The tetrahedral carbon atom

The earliest demonstration of the regular tetrahedral arrangement of carbon bonds was provided by the analysis of the crystal structure of diamond. In this crystal 

Many simple carbon compounds have been studied by diffraction or spectroscopic methods, and in all molecules Ca the interbond angles have the regular tetrahedral value (109°28 ) to within the experimental error. Some reliable values of bond lengths in simple molecules of carbon and other Group IV elements are listed in Table 21.1. 

Boiling-points of hydrocarbons, fluorocarbons, and noble gases. 

For carbon forming one double and two single bonds the bond angles 

Carbonyl halides and thiocarbonyl halides. All the compounds COCl2/ and COBr2/ have been studied in the vapour state by e.d. and/or m.w., and COCI2 (phosgene) has also been studied in the crystalline state/ The C-X bond lengths are close to the values expected for single bonds, while the C=0 

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The Tetrahedral Carbon Atom.—We have thus derived the result that an atom in which only s and p eigenfunctions contribute to bond formation and in which the quantization in polar coordinates is broken can form one, two, three, or four equivalent bonds, which are directed toward the corners of a regular tetrahedron (Fig. 4). This calculation provides the quantum mechanical justification of the chemist s tetrahedral carbon atom, present in diamond and all aliphatic carbon compounds, and for the tetrahedral quadrivalent nitrogen atom, the tetrahedral phosphorus atom, as in phosphonium compounds, the tetrahedral boron atom in B2H6 (involving single-electron bonds), and many other such atoms. 

Thus we have shown that when s and p orbitals are available and s—p quantization is broken an atom can form four (or fewer) equivalent bonds which are directed towards tetrahedron corners. To the approximation involved in these calculations the strength of a bond is independent of the nature of other bonds. This result gives us at once the justification for the tetrahedral carbon atom and other tetrahedral atoms, such as silicon, germanium, and tin in the diamond-type crystals of the elements and, in general, all atoms in tetrahedral structures. 

The Dependence of Bond Angles on Single Bond-Double Bond Resonance.—In a molecule such as phosgene or 1,1-dichloroethylene the value 125°16 for the angle Cl-C-0 (0) is predicted by the theory of the tetrahedral carbon atom in case that the C-Cl bonds have no double bond character. If the double bond resonates equally among all three positions, giving the Cl-C bond one-third double bond character, we expect from symmetry... 

The results shown in the table provide further evidence of the extraordinary extent to which the tetrahedral carbon atom of van t Hoff and Le Bel determines the structure of organic molecules. 

Figure 5.4 The tetrahedral carbon atom of 2-butanol that bears four different groups. [By convention such atoms are often designated with an asterisk ( )].

The Mills-Nixon hypothesis that small ring annelation on benzene would induce bond fixation (bond alternation) by trapping out one Kekul6 tautomer is a casualty of early twentieth century structural chemistry. Due to a lack of direct methods for analyzing molecular structure, structural postulates of that time were often supported by an analysis of product distributions. An experimental observable such as product selectivity or isomer count was correlated to an unobservable structural feature derived on the basis of a chemical model. Classical successes of this method are van t Hoff s proof of the tetrahedral carbon atom and Fischer s proof for the configuration of sugars. In the case of Mills and Nixon, however, the paradigm broke down. 

The properties of a substance depend in part upon the type of bonds, between the atoms of the substance and in part upon the atomic arrangement and the distribution of the bonds. The atomic arrangement is itself determined to a great extent by the nature of the bonds the directed character of covalent bonds (as in the tetrahedral carbon atom) plays an especially important part in determining the configura-... 

HYBRID BOND ORBITALS THE TETRAHEDRAL CARBON ATOM... 

The postulate of the tetrahedral carbon atom in classical stereochemistry requires that the atom have a configuration that is tetrahedral but is not necessarily that of a regular tetrahedron so long as... 

The ideas involved in modem structural chemistry are no more difficult and require for their understanding no more, or little more, mathematical preparation than the familiar concepts of chemistry. Some of them may seem strange at first, but with practice there can be developed an extended chemical intuition which perir-its the new concepts to be used just as confidently as the older ones of the valence bond, the tetrahedral carbon atom, etc., which form the basis of classical structural chemistry. 

The classical valency concept of the tetrahedral carbon atom has been more than fully verified by its success in explaining the chemistry of countless thousands of organic compounds. The first direct physical confirmation of the tetrahedral distribution of carbon valency bonds, however, came with the elucidation of the structure of diamond by W. H. and W. L. Bragg (1913) using the newly discovered method of X-ray diffraction. 

Pasteur s famous experiments with tartrate crystals have been described,161 the sesqui-centenary of their start being marked by a paper that examined missed opportunities in stereochemistry and, in particular, the work by Mitscherlich which nearly anticipated Pasteur.162 The centenary in 1995 of Pasteur s death prompted publication of several papers.163-165 His observations, and those of le Bel and van t Hoff, are described in a paper outlining the reasoning that led to the momentous recognition of the tetrahedral carbon atom.166 The reception of a tetrahedral carbon atom was varied. Its application to the relatively new Kekule structure for benzene was made by van t Hoff himself and more particularly by Wilhelm Komer.167 Eventual support came from Wislicenus, a widely ranging organic chemist, noted specially for his work on isomerism.168... 

Van t Hoff s 1874 pamphlet, reprinted in Peter J. Ramberg and Geert J. Somsen, The Young J. H. van t Hoff The Background to the Publication of His 1874 Pamphlet on the Tetrahedral Carbon Atom, Together with a New English Translation, Annals of Science 58 (2001) 51—74. 

The discovery of stereochemistry was one of the most important breakthroughs in the structural theory of organic chemistry. Stereochemistry explained why several types of isomers exist, and it forced scientists to propose the tetrahedral carbon atom. In this... 

The resonance concept thus removes both difficulties. In fact, if Kekule had arrived on experimental grounds at the hypothesis that the oscillation between the two structures might at the same time be the cause of the stabilization, then the resonance concept would have been anticipated in the same way as the tetrahedral carbon atom of Van 5t Hoff and Le Bel anticipated the wave-mechanical theory of mixed wave functions. Now the resonance concept can, however, like the tetrahedral carbon atom, be operated even without the wave mechanical theories, which lie at the basis of these concepts, being always applied explicitly. 

Fhst, the number of valence functions (or frontier orbitals) and valence elechons (frontier orbital occupancy) determines the tendency toward cluster bonding. It is instructive to recall that the structural motif in elemental boron is the icosahedron with six-connected boron atoms see Borides Solid-state Chemistry), it is the tetrahedral carbon atom in the diamond form of elemental carbon with four-coimected carbon atoms and it is three-connected phosphorus atoms in the sheets of elemental black phosphorus (see Phosphides Solid-state Chemistry). Boron has more valence orbitals than valence elechons, naturally leading to orbitally rich cluster formation for example, BH has three orbitals and two elechons and forms... 

The rigorous group theoretical requirement for the existence of chirality in a crystal or a molecule is that no improper rotation elements be present. This definition is often trivialized to require the absence of either a reflection plane or a center of inversion in an object, but these two operations are actually the two simplest improper rotation symmetry elements. It is important to note that a chiral object need not be totally devoid of symmetry (i.e., be asymmetric), but that it merely be diss)nn-metric (i.e., containing no improper rotation symmetry elements). The tetrahedral carbon atom bound to four different substituents may be asymmetric, but the reason it represents a site of chirality is by virtue of dissymmetry. 

The electronic structure of the ammonium ion is similar to that in the tetrahedral carbon atom and, therefore, sp hybridization becomes possible. 

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