Bonding in Methane and Orbital Hybridization

For a molecule as simple as H2, it is hard to see much difference between the valence bond and molecular orbital methods. The most important differences appear in molecules with more than two atoms—a very common situation indeed. In those cases, the valence bond method continues to view a molecule as a collection of bonds between connected atoms. The molecular orbital method, however, leads to a picture in which the same electron can be associated with many, or even all, of the atoms in a molecule. 

In the remaining sections of this chapter we will use a modification of valence bond theory to describe CH and CC bonds in some fundamental types of organic compounds. 

FIGURE 1.20 (a) Electron configuration of carbon in its most stable state, (b) An electron is promoted from the 2s orbital to the vacant 2p orbital, (c) The 2s orbital and the three 2p orbitals are combined to give a set of four equal-energy sp -hybridized orbitals, each of which contains one electron. 

The peculiar shape of sp hybrid orbitals turn out to have an important consequence. Since most of the electron density in an sp hybrid orbital lies to one side of a carbon atom, overlap with a half-filled 1 orbital of hydrogen, for example, on that side produces a stronger bond than would result otherwise. If the electron probabilities were equal on both sides of the nucleus, as it would be in a p orbital, half of the time the electron would be remote from the region between the bonded atoms, and the bond would be weaker. Thus, not only does Pauling s orbital hybridization proposal account for carbon forming four bonds rather than two, these bonds are also stronger than they would be otherwise. 

Combine one 2.5 and three 2p orbitals to give four equivalent sp hybrid orbitals  

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Figure 1.5 Directional characteristics of sp hybrid orbitals of carbon and the formation of C—H bonds in methane (CH4). The hybrid orbitals point toward the corners of a regular tetrahedron. Hydrogen 1 s orbitals are illustrated in position to form bonds by overlap with the major lobes of the hybrid orbitals.

Section 2.6 Bonding in methane is most often described by an orbital hybridization model, which is a modified for m of valence bond theory. Four equivalent 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 I5 orbital gives a a bond. 

FIGURE 3.14 Each C H bond in methane is formed by the pairing of an electron in a hydrogen U-orbital and an electron in one of the four sp hybrid orbitals of carbon. Therefore, valence-bond theory predicts four equivalent cr-bonds in a tetrahedral arrangement, which is consistent with experimental results. 

There is also a third type of reactive species that we shall discuss in detail in Chapter 9, namely radicals. Briefly, radicals are uncharged entities that carry an unpaired electron. A methyl radical CH3 results from the fission of a C-H bond in methane so that each atom retains one of the electrons. In the methyl radical, carbon is sp hybridized and forms three CT C-H bonds, whilst a single unpaired electron is held in a 2/ orbital oriented at right angles to the plane containing the ct bonds. The unpaired electron is always shown as a dot. The simplest of the radical species is the other fission product, a hydrogen atom. 

More complicated hybrid orbitals are used in many other problems. For example, the bonding in methane is best described by combinations of one s orbital and three p orbitals, which make a set of four equivalent orbitals which point to the comers of a tetrahedron ... 

The interaction of the Is orbital of a hydrogen atom with an sp3 hybrid on carbon leads to a crCH-bonding orbital or a (j CH-antibonding orbital (Fig. 1.17). Four of the bonding orbitals, with two electrons in each, point towards the corners of a regular tetrahedron, and give rise to the familiar picture for the bonds in methane shown in Fig. 1.18a. 

What then of the p orbitals that did not participate in the formation of sp2 hybrid orbitals These remain as p orbitals, one at each carbon, and each p orbital contains one electron. Together they form a bond, termed a n bond, between the carbon atoms. The mode of overlap is sideways on . This contrasts with the end-on overlap that results in formation of a bonds, and which in the present context involves C-H bonds in methane (Figure 1.2) and ethene, and the other bond between carbon and carbon in ethene. 

The correct answer is (D). According to electron configuration of carbon, the carbon atom shouldhave two electrons in the 2s orbital and one in each of the two 2p orbitals. The four carbon-hydrogen bonds in methane should be different because of the different orbitals, yet experimental evidence shows them to be the same. The solution is that one of the 2s electrons is raised to ap orbital, and the result is the fonnation of four identical hybridized sp orbitals. 

To explain bonding in methane, VB theory uses hypothetical hybrid orbitals, which are atomic orbitals obtained when two or more nonequivalent orbitals of the same atom combine in preparation for covalent bond formation. Hybridization is the term applied to the mixing of atomic orbitals in an atom (usually a central atom) to generate a set of hybrid orbitals. We can generate four equivalent hybrid orbitals for carbon by mixing the 2s orbital and the three 2p orbitals ... 

We have managed to account for the observation that carbon forms four covalent bonds, but what accounts for the fact that the four C—H bonds in methane are identical Each has a bond length of 1.10 A, and breaking any one of the bonds requires the same amount of energy (105 kcal/mol, or 439 kJ/mol). If carbon used an s orbital and three p orbitals to form these four bonds, the bond formed with the s orbital would be different from the three bonds formed withp orbitals. How can carbon form four identical bonds, using one 5 and three p orbitals The answer is that carbon uses hybrid orbitals. 

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