Institut für Physik, Universität Rostock, Rostock, Germany.
J Phys Condens Matter. 2010 Apr 7;22(13):135401. doi: 10.1088/0953-8984/22/13/135401. Epub 2010 Mar 17.
An anharmonic extension of the Einstein model is developed in order to describe the effect of translational zero point motion on structural and thermodynamic properties of para-H(2) and ortho-D(2) crystals in the zero temperature limit. Accordingly, the molecules carry out large amplitude translational motions in their matrix cage, which are formed by the frozen environment of all other molecules. These translations lead from the molecular equilibrium positions via the harmonic to the anharmonic domain of the potential energy surface. The resulting translational distributions are roughly isotropic, and they have approximately Gaussian shapes, with rather broad full widths at half-maximum, FWHM(para-H(2)/ortho-D(2)) = 1.36/1.02 Å. The translational zero point energies induce expansions of the crystals, in nearly quantitative agreement with experimental results. Furthermore, they make significant contributions to the sublimation energies and zero pressure bulk moduli. These quantum effects decrease with heavier molecular masses. The corresponding isotope effects for ortho-D(2) compared to para-H(2) are confirmed by application of the model to Ar crystals. The results imply consequences for laser induced reaction dynamics of dopants with their host crystals.
为了描述平移零点运动对零温极限下 para-H(2)和 ortho-D(2)晶体结构和热力学性质的影响，发展了爱因斯坦模型的非谐扩展。相应地，分子在由所有其他分子的冻结环境形成的基质笼中进行大振幅平移运动。这些平移运动使分子从平衡位置通过谐和区进入势能面的非谐区。得到的平移分布大致各向同性，具有近似高斯形状，半峰全宽（para-H(2)/ortho-D(2)）较宽，为 1.36/1.02 Å。平移零点能引起晶体的膨胀，与实验结果几乎完全一致。此外，它们对升华能和零压体弹模量有重要贡献。这些量子效应随着分子质量的增加而减小。通过将模型应用于 Ar 晶体，证实了 ortho-D(2)相对于 para-H(2)的同位素效应。这些结果对掺杂剂与其宿主晶体的激光诱导反应动力学产生了影响。
