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Symmetry specified enumeration of substituted derivatives: an easy solution to the complex problemстатья
Информация о цитировании статьи получена из
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Дата последнего поиска статьи во внешних источниках: 18 июля 2013 г.
- Авторы: Tratch S.S., Zefirov N.S.
- Журнал: Russian Chemical Bulletin
- Том: 57
- Номер: 2
- Год издания: 2008
- Издательство: Springer Nature
- Местоположение издательства: Switzerland
- Первая страница: 235
- Последняя страница: 252
- DOI: 10.1007/s11172-008-0038-3
- Аннотация: Several sophisticated methods to solution of symmetry specified enumeration problems are available in the modern literature. In this paper we propose a simple technique that allows one to manually compute the exact numbers of fixed-symmetry derivatives for a given structure either with inclusion or ignoring the substitution patterns. The basic idea of the method suggested consists in the derivation of PA(3)lya-like cycle indices for the automorphism groups of specially constructed orbit partition graphs; the expansion of these indices and subsequent simple calculations result in the desired numbers of substituted derivatives with achiral substituents. Limitations of the new technique (and a method suggested earlier) depend on the relevance of the orbit partitions for particular subgroups of the point symmetry group. For illustration purposes, the results obtained for the prismane (D (3h) ) and adamantane (T (d) ) structures are discussed. In the former case the numbers of substituted derivatives can be found for all subgroups of the D (3h) group, whereas in the latter case these numbers can be determined for eight out of eleven subgroups of the T (d) point symmetry group.
- Добавил в систему: Зефиров Николай Серафимович