Chemist Who Thinks Like Mathematician

Jeremy Richardson doesn't look like a revolutionary - more like professionalism personified. He speaks about his scientific work with calmness, wit, courteousness and something approaching reluctance. And yet, his work is groundbreaking and has the potential to radically alter the perspectives of many chemists.

Until now, only a handful of chemists had suspected that even heavy atoms like oxygen could take a shortcut during a chemical reaction - that instead of crossing a quantum mechanical barrier, they can simply tunnel under it.

Tunnelling was previously associated primarily with small particles like electrons or very small atoms like hydrogen. But Richardson was able to use his calculations to demonstrate the same phenomenon in oxygen, which is 16 times heavier than hydrogen. Yesterday, Richardson was awarded the ETH Zurich Rössler Prize.

Physics and computer science in chemical research

He arrived at ETH ten years ago as a 30-year-old, taking up the role of Assistant Professor of Theoretical Chemistry. "Most chemists work in laboratories, wearing white coats. But there's a few of us who are different and try to combine chemistry with ideas from physics, mathematics and computer science," he explains. It might not sound exciting to outsiders, but this couldn't be further from the truth, and anyone who listens to the researcher will quickly share his infectious enthusiasm.

Richardson has a diverse range of interests, which isn't just evident from his research. Even as a child, he was programming computer games. Whilst studying chemistry at the University of Cambridge, he was a member of the university croquet team. He played violin and piano to a high level over many years and, until the age of 21, was a member of the National Youth Orchestra of Wales, where he's from. He doesn't find himself playing music as much nowadays, by his own admission. He still finds a musical outlet though, performing as a tenor in an aspiring vocal ensemble.

Not all oxygen is the same

Richardson's scientific endeavours are centred on a fundamental question within the field of chemistry: why do some reactions happen quickly and others slowly? In many cases, the answer predominantly lies in how much energy has to be expended for a reaction. However, sometimes a chemical reaction involves a transition between two quantum mechanical states of a molecule. The more difficult the transition is between these two states, the more unlikely it is to happen.

It's precisely these complex cases involving quantum mechanics that appealed to Richardson. To understand the example with oxygen, we first have to clear up a few details. The vast majority of oxygen molecules in the air are in a specific quantum mechanical state called the triplet state. But when these molecules absorb energy - for example via sunlight - the electrons in the molecules rearrange themselves. Their quantum mechanical state changes. Scientists call this new state the singlet state.

Triplet and singlet oxygen differ: triplet oxygen is chemically sluggish, whereas singlet oxygen is highly reactive. Especially in biochemistry, this is crucial: singlet oxygen reacts with numerous substances in our bodies.

A seemingly impossible process happens all the time

The question now is: what happens to the singlet oxygen if it doesn't react with other substances? This is where it gets interesting, as traditional theoretical explanations don't neatly map onto what actually happens in practice. According to prevailing theories, a singlet oxygen molecule ought to live forever, because, as these theories dictate, a return from the singlet to the triplet state is so extremely improbable that it would only occur after several dozen trillion years. Theoretically speaking, this means that the reaction would take longer than the universe has existed.

Nevertheless, these theories don't bear the scrutiny of reality: in practice, singlet oxygen has a short lifespan and returns to a triplet state within just a few millionths of a second. The idea that something which seems impossible in theoretical terms nevertheless happens all the time in nature is explained by Richardson with the help of tunnelling. The barrier which is tunnelled under here is the quantum mechanical difficulty of transitioning from one electronic state to another.

One hundred quintillion times quicker

Over the past few years, Richardson has developed a theory which shows that, under certain conditions, atoms like oxygen can also make use of the tunnel shortcut. His calculations indicate that oxygen atoms in fact do exactly this and that it's the tunnelling process which accelerates the transition from single to triplet oxygen to such an incredible extent - from the several dozen trillion years needed in theory down to just microseconds in reality.

Working out these calculations was anything but simple though, and required Richardson's mathematical expertise. When he explains his work to someone, he will sometimes write a complex mathematical formula on the board say: "This formula contains the whole of chemistry. Unfortunately, it's such a terribly difficult formula that nobody can solve it in its current guise."

The search for "magic paths"

If you want to take into account all quantum mechanically possible motion paths of nuclei and electrons, it's not really possible to calculate the transition from singlet to triplet oxygen on a computer. Depending on the degree of accuracy required, a calculation like this would take an unrealistically long time, several years or even much longer.

In view of this, Richardson pursued the idea of not calculating all conceivable motion paths, but only those likely to have the greatest influence on the chemical reaction - the "magic paths" as he calls them. Using a mathematical model he developed himself, he can identify which paths these are.

As a result, a computer no longer needs to calculate the entire problem, just the crucial steps. And with that, a practically unsolvable calculation is transformed into a solvable one. "We use mathematics to turn a difficult quantum problem into a simple one," Richardson summarises. In doing so, he doesn't simplify the problem purely by making more approximate calculations; he uses mathematics to find out which motion paths are decisive and which can be ignored.

Many reactions misunderstood up to now

Having demonstrated quantum tunnelling in oxygen, Richardson has now turned his attention to finding where else it occurs. He suspects that many researchers have so far misunderstood certain chemical reactions because they haven't taken the tunnel effect into account. As part of his search, he wants to focus in particular on biology and biochemistry "It would be fascinating to identify a process in the human body that wouldn't take place without tunnelling," explains Richardson.

"If we can understand when and how molecules make use of tunnelling paths, we could use this in targeted ways," he says. For example, he envisages being able one day to trigger chemical reactions via quantum tunnelling or to accelerate industrial processes this way. But that's a long way off yet. Even so, someone who's capable, as Richardson is, of thinking in such an interconnected way and of radically simplifying complex ideas has a good chance of revolutionising not only the theory of chemistry, but its applications too.