The trends of
formation energy versus $x$, M and {\delta} and the correlation with O
2$p$-band center are explained in terms of oxidation chemistry and electronic
structure.
