Nuclear quantum effects on proton diffusivity in perovskite oxides

In the present study, nuclear quantum effects (NQEs) on proton diffusivity in oxides were evaluated by molecular dynamics (MD) simulations with a quantum thermal bath based on Langevin dynamics. We employed the proton diffusion in barium zirconate ($\mathrm{BaZr}{\mathrm{O}}_{3}$) with the cubic perovskite structure as the model system, in which protons migrate by rotation around single oxide ions and by hopping between adjacent oxide ions. MD simulations with the standard classical thermal bath and phonon calculations were also conducted to verify the conventionally used classical harmonic transition state theory (classical h-TST), in which the transition state theory, the harmonic approximation, and the classical approximation are assumed. As a result, the h-TST is reasonable for the proton rotation, while significantly overestimating the activation energy and the preexponential factor of the jump frequency for the proton hopping. Furthermore, the classical approximation makes the proton jump frequencies close to linear in the Arrhenius plots, which should actually be nonlinear by the NQEs in the temperature range of 500--2000 K. This suggests the necessity of the treatment beyond the classical h-TST for accurate evaluation of the proton diffusivity in oxides even in the intermediate temperature range (573--873 K).