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首页> 外文期刊>Bulletin of the Chemical Society of Japan >Categorization and Enumeration of Achiral and Chiral Alkanes of a Given Carbon Content by Considering Internal Branching
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Categorization and Enumeration of Achiral and Chiral Alkanes of a Given Carbon Content by Considering Internal Branching

机译：考虑内部分支的给定碳含量的非手性和手性烷烃的分类和列举

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Combinatorial enumeration of alkanes as three-dimensional structures has been investigated, where the degrees of internal branching have been taken into consideration by introducing branching indicators (BIs, i.e., q, t, s, and p). After generating functions for counting preformed alkyl moieties (PAMs) were calculated by following Fujita's proligand method (S. Fujita, Theor. Chem. Acc. 2005, 1137 73; 2005, 113, 80; 2006, 115, 37), they have been introduced into functional equations for counting alkanes so as to give the corresponding generating functions, where such alkanes Of carbon content k have been categorized into four cases in terms of centroidal/bicentroidal nature and achirality/chirality. Thereby, the generating functions of the respective cases have given the numbers of alkanes, where each number appears as the coefficient of the term called a branching monomial (BM) q(nq)t(nt)s(ns)p(np)x(k), when such an alkane contains n(q) quaternary, n(t) tertiary, n(s) secondary, and n(q) quaternary carbons (k = n(q) + n(t) + n(s) + n(p)). The results of the enumeration have been verified by drawing alkanes of several representative cases, where a mode of divergence, i.e., [n(q), n(t), n(s), and n(p)], has been used for the purpose of qualitative discussions. Previous approaches without considering BIs have been derived by disregarding the effect of internal branching. Moreover, the functional equations for counting 3D structures have been systematically reduced into those for counting graphs, where graph-reduction conditions have been formulated to rationalize the reduction processes. Thereby, Polya's theorem for Counting graphs has been shown to be a special case of Fujita's proligand method for counting 3D structures. As a result, difference between stereoisomers (3D Structures) and constitutional isomers (graphs) has been discussed by the common criterion due to BMs (or modes of divergence), which provides more detailed enumerations that) previous enumerations due to Carbon contents (or constitutions).
机译：已经研究了烷烃的组合列举为三维结构，其中通过引入支化指示剂（BI，即q，t，s和p）考虑了内部支化度。根据Fujita的proligand方法（S. Fujita，Theor。Chem。Acc。2005，1137 73; 2005，113，80; 2006，115，37）生成用于计算预先形成的烷基部分（PAM）的函数后，引入到用于计算烷烃的函数方程式中以给出相应的生成函数，其中，这种碳含量为k的烷烃根据质心/双质心性质和非手性/手性分为四种情况。因此，相应情况的生成函数给出了烷烃的数目，其中每个数目都显示为称为支链单项式（BM）q（nq）t（nt）s（ns）p（np）x的项的系数（k），当此类烷烃包含n（q）个季碳，n（t）个叔碳，n（s）个仲碳和n（q）个季碳时（k = n（q）+ n（t）+ n（s ）+ n（p））。枚举的结果已通过绘制几种代表性情况的烷烃进行了验证，其中使用了一种发散模式，即[n（q），n（t），n（s）和n（p）]。为了进行定性讨论。通过不考虑内部分支的影响而获得了不考虑BI的先前方法。此外，用于计数3D结构的功能方程已被系统地简化为用于计算图形的方程，其中已制定了图形缩小条件以合理化缩小过程。因此，Polya的计数图定理已被证明是Fujita的3D结构计数的proligand方法的特例。结果，由于BM（或发散模态），通过通用标准讨论了立体异构体（3D结构）和结构异构体（图形）之间的差异，该标准提供了更详细的枚举，该枚举是由于碳含量（或构造）而先前的枚举）。

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