molecular orientation

https://doi.org/10.1351/goldbook.MT07422
Absorption probability (referred to electric dipolar absorption) for a molecular transition with its electric transition (dipole) moment at an angle θ with the electric vector of the light is proportional to cos2⁡θ. For the whole sample it is proportional to the orientation factor Kθ=<cos2⁡θ>, 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 θ=α,β,γ with the light electric vector in the z direction, all orientation effects induced by light absorption are contained in Kθθ=Kθ. Since the sum of Kθ 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: Sθ=(3Kθ−1)/2 The principal (molecular) coordinate system (x, y, z) forming angles θ=α,β,γ with the light electric vector should be chosen such that the matrix K and the tensor Sθ 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.
Source:
PAC, 2007, 79, 293. (Glossary of terms used in photochemistry, 3rd edition (IUPAC Recommendations 2006)) on page 371 [Terms] [Paper]
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. https://doi.org/10.1351/goldbook.MT07422 RIS BibTex EndNote
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Last revised: February 24, 2014