According to valence bond theory, a covalent bond results when: (1) an orbital on one atom overlaps an orbital on a second atom, and (2) the single electrons in each orbital combine to form an electron pair. The strength of a covalent bond depends on the extent of overlap of the orbitals involved. Maximum overlap is possible when the orbitals overlap on a direct line between the two nuclei.

A σ bond (single bond in a Lewis structure) is a covalent bond in which the electron density is concentrated in the region along the internuclear axis. A π bond is a covalent bond that results from the side-by-side overlap of two p orbitals. In a π bond, the regions of orbital overlap lie on opposite sides of the internuclear axis, while there is a node (a plane with no probability of finding an electron) along the axis. All single bonds are σ bonds, while multiple bonds consist of both σ and π bonds.

When atoms are bound together in a molecule, the wave functions for atomic orbitals can combine to produce new mathematical descriptions that have different shapes. This process is called hybridization and is mathematically accomplished by the linear combination of atomic orbitals. The resulting new orbitals are called hybrid orbitals.

The shapes and orientations of hybrid orbitals, which are formed only in covalently bonded atoms, are different from those of atomic orbitals in isolated atoms. The number of hybrid orbitals is equal to the number of atomic orbitals that were combined to generate them. All orbitals in a set of hybrid orbitals are equivalent in shape and energy, and their orientation is predicted by the VSEPR theory. Hybrid orbitals overlap to form σ bonds, while unhybridized orbitals overlap to form π bonds.

For instance, in the excited state of carbon, the one 2s and three 2p orbitals undergo hybridization yielding four degenerate hybrid sp³ orbitals oriented tetrahedrally. In a methane molecule, the 1s orbital of each of the four hydrogen atoms overlaps with one of the four sp³ orbitals of the carbon atom to form a sigma (σ) bond.

Similarly, the mixing of one 2s and two of the 2p orbitals of carbon generates three equivalent sp² hybrid orbitals with trigonal planar geometry, while the hybridization of one 2s and one of the 2p orbitals creates two sp orbitals oriented at 180° to each other.

For atoms that have d orbitals in their valence subshells, hybridization of five valence shell atomic orbitals (one s, three p, and one of the d orbitals) gives five sp³d hybrid orbitals with trigonal bipyramidal geometry. An octahedral arrangement of six hybrid orbitals is obtained by the mixing of six valence shell atomic orbitals (one s, three p, and two of the d orbitals), which yields six sp³d² hybrid orbitals.

This text has been adapted fromOpenstax, Chemistry 2e, Section 8.1 Valence Bond TheoryandSection 8.2 Hybrid Atomic Orbitals.