Hydrogen clathrate hydrates are ice-like crystalline substances in which hydrogen molecules are trapped inside polyhedral cages formed by the water molecules. Small cages can host only a single H2 molecule, while each large cage can be occupied by up to four H2 molecules. Here, we present a neutron scattering study on the structure of the sII hydrogen clathrate hydrate and on the low-temperature dynamics of the hydrogen molecules trapped in its large cages, as a function of the gas content in the samples. We observe spectral features at low energy transfer (between 1 and 3 meV), and we show that they can be successfully assigned to the rattling motion of a single hydrogen molecule occupying a large water cage. These inelastic bands remarkably lose their intensity with increasing the hydrogen filling, consistently with the fact that the probability of single occupation (as opposed to multiple occupation) increases as the hydrogen content in the sample gets lower. The spectral intensity of the H2 rattling bands is studied as a function of the momentum transfer for partially emptied samples and compared with three distinct quantum models for a single H2 molecule in a large cage: (i) the exact solution of the Schrödinger equation for a well-assessed semiempirical force field, (ii) a particle trapped in a rigid sphere, and (iii) an isotropic three-dimensional harmonic oscillator. The first model provides good agreement between calculations and experimental data, while the last two only reproduce their qualitative trend. Finally, the radial wavefunctions of the three aforementioned models, as well as their potential surfaces, are presented and discussed.

中文翻译：

---

sII 笼形水合物中氢分子的大笼占据和量子动力学

氢笼形水合物是冰状结晶物质，其中氢分子被捕获在水分子形成的多面体笼内。小笼只能容纳一个 H2 分子，而每个大笼最多可以容纳四个 H2 分子。在这里，我们对 sII 氢笼形水合物的结构以及被困在其大笼中的氢分子的低温动力学（作为样品中气体含量的函数）进行了中子散射研究。我们观察了低能量转移（1 至 3 meV 之间）的光谱特征，并表明它们可以成功地归因于占据大水笼的单个氢分子的嘎嘎运动。随着氢填充量的增加，这些非弹性带的强度显着降低，这与随着样品中氢含量降低而单一占据（而不是多重占据）的概率增加的事实一致。研究了 H2 振动带的光谱强度作为部分清空样品动量传递的函数，并与大笼中单个 H2 分子的三个不同量子模型进行比较：(i) 薛定谔方程的精确解经过充分评估的半经验力场，(ii) 被困在刚性球体中的粒子，以及 (iii) 各向同性三维谐振子。第一个模型在计算和实验数据之间提供了良好的一致性，而后两个模型仅再现了它们的定性趋势。最后，提出并讨论了上述三个模型的径向波函数及其势表面。