Path integral simulation study of quantum dynamics of hydrogen doped inside carbon nanotubes

对碳纳米管内的对氢体系进行了质心路径积分分子动力学（CMD）模拟。针对这些模拟，开发了CMD数值计算源程序。我们采用了等温-等压系综分子动力学技术来保持沿z方向的压力张量和各自由度产生的温度恒定。为此，采用了andersen型等温技术和Nose-Hoover链型等温技术。对于分子相互作用，Silvera-Goldman势和Lennard-Jones势分别适用于氢-氢和氢-碳相互作用。对于后一种相互作用，纳米管内壁在整个空间范围内被光滑化，使纳米管壁具有平坦均匀的表面，而不识别碳原子。在氢分子数为312、温度为8 ~ 15 K、Trotter数为100的条件下，对该模型进行了CMD模拟。通过对氢分子虚时程积分质心的均方位移和速度自相关函数的分析，阐明了动力学的各向异性。此外，还发现纳米管内的氢比体体系具有更高的熔化温度。作为纳米管氢体系的参考，本文综述了通过CMD模拟所揭示的大块氢的物理性质。

The centroid path integral molecular dynamics (CMD) simulations have been carried out for the systems of para-hydrogen contained inside the carbon nanotubes. For these simulations the CMD source program for numerical calculations has newly been developed. We have employed the isothermal-isobaric ensemble molecular dynamics technique to keep the pressure tensor along the z-direction constant and the temperature arising from all the degrees of freedom constant as well. The Andersen-type isobaric technique and the Nose-Hoover chain-type isothermal technique have been employed for this purpose. As for molecular interaction, the Silvera-Goldman potential and the Lennard-Jones potential have been assumed to be valid for the hydrogen-hydrogen and the hydrogen-carbon interaction, respectively. For the latter interaction, the nanotube inner wall has been smoothed out over the whole spatial range so that the nanotube wall should have flat and uniform surface without identification of carbon atoms. The CMD simulations for this model have been performed at the condition that the number of hydrogen molecules is 312, the temperature is 8-15 K, and Trotter number is 100. The anisotropy of dynamics has been clarified on the basis of the analysis of the mean square displacement and the velocity autocorrelation function of imaginary time path integral centroids of hydrogen molecules. Furthermore, it has been found that the hydrogen inside the nanotube tends to have higher melting temperature than the bulk system. As a reference of the nanotube hydrogen system, the physical properties of bulk hydrogen revealed by means of the CMD simulations have been reviewed as well.