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Yttrium-doped barium zirconate is one of the fastest solid-state proton conductors. While previous studies suggest that proton–tuples move as pairs in yttrium-doped barium zirconate, a systematic catalog of possible close proton–tuple moves is missing. Such a catalog is essential to simulating dual proton conduction effects. Density functional theory with the Perdew–Burke–Ernzerhof functional is utilized to obtain the total electronic energy for each proton–tuple. The conjugate gradient and nudged elastic band methods are used to find the minima and transition states for proton–tuple motion. In the lowest-energy configuration, protons are in close proximity to each other and the dopant, significantly affecting the backbone structure. The map of moves away from the global minimum proton–tuple shows that the most critical move for long-range proton conduction is a rotation with a barrier range of 0.31–0.41 eV when the two protons are in close proximity.