Title: molecular orientation
Long Title: IUPAC Gold Book - molecular orientation
DOI: 10.1351/goldbook.MT07422
Status: current

Definition
Absorption probability (referred to electric dipolar absorption) for a molecular transition with its electric transition moment at an angle \(\theta\) with the electric vector of the light is proportional to \(\cos^{2}\theta\). For the whole sample it is proportional to the orientation factor \(K_{\theta} = \:< \cos^{2}\theta >\), averaged over all sample molecules. This average is \(1\) for a sample with all transition moments perfectly aligned along the electric vector of the light, \(1/3\) for an isotropic sample and \(0\) for a sample where all transition moments are perpendicular to the electric vector.

Notes
1) The directional cosines provide, especially for uniaxial samples, a simple description of exactly those orientation properties of the sample that are relevant for light absorption. With the principal coordinate system (\(x\), \(y\), \(z\)), forming angles \(\theta = \alpha,\:\beta,\:\gamma\) with the light electric vector in the \(z\) direction, all orientation effects induced by light absorption are contained in \(K_{\theta\theta} = K_{\theta}\). Since the sum of \(K_{\theta}\) for three perpendicular molecular axes is equal to \(1\), only two independent parameters are required to describe the orientation effects on light absorption.
2) A related, commonly used description is based on diagonalized Saupe matrices: \[S_{\theta} = (3K_{\theta} -1)/2\] The principal (molecular) coordinate system (\(x\), \(y\), \(z\)) forming angles \(\theta = \alpha,\:\beta,\:\gamma\) with the light electric vector should be chosen such that the matrix \(K\) and the tensor \(S_{\theta}\) are diagonal.To describe processes involving two or more photons, such as luminescence of a uniaxial, aligned sample, an expansion of the directional cosines to the fourth power is required.
3) Order parameters (related to 'Wigner matrices') are an alternative to the directional cosine-based description of molecular alignment. Order-parameter methods also work well for non-uniaxial samples and provide a seemingly more complex, but in other ways convenient, description of molecular orientation distributions. Wigner matrices are used as a basis set for an expansion of the orientation–distribution function.

Related Terms
- angle: https://goldbook.iupac.org//terms/view/A00346
- basis set: https://goldbook.iupac.org//terms/view/BT06999
- isotropic: https://goldbook.iupac.org//terms/view/I03353
- luminescence: https://goldbook.iupac.org//terms/view/L03641
- power: https://goldbook.iupac.org//terms/view/P04792
- probability: https://goldbook.iupac.org//terms/view/P04855
- transition moment: https://goldbook.iupac.org//terms/view/T06460

Source
- PAC, 2007, 79, 293. 'Glossary of terms used in photochemistry, 3rd edition (IUPAC Recommendations 2006)' on page 371 (https://doi.org/10.1351/pac200779030293)

Other Outputs
- html: https://goldbook.iupac.org/terms/view/MT07422/html
- json: https://goldbook.iupac.org/terms/view/MT07422/json
- xml: https://goldbook.iupac.org/terms/view/MT07422/xml

Citation: Citation: 'molecular orientation' in IUPAC Compendium of Chemical Terminology, 5th ed. International Union of Pure and Applied Chemistry; 2025. Online version 5.0.0, 2025. 10.1351/goldbook.MT07422
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Accessed: 2026-05-28T07:24:33+00:00