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.