## molecular orientation

https://doi.org/10.1351/goldbook.MT07422
Absorption @P04855@ (referred to electric dipolar absorption) for a molecular transition with its electric @T06460@ at an @A00346@ $$\theta$$ 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 @I03353@ 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 @L03641@ of a uniaxial, aligned sample, an expansion of the directional cosines to the fourth @P04792@ is required.
3. Order parameters (related to @WT07498@) 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. @WT07498@ are used as a @BT06999@ 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]