molecular orientation

https://doi.org/10.1351/goldbook.MT07422
Absorption @[email protected] (referred to electric dipolar absorption) for a molecular transition with its electric @[email protected] at an @[email protected] \(\theta\) 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 @[email protected] 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 @[email protected] of a uniaxial, aligned sample, an expansion of the directional cosines to the fourth @[email protected] is required.
  3. 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.
Source:
PAC, 2007, 79, 293. (Glossary of terms used in photochemistry, 3rd edition (IUPAC Recommendations 2006)) on page 371 [Terms] [Paper]