Algebraic Description of Coordination Sequences and Exact TopologicalDensities for Zeolites
Algebraic Description of Coordination Sequences and Exact TopologicalDensities for Zeolites
复制标题
沸石配位序列和精确拓扑密度的代数描述
DOI：
10.1107/s0108767396007519
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发表时间：
1996
期刊：
影响因子：
--
通讯作者：
N. Sloane
中科院分区：
文献类型：
--
作者：
R. Grosse;G. Brunner;N. Sloane
已计算了所有经批准的沸石拓扑、所有致密 SiO2 多晶型物和 16 种选定的非四面体结构的配位序列 (CS)，并对这些 CS 的代数结构进行了分析。给出了配位序列的两种代数描述。一种描述使用周期性二次方程组，并且已经在文献中建立。第二个描述采用了生成函数，生成函数在组合学中是众所周知的，但在这里首次与协调序列一起使用。事实证明，基于生成函数的代数分析比其他方法更强大。基于代数分析，得出所有研究结构的精确拓扑密度并制成表格。此外，“n 维方钠石”被观察到具有特别简单的 n 维图。
Coordination sequences (CS) have been calculated for all approved zeolite topologies, all dense SiO2 polymorphs and 16 selected non-tetrahedral structures and the algebraic structure of these CS's has been analyzed. Two algebraic descriptions of coordination sequences are presented. One description uses periodic sets of quadratic equations and is already established in the literature. The second description employs generating functions, which are well known in combinatorics but are used here for the first time in connection with coordination sequences. The algebraic analysis based on generating functions turns out to be more powerful than the other approach. Based on the algebraic analyses, exact topological densities are derived and tabulated for all the structures investigated. In addition, `n-dimensional sodalite' is observed to have an especially simple n-dimensional graph.