Hybridization and Molecular Geometry

Carbon's ground-state electron configuration is $1s^2 2s^2 2p^2$. If you look at the valence shell, there are only two unpaired electrons in the $p$ orbitals. This suggests carbon should only form two bonds. However, in nature, carbon is tetravalent, forming four stable bonds (like in $CH_4$). To solve this, carbon undergoes excitation, promoting one $2s$ electron to the empty $2p_z$ orbital. But since $s$ and $p$ orbitals have different shapes and energies, carbon must 'blend' them. This process is called hybridization, creating new, identical hybrid orbitals that allow for symmetrical bonding.

When carbon forms four single bonds, it mixes its one $2s$ orbital and all three $2p$ orbitals. This results in four identical **$sp^3$ hybrid orbitals. According to VSEPR theory, these orbitals push away from each other as far as possible, pointing toward the corners of a tetrahedron**. This geometry creates a bond angle of exactly $109.5^\circ$. These orbitals form **$\sigma$ (sigma) bonds**, which are characterized by head-on overlap along the axis between the two nuclei.

In double bonds, carbon only needs three hybrid 'landing pads.' It mixes one $s$ and two $p$ orbitals to form three **$sp^2$ hybrid orbitals**, leaving one $p$ orbital unhybridized. This creates a trigonal planar shape ($120^\circ$). In triple bonds, carbon mixes one $s$ and one $p$ orbital to form two **$sp$ hybrid orbitals**, leaving two $p$ orbitals unhybridized. This results in a linear geometry ($180^\circ$). The unhybridized $p$ orbitals are the key to forming **$\pi$ (pi) bonds**, which overlap 'side-by-side' above and below the $\sigma$ bond.

While a double bond is stronger than a single bond, a **$\pi$ bond is actually weaker than a $\sigma$ bond** because the side-on overlap is less efficient than head-on overlap. However, $\pi$ bonds provide a critical feature: they restrict rotation. While single bonds can spin freely, double and triple bonds are rigid. This rigidity is what allows for isomers (different shapes of the same molecule) to exist in organic chemistry, which is vital for the function of biological molecules like fats and proteins.