  The vibrational spectra and short-range structure of the brownmillerite-type
oxide Ba$_{2}$In$_{2}$O$_{5}$ and its hydrated form BaInO$_{3}$H, are
investigated by means of Raman, infrared, and inelastic neutron scattering
spectroscopies together with density functional theory calculations. For
Ba$_{2}$In$_{2}$O$_{5}$, which may be described as an oxygen deficient
perovskite structure with alternating layers of InO$_{6}$ octahedra and
InO$_{4}$ tetrahedra, the results affirm a short-range structure of $Icmm$
symmetry, which is characterized by random orientation of successive layers of
InO$_{4}$ tetrahedra. For the hydrated, proton conducting, form, BaInO$_{3}$H,
the results suggest that the short-range structure is more complicated than the
$P4/mbm$ symmetry that has been proposed previously on the basis of neutron
diffraction, but rather suggest a proton configuration close to the lowest
energy structure predicted by Martinez et al. [J.-R. Martinez, C. E. Moen, S.
Stoelen, N. L. Allan, J. of Solid State Chem. 180, 3388, (2007)]. An intense
Raman active vibration at 150 cm$^{-1}$ is identified as a unique fingerprint
of this proton configuration.
