Proton transfer (PT) in proton-conducting oxides is an intrinsically quantum phenomenon, due to the very strong quantization of the OH stretching vibration (ℏω~ 0.4 eV). Up to high temperatures, the proton is frozen in the ground state associated with the OH stretching motion, and thus does not undergo the thermal agitation for this vibration. Therefore, these are the thermal fluctuations of the (heavier) lattice atoms which make PT possible, at least above ~ half the Debye temperature of the lattice. These fluctuations may occasionally and randomly produce specific lattice configurations in which the quantum protonic ground levels in the two wells are equalized (coincidence), making PT possible, however with a certain probability. An analytical expression of this transfer probability may be obtained as the solution of a curve-crossing quantum-mechanical problem, and thus described by the Landau-Zener (LZ) formula. Two lattice vibrations play a fundamental role in intra-octahedral PT: (i) a reorganization of the lattice, that sends the protonated system from its initial self-trapped configuration up to the coincidence manifold, and (ii) a reduction of the (donor) oxygen - (acceptor) oxygen distance Q, which facilitates PT by leading the system to coincidence configurations with smaller proton barrier, and thus larger LZ probability. In cubic perovskites, the set of the coincidence configurations plays the role of the transition state for PT. The implementation of this theory of proton transfer [G. Geneste, Solid State Ionics 323, 172 (2018)] is here strongly improved on several points: description of the coincidence configurations, proton zero-point energies and proton potential at coincidence. It is then re-applied to barium zirconate (BZO), and also to potassium tantalate (KTO), with parameters derived from density-functional theory (DFT) calculations. The theory confirms the adiabatic PT regime in BZO, common to most proton conductors, with a negligible contribution of non-adiabatic tunneling transfers to the transfer rate. In KTO, by contrast, the relative contribution of non-adiabatic tunneling transfers is larger than in BZO, especially below ~ 250–300 K. The present work helps to characterize intrinsic features common to most proton conductors, at least from the point of view of proton mobility within the lattice. The activations energies for proton transfer at high temperature are predicted at 0.11 eV (BZO) and 0.25 eV (KTO).

质子在质子传导氧化物转移（PT）是固有量子现象，由于OH拉伸振动的非常强的量化（ℏ ω〜0.4 eV）。在高达高温下，质子在与OH拉伸运动相关的基态下被冻结，因此不会因振动而受到热搅动。因此，这些是（较重的）晶格原子的热涨落，使得PT成为可能，至少在晶格的德拜温度的一半以上。这些波动可能偶尔随机产生特定的晶格配置，其中两个阱中的量子质子基能级相等（重合），但是使PT成为可能，但是具有一定的可能性。可以通过交叉量子力学问题的解决方案来获得这种转移概率的解析表达式，因此可以用Landau-Zener（LZ）公式进行描述。在八面体内PT中，两个晶格振动起着基本作用：（i）a晶格的重组，将质子化的系统从其初始的自陷构型发送到重合流形；以及（ii）减少（供体）氧-（受体）氧距离Q，这通过引导系统促进了PT具有较小质子势垒的重合构型，从而具有更大的LZ概率。在立方钙钛矿中，一组重合构型起着PT过渡态的作用。这种质子转移理论的实施［G．Geneste，固态离子323，172（2018）]在以下几点上进行了重大改进：重合配置，质子零点能量和重合质子势的描述。然后将其重新应用于锆酸钡（BZO）和钽酸钾（KTO），并使用从密度泛函理论（DFT）计算得出的参数。该理论证实了BZO绝热的PT制度，这是大多数质子导体所共有的，其非绝热隧穿转移对转移速率的贡献可忽略不计。相比之下，在KTO中，非绝热隧穿转移的相对贡献要大于BZO，尤其是在〜250–300 K以下时。至少从观点来看，本研究有助于表征大多数质子导体共有的固有特征。在晶格内的质子迁移率。