Q.Distinguish between a sigma and a pi bond.

The key idea is that sigma ($\sigma$) and pi ($\pi$) bonds differ in their orbital overlap geometry and electron density distribution.

Step 1: Sigma bond — formed by end-to-end (head-on) overlap of orbitals along the internuclear axis. This can involve $s$-$s$, $s$-$p$, or $p$-$p$ orbitals. The electron density is concentrated between the two nuclei.

Step 2: Pi bond — formed by sideways (lateral) overlap of parallel $p$ orbitals above and below the internuclear axis. The electron density lies in two lobes off the axis, making it weaker than a sigma bond. …

The Concept: Bonding Through Overlap

When two atoms come close enough to form a bond, their atomic orbitals overlap. The type of overlap determines whether the bond is sigma or pi. Think of it like two hands shaking: a sigma bond is a direct, head-on handshake along a straight line; a pi bond is like two hands clasping sideways, with palms facing each other but not directly aligned.

The internuclear axis is the imaginary straight line connecting the two nuclei. This axis is the reference for all bond classification.

Step-by-Step Breakdown

1. Sigma ($\sigma$) bonds: End-to-end overlap

   • The overlap occurs directly along the internuclear axis.
   • Orbitals involved: $s$–$s$, $s$–$p$, $p$–$p$ (head-on), or hybrid orbitals ($sp$, $sp^2$, $sp^3$).
   • The electron density is concentrated between the two nuclei, along the axis.
   • Result: A sigma bond is the first bond formed between any two atoms. It is strong because the overlap is large and direct.
   • Example: In $\mathrm{H_2}$, the $1s$–$1s$ overlap is sigma. In $\mathrm{Cl_2}$, the $3p$–$3p$ head-on overlap is sigma.

2. Pi ($\pi$) bonds: Sideways overlap

   • The overlap occurs above and below the internuclear axis, not along it.
   • Orbitals involved: unhybridized $p$ orbitals (or $d$ orbitals in some cases) that are parallel to each other.
   • The electron density is concentrated in two lobes — one above and one below the plane of the nuclei.
   • Result: A pi bond is weaker than a sigma bond because the overlap is less direct and the electrons are farther from the nuclei. It can only form after a sigma bond already exists.
   • Example: In $\mathrm{O_2}$, the double bond consists of one sigma bond (from $p$–$p$ head-on) and one pi bond (from sideways overlap of the remaining $p$ orbitals).

3. Key structural difference

   • Sigma bonds allow free rotation around the bond axis because the overlap is cylindrical.
   • Pi bonds prevent rotation — rotating would break the sideways overlap, so double and triple bonds are rigid.