  A study based on density functional theory calculations was performed for the
three charge states of interstitial hydrogen in Yttria. The present
calculations were carried out by employing the GGA-PBE and the HSE06
exchange-correlation functional. It is observed that the ground state H$^0$ and
H$^-$ configurations are similar in behaviour; these prefer to relax in the O
vacant site, with limited structural relaxation. For the neutral and the
negative charged systems more two different geometrical configurations occur
with higher energies, which evidence the existence of metastable sites of H in
the Yttria lattice. The H$^+$ equilibrium state is found only when a strong
bond between the impurity ion and an anion, O-H bond of $\sim$1 \AA, is formed.
The formation energy of the interstitial impurity is studied, for which
amphoteric behaviour is found for this defect and for the ground state
structures. These results evidence that hydrogen counteracts the prevailing
conductivity of the host lattice, thus passivating any existing electrical
levels originated from other doping sources. To compare results with
non-equilibrium and short time-scale $\mu$SR measurements, the formation energy
of the higher energy configurations were also evaluated. For the Bond O
geometrical site, H evidences a donor-dopant behaviour, hence enabling the
coexistence of donor behaviour with the ground-state amphoteric behaviour. From
the density of states results, and for the H$^0$ and H$^-$ charge states, a
defect level was observed in the band gap. For the ground state Vacant O
configuration and the metastable Interstitial structure the defect level was
found to be slightly above the valence band maximum, hence indicating no
dopant-donor character for the Yttria material. But, for the Bond O,
local-minimum, configuration, the defect level is located above the middle of
the band gap, closer the conduction band.
