Written in a clear and understandable manner, this book provides a comprehensive, yet non-mathematical, treatment of the topic, covering the basic principles of symmetry and the important spectroscopic techniques used to probe molecular structure.
The chapters are extensively illustrated and deal with such topics as symmetry elements, operations and descriptors, symmetry guidelines, high-fidelity pseudosymmetry, crystallographic symmetry, molecular gears, and experimental techniques, including X-ray crystallography and NMR spectroscopy. As an additional feature, 3D animations of most of the structures and molecules covered are available online at wiley.com. As a result, chemists learn how to understand and predict molecular structures and reactivity.
Authored by a renowned expert with numerous publications and an excellent track record in research and teaching, this is a useful source for graduate students and researchers working in the field of organic synthesis, physical chemistry, biochemistry, and crystallography, while equally serving as supplementary reading for courses on stereochemistry, organic synthesis, or crystallography.
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Yes, you can access Symmetry, Spectroscopy, and Crystallography by Robert Glaser in PDF and/or ePUB format, as well as other popular books in Naturwissenschaften & Organische Chemie. We have over one million books available in our catalogue for you to explore.
Chapter 1 Symmetry/Pseudosymmetry: Chirality in Molecules,in Nature, and in the Cosmos
1.1 Introduction
Symmetry and emulation of symmetry (pseudosymmetry) play a major role in the world of esthetics and science. In our macro-surroundings, symmetry and pseudosymmetry are an ever-present source of āvisual pleasureā whose origins may arise from our genes. At times, prior to the achievements of modern medical science, symmetrical appearance of a prospective mate may have symbolized physical well-being (health) ā an essential attribute for both the child bearer/parent and the successful hunter/defender. Often, our perception of beauty and form is related to the observation of physical proportions whose ratio approximates the āgolden ratioā Ļ (an irrational number (1 + ā5)/2) where
The golden ratio is derived from a Fibonacci sequence of numbers 0,1,1,2,3,5,8,13,21,ā¦,a,b whereby
.
Leonardo da Vinci's āVitruvian Manā drawing (1) illustrates the beauty of ideal human proportions as described by Vitruvius, an architect in ancient Rome. The proportions of the circle's radius (centered at the navel) and the square's side (the human figure's height) are 1.659, which approximates the 1.618 value of the golden ratio. It is doubtful whether da Vinci and other great artists thought to themselves that they should paint figures and objects according to the dimensions specified by the golden ratio. Instead, they knew in their creative minds āwhat looks goodā in their mind's eye in terms of proportions. They were probably gifted from birth (i.e., their genes) and did not have to learn about the importance of painting with the golden ratio as a novice students in art school.
Prehistoric man's predilection to symmetry can be seen in anthropological findings of stone axe-heads. Increasingly symmetric stone axe-heads were unearthed at sites populated by progressively more developed societies. As the society of early prehistoric man matured, these finds seem to suggest that the hunter-gatherer crafted increasingly more functional hand tools that were also more visually pleasing [1]. David Avnir and coworkers have developed algorithms to measure distortion from an ideal symmetry and applied them to a morphological study of stone axe-heads unearthed at Pleistocene Age sites in the Jordan Valley. This enabled a quantitative correlation between increasing stone axe-head mirror pseudosymmetry and the decreasing age of the site. Illustrations 2ā4 depict axe-heads dated 1.84 million years ago (the oldest site, (2)) 0.6(2) million years ago (intermediate aged site, (3)), and 0.3(2) million years ago (the youngest site, (4)) [1].
The visual pleasure we receive from the āclassic proportionsā of the Municipal Arch (5, photo: Yael Glaser) in the Roman ruins of Glanum (Provence) is undoubtedly related to the golden ratio of its dimensions (8.8 m width and 5.5 m height). It is clear that its intimately related symmetry and esthetics were concepts well understood by talented architects in ancient times.
Our ancestors seem to have been greatly fascinated by objects of āhigh symmetryā (i.e., objects with more than one Cn rotation axis of order n ā„ 3, where n denotes the number of times the rotation is performed on a subunit in order to return it to its original orientation). Gray illustration 6 illustrates a late Neolithic/Bronze Age (about 4500ā5200 years ago) elaborately carved regular tetrahedron stone specimen with three of its knobs decorated with spirals or dots and rings. It was unearthed at Towie in Aberdeenshire, North-East Scotland. Simple carved regular tetrahedron (7) and octahedron (8) geometry objects were also unearthed in Aberdeenshire (hedron means āfaceā in Greek). The esthetically pleasing five convex regular polyhedra (tetrahedron, hexahedron, octahedron, dodecahedron, and icosahedron) were a source of learning, contemplation, and discussion for Plato and his students. In modern times, these geometrical structures were the impetus for creative organic syntheses of high-symmetry hydrocarbon molecules [2, 3].
1.2 Rudimentary Group Theory, Isometry, and Symmetry
Symmetry is based upon mathematical transforms, and to understand it, a short introduction to simple Group Theory will be presented. The elements (members) of a mathematical set all share some common trait. For example, the elements of a symmetry set are all the symmetry operations that can be performed for a particular object. This set may be acted upon by a mathematical operation (multiplication or successive application, that is, performing one operation followed by another). The combination of a set and an operation defines a mathematical group. The identity (E) element must be present in the set of every group. Multiplication of two elements always affords a third element that must also be an element of the set. For example, in the symmetry group C2, the elements E and C2 (
rotation ...
Table of contents
Cover
Title Page
Related Titles
Copyright
Table of Contents
Dedication
From the Author's Desk
Chapter 1: Symmetry/Pseudosymmetry: Chirality in Molecules,in Nature, and in the Cosmos
Chapter 2: Enantiospecificity of Pheromones, Sweeteners, Fragrances, and Drugs
Chapter 3: Bonding Parameters and the Effect of Local Environment on Molecular Structure
Chapter 4: Historical Development of Structural Chemistry: From Alchemy to Modern Structural Theory
Chapter 5: Chiroptical Properties
Chapter 6: Symmetry Comparison of Molecular Subunits: Symmetry in Nuclear Magnetic Resonance Spectroscopy and in Dynamic NMR
Chapter 7: Prochirality, Asymmetric Hydrogenation Reactions, and the CurtināHammett Principle
Chapter 8: Stereogenic Elements, Chirotopicity, Permutational Isomers, and Gear-Like Correlated Motion of Molecular Subunits
Chapter 9: Symmetry in Extended Periodic Arrays of Molecular Crystals and the Relevance of Penrose Tiling Rules for Nonperiodic Quasicrystal Packing
Chapter 10: Multiple Molecules in the Asymmetric Unit, āFaking Itā; Pseudosymmetry Emulation of Achiral Higher Order Space Filling in Kryptoracemate Chiral Crystals
Chapter 11: Platonic-Solid Geometry Molecules and Crystallographic Constraints upon Molecular Geometry, Symmetry Distortions from Ideality
Chapter 12: Solid-State NMR Spectroscopic/X-Ray Crystallographic Investigation of Conformational Polymorphism/Pseudopolymorphism in Crystalline Stable and Labile Hydrated Drugs
Chapter 13: NMR Spectroscopic Differentiation of Diastereomeric Isomers Having Special Positions of Molecular Symmetry
Chapter 14: Stereochemistry of Medium Ring Conformations
Chapter 15: The Pharmacophore Method for Computer Assisted Drug Design
Chapter 16: The X-Ray StructureāBased Method of Rational Design
