# AN EMPIRICAL SUM RULE FOR VIBRATION FREQUENCIES IN HOMOLOGUES

Please use this identifier to cite or link to this item: http://hdl.handle.net/1811/14310

Files Size Format View
1952-F-03.jpg 155.2Kb JPEG image

 Title: AN EMPIRICAL SUM RULE FOR VIBRATION FREQUENCIES IN HOMOLOGUES Creators: Bernstein, H. J.; Pullin, A. D. E. Issue Date: 1952 Publisher: Ohio State University Abstract: It is shown empirically that the zero point energy in homologous series may be treated as an additive property when account is taken of interaction between nonbonded atoms. Thus, the sum of the vibration frequencies ($\Sigma \nu$) of, inter alia, some 20 chloro-bromo-fluoro substitued methanes are found to have the predicted quadratic dependence on the number of substituents. It follows that in an isotopic homologous series, the zero point energy and $\Sigma \nu$ should be a linear function of the number of substituents. Inspection of the rule for deuterium substituted acetylenes, benzenes, ethylenes and methanes shows that not only $\Sigma \nu$ but $\Sigma \nu^{3/2}, \Sigma \nu^{2}$, and $\Sigma \nu^{3}$ are all very nearly linear in the number of deuterium atoms, with $\Sigma \nu$ giving the best, and the higher powers a progressively worse straight-line relationship. Decius and Wilson, and independently Sverdlov have derived theoretically a sum rule giving the linearty of $\Sigma \nu^{2}$ when the summation is taken over all the fundamental frequencies or over certain symmetry-factor groups where these exist. It has been found empirically that $\Sigma \nu$ can be used instead of $\Sigma \nu^{2}$ in all cases covered by the above rule with comparable accuracy and considerable saving in labour. This suggests that $\Sigma \nu^{2}$ for the nonisotopically substituted methanes, could be shown theoretically to be a quadratic function of the number of substituents. Applications are given where the $\Sigma \nu$ rule is used as a criterion for the correct choice of fundamentals. Description: Author Institution: Division of Chemistry, National Research Council URI: http://hdl.handle.net/1811/14310 Other Identifiers: 1952-F-3