Exploring Proton Pair Motion Away from the Global Proton-Tuple Energy Minimum in Yttrium-Doped Barium Zirconate

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.