M. Hargittai, I. Hargittai - Symmetry through the Eyes of a Chemist (793765), страница 2
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. . . . . . . . . . . . . . . . . . . . . .6.3.1. Constructing Molecular Orbitals . . . . . . . . . . .6.3.2. Electronic States . . . . . . . . . . . . . . . . . . . . . . . .6.3.3. Examples of MO Construction . . . . . . . . . . . . .6.4. Quantum Chemical Calculations . . . .
. . . . . . . . . . . . . .6.5. Influence of Environmental Symmetry . . . . . . . . . . . . .6.6. Jahn–Teller Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2522522612632872902943087 Chemical Reactions . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . .7.1. Potential Energy Surface . . . . . . . . . . . . . . . . . . . . . . . . .7.1.1. Transition State, Transition Structure . . . . . . .7.1.2. Reaction Coordinate . . . . . . . . . . . . . . . . . . . . .7.1.3. Symmetry Rules for the Reaction Coordinate7.2. Electronic Structure . . .
. . . . . . . . . . . . . . . . . . . . . . . . . .7.2.1. Changes During a Chemical Reaction . . . . . . .7.2.2. Frontier Orbitals: HOMO and LUMO . . . . . . .7.2.3. Conservation of Orbital Symmetry . . . . . . . . .7.2.4. Analysis in Maximum Symmetry . . . . . . . .
. .7.3. Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7.3.1. Cycloaddition . . . . . . . . . . . . . . . . . . . . . . . . . . .7.3.2. Intramolecular Cyclization . . . . . . . . . . . . . . . .7.3.3. Generalized Woodward–Hoffmann Rules . . .
.7.4. Hückel–Möbius Concept . . . . . . . . . . . . . . . . . . . . . . . . .7.5. Isolobal Analogy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3133153163193203243243253263273283283433503503563648 Space-Group Symmetries .
. . . . . . . . . . . . . . . . . . . . . . . . . . .8.1. Expanding to Infinity . . . . . . . . . . . . . . . . . . . . . . . . . . . .8.2. One-Sided Bands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8.3. Two-Sided Bands . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . .8.4. Rods, Spirals, and Similarity Symmetry . . . . . . . . . . . .8.5. Two-Dimensional Space Groups . . . . . . . . . . . . . . . . . . .8.5.1. Simple Networks . . . . . . . . . . . . . . . . . . . . . . . .8.5.2. Side-Effects of Decorations . . . .
. . . . . . . . . . .8.5.3. Moirés . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .371371375378381395401406408410xiiContents9 Crystals . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . .9.1. Basic Laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9.2. The 32 Crystal Groups . . . . . . . . . . . . . . . . . . . . . . . . . . .9.3. Restrictions . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . .9.4. The 230 Space Groups . . . . . . . . . . . . . . . . . . . . . . . . . . .9.4.1. Rock Salt and Diamond . . . . . . . . . . . . . . . . . .9.5. Dense Packing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9.5.1. Sphere Packing .
. . . . . . . . . . . . . . . . . . . . . . . . .9.5.2. Icosahedral Packing . . . . . . . . . . . . . . . . . . . . . .9.5.3. Connected Polyhedra . . . . . . . . . . . . . . . . . . . . .9.5.4. Atomic Sizes . . . . . . . . . . . . . . . . . . . . . . . . . . .9.6. Molecular Crystals . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . .9.6.1. Geometrical Model . . . . . . . . . . . . . . . . . . . . . .9.6.2. Densest Molecular Packing . . . . . . . . . . . . . . .9.6.3. Energy Calculations and Structure Predictions9.6.4. Hypersymmetry . . . . . . . .
. . . . . . . . . . . . . . . . .9.6.5. Crystal Field Effects . . . . . . . . . . . . . . . . . . . . .9.7. Beyond the Perfect System . . . . . . . . . . . . . . . . . . . . . . .9.8. Quasicrystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
.9.9. Returning to Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . .References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .413417423424432438440442446449453456457466470474476483489494496Epilogue . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . 505Other Titles by the Authors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 507Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 509Chapter 1IntroductionArtists treat facts as stimulifor the imagination,while scientists use their imaginationto coordinate facts.Arthur Koestler [1]Fundamental phenomena and laws of nature are related to symmetryand, accordingly, symmetry is one of science’s basic concepts.Perhaps it is so important in human creations because it is omnipresentin the natural world. Symmetry is beautiful although alone it may notbe enough for beauty, and absolute perfection may even be irritating.Function, utility, and aesthetic appeal are the reasons for symmetry intechnology and the arts.Much has been written about symmetry, for example, in BélaBartók’s music [2].
