Sigma Bond Formation:
In a double bond, the sigma bond is formed by the head-on overlap of two \(sp^2\) hybrid orbitals from each carbon atom. The \(sp^2\) hybrid orbitals result from the mixing of one \(s\) orbital and two \(p\) orbitals, leading to a trigonal planar arrangement of the atoms around the double bond.
Pi Bond Formation:
The pi bond in a double bond is formed by the sideways overlap of two \(p\) orbitals from each carbon atom. These \(p\) orbitals are perpendicular to the plane of the sigma bond and to each other. The electron density of the pi bond is concentrated above and below the plane of the sigma bond, creating a cylindrical electron cloud.
The rigidity of the double bond arises from the nature of the pi bond. The \(p\) orbitals involved in the pi bond have a dumbbell shape with electron density concentrated in two lobes on opposite sides of the nucleus. This shape restricts rotation around the double bond because any attempt to rotate would disrupt the overlap of the \(p\) orbitals and weaken the pi bond. Breaking the pi bond would require significant energy input, making rotation around the double bond highly unfavourable.
In contrast, single bonds formed by the overlap of \(sp^3\) hybrid orbitals allow for free rotation because the electron density is distributed more symmetrically around the bond axis. The \(sp^3\) orbitals can rotate without significantly disrupting the bond, allowing for the different conformations of molecules with single bonds.
Therefore, the presence of the pi bond and the restricted rotation around the double bond play crucial roles in determining the molecular geometry, stability, and properties of compounds containing double bonds.
