Hydrogen Is orbital

Section 2 6 Bonding m methane is most often described by an orbital hybridization model which is a modified form of valence bond theory Four equiva lent sp hybrid orbitals of carbon are generated by mixing the 2s 2p 2py and 2p orbitals Overlap of each half filled sp hybrid orbital with a half filled hydrogen Is orbital gives a ct bond... 

Fig. 1.29. Interactions between two hydrogen Is orbitals and carbon 2p orbitals stabilize the eclipsed confonnation of propene.

A similar analysis of the 1,5-sigmatropic shift of hydrogen leads to the opposite conclusion. The relevant frontier orbitals in this case are the hydrogen Is orbital and ij/j of the pentadienyl radical. The suprafacial mode is allowed whereas the antarafacial mode is forbidden. The suprafacial shift corresponds to a favorable six-membered ring. 

FIGURE 2.9 Each half-filled sp orbital overlaps with a half-filled hydrogen Is orbital along a line between them giving a tetrahedral arrangement of four a bonds. Only the major lobe of each sp orbital is shown. Each orbital contains a smaller back lobe, which has been omitted for clarity. 

Why stop with a single hydrogenic Is orbital on either centre A little thought shows that the 2s and 2po- orbitals might also make a contribution to the bonding, and so we could write... 

In this table, eis is the energy of a hydrogenic Is orbital, fi2s the energy of a hydrogenic 2s orbital. Before we worry about comparison with experiment, there are a couple of loose ends that have to be tidied up. 

At this stage, it looks as though electron promotion should result in two different types of bonds in methane, one bond from the overlap of a hydrogen ls-orbital and a carbon 2s-orbital, and three more bonds from the overlap of hydrogen Is-orbitals with each of the three carbon 2/ -orbitals. The overlap with the 2p-orbitals should result in three cr-bonds at 90° to one another. However, this arrangement is inconsistent with the known tetrahedral structure of methane with four equivalent bonds. 

Figure 3.14 Hybrid orbitals h, and Ii2 formed from the s and p orbitals of the oxygen atom to correspond to the bond angle of 104.5°. These orbitals have a greater overlap with the hydrogen Is orbitals than the atomic 2p orbitals and so form stronger bonds.

Consideration of the feasibility of these shifts as concerted processes, i.e. via cyclic transition states, requires as usual a consideration of the symmetry of the orbitals involved. A model related to the transition state can be constructed by the device of assuming that the C—H a bond that is migrating can be broken down into a hydrogen Is orbital and a carbon 2p orbital. For the case where x = 1 in (36), the T.S. can then be considered as being made up from a pentadienyl radical (38), with a hydrogen atom (one electron in a Is orbital) migrating between the terminal carbon atoms of its Site system (i.e. a 6e system overall is involved) ... 

In each of the B-H-B bridges, only two electrons bond the three atoms together by having the orbitals on the boron atoms simultaneously overlap the hydrogen Is orbital. A bond of this type is known as a two-electron three-center bond. In terms of molecular orbitals, the bonding can be described as the combination of two boron orbitals and one hydrogen orbital to produce three molecular orbitals, of which only the one of lowest energy is populated ... 

Carbon atoms (1) and (4) use sp3 hybrid orbitals to form four sigma bonds, three by overlap with the hydrogen Is orbitals and one by overlap with an sp2 orbital from the central carbon (2). The two carbon atoms involved in the double bond undergo sp2 hybridization. They form C-H bonds by overlapping with Is orbitals of the H atoms. The C=C double bond is formed similarly to that described in (a). 

The electronic states introduced by hydrogen in the band structure of Si are quite different depending upon the location of the impurity in the lattice. For H at the bond center we can, to a first approximation, treat the problem as involving only three states (Schaad, 1974 Fisch and Licciardello, 1978) the semiconductor bonding (b) and antibonding (a) states (which, in turn, are symmetric and antisymmetric combinations of hydrid orbitals on the two atoms) and the hydrogen Is orbital. The cor-... 

The hydrogenic Is orbital is therefore unique in presenting no strong angular or radial barriers toward approaching atoms.75... 

The hydrogen Is orbital encloses a positively charged nucleus that repels other nuclei by a Coulombic R 1 potential. However, such a Coulombic barrier between nuclei is much weaker than the steric repulsion between electronic cores, which varies exponentially with distance. 

The shape of the CH4 molecule is tetrahedral. A tetrahedral orientation of equal bonds (which are formed from the overlap of the identical sp3 hybrid orbitals and the hydrogen Is orbitals) gives a bond angle of 109.5° (Figure 6). 

Each external (i.e., terminal) B-H bond is regarded as a typical two-center two-electron single bond requiring the hydrogen Is orbital, one hybridized boron orbital, and one electron each from the H and the B atoms. Because of the small electronegativity difference between hydrogen and boron, these bonds are assumed to be non-polar. In the polynuclear boron hydrides every boron atom may form zero or one but never more than two such external B-H bonds. 

We have already explained. In terms of hybridisation, how a carbon atom can form four sp hybrid orbitals (see p. 47). We can apply this concept to explain the bonding in alkanes. Ethane is taken as an example of a typical alkane. The four sp hybrid orbitals on each carbon atom will overlap end-on with four other orbitals three hydrogen Is orbitals and one sp hybrid orbital on the other carbon atom. Four cr bonds will be formed and they will adopt a tetrahedral arrangement. This is illustrated for ethane in the diagram. 

Problem 8-15. A normalized hydrogenic Is orbital for a one-electron atom or ion of nuclear charge Z has the form ... 

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