Rehybridization

For a crystal having the symmetry of diamond or /.incblende (thus having cubic elasticity), there are three independent clastic constants, c, t 12, and C4.4. The bulk modulus that was discussed in Chapter 7 is B = (c, + 2c,2)/3. We can discuss the bulk modulus, and the combination c, — c,2, entirely in terms of rigid hybrids, and therefore the two elastic constants c, and c,2 do not require deviations from this simple picture. This will not be true for the strain, which is relevant to c 44, and this is a complication of some importance. 

Let us consider the displacements of the four neighbors nearest to the central atom. These have components that rotate the entire tetrahedron, the first complication. These complicate the geometry slightly but do not affect the energy. They may be subtracted out, leaving the displacements shown in Fig. 8-6. 

We see immediately that these residual displacements have components along the bonds so that, in contrast with the Ci, — c,2 shear, the radial interaction contributes to the shear constant. This is the second complication. 

The third is the po.ssibility of rehybridization. Note that the nonradial components of that drsplacement tend to pull the bonds to atoms a and c apart and tend to pull those to b and d together, as illustrated in Fig. 8-6. In order to avoid the misalignment of hybrids of the type shown in Fig. 8-3, it becomes favorable to decrease the content of orbitals (the. x-direction is indicated in Fig. 8-6) in 

Atoms a and c lie in the positive. --dii cction from the origin atom by rt/4 atoms h and d lie in the negative x-dircction by the same amount. For zincbicnde the shaded atoms might be Zn and the empty atoms S. 

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Fladdon R C, Brus L E and Raghavaohari K 1986 Rehybridization and n-orbital alignment the key to the existenoe of spheroidal oarbon olusters Chem. Rhys. Lett. 131 165... 

The MO picture predicts that the reaction will proceed with inversion of configuration because the development of the transition state is accompanied by rehybridization of the carbon to the trigonal bipyramidal geometry. As the reaction proceeds on to product and sp hybridization is reestablished, the product is formed with inversion of configuration. 

The phenyl cation is an extremely unstable cation, as is reflected by the high hydride affinity shown in Table 5.2. In this case, the ring geometry opposes rehybridization so the vacant orbital retains sp character. Because the empty orbital is in the nodal plane of the ring, it receives no stabilization firom the n electrons. 

The deviation from planarity that is present in a structure such as 1 raises the question of how severely a conjugated system can be distorted from the ideal coplanar alignment of p orbitals and still retain aromaticity. This problem has been analyzed by determining the degree of rehybridization necessary to maximize p orbital overlap in 1. It is found that rehybridization to incorporate fractional amounts of s character can improve orbital alignment substantially. Orbitals with about 6% s character are suggested to be involved... 

The hypothesis that electron-pair donation from the a atom will stabilize this transition state leads to the difficulty that the attacking atom must carry more bonds than conventional valence bond symbolism admits. Despite this problem, the general idea is expressed by 7 and its relationship to 6 by resonance. It is possible that transition state stabilization can be obtained in this way by rehybridization of the entire molecule. Klopman et al. suggest that the a effect arises from... 

We can imagine the transition state for alkene protonation to be a structure in which one of the alkene carbon atoms has almost completely rehybridized from sp2 to sp- and in which the remaining alkene carbon bears much of the positive charge (Figure 6.16). This transition state is stabilized by hyperconjuga-lion and inductive effects in the same way as the product carbocation. The more alkyl groups that are present, the greater the extent of stabilization and the faster the transition state forms. 

In the Diels-Alder transition state, the two alkene carbons and carbons 1 and 4 of the diene rehybridize from sp2 to sp 5 to form two new single bonds, while carbons 2 and 3 of the diene remain sp2-hybridized to form the new double bond in the cyclohexene product. We ll study this mechanism at greater length in Chapter 30 but will concentrate for the present on learning more about the characteristics and uses of the Diels-Alder reaction. 

The most common reaction of aldehydes and ketones is the nucleophilic addition reaction, in which a nucleophile, Nu , adds to the electrophilic carbon of the carbonyl group. Since the nucleophile uses an electron pair to form a new bond to carbon, two electrons from the carbon-oxygen double bond must move toward the electronegative oxygen atom to give an alkoxide anion. The carbonyl carbon rehybridizes from sp2 to sp3 during the reaction, and the alkoxide ion product therefore has tetrahedral geometry. 

As we saw in A Preview of Carbonyl Compounds, the most general reaction of aldehydes and ketones is the nucleophilic addition reaction. A nucleophile, Nu-, approaches along the C=0 bond from an angle of about 75° to the plane of the carbonyl group and adds to the electrophilic C=0 carbon atom. At the same time, rehybridization of the carbonyl carbon from sp2 to sp3 occurs, an electron pair from the C=0 bond moves toward the electronegative oxygen atom, and a tetrahedral alkoxide ion intermediate is produced (Figure 19.1). 

A nucleophilic addition reaction to an aldehyde or ketone. The nucleophile approaches the carbonyl group from an angle of approximately 75° to the plane of the sp2 orbitals, the carbonyl carbon rehybridizes from sp2 to sp3, and an alkoxide ion is formed. 

O An electron pair from the nucleophile adds to the electrophilic carbon of the carbonyl group, pushing an electron pair from the C=0 bond onto oxygen and giving an alkoxide ion intermediate. The carbonyl carbon rehybridizes from sp2 to sp3. 

One consequence of tetrahedral geometry is that an amine with three different substituents on nitrogen is chiral, as we saw in Section 9.12. Unlike chiral carbon compounds, however, chiral amines can t usually be resolved because the two enantiomeric forms rapidly interconvert by a pyramidal inversion, much as an alkyl halide inverts in an Sfg2 reaction. Pyramidal inversion occurs by a momentary rehybridization of the nitrogen atom to planar, sp2 geometry, followed by rehybridization of the planar intermediate to tetrahedral, 5p3 geometry... 

Steric factors fall into four main categories 27 (a) The release or occurrence of steric compression due to rehybridization in the transition state where the attacking radical and site of attack are each undergoing rehybridization (from sp1 - sp1 and sp1 - sp respectively for aliphatic carbons - refer Figure 1.6). As a consequence, substituents on the attacking radical are brought closer together while those at the site of attack... 

It is thus anticipated that compressive stress inhibits while tensile stress promotes chemical processes which necessitate a rehybridization of the carbon atom from the sp3 to the sp2 state, regardless of the reaction mechanism. This tendency has been verified for model ring-compounds during the hydrogen abstraction reactions by ozone and methyl radicals the abstraction rate increases from cyclopropane (c3) to cyclononane (c9), then decreases afterwards in the order anticipated from Es [79]. The following relationship was derived for this type of reactions ... 

The K conjugate molecules usually have planar geometries and no difference between the two faces above and below the molecular plane. When substitutions break the symmetry with respect to the plane, n orbitals mix a orbitals orthogonal prior to the substitution. Rehybridization occurs and the unsaturated bonds have... 

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