Hydrogen exhibits qualitatively different charge states depending on the host material, as nicely explained by the state-of-the-art impurity-state calculation. Motivated by a recent experiment [Nature 546, 124 (2017)], we show that the complex oxide SrCoO$_{2.5}$ represents an interesting example, in which the interstitial H appears as a deep-level center according to the commonly-used transition level calculation, but no bound electron can be found around the impurity. Via a combination of charge difference analysis, density of states projection and constraint magnetization calculation, it turns out that the H-doped electron is spontaneously trapped by a nonunique Co ion and is fully spin-polarized by the onsite Hunds rule coupling. Consequently, the doped system remains insulating, whereas the antiferromagnetic exchange is slightly perturbed locally.
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