Difference between revisions of "Orbital overlap"
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'''Orbital overlap''' is a concept in the [[Molecular orbital theory|molecular orbital]] description of [[chemical bond]]ing. In the simplest terms, a [[covalent bond]] can only form between two atoms if there is significant overlap between [[atomic orbital]]s on the atoms. | '''Orbital overlap''' is a concept in the [[Molecular orbital theory|molecular orbital]] description of [[chemical bond]]ing. In the simplest terms, a [[covalent bond]] can only form between two atoms if there is significant overlap between [[atomic orbital]]s on the atoms. | ||
| − | Orbital overlap can be expressed in qualitative terms through empirical rules, or quantitatively through [[overlap integral]]s ''S<sub>ab</sub> | + | Orbital overlap can be expressed in qualitative terms through empirical rules, or quantitatively through [[overlap integral]]s ''S''<sub>ab</sub> (where a and b represent atomic orbitals). |
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| + | ==Overlap integral== | ||
| + | {{main|Overlap integral}} | ||
| + | The overlap integral ''S''<sub>ab</sub> is the name given to an integral of the form | ||
| + | :<math>S_{\rm ab} = \int \varphi_{\rm a}^\ast \varphi_{\rm b} {\rm d}\tau</math> | ||
| + | where φ<sub>a</sub> and φ<sub>b</sub> are the [[wavefunction]]s corresponding to the atomic orbitals a and b and dτ indicates that the integral is to be taken over all space. In [[Dirac notation]], ''S''<sub>ab</sub> = <φ<sub>a</sub>|φ<sub>b</sub>>, usually written as simply <a|b>. | ||
| + | |||
| + | ===Graphical representation=== | ||
==Notes and references== | ==Notes and references== | ||
Revision as of 20:15, 11 September 2010
Orbital overlap is a concept in the molecular orbital description of chemical bonding. In the simplest terms, a covalent bond can only form between two atoms if there is significant overlap between atomic orbitals on the atoms.
Orbital overlap can be expressed in qualitative terms through empirical rules, or quantitatively through overlap integrals Sab (where a and b represent atomic orbitals).
Contents
Overlap integral
The overlap integral Sab is the name given to an integral of the form
- <math>S_{\rm ab} = \int \varphi_{\rm a}^\ast \varphi_{\rm b} {\rm d}\tau</math>
where φa and φb are the wavefunctions corresponding to the atomic orbitals a and b and dτ indicates that the integral is to be taken over all space. In Dirac notation, Sab = <φa|φb>, usually written as simply <a|b>.
Graphical representation
Notes and references
Notes
References
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