A Model for Combinatorial Organic Chemistry
详细信息 查看全文
- 作者：Sherif El-Basil
- 刊名：Journal of Chemical Information and Modeling
- 出版年：2000
- 出版时间：May 2000
- 年：2000
- 卷：40
- 期：3
- 页码：572 - 579
- 全文大小：136K
- 年卷期：v.40,no.3(May 2000)
- ISSN：1549-960X
文摘
The set of coset representations, CR's, of a group G, {G(/G1), G(/G2), ..., G(/Gs)}, where G1 = {I}, Gs =G, the marks, mij of subgroup Gj on a given G(/Gi), 1 
i s, and the subduction of G(/Gi) by Gj, j i,G(/Gi) 
Gj, are essential tools for the enumeration of stereoisomers and their classification according totheir subgroup symmetry (Fujita, S. Symmetry and Combinatorial Enumeration in Chemistry; Springer-Verlag: Berlin, 1991). In this paper, each G(/Gi) is modeled by a set of colored equivalent configurations(called homomers), H = {h1, h2, ..., hr}, r = 
G/Gi, such that a given homomer, hk, remains invariant onlyunder all g 
Gi, where g is an element of symmetry. The resulting homomers generate the correspondingset of marks almost by inspection. The symmetry relations among a set H can be conveniently stored in aCayley-like diagram (Chartrand, G. Graphs as Mathematical Models; Prindle, Weber and SchmidtIncorporated: Boston, MA, 1977; Chapter 10), which is a complete digraph on r vertices so that an arcfrom vertex vi to vertex vj is colored with the set Sij of symmetry elements such that hi 
hj,gij Sij. Inaddition, each vertex, vi, is associated with a loop that is colored with a set Sii so that gii Sii stabilizes hi.A Cayley-like diagram of a given CR, G [G(/Gi)], leads to graphical generation of G(/Gi) Gj for all valuesof j and also to all mij's. Several group-theoretical results are rederived and/or became more envisagablethrough this modeling. The approach is examplified using C2, C3, D2, T, and D3 point groups and is appliedto trishomocubane, a molecule that belongs to the D3 point group.
i s, and the subduction of G(/Gi) by Gj, j i,G(/Gi) Gj, are essential tools for the enumeration of stereoisomers and their classification according totheir subgroup symmetry (Fujita, S. Symmetry and Combinatorial Enumeration in Chemistry; Springer-Verlag: Berlin, 1991). In this paper, each G(/Gi) is modeled by a set of colored equivalent configurations(called homomers), G/Gi, such that a given homomer, hk, remains invariant onlyunder all g Gi, where g is an element of symmetry. The resulting homomers generate the correspondingset of marks almost by inspection. The symmetry relations among a set hj,gij Sij. Inaddition, each vertex, vi, is associated with a loop that is colored with a set Sii so that gii Sii stabilizes hi.A Cayley-like diagram of a given CR, Gj for all valuesof j and also to all mij's. Several group-theoretical results are rederived and/or became more envisagablethrough this modeling. The approach is examplified using C2, C3, D2, T, and D3 point groups and is appliedto trishomocubane, a molecule that belongs to the D3 point group.