Methane hybrid orbitals

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... 

We are now ready to account for the bonding in methane. In the promoted, hybridized atom each of the electrons in the four sp3 hybrid orbitals can pair with an electron in a hydrogen ls-orbital. Their overlapping orbitals form four o-bonds that point toward the corners of a tetrahedron (Fig. 3.14). The valence-bond description is now consistent with experimental data on molecular geometry. 

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. 

Although the hybrid orbitals discussed in this section satisfactorily account for most of the physical and chemical properties of the molecules involved, it is necessary to point out that the sp orbitals, for example, stem from only one possible approximate solution of the Schrddinger equation. The i and the three p atomic orbitals can also be combined in many other equally valid ways. As we shall see on page 12, the four C—H bonds of methane do not always behave as if they are equivalent. 

Any hybrid orbital is named from the atomic valence orbitals from which It Is constmcted. To match the geometry of methane, we need four orbitals that point at the comers of a tetrahedron. We construct this set from one s orbital and three p orbitals, so the hybrids are called s p hybrid orbitais. Figure 10-8a shows the detailed shape of an s p hybrid orbital. For the sake of convenience and to keep our figures as uncluttered as possible, we use the stylized view of hybrid orbitals shown in Figure 10-8Z). In this representation, we omit the small backside lobe, and we slim down the orbital in order to show several orbitals around an atom. Figure 10-8c shows a stylized view of an s p hybridized atom. This part of the figure shows that all four s p hybrids have the same shape, but each points to a different comer of a regular tetrahedron. 

Methane forms from orbital overlap between the hydrogen 1 S orbitals and the s hybrid orbitals of the carbon atom. 

We generate hybrid orbitals on inner atoms whose bond angles are not readily reproduced using direct orbital overlap with standard atomic orbitals. Consequently, each of the electron group geometries described in Chapter 9 is associated with its own specific set of hybrid orbitals. Each type of hybrid orbital scheme shares the characteristics described in our discussion of methane ... 

The hybridized orbital approach is a simplified way of predicting the geometry of a molecule by mixing the valence orbitals of its atoms. For example, methane (CH ) is composed of a carbon atom with an electron configuration of Is 2s 2p. The hydrogen atom has an electron configuration of Is. The geometry of the methane... 

It will thus be apparent why the use of hybrid orbitals, e.g. sp3 hybrid orbitals in the combination of one carbon and four hydrogen atoms to form methane, results in the formation of stronger bonds. 

Figure 1.12 The hypothetical formation of methane from an sp -hybridized carbon atom. In orbital hybridization we combine orbitals, not electrons. The electrons can then be placed in the hybrid orbitals as necessary for bond formation, but always in accordance with the Pauli principle of no more than two electrons (with opposite spin) in each orbital. In this illustration we have placed one electron...

For example, in the methane molecule (CH4), the four sp3 hybrid orbitals of the carbon atom overlap end to end with one Is orbital from each hydrogen atom to form four C — H bonds. Those bonds are all o bonds. 

Fig. 4.4 The sp hybridized orbital on single carbon atoms terminated by four hydrogen atoms forms molecule of methane - CH,...

The single 2s orbital combines with the three 2p orbitals to create four identical sp hybrid orbitals. The fact that each sp orbital is identical is important because VSEPR theory can now explain the symmetrical shape of methane the tetrahedron. 

Although this phenomenon represents an exception to the rules, it s somewhat less annoying than other exceptions because hybridization allows for the nicely symmetrical orbital geometries of actual atoms within actual molecules. VSEPR theory presently clears its throat to point out that the negative charge of the electrons within the hybridized orbitals causes those equivalent orbitals to spread as far apart as possible from one another. As a result, the geometry of sp -hybridized methane (CH ), for example, is beautifully tetrahedral. 

We will explain how to do this by taking the specific example of methane. Methane has a central carbon atom which is a-bonded to four hydrogen atoms with each a-bond pointing to one of the comers of a tetrahedron. We therefore require four hybrid orbitals on the carbon atom which similarly point to the comers of a tetrahedron. Since the four bonds are indistinguishable, the four hybrids must be equivalent, that is to say they must be identical in all respects except for their orientation. For the reasons given in 11-2, they will be taken to be linear combinations of the atomic orbitals of carbon, which are... 

Fig. 11-3.1. A set of vectors v1( va, V , and v4 representing the four o hybrid orbitals used by carbon to bond the four hydrogens in methane.

First then, for methane, we must obtain I 71. To do this let us associate with each carbon hybrid orbital a vector pointing in the appropriate direction and let us label these vectors vv vs, v , v4 (see Fig. 11-3.1). All of the symmetry properties of the four hybrid orbitals will be identical to those of the four vectors. The reducible representation using these vectors (or hybrids) as a basis can be obtained from 4... 

For methane we have seen that there are four hybrid orbitals Yu Yt Yt an< Yi (see Fig 11-5-2) each composed of an s-orbital belonging to P-1 and three p-orbitals p, p , and p belonging to rT for the choice of ar, y, and z axes see Fig. 11-5.2. Using the relevant projection operators, we obtain the following combinations ... 

Mathematically, the formation of sp3 or tetrahedral orbitals for methane is more complicated but not basically different. The results are four equivalent hybrid orbitals, each containing one part s to three parts p in each wave function, directed to the corners of a tetrahedron. As in the case of sp hybrids, the hybridization of s and p has... 

The first three geometries involve the tetrahedral, trigonal, and digonal hybrids discussed above and the fourth involves the use of pure s and p orbitals as discussed on page 149. The last structure contains three equivalent bonds at mutual angles of 60 and a fourth bond at an angle of approximately 145° to the others. U is impossible to construct s-p hybrid orbitals with angles less than 90°, and so structure V is ruled out. In this sense it may be sard that hybridization does not allow" structure V, but it may not be said that it "chooses ore of the others. Carbon hybridizes sp, sp2, and spJ in various compounds, und the choice of sp3 in methane is a result of the foot that the tetrahedral structure is the most stable possible. 

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