Symmetry-Itemized Enumeration of Cubane Derivatives as Three-Dimensional Entities by the Elementary-Superposition Method of the USCI Approach

Fujita Shinsaku

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Symmetry-Itemized Enumeration of Cubane Derivatives as Three-Dimensional Entities by the Elementary-Superposition Method of the USCI Approach

机译：USCI方法的基本叠加方法对称衍生物作为三维实体的对称性序列枚举

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Cubane derivatives with a given chemical formula and a given symmetry are enumerated by applying the elementary-superposition method (S. Fujita, Theo,: Chim. Acta 1992, 82, 473-498) of the unit-subduced-cycle-index (USCI) approach to a cubane skeleton of the point group O-h. A cycle index (Cl) for a regular or an irregular case of chiral and achiral ligands is calculated in accord with such a given chemical formula. The CI is superposed elementarily onto respective subduced cycle indices with chirality fittingness (SCI-CFs), which are calculated by starting from unit subduced cycle indices with chirality fittingness (USCI-CFs). Thereby, the numbers of fixed points (derivatives) are obtained with respect to the respective SCI-CFs to give a fixed-point vector (FPV). The resulting FPV is multiplied by an inverse matrix of the mark table of O-h to give an isomer-counting vector (ICV), which contains the numbers of 3D-structural isomers in an itemized fashion with respect to point-group symmetries. The concept of prochirality is examined by using cubane derivatives enumerated by the ICV.

机译：通过施加基本叠加方法（S. Fujita，TheO：Chim）来列举具有给定化学式和给定对称的亚甘蔗衍生物。委员会统一 - 循环指数的Acta 1992,82,473-498）（USCI ）接近点群的Cubane骨架哦。用于常规或不规则性的手性和成分配体的循环指数（CL）根据这种给定的化学式计算。 CI基本上叠加在具有手性拟合（SCI-CFS）的各个频级索引上，通过从具有手性拟合（USCI-CFS）的单位频循环索引来计算。由此，相对于各个SCI-CF获得固定点（衍生物）的数量以提供定点载体（FPV）。得到的FPV通过O-H的标记表的反向矩阵乘以，以给出异构体计数矢量（ICV），其包含关于点组对称的逐个逐项的三维结构异构体的数量。通过使用ICV枚举的Cubane衍生品来检查促进概念。

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《Bulletin of the Chemical Society of Japan》 |2012年第7期|共11页
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Fujita Shinsaku;
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1. Symmetry-Itemized Enumeration of Cubane Derivatives as Three-Dimensional Entities by the Elementary-Superposition Method of the USCI Approach [J] . Fujita Shinsaku Bulletin of the Chemical Society of Japan . 2012,第7期

机译：USCI方法的基本叠加方法对称衍生物作为三维实体的对称性序列枚举
2. Symmetry-Itemized Enumeration of Cubane Derivatives as Three-Dimensional Entities by the Partial-Cycle-Index Method of the USCI Approach [J] . Fujita Shinsaku Bulletin of the Chemical Society of Japan . 2012,第7期

机译：通过USCI方法的部分循环索引方法将Cubane衍生物作为三维实体的对称性逐项列举
3. Symmetry-Itemized Enumeration of Cubane Derivatives as Three-Dimensional Entities by the Fixed-Point Matrix Method of the USCI Approach [J] . Fujita Shinsaku Bulletin of the Chemical Society of Japan . 2011,第11期

机译：通过USCI方法的定点矩阵方法将Cubane衍生物作为三维实体的对称性逐项列举
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8. A Recursive Approach to the Implementation of Enumerative Methods [R] . Lenstra, J. K., Rinnooykan, A. H. G. 1980

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Symmetry-Itemized Enumeration of Cubane Derivatives as Three-Dimensional Entities by the Elementary-Superposition Method of the USCI Approach

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