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 cos 2θ. For the whole sample it is proportional to the orientation factor Kθ = < cos^2 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: **

*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)

- 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.
- 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 θ = α, β, γ with the light electric vector should be chosen such that the matrix K and the tensor S θ are diagonal.

To describe processes involving two or more photons, such as @[email protected] of a uniaxial, aligned sample, an expansion of the directional cosines to the fourth @[email protected] is required. - Order parameters (related to @[email protected]) 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. @[email protected] are used as a @[email protected] for an expansion of the orientation–distribution function.

PAC, 2007,