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molecular orientation

Absorption probability (referred to electric dipolar absorption) for a molecular transition with its electric transition (dipole) moment at an angleθ with the electric vector of the light is proportional to cos 2 θ. For the whole sample it is proportional to the orientation factor K θ = < 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.
  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 K θ θ = K θ. Since the sum of K θ 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 θ = ( 3 K θ − 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 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.
PAC, 2007, 79, 293 (Glossary of terms used in photochemistry, 3rd edition (IUPAC Recommendations 2006)) on page 371
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IUPAC. Compendium of Chemical Terminology, 2nd ed. (the "Gold Book"). Compiled by A. D. McNaught and A. Wilkinson. Blackwell Scientific Publications, Oxford (1997). XML on-line corrected version: (2006-) created by M. Nic, J. Jirat, B. Kosata; updates compiled by A. Jenkins. ISBN 0-9678550-9-8.
Last update: 2014-02-24; version: 2.3.3.
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