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{{Short description|Concentration of chemical orbitals on adjacent atoms}}
In [[chemical bond]]s, an '''
A quantitative measure of the overlap of two atomic orbitals Ψ<sub>A</sub> and Ψ<sub>B</sub> on atoms A and B is their '''overlap integral''', defined as
▲'''Orbital overlap''' was an idea first introduced by [[Linus Pauling]] to explain the molecular [[bond angle]]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>
where the integration extends over all space. The star on the first orbital wavefunction indicates the function's [[complex conjugate]] ==Overlap matrix==
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:<math>\mathbf{S}_{jk}=\left \langle b_j|b_k \right \rangle=\int \Psi_j^* \Psi_k \, d\tau</math>
where
:<math>\left |b_j \right \rangle</math> is the ''j''-th basis [[Bra-ket notation|ket]] ([[vector (geometric)|vector]]), and
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:<math>\Psi_j</math> is the ''j''-th [[wavefunction]], defined as :<math>\Psi_j(x)=\left \langle x | b_j \right \rangle</math>.
In particular, if the set is normalized (though not necessarily orthogonal) then the diagonal elements will be identically 1 and the magnitude of the [[off-diagonal
==See also==
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*[[Roothaan equations]]
*[[Hartree–Fock method]]
*[[Pi bond]]
*[[Sigma bond]]
==References==
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[[Category:Chemical bonding]]
[[Category:Molecular geometry]]
[[ar:مصفوفة التداخل]]
[[it:Matrice di sovrapposizione]]
[[sv:Överlappsmatris]]
[[zh:重叠矩阵]]
{{quantum-chemistry-stub}}
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