The quantum motion of clusters of up to four deuterium molecules under confinement in a single-wall (1 nm diameter) carbon nanotube is investigated by applying a highly accurate full quantum treatment of the most relevant nuclear degrees of freedom and an ab initio-derived potential model of the underlying dispersion-dominated intermolecular interactions. The wave functions and energies are calculated using an ad hoc-developed discrete variable representation (DVR) numerical approach in internal coordinates, with the space grid approaching a few billion grid points. We unambiguously demonstrate the formation of a solid-like pyramidal one-dimensional chain structure of molecules under the cylindrical nanotube confinement. The onset of solid-like packing is explained by analyzing the potential minima landscape. The stabilization of collective rotational motion through “rigid rotations” of four deuterium molecules provides conclusive evidence for the onset of a quantum solid-like behavior resembling that of quantum rings featuring persistent current (charged particles) or persistent flow (neutral particles).

中文翻译：

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从分子聚集到直径为1 nm的碳纳米管内的氘的一维量子晶体。

通过对最相关的核自由度和从头算来的势进行高度精确的全量子处理，研究了限制在一个单壁（直径为1 nm）碳纳米管中的最多四个氘分子簇的量子运动。潜在的以色散为主的分子间相互作用的模型。波函数和能量使用临时计算-在内部坐标中开发了离散变量表示（DVR）数值方法，其中空间网格接近数十亿个网格点。我们明确地证明了在圆柱形纳米管约束下分子的固体状金字塔一维链结构的形成。通过分析潜在的极小景观来解释固体堆积的发生。通过四个氘分子的“刚性旋转”来稳定集体旋转运动，提供了确凿的证据来证明类似于具有持久性电流（带电粒子）或持久性流动（中性粒子）的量子环的量子固体行为。