Thermodynamics of some proton-transfer reactions. Dynamic ion structures and the measurement of entropies of ‘internal translation’

Abstract

Entropies well in excess of expected values have been measured for some protonated aromatic compounds (benzene, halogenobenzenes, halogeno-toluenes and xylenes). It is proposed that this occurs only when very facile proton migration is possible and that the large excess arises out of rapid ‘internal translation’ of the proton across a broad potential well within the molecule. An attempt has been made to model these systems, using a ‘particle-in-a-box’ approach to estimate the molecular partition functions. It was possible to generate sections of the potential-energy surfaces involved by using ab initio calculations at the 4–31G basis set level. The ideas presented are consistent with independent experimental evidence not based on thermodynamic measurements. In particular, the measurements and calculations involving protonated benzene in the gas phase can be compared with a low-temperature study in the liquid phase, using n.m.r. spectroscopy. Making some assumptions with regard to the total excess entropy available in the dynamic protonated species, it is possible to estimate barrier heights for proton migration. The general implications are that such barriers are probably somewhat lower than those currently predicted by the best ab initio methods and that the relative proton affinities measured are not ground-state values and may therefore appear to be significantly lower than expected. Although the idea of ‘internal translation’ has been used in the past in the context of the transition-state theory, the concept of a stable, but dynamic ion structure, as suggested here, is new.