Orbital overlap

In chemical bonds, an orbital overlap is the concentration of orbitals on adjacent atoms in the same regions of space. Orbital overlap can lead to bond formation. Linus Pauling explained the importance of orbital overlap in the molecular bond angles observed through experimentation; it is the basis for orbital hybridization. As s orbitals are spherical (and have no directionality) and p orbitals are oriented 90° to each other, a theory was needed to explain why molecules such as methane (CH₄) had observed bond angles of 109.5°.^[1] Pauling proposed that s and p orbitals on the carbon atom can combine to form hybrids (sp³ in the case of methane) which are directed toward the hydrogen atoms. The carbon hybrid orbitals have greater overlap with the hydrogen orbitals, and can therefore form stronger C–H bonds.^[2]

A quantitative measure of the overlap of two atomic orbitals Ψ_A and Ψ_B on atoms A and B is their overlap integral, defined as

${\displaystyle \mathbf {S} _{\mathrm {AB} }=\int \Psi _{\mathrm {A} }^{*}\Psi _{\mathrm {B} }\,dV,}$

where the integration extends over all space. The star on the first orbital wavefunction indicates the function's complex conjugate, which in general may be complex-valued.