A statistical‐mechanical analysis of group additivity. Calculation of thermochemical values from frequency distributions

Abstract

AbstractMolecular vibrational frequencies of homologous series plotted as cumulative frequency distributions are very similar, and the fine structure of the distributions exhibit identical features. An obvious explanation is that the changes in the molecular frequency distributions (MFDs) from one homologue to the next is independent of the chain length and of the functional groups in the molecule. Since group additivity is valid for the chosen homologous series there is here an explanation for the linearity of thermochemical values expressed by group additivity. For these properties the following hypothesis is proposed: group additivity is observed when the MFD is a sum of group frequency distributions (GFDs). This leads to additivity for the zero‐point vibrational energy which is confirmed by analysis of the frequencies of 126 organic molecules from 11 homologous series. The frequency distribution for a methylene group is estimated from that of octadecane. From this GFD combined with 11 different MFD it is possible to calculate model frequencies for the homologous series which are in good agreement with frequencies from ab initio calculations. For three thermochemical parameters (the logarithm of the vibrational partition function, the vibrational excitation energy and the vibrational heat capacity), the combination of the estimated methylene GFD with 11 different MFDs lead to group additivity values for a methylene group which are identical over a wide temperature range. The derivation of Benson additivity for thermochemical functions from frequency distributions is at step towards a better understanding of Benson additivity. Copyright © 2008 John Wiley & Sons, Ltd.