期刊名称：Hyle : International Journal for Philosophy of Chemistry
印刷版ISSN：1433-5158
出版年度：1997
卷号：3
页码：29-49
出版社：HYLE Publications, Karlsruhe and University of Karlsruhe
摘要：Molecules have more or less symmetric and complex structures which can be defined in the mathematical framework of topology, group theory, dynamical systems theory, and quantum mechanics. But symmetry and complexity are by no means only theoretical concepts of research. Modern computer aided visualizations show real forms of matter which nevertheless depend on the technical standards of observation, computation, and represen-tation. Furthermore, symmetry and complexity are fundamental interdiscipli-nary concepts of research inspiring the natural sciences since the antiquity
关键词：molecular structure; symmetry; symmetry breaking; complexity; non-;linearity. ;1. Molecular Structure in Topology and Quantum ;Mechanics ;The molecular structure hypothesis states that a molecule is a collection of ;atoms linked by a network of bonds. Since the 19th century the molecular ;structure hypothesis has been a successful concept of ordering and classifying ;the observations of chemistry. But this hypothesis cannot directly be derived ;from the physical laws governing the motions of the nuclei and electrons that ;make up the atoms and the bonds. It must be justified that all atoms exist in ;molecules as separate definable pieces of the three-dimensional ('real') space ;with properties which can be predicted and computed by the laws of quantum ;mechanics. ; var currentpos;timer; function initialize() { timer=setInterval("scrollwindow()";10);} function sc(){clearInterval(timer); }function scrollwindow() { currentpos=document.body.scrollTop; window.scroll(0;++currentpos); if (currentpos != document.body.scrollTop) sc();} document.onmousedown=scdocument.ondblclick=initialize30 ;Klaus Mainzer ;The well-known models of molecules with different information for a ;chemist are derived from the molecular structure hypothesis: a) The three-;dimensional ball-and-stick model with balls for the atomic nuclei; sticks for ;the atomic bonds and their angles; b) its 2-dimensional representation as ;structural formula; and c) its 1-dimensional representation as linguistic name ;which can be derived from the structural formula. Graphic models are ;applications of mathematical graph theory which is a part of combinatorical ;topology. This mathematical theory became fundamental for chemistry; when ;in the midst of the last century the molecular structure of chemical sub-;stances were discovered (e.g.; Biggs et al. 1976; p. 55). L. Pasteur recognized ;that the relationship between symmetry of reflection and optical activity is ;not a function of the crystal structure of a substance. With certain water-;soluble crystals; for example; the symmetry of reflection can be demonstrated ;both in the solid state and in the liquid state. Pasteur investigated tartaric acid ;and found a counterclockwise and a clockwise form; which are called L-;tartaric acid and D-tartaric acid (D = dextro = right) respectively. He also ;isolated a third form of tartaric acid (meso-tartaric acid); which cannot be ;separated into one of the other forms. To explain the optical activity; it was ;therefore necessary to investigate more fundamental structures than crystals; ;or even molecules and the orientation of atoms. R.J. Haüy had already ;suspected that the form of crystals and their constituent components were ;images of one another. Pasteur therefore inferred the symmetric form of the ;crystal's components from the crystal reflections. ;Another important step was A. Kekulé's investigation of quadrivalent ;carbon atoms; for whose multiple bonds he also introduced a structural ;formula notation which is still used in today's organic chemistry. An essential ;advance occurred in 1864; when the Edinburgh chemist A. Crum Brown ;introduced his version of the graphic notation. Each atom was shown ;separately; represented by a letter enclosed in a circle; and all single and ;multiple bonds were marked by lines joining the circles. Crum Brown's ;system is more or less the one in use today; except that the circles are now ;usually omitted. His notation was soon accepted everywhere; after some ;resistance from Kekulé and others. Its acceptance was partly due to its ;success in explaining the strange fact that there are pairs of substances which ;have the same chemical composition; although their physical properties are ;different. The graphic notation made it clear that this is because the atoms are ;arranged in different ways in the different substances. This well-known ;chemical phenomenon is called isomerism; and in many cases there are more ;than two isomers with the same constitutional formula. In 1874; the great ;British mathematician A. Cayley wrote a paper 'On the mathematical theory ;of isomers' inspired by the fusion of chemical and mathematical ideas.
