'''Orbital overlap''' was an idea first introduced by [[Linus Pauling]] to explain the molecular [[bond anglesangle]]s observed through experimentation and is the basis for the concept of [[orbital hybridisation]]. ''s'' orbitals are spherical and have no directionality while ''p'' orbitals are oriented 90° to one another. A theory was needed therefore to explain why molecules such as [[methane]] (CH<sub>4</sub>) had observed bond angles of 109.5°.<ref>Anslyn, Eric V./Dougherty, Dennis A. (2006). ''Modern Physical Organic Chemistry''. University Science Books.</ref> Pauling's theory was that bonds are created by the overlap of adjacent atomic orbitals of two atoms. The greater the overlap of the two orbitals, the stronger the bond. The resulting bond is known as an [[sp hybrid]] and it exhibits strength greater than that of an s or p orbital.<ref>Pauling, Linus. (1960). ''The Nature Of The Chemical Bond''. Cornell University Press.</ref>
A quantitative measure of the overlap of two atomic orbitals on atoms A and B is their '''overlap integral''', defined as <math>\mathbf{S}_\mathrm{AB}=\int \Psi_APsi_\mathrm{A}^* \Psi_BPsi_\mathrm{B} \, dV,</math> where the integration extends over all space. The star on the first orbital wavefunction indicates the [[complex conjugate]] of the function, which in general may be [[complex-valued]].
, where the integration extends over all space. The star on the first orbital wavefunction indicates the [[complex conjugate]] of the function, which in general may be [[complex-valued]].
