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  Home > JCE Print > Journal of Chemical Education > Issues > 2004  > June  >
Research: Science and Education
Using Rotational Averaging To Calculate the Bulk Response of Isotropic and Anisotropic Samples from Molecular Parameters
Steven S. Andrews
Department of Chemistry, Stanford University, Stanford, CA 94305
Cover
June 2004
Vol. 81 No. 6
p. 877
Abstract
Most physical chemistry experiments analyze bulk samples, rather than single molecules, with the result that each measurement yields an average response from many molecules. In particular, investigation of vector or matrix molecular properties, such as dipole moments or polarizabilities, leads to results that are averaged over a range of molecular orientations. This article presents mathematical methods for calculating these averages for isotropic and partially oriented samples, where the latter might arise from external electric or magnetic fields, flow gradients, or photoselection. Rotational averaging is demonstrated with several examples, including calculations for the potential energy of fixed and mobile molecules in an electric field and quantitative absorption and fluorescence spectroscopy. In the process, the fluorescence anisotropy and the Langevin function are derived. A table of direction cosine averages allows the method to be used for new experiments.
More Information
*  Citation
 Andrews, Steven S. J. Chem. Educ. 2004 81 877.
*  Keywords
 Fluorescence Spectrometry; Lasers / Laser Spectroscopy; Physical Chemistry; Statistical Mechanics; UV-Vis Spectroscopy
*  History
 Created:
Last Updated:		 May 2, 2004
January 21, 2005
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