Theoretical Chemists Unlock One of Water's Mysteries

Water cluster model showing configurations of oxygens and hydrogens
A low-probability ion-pair water cluster showing the three hydrogen-bonded water-dimer buttresses that separate hydronium (+; left) and hydroxide (-; right) ions. Image: Frank Weinhold

For the first time, an international team of researchers from UW-Madison, University of Bonn (Germany), and University of Rostock (Germany) has determined the ion product of water using theoretical methods. The work is reported today (Aug. 31) in the journal Scientific Reports in a paper titled “Predicting the Ionic Product of Water.”

The ion product of water is a very small number that quantifies the number of ions found among the molecules of water. This number determines the product of concentrations of the positively and negatively charged ionic particles in water. This number also is connected with the pH value of water, which measures its acidity or alkalinity.

The ion product of water is an extremely small number with thirteen zeros behind the decimal point, far below what can be determined by conventional simulation methods. Only 18 of every 10 billion water particles are found to be in the form of negatively charged hydroxide or positively charged hydronium ions. The measurable pH can also be described as the “self-dissociation” (autoprotolysis) property of water, the self-splitting of neutral water molecules into charged ions.

Prof. Frank Weinhold

“I think it’s fair to say that this is the deepest mystery of the most important and interesting fluid in the natural world,” says Frank Weinhold, an emeritus professor of chemistry at UW-Madison who collaborated in the effort.

The research team has now succeeded in using quantum chemical methods and a sophisticated cluster model to calculate this small number. The team first identified specific water clusters in which separated ions can persist alongside the dominant neutral water molecules (H2O), supported by a complex “buttressing” structure of hydrogen bonds. These clusters are energetically unfavorable and able to survive only in faint traces in the thermodynamic cluster model. Calculating the thermodynamic survival probability of these feeble clusters leads directly to the ion product of water. Molecular-level details of the cluster model then make it possible to analyze the specific water configurations and mechanisms by which the hydroxide and hydronium ions can persist.

The research team was also successful in theoretically predicting the temperature dependence of the ion product. For example, between the freezing point and boiling point of water (0-100°C) the self-dissociation of water is predicted to increase by approximately a thousand-fold, in agreement with experiment.

The international research team consists of Eva Perlt, Michael von Domaros, and Barbara Kirchner of the University of Bonn, Ralf Ludwig of the University of Rostock, and Frank Weinhold of UW-Madison.