Hybrid Orbitals

sp³ hybridization

A problem arises when we apply the valence bond theory method of orbital overlap to even simple molecules like methane (CH₄) (Figure 1 “Methane”). Carbon (1s² 2s² 2p²) only has two unpaired valence electrons that are available to be shared through orbital overlap, yet CH₄ has four C-H σ bonds!

Figure 1. Methane.

Figure 9.9. Nobel laureate Linus Pauling.

In 1931, Linus Pauling (Figure 9.9) proposed a mathematical mixing of atomic orbitals known as hybridization. The 2s and three 2p orbitals are averaged mathematically through hybridization to produce four degenerate sp³ hybrid orbitals (Figure 1 “Hybridization of carbon to generate sp³ orbitals”). Note that in hybridization, the number of atomic orbitals hybridized is equal to the number of hybrid orbitals generated.

Figure 1. Hybridization of carbon to generate sp³ orbitals.

The sp³ orbitals, being a combination of a spherical s orbital and propeller- (or peanut-) shaped p orbital, give an unsymmetrical propeller shape where one lobe of the orbital is larger (fatter) than the other (Figure 2 “An sp³ hybridized atomic orbital”). This larger lobe is typically used for orbital overlap in covalent bonding.

Figure 2. An sp³ hybridized atomic orbital.

According to VSEPR theory, the four degenerate orbitals will arrange as far apart from each other as possible, giving a tetrahedral geometry with each orbital 109.5^o apart (Figure 3 “A carbon atom’s four tetrahedral sp³ hybridized orbitals”).

Figure 3. A carbon atom’s four tetrahedral sp³ hybridized orbitals