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Titlebook: Mathematical Concepts in Organic Chemistry; Ivan Gutman,Oskar E. Polansky Textbook 1986 Springer-Verlag Berlin Heidelberg 1986 algebra.che

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发表于 2025-3-21 18:24:57 | 显示全部楼层 |阅读模式
书目名称Mathematical Concepts in Organic Chemistry
编辑Ivan Gutman,Oskar E. Polansky
视频video
图书封面Titlebook: Mathematical Concepts in Organic Chemistry;  Ivan Gutman,Oskar E. Polansky Textbook 1986 Springer-Verlag Berlin Heidelberg 1986 algebra.che
描述The present book is an attempt to outline some, certainly not all, mathematical aspects of modern organic chemistry. We have focused our attention on topological, graph-theoretical and group-theoretical features of organic chemistry, Parts A, B and C. The book is directed to all those chemists who use, or who intend to use mathe­ matics in their work, and especially to graduate students. The level of our exposition is adjusted to the mathematical background of graduate students of chemistry and only some knowledge of elementary algebra and calculus is required from the readers of the book. Some less well-known. but still elementary mathematical facts are collected in Appendices 1-4. This, however, does not mean that the mathematical rigor and numerous tedious, but necessary technical details have been avoided. The authors‘ intention was to show the reader not only how the results of mathematical chemistry look, but also how they can be obtained. In accordance with this, Part 0 of the book contains a few selected advanced topics which should give the reader the flavour of the contemporary research in mathe­ matical organic chemistry. One of the authors (I.G.) was an Alexander von Hu
出版日期Textbook 1986
关键词algebra; chemistry; knowledge; mutation; organic chemistry; stability
版次1
doihttps://doi.org/10.1007/978-3-642-70982-1
isbn_softcover978-3-642-70984-5
isbn_ebook978-3-642-70982-1
copyrightSpringer-Verlag Berlin Heidelberg 1986
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Some Interrelations between Symmetry and Automorphism Groupsatoms about their mean positions are discussed in terms of . (see paragraph 8.4.3). This concept begins to break down when an internal degree of freedom (e.g. the torsion of a methyl group) becomes fully excited. As the shall show later, automorphism groups of the molecular graph are well-suited to treat the symmetry in non-rigid molecules.
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Fundamentals of Graph Theoryf molecular graphs. The present chapter will, finally, provide a precise mathematical characterization of a graph. We shall list here a number of additional graph-theoretical definitions and mention a few basic properties of graphs.
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Graph Theory and Molecular Orbitalsmolecules. The wave function for a .-electron is presented in the LCAO form . where {.> symbolizes a .-vorbital located on the .-th atom of the conjugated molecule, and the summation goes over all . atoms which participate in the conjugation.
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Topological Indicesthe information contained in the molecular graph into a numerical characteristic. Every number which is uniquely determined by a graph is called a graph invariant. Those invariants of molecular graphs which are used for structure-property or structure-activity correlations are usually called topological indices (of the corresponding molecule).
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Topological Aspects in ChemistrySince the time of ., chemists are used to thinking about molecules as geometric objects in which atoms have a certain spatial arrangement. The geometric parameters of molecules (interatomic distances, bond angles, dihedral angles, etc.) can be measured with a rather high degree of accuracy and are indeed known in a considerable number of cases.
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Special Molecular GraphsIn graph theory a connected acyclic graph is called a tree. Hence we may say that the topology of acyclic molecules is represented by trees; the essential topological properties of acyclic molecules coincide with those of trees. In the following we shall get acquainted with the basic properties of trees.
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Fundamentals of Group TheoryGroups are sets of elements amended with a combination law that satisfies certain conditions (axioms).
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