A new research paper has solved one of the top theoretical problems in chemical physics as ranked by the National Research Council in 1995.

Credit: Professor Vincent Rotello, University of Massachusetts at Amherst

It’s not the problem of why water freezes quicker when hot – that research is still ongoing – however, scientists have found a way to more accurately predict the dynamic behaviour of electrons in atoms and molecules in chemical reactions that govern a wide range of phenomena, such as the fuel efficiency of combustion engines and the depletion of the atmospheric ozone.

David Mazziotti, professor in chemistry at the University of Chicago, has solved what specialists call the “N-representability problem.” The paper has been described as a “striking advance”, “an elegant theory”, and “a remarkable achievement” by Robert Erdahl, a mathematician at Queens University in Canada and a leading authority on the N-representability problem.

Mr Erdahl noted that theoretical interpretations of the problem have advanced down very different lines over the past 60 years. He said: “Work in both directions has proceeded independently even though it was widely understood that a unified approach was required to achieve a clear understanding. However, no one has been able to construct a theory where both paths enter in partnership. In his recent work Mazziotti has achieved precisely that.”

Molecules can have tens to thousands of electrons, and the complexity of simulating their behaviour grows exponentially with the number of strongly correlated electrons. Mr Mazziotti looked to accurately calculate the properties of many-electron systems via a two-electron technique, where the two electrons represent the other electrons in the system.

His recent paper plugs the gap between two sets of research in the area, making the two-electron model a powerfully complete theory for mapping many-electron systems. He said: “We can achieve much greater accuracy in our calculations by adding some of these new conditions that we’ve discovered.

“It’s exciting because it’s something I’ve been looking for since I started thinking about this in 1995.”