dc.creator Stidham, Howard D. en_US dc.date.accessioned 2006-06-15T14:48:55Z dc.date.available 2006-06-15T14:48:55Z dc.date.issued 1983 en_US dc.identifier 1983-RG-10 en_US dc.identifier.uri http://hdl.handle.net/1811/11922 dc.description $^{1}$R.F. Schaufele and T. Shimanouchi, J. Chem. Phys. 47, 3605(1967). en_US dc.description Author Institution: Department of Chemistry, University of Massachusetts en_US dc.description.abstract Schaufele and $Shimanouchi^{1}$ frist showed that low frequency Raman active vibrations of long chain hydrocarbons could be explained as longitudinal acoustic modes associated with odd numbers of nodes, or zeroes of the motion, along the hydrocarbon chain. The experimental which a polarization dependence of the from $$\alpha=\alpha_{0}+\alpha_{1}\sum\nolimits_{i}\Delta\ell_{i}+\cdots$$ was assumed. To the extent that this bond polarizability model can be applied to real molecules, there is a precise intensity sum rule which is embedded in the mathematics of the transformation from the basis coordinates $\Delta\ell_{i}$ to the normal coordinates $Q_{m}$ appropriate to such iterated virgulate structures. If $\mu$ is the reduced mass for motio-n $\Delta\ell_{i}$, the sum rule has the from $$\frac{1}{2\mu\alpha_{1}^{2}}\sum\limits^{n-1 \hbox{ or } n-2}_{m_{ odd}{=1}}(\partial\alpha/\partial Q_{m})^{2} =1$$ In this paper, this intensity sum rule will be derived, and the scope of applicability will be discussed. Some real physical examples will be presented. en_US dc.format.extent 106880 bytes dc.format.mimetype image/jpeg dc.language.iso English en_US dc.publisher Ohio State University en_US dc.title INTENSITY SUM RULE FOR ITERATED VIRGULATE STRUCTURES en_US dc.type article en_US
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