  Y-doped BaZrO$_3$ is a promising proton conductor for intermediate
temperature solid oxide fuel cells. In this work, a combination of static DFT
calculations and DFT based molecular dynamics (DFT-MD) was used to study proton
conduction in such a material. Geometry optimisations of 100 structures with a
12.5% dopant concentration allowed us to identify a clear correlation between
the bending of the metal-oxygen-metal angle and the energies of the simulated
cells. Depending on the type of bending, two configurations, designated as
inwards bending and outwards bending, were defined. The results demonstrate
that a larger bending decreases the energy and that the lowest energies are
observed for structures combining inwards bending with protons being close to
the dopant atoms. These lowest energy structures are the ones with the
strongest hydrogen bonds. DFT-MD simulations in cells with different yttrium
distributions provide complementary microscopic information on proton diffusion
as they capture the dynamic distortions of the lattice caused by thermal
motion. A careful analysis of the proton jumps between different environments
confirmed that the inwards and outwards bending states are relevant for the
understanding of proton diffusion. Indeed, intra-octahedral jumps were shown to
only occur starting from an outwards configuration while the inwards
configuration seems to favor rotations around the oxygen. On average, in the
DFT-MD simulations, the hydrogen bond lengths are shorter for the outwards
configuration which facilitates the intraoctahedral jumps. Diffusion
coefficients and activation energies were also determined and compared to
previous theoretical and experimental data showing a good agreement with
previous data corresponding to local proton motion.
