Knowledge Bank

Schaufele and $Shimanouchi1$ 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 \begin{equation} \alpha=\alpha_{0}+\alpha_{1}\sum\nolimits_{i}\Delta\ell_{i}+\cdots \end{equation} 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 $Qm$ appropriate to such iterated virgulate structures. If $\mu$ is the reduced mass for motio-n $\Delta \ell i$, the sum rule has the from \begin{equation} \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 \end{equation} 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.