We shall elaborate this definition by explaining our use of the terms description and particles. A description may take many forms. It may be verbal, or it may be visual—as, for example, through the use of molecular models. The most accurate descriptions are also the most complex: These are the equations which describe the motion of the particles as a function of time and spatial position. There are two kinds of submolecular particles which are of interest to the organic chemist: the electrons and the nuclei.

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We shall elaborate this definition by explaining our use of the terms description and particles. A description may take many forms. It may be verbal, or it may be visual—as, for example, through the use of molecular models. The most accurate descriptions are also the most complex: These are the equations which describe the motion of the particles as a function of time and spatial position. There are two kinds of submolecular particles which are of interest to the organic chemist: the electrons and the nuclei.

Wave-mechanical arguments lead to a description of electronic structure as a probability distribution of negative charge, i. In contrast, the distribution of nuclei in space may be discussed more nearly in classical terms, i. These vibrations are completely analogous to the quivers executed by two weights connected by a spring: the coulombic and exchange forces in the molecule simply take the place of the mechanical restoring force in the spring.

It might therefore be appropriate to begin our discussion of structure and symmetry by analyzing the case of the hydrogen molecule. In the formation of that molecule, two protons and two electrons have been brought together. The electrons distribute themselves so that the position of the protons assumes an equilibrium value. This distribution of protons and electrons is indicated in Figure 1—1, which shows a cross section of the molecule made by a plane which contains the nuclei.

This plane shows contour lines of equal electronic charge density, and the three-dimensional contour surfaces may be developed by rotation around the internuclear line x. Note that well-defined positions are assigned to the protons, whereas the electrons can only be described in terms of the over-all charge density.

The molecule may be pictured as a roughly cigar-shaped region of electron density within which the two protons are buried. As shown by the contour lines, the density is highest at points on the x-axis corresponding to the positions of the nuclei, falls off at all distances, but remains high in the region between the nuclei. This region of electron localization between the nuclei coincides in direction with the internuclear line.

This description of the distribution of two electrons in the field of the two protons corresponds to the bonding molecular orbital MO of hydrogen molecule. The protons jiggle about but maintain an equilibrium distance r, the bond length.

The bond length The potential energy of the molecule is raised whenever the bond is stretched say to We shall now consider symmetry in simple molecules. Every molecule may be classified according to its symmetry, and each particular symmetry class is characterized by the number and type of symmetry elements present in such a molecule.

Objects like idealized forks, spoons, hammers, and cups have just one plane of symmetry, and so do molecules like nitrosyl chloride Figure 1—2 , bromocyclopropane and vinyl chloride.

For example, water has a twofold axis of symmetry and ammonia a threefold axis, as indicated in Figure 1—2. It is important to note that planes and axes of symmetry are often both encountered in the same molecule. For example, while nitrosyl chloride does not have an axis of symmetry the trivial one-fold axis C1 is never considered , water and ammonia have, respectively, two and three planes of symmetry Figure 1—2 which intersect at the Cn axis. Let us now apply a similar analysis to the case of the hydrogen molecule.

In addition to the above-mentioned planes there also exists a plane which is perpendicular to the internuclear axis, which bisects the molecule, and which contains an infinite number of C2 axes.

Molecules such as oxygen and carbon dioxide have that kind of symmetry which is called cylindrical symmetry. Objects such as idealized hourglasses, footballs American , and doughnuts also have cylindrical symmetry.

Conical symmetry is a closely related kind of axial symmetry. In molecules possessing conical symmetry, e. Objects like idealized funnels, saucers, soda bottles, pins, and eggs have conical symmetry. Cylindrically and conically symmetrical objects have one C, axis. We shall elaborate on the subject of symmetry elements in Section 1—4. A carbon nucleus, one or more other nuclei, and the appropriate number of electrons are brought together, and the electrons are allowed to distribute themselves in a fashion which stabilizes the equilibrium configuration of all the nuclei.

As in hydrogen molecules, there exist regions of high electron density between the nuclei which generally coincide in direction with the internuclear lines. The atoms thus bonded to the central carbon atom are called ligand atoms. The nonbonding electrons, e. The number of ligand atoms defines the coordination number. Carbon in its various stable combinations may exhibit coordination numbers varying from one to four. We shall discuss the geometry of bonding separately for each coordination number.

These molecules have conical symmetry and in that respect resemble hydrogen chloride. First, the ligand atoms may be equivalent or they may be nonequivalent.

Second, the molecular array may be linear or nonlinear. As it happens, the latter question rarely arises in practice, for stable compounds of carbon in which carbon exhibits a coordination number of two are linear. Carbon dioxide is a linear molecule in which the ligand atoms are equivalent and in which the bond lengths are equal 1. Carbonyl sulfide, hydrogen cyanide, and acetylene are linear molecules in which the ligand atoms are not equivalent and in which the two bond lengths of carbon must therefore be different.

