A Sum Rule for the Vibrational Frequencies of Homologs

Abstract

It is shown empirically that the zero‐point energy in substituted methanes may be treated as a constitutive property when account is taken of the interaction between nonbonded atoms. Thus, the sum of the vibration frequencies (Σν) of the halogenated methanes is found to have the predicted quadratic dependence on the number of substituents. This reduces to a linear dependence in the case of isotopically substituted homologs, compared to the linear dependence for Σν² found theoretically by Decius and Wilson, and Sverdlov. Both Σν and Σν² give good agreement between observed and calculated results. Various applications are given for the Σν rule and it is shown further that Σν, Σν², Σ1/ν, Σ1/ν² are all approximately constitutive properties of the halogenated methanes.