Hydrogen diffusion on metals exhibits rich quantum behavior, which is not yet fully understood. Using simulations, we show that many hydrogen diffusion barriers can be categorized into those with parabolic tops and those with broad tops. With parabolic-top barriers, hydrogen diffusion evolves gradually from classical hopping, to shallow tunneling, to deep tunneling as the temperature ($T$) decreases, and noticeable quantum effects persist at moderate $T$. In contrast, with broad-top barriers quantum effects become important only at low $T$ and the classical-to-quantum transition is sharp, at which classical hopping and deep tunneling both occur. This coexistence indicates that more than one mechanism contributes to the quantum reaction rate. The conventional definition of the classical-to-quantum crossover $T$ is invalid for the broad tops, and we give a new definition. Extending this, we propose a model to predict the transition $T$ for broad-top diffusion, providing a general guide for theory and experiment.

中文翻译：

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同时进行深隧穿和经典跳变对金属进行氢扩散

氢在金属上的扩散表现出丰富的量子行为，目前尚不完全清楚。通过模拟，我们显示出许多氢扩散阻挡层可以分为具有抛物线顶部的氢扩散阻挡层和具有宽顶部的氢扩散阻挡层。借助抛物线型顶部势垒，随着温度的升高，氢的扩散逐渐从经典的跳跃跃迁到浅隧道效应，再到深隧道效应（$Ť$）减小，并且明显的量子效应在中等强度下持续存在 $Ť$。相比之下，利用宽广的壁垒，量子效应仅在低水平时才变得重要$Ť$并且经典到量子的跃迁是尖锐的，这时会发生经典跳变和深隧道效应。这种共存表明，不止一种机制有助于量子反应速率。经典到量子交叉的常规定义$Ť$对于宽顶无效，我们给出一个新的定义。对此进行扩展，我们提出了一个模型来预测过渡$Ť$ 为宽顶扩散提供理论和实验的一般指南。