Hybridization of Atomic Orbitals II

The trigonal bipyramidal, octahedral, and other molecular shapes can be explained by assuming the participation of 3d orbitals in the process of hybridization.

The phosphorus pentachloride molecule has a trigonal bipyramidal shape, and it contains 5 valence electrons. Phosphorus uses the 3s orbital, the three 3p orbitals, and one of the 3d orbitals to form five sp³d hybrid orbitals that are involved in the phosphorus–chlorine bonds.

Sulfur hexafluoride has an octahedral structure and it contains 6 valence electrons. The 3s orbital, the three 3p orbitals, and two of the 3d orbitals on sulfur form six equivalent sp³d² hybrid orbitals. These six sp³d² orbitals form an octahedral structure around sulfur and participate in the formation of sulfur–fluorine bonds.

The concept of hybridization also provides an explanation for the formation of multiple bonds. The side-on overlap of two p orbitals gives rise to a π bond. 

However, a π-bond can only be formed in double and triple bonds when a σ bond already exists between two atoms. Because the π bond exists on opposite sides of the internuclear axis, π bonds are unable to rotate around this axis.

In the ethene molecule, both carbons exhibit sp² hybridization. The mixing of one s orbital and two p orbitals of a carbon atom produce three identical sp² hybrid orbitals, and one p orbital remains unhybridized.

The carbon–carbon σ bond is formed by the overlap of two sp² hybrid orbitals, one on each carbon atom.

The two carbon–hydrogen σ bonds on each carbon are formed by the overlap of two sp² hybrid orbitals with the 1s orbitals on the hydrogen atom. Thus, five σ bonds are formed in the ethene molecule. 

The unhybridized 2p orbitals on the carbons overlap sideways with each other to produce a π bond. All six atoms lie in the same plane, and therefore 2p orbitals can overlap effectively.

Thus, the double bond in ethene consists of one σ and one π bond.

The triple bonds and the linear geometry of ethyne can be explained using sp hybridization. The 2s and 2p orbitals of both carbon atoms undergo hybridization to produce two sp orbitals each, and two p orbitals remain unhybridized. 

One of the sp-orbitals forms a σ bond with the other carbon atom, whereas the remaining sp orbital forms a σ bond with a hydrogen atom. The two unhybridized 2p orbitals are perpendicular and intersect at the principal axis of the sp hybrid orbitals. 

These 2p orbitals overlap sideways with the 2p orbitals of the other carbon atom resulting in the formation of two π bonds. Therefore, the triple bond in ethyne consists of one σ bond and two π bonds between the two carbon atoms.