刚性分子间相互作用核的对称一致展开
Symmetry-consistent expansion of interaction kernels between rigid molecules
摘要：
讨论了各向异性刚性分子间相互作用核的展开。该扩展将相关的取向变量叠加，以便可以利用它来导出宏观模型。两种类型的对称被认为是。首先，我们研究了相互作用集群的对称性，包括整个集群的平移和旋转，以及集群内的标签排列。展开式用对称无迹张量表示，并确定了线性无关项。然后，我们研究了$O(3)$中由点群表征的分子对称性。适当的旋转决定了什么样的对称无痕张量可以出现。不适当的旋转将这些张量分解成两个子空间，并确定两个子空间中的张量如何耦合。对于每个点群，我们确定两个子空间，从而建立与点群一致的展开式。
英文摘要：
We discuss the expansion of interaction kernels between anisotropic rigid molecules. The expansion decouples the correlated orientational variables so that it can be utilized to derive macroscopic models. Symmetries of two types are considered. First, we examine the symmetry of the interacting cluster, including the translation and rotation of the whole cluster, and label permutation within the cluster. The expansion is expressed by symmetric traceless tensors, and the linearly independent terms are identified. Then, we study the molecular symmetry characterized by a point group in $O(3)$. The proper rotations determine what symmetric traceless tensors can appear. The improper rotations decompose these tensors into two subspaces and determine how the tensors in the two subspaces are coupled. For each point group, we identify the two subspaces, so that the expansion consistent with the point group is established.
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