Significance of Group Frequency Distributions for Group Additivity

The following hypothesis is proposed: When additivity is valid, the molecular frequency distribution (MFD) is a weighted sum of group frequency distributions (GFDs). On the basis of the transformation rules for distribution functions from statistical theory and the rigid-rotator harmonic oscillator approximation, it is shown analytically that the hypothesis leads to group additivity of vibrationally dependent thermochemical parameters. Graph theory has been used to find the structure of the matrices used to determine group additivity values, and the results show that, within the rigid-rotator harmonic oscillator approximation, additivity of the vibrational contributions leads to the experimentally observed group additivity of the total group contributions. Support for the hypothesis is obtained from ab initio and DFT frequency calculations of a total 182 different compounds from seven polymeric series. In agreement with the hypothesis, remarkable similarities of the MFDs are observed throughout each series. Molecular frequencies can be satisfactorily calculated from model calculations based on the hypothesis, and temperature dependent heat capacities for the monomeric units can be derived that are in agreement with experimental values.