Valence Bond Theory and Hybridized Orbitals

A sigma bond forms through head-to-head overlap of atomic orbitals along the internuclear axis. The electron density concentrates in the region between the two nuclei, creating a strong covalent bond. All single bonds are sigma bonds, making them the most common type of covalent bond in molecules.

Hybridization occurs when atomic orbitals recombine to form new hybrid orbitals with different shapes. These hybrid orbitals have directional lobes that enable more effective overlap with other atoms' orbitals. The orientation of hybrid orbitals is predicted by valence shell electron pair repulsion theory, explaining why molecules adopt specific three-dimensional shapes.

sp3 hybridization combines one s and three p orbitals, creating four equivalent hybrid orbitals with tetrahedral geometry. sp2 hybridization mixes one s and two p orbitals, yielding three trigonal planar orbitals. sp hybridization combines one s and one p orbital, producing two linear orbitals oriented at 180 degrees. Each type determines the molecular shape and bonding arrangement.

A pi bond results from side-on overlap of p orbitals and exists on opposite sides of the internuclear axis. Pi bonds cannot rotate around the internuclear axis due to their geometry. A sigma bond must first establish the direct connection between atoms; pi bonds then form alongside it in double and triple bonds.

The number of hybrid orbitals generated always equals the number of atomic orbitals that combined to form them. For example, mixing one s and three p orbitals produces four sp3 hybrid orbitals. This conservation principle ensures that no orbitals are lost during hybridization, maintaining the total electron capacity.

Hybrid orbitals form sigma bonds through overlap with orbitals from other atoms, while unhybridized p orbitals form pi bonds. The directional lobes of hybrid orbitals concentrate electron probability density, enabling stronger and more effective overlap. In methane, carbon's four sp3 orbitals each overlap with hydrogen's 1s orbital to create four sigma bonds.

Atoms with d orbitals in their valence subshells can undergo expanded hybridization. Mixing one s, three p, and one d orbital creates five sp3d hybrid orbitals with trigonal bipyramidal geometry. Combining one s, three p, and two d orbitals produces six sp3d2 hybrid orbitals with octahedral arrangement, enabling complex bonding in transition metal compounds.