Quantum cluster equilibrium theory treatment of hydrogen-bonded liquids: water, methanol and ethanol

The quantum cluster equilibrium (QCE) theory was used in order to predict the composition of the hydrogen bonded liquids: water, methanol and ethanol. The calculations were based on high accuracy theoretical data obtained at the DFT/B3LYP/6-311G(d,p) level of theory. All investigated liquids are predicted to be composed of big clusters: hexamers in the case of water, tetramers, pentamers, hexamers and heptamers in the case of methanol and pentamers in the case of ethanol. The content of big clusters in a liquid phase as predicted by QCE is overestimated. We have found two confirmations of this. First of all, the behaviour of the liquid water isobar clearly demonstrates that there should be a substantial amount of small clusters in order to obtain the correct temperature dependence of the molar volume. Indeed, the theoretical molar volume close to the boiling point is by about 0.6 cm(3) lower than the experimental one. The molar volume is too low due to the overestimated population of big clusters resulting in too high a liquid density. Second, the temperature dependence of the chemical shift of the hydroxyl protons in liquid methanol and ethanol, obtained as the population weighted average of the chemical shift of individual clusters, is shifted down field as compared to experiment by as much as 2 ppm. This is because big clusters with strongly deshielded hydroxyl protons contribute too much to the weighted average. Possible shortcomings of the QCE approach are discussed.