Bonding in methane and orbital hybridization
A vexing puzzle in the early days of valence bond theory concerned the bonding in methane (CH4). Since covalent bonding requires the overlap of half-filled orbitals of the connected atoms, carbon with an electron configuration of 1s22s22px12py1 half-filled orbitals (Figure 1.a), so how can it have bonds to four hydrogens?
Figure 1. 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 sp3-hybridized orbitals, each of which contains one electron.
In the 1930s Linus Pauling offered an ingenious solution to the puzzle. He began with a simple idea: “promoting” one of the 2s electrons to the empty 2pz orbital gives four half filled orbitals and allows for four C – H bonds (Figure 1.b). The electron configuration that results (1s22s22px12py12pz1), however, is inconsistent with the fact that all of these bonds are equivalent and directed toward the corners of a tetrahedron. The second part of Pauling’s idea was novel: mix together (hybridize) the four valence orbitals of carbon (2s, 2px, 2py, and 2pz) to give four half-filled orbitals of equal energy (Figure 1.c). The four new orbitals in Pauling’s scheme are called sp hybrid orbitals because they come from one s orbital and three p orbitals.
Figure 2 depicts some of the spatial aspects of orbital hybridization. Each sp3 hybrid orbital has two lobes of unequal size, making the electron density greater on one side of the nucleus than the other. In a bond to hydrogen, it is the larger lobe of a carbon sp orbital that overlaps with a hydrogen 1s orbital. The orbital overlaps corre-sponding to the four C–H bonds of methane are portrayed in Figure 3. Orbital overlap along the internuclear axis generates a bond with rotational symmetry-in this case a C(2sp3) H(1s) Sigma bond. A tetrahedral arrangement of four bonds is characteristic of sp -hybridized carbon.
The peculiar shape of sp3 hybrid orbitals turn out to have an important consequence. Since most of the electron density in an sp3 hybrid orbital lies to one side of a carbon atom, overlap with a half-filled 1s 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 2s and three 2p orbitals to give four equivalent sp hybrid orbitals:
The two lobes of each sp3hybrid orbital are of different size. More of the electron density is concentrated on one side of the nucleus than on the other.
Figure 2. Representation of orbital mixing in sp3 hybridization. Mixing of one s orbital with three p orbitals generates four sp3 hybrid orbitals. Each sp3 hybrid orbital has 25% s character and 75% p character. The four sp3 hybrid orbitals have their major lobes directed toward the corners of a tetrahedron, which has the carbon atom at its center.
Figure 3. The sp3 hybrid orbitals are arranged in a tetrahedral fashion around carbon. Each orbital contains one electron and can form a bond with a hydrogen atom to give a tetrahedral methane molecule. (Note: Only the major lobe of each sp3 orbital is shown. As indicated in Figure 2, each orbital contains a smaller back lobe, which has been omitted for the sake of clarity.)
Figure 4. a) A framework (tube) molecular model of methane (CH4 ). A framework model shows the bonds connecting the atoms of a molecule, but not the atoms themselves. b) A ball-and-stick (ball-and-spoke) model of methane. c) A space-filling model of methane. d) An electrostatic potential map superimposed on a ball-and-stick model of methane. The electrostatic potential map corresponds to the space-filling model, but with an added feature. The colors identify regions according to their electric charge, with red being the most negative and blue the most positive.