It is not known, however, whether he consciouslyapplied symmetry or was simply led intuitively to the golden ratioso often present in his music. Another unanswerable question is howthese symmetries contribute to the appeal of Bartók’s music, and howmuch of this appeal originates from our innate sensitivity to symmetry.Bartók declined to discuss the technicalities of his composing andmerely stated that he created after nature.The world around us abounds in symmetries and they have beenstudied for centuries. More recently, research has probed into the roleof symmetry in human interactions along with representatives of theanimal kingdom.
Special attention has been given to mate selection.One of the first appearances of this facet of symmetry in the popularpress was an article in The New York Times, with an intriguing title,“Why Birds and Bees, Too, Like Good Looks” [3].M. Hargittai, I. Hargittai, Symmetry through the Eyes of a Chemist, 3rd ed.,C Springer Science+Business Media B.V.
2009DOI: 10.1007/978-1-4020-5628-4 1, 121 IntroductionThe above examples illustrate that we like to consider symmetry ina broader sense than how it just appears in geometry. The symmetryconcept provides a good opportunity to widen our horizons and tobring chemistry closer to other fields of human activities. An interesting aspect of the relationship of chemistry with other fields wasexpressed by Vladimir Prelog in his Nobel lecture [4]:Chemistry takes a unique position among thenatural sciences for it deals not only with materialfrom natural sources but creates the major parts ofits objects by synthesis.
In this respect, as statedmany years ago by Marcelin Berthelot, chemistryresembles the arts; the potential of creativity isterrifying.Of course, even the arts are not just for the arts’ sake and chemistry is certainly not done just for chemistry’s sake. But in additionto creating new medicines, heat-resistant materials, pesticides, andexplosives, chemistry is also a playground for the organic chemist tosynthesize exotica including propellane and cubane, for the inorganicchemist to prepare compounds with multiple metal–metal bonds, forthe stereochemist to model chemical reactions after a French parlortrick (cf.
Section 2.7), and for the computational chemist to createundreamed-of molecules and to write detailed scenarios of as yetunknown reactions. Symmetry considerations play no small role inall these activities. The importance of blending fact and fantasy wassuccinctly expressed by Arthur Koestler in the chapter-opening quotation. Lucretius gave an early illustration of an imaginative use ofthe concept of shape in the first century BCE: “atoms with smoothsurfaces would correspond to pleasant tastes, such as honey; but thosewith rough surfaces would be unpleasant” [5].Chemical symmetry has been noted and investigated for centuriesin crystallography which is at the border between chemistry andphysics.
It was more physics when crystal morphology and other properties of the crystal were described. It was more chemistry when theinner structure of the crystal and the interactions between its buildingunits were considered. Later, descriptions of molecular vibrationsand the establishment of selection rules and other basic principleshappened in all kinds of spectroscopy. This led to another uniquelyimportant place for the symmetry concept in chemistry with practicalimplications.1 Introduction3The discovery of handedness, or chirality, in crystals and moleculesbrought the symmetry concept nearer to the chemical laboratory.All this, however, concerned more the stereochemist, the structuralchemist, the crystallographer, and the spectroscopist rather than thesynthetic chemist. Symmetry used to be considered to lose its significance as soon as the molecules entered the chemical reaction.
Orbitaltheory and the discovery of the conservation of orbital symmetryhave encompassed even this area. It was signified by the 1981 NobelPrize in chemistry awarded to Kenichi Fukui and Roald Hoffmann(Figure 1-1): “for their theories, developed independently, concerningthe course of chemical reactions” [6].During the past half a century, fundamental scientific discoverieshave been aided by the symmetry concept. They have played a role inthe continuing quest for establishing the system of fundamental particles [7]. It is an area where symmetry breaking has played as important a role as symmetry.
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