Density functional theory calculations are used to study the equilibrium energetics of protons on the surface and in the bulk of Y-doped BaZrO_3. It is shown that protonic species in direct contact with Y dopants have energies lower than in perfect BaZrO_3 by up to 0.4 eV. This energetic stabilization is achieved when the protonic species is in direct contact with two Y dopants. On the (001) surface of BaZrO_3, protonic species are found to be energetically more stable than in the bulk by 1.1 eV and 1.6 eV on the BaO and ZrO_2 surface terminations, respectively. At these terminations, the energy of protons recover the bulk value after penetrating three surface layers, and the energy cost associated with bulk incorporation is larger than 1 eV.
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