Pinsky Mark, Avnir David
Institute of Chemistry and The Lise Meitner Minerva Center for Computational Quantum Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel.
Inorg Chem. 1998 Oct 19;37(21):5575-5582. doi: 10.1021/ic9804925.
The continuous symmetry measures approach, designed to assess quantitatively the degree of any symmetry within any structure, is extended to the important class of the polyhedra. For this purpose, we developed a general methodology and a general computational tool, which identify the minimal distance of a given structure to a desired general shape with the same number of vertexes. Specifically, we employ this tool to evaluate quantitatively the degree of polyhedricity within distorted polyhedra, taking as examples the most central and abundant polyhedral structures in chemistry in general and in coordination chemistry in particular, namely the tetrahedron, the bipyramid, the octahedron, the cube, the icosahedron, and the dodecahedron. After describing the properties of the symmetry measurement tool, we show its application and versatility in a number of cases where the deviation from exact symmetry has been an issue, including z-axis Jahn-Teller type polyhedral distortions, tantalum hydride complexes, pentacoordinated zinc complexes, tetrahedral/octahedral Sn complexes, and icosahedrally distorted C(60)-fullerene anions.
旨在定量评估任何结构内对称性程度的连续对称度量方法，被扩展到多面体这一重要类别。为此，我们开发了一种通用方法和一个通用计算工具，该工具可确定给定结构到具有相同顶点数的所需一般形状的最小距离。具体而言，我们使用此工具定量评估畸变多面体内的多面性程度，以化学领域尤其是配位化学中最核心且最丰富的多面体结构为例，即四面体、双锥体、八面体、立方体、二十面体和十二面体。在描述了对称测量工具的属性之后，我们展示了它在一些偏离精确对称性成为问题的情况下的应用及其通用性，这些情况包括z轴 Jahn-Teller 型多面体畸变、氢化钽配合物、五配位锌配合物、四面体/八面体锡配合物以及二十面体畸变的C(60)-富勒烯阴离子。
