AI 中文总结
该研究基于Schur-Weyl框架，结合杨表相关规则提出一种组合方法，可确定多原子分子的核自旋对称种类与统计权重，适用于多种分子且可自动化，为振转谱线强度建模提供支持。
AI 中文摘要
分子光谱中的核自旋统计权重和选择定则由全同核的置换对称性决定，尽管刚性和半刚性分子通常仅实现全对称群的真子群。基于Schmiedt、Jensen和Schlemmer的Schur-Weyl框架，我们将该方法扩展到其振转运动实现循环和二面体置换子群的分子几何结构。结合n自旋希尔伯特空间的Schur-Weyl分解与Kraśkiewicz-Weyman-Adin-Roichman主指标分支规则（用于S_N↓C_m的限制），我们得到一种完全组合的方法来确定核自旋对称种类和统计权重。每个标准杨表对应由其主指标确定的确定循环特征，反射则产生相关的二面体对称性，因此核自旋种类可直接由杨表数据得出，无需投影算子或特定情况的构造。将该方法应用于XeOF₄、SF₄、苯、氘代苯和 tropylium阳离子，证明其可统一适用于现实的分子点群，重现已确立的统计权重，同时提供透明的自旋分辨结构。该方法为振转谱线强度建模提供所需的对称性信息，并为多原子分子的核自旋对称性分析提供实用、可自动化的框架。
英文摘要
Nuclear-spin statistical weights and selection rules in molecular spectroscopy are governed by the permutation symmetry of identical nuclei, although rigid and semi-rigid molecules typically realize only a proper subgroup of the full symmetric group. Building on the Schur-Weyl framework of Schmiedt, Jensen, and Schlemmer, we extend this approach to molecular geometries whose rovibrational motion realizes cyclic and dihedral permutation subgroups. By combining the Schur-Weyl decomposition of the $n$-spin Hilbert space with the Kraśkiewicz-Weyman-Adin-Roichman major-index branching rule for the restriction $S_N \downarrow C_m$, we obtain a fully combinatorial method for determining nuclear-spin symmetry species and statistical weights. Each standard Young tableau corresponds to a definite cyclic character determined by its major index, with reflections yielding the associated dihedral symmetry, so that nuclear-spin species follow directly from tableau data without projection operators or case-specific constructions. Applications to $XeOF_4$, $SF_4$, benzene, deuterated benzene, and the tropylium cation demonstrate that the method applies uniformly to realistic molecular point groups and reproduces established statistical weights while providing a transparent spin-resolved structure. The approach supplies the symmetry information required for rovibrational line-intensity modeling and provides a practical, automatable framework for nuclear-spin symmetry analysis in polyatomic molecules.
Journal refJ. Chem. Phys. 21 May 2026; 164 (19): 194120