Carbon suboxide contains one carbon atom with two equivalent ligands and two carbon atoms with different ligands see Formula I. It may be noted that carbon dioxide, carbon suboxide, and acetylene have the cylindrical symmetry of hydrogen molecule, while hydrogen cyanide and carbonyl sulfide have the conical symmetry of hydrogen chloride.

However, with the exception of carbanions and possibly radicals , in which the unshared electrons may be regarded as occupying an additional position on the coordination sphere, the most stable groupings containing carbon bonded to three atoms are planar, and our discussion is therefore considerably simplified.

Groupings of this type in which carbon is attached to three identical ligands as in graphite are quite exceptional. Methyl cation has trigonal symmetry, the chief attributes of which are summarized in Figure 1—4. However, in the vast majority of compounds containing tricoordinate carbon, the carbon atom is attached to noneVCquivalent ligands. Hence, the totality of the interactions of the three ligands including nuclei, bonding, and nonbonding electrons with each other no longer has regular trigonal symmetry Figure 1—5.

It cannot be doubted that such differences, though they might perhaps be too small to be observable with currently available measuring techniques, would nevertheless be finite and could in principle be detected by more sensitive devices. It must be re-emphasized that the nature and magnitude of the electronic interactions are completely immaterial to the validity of such arguments and become important only when we attempt to predict or justify the direction and magnitude of the observed effects.

In diamond these ligands are identical. As shown by a great variety of physical measurements, the atoms attached to carbon in compounds of type CX4 are completely equivalent. A square planar array of four X groups with a carbon atom at the center does not meet these specifications. It may be shown that equivalence in three dimensions signifies regular tetrahedral symmetry, an analysis of which is given in Figure 1—6.

This figure shows a carbon atom, called the tetrahedral carbon atom, attached to four hydrogen atoms numbered 1 through 4. Inspection of the figure shows that there are four C3 axes, one for each of the C—H bonds. In this respect we are reminded of the case of ammonia Figure 1—2C.

These six planes may be ordered into the three pairs shown in Figure 1—6. In each pair the two planes are perpendicular to each other and they intersect to form a C2 axis.

The three resulting C2axes are mutually perpendicular, and they bisect the six tetrahedral angles. Expressed in degrees, this is approximately As soon as the ligands are no longer equivalent, the regular tetrahedral symmetry vanishes since the various interactions of the ligands around the central carbon are no longer identical.

It follows that the bond angles can also no longer be The conclusion of this symmetry argument is borne out by numerous experimental observations. The regular tetrahedral angle is therefore the exception rather than the rule in organic chemistry. The electronic distributions in the atoms i. These four orbitals are the 2s and the three 2p orbitals.

In its lowest energy state, the carbon atom has two electrons in the 2s orbital and two electrons in the 2p orbitals, so that the description of the electron configuration is 1s22s2p2. Like all s-orbitals, the 2s-orbital is spherically symmetrical and has its highest charge density at the nucleus.

Each p-orbital, however, is cylindrically symmetrical, and the charge density at the nucleus is zero. The three p-orbitals differ only in direction in space and the three cylindrical axes define a Cartesian coordinate system x, y, and z.

Figure 1—7A shows projected contour lines of equal electronic charge density for the 2pz AO. It is seen that the charge density is concentrated in the lobes, two separated distorted ellipsoids which float above and below the nodal xy-plane. This does not correspond to any experimentally observed geometry of carbon bonding orbitals. It follows, therefore, that the wave function i. Excerpted from Introduction to Stereochemistry by Kurt Mislow.

Excerpted by permission of Dover Publications, Inc.. All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher. Excerpts are provided by Dial-A-Book Inc.


Introduction to Stereochemistry

Its focus lies in the fundamentals of structural stereochemistry, rather than the dynamic aspects that are more relevant to reaction mechanisms. The three-part treatment deals with structure and symmetry, stereoisomerism, and the separation and configuration of stereoisomers. The first section reviews molecular architecture, relating empirical bonding geometries to the hybridization of the central carbon atom. Students receive a nonrigorous treatment of symmetry elements and point groups, with particular focus on the presence or absence of reflection symmetry. The second section classifies stereoisomers according to symmetry properties and to the nature of their barriers; it also discusses the dependence of optical activity on structure and concludes with an examination of topological isomerism. The third and final section explores the conceptual basis of asymmetric syntheses and kinetic resolutions.





0486425304 - Introduction to Stereochemistry Dover Books on Chemistry by Kurt Mislow


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