Physicists Observe Molecules Forming Through Quantum Tunneling for the First Time

Quantum mechanics allows particles due to their quantum mechanical wave properties to break through the energetic barrier (wall) and a reaction occurs.

Tunneling reactions in chemistry are very difficult to predict. The quantum mechanically exact description of chemical reactions with more than three particles is difficult, with more than four particles it is almost impossible. 

Theorists simulate these reactions with classical physics and must neglect quantum effects. 

But where is the limit of this classical description of chemical reactions, which can only provide approximations?

Quantum theory does provide a workaround if you're patient. And a team of researchers from the University of Innsbruck in Austria has finally seen the quantum tunneling in action in a world-first experiment measuring the merger of deuterium ions with hydrogen molecules.

Tunneling is a quirk of the quantum universe that makes it seem like particles can pass through obstacles that are ordinarily too hard to overcome.

In chemistry, this obstacle is the energy required for atoms to bond with one another, or with existing molecules.

Yet theory says that, in extremely rare instances, it's possible for atoms in close proximity to 'tunnel' their way through this energy barrier and connect without any effort.

"Quantum mechanics allows particles to break through the energetic barrier due to their quantum mechanical wave properties, and a reaction occurs," says first author Robert Wild, an experimental physicist from the University of Innsbruck.

Quantum waves are the ghosts that drive the behaviors of objects like electrons, photons, and even entire groups of atoms, blurring their existence before any observation so they sit not in any one precise place but occupy a continuum of possible positions.

This blurring is insignificant for larger objects like molecules, cats, and galaxies. But as we zoom in on individual subatomic particles, the range of possibilities expands, forcing the location states of various quantum waves to overlap.

When that happens, particles have a slight chance of appearing where they have no business being, tunneling into regions that would otherwise require a great deal of force to enter.

One of those regions for an electron might be within the bonding-zone of a chemical reaction, welding together neighboring atoms and molecules without the boom-crash-crush of heat or pressure.

Understanding the role quantum tunneling plays in the building and rearrangements of molecules could have important ramifications in the calculations of energy release in nuclear reactions, such as those involving hydrogen in stars and fusion reactors here on Earth.

While we've modeled this phenomenon for examples involving reactions between a negatively charged form of deuterium – an isotope of hydrogen containing a neutron – and dihydrogen or H2, proving the numbers experimentally requires a challenging level of precision.

To accomplish this, Wild and his colleagues cooled negative deuterium ions to a temperature that brought them close to a standstill before introducing a gas made of hydrogen molecules.

Without heat, the deuterium ion was far less likely to have the energy required to force hydrogen molecules into a rearrangement of atoms. Yet it also forced the particles into sitting quietly near one another, giving them more time to bond through tunneling.

"In our experiment, we give possible reactions in the trap about 15 minutes and then determine the amount of hydrogen ions formed. From their number, we can deduce how often a reaction has occurred," Wild explains.

That figure is just over 5 x 10-20 reactions per second taking place in each cubic centimeter, or around one tunneling event for around every hundred billion collisions. So not a lot. Though the experiment does back up previous modeling, confirming a benchmark that can be used in predictions elsewhere.

Given tunneling plays a fairly important role in a diverse range of nuclear and chemical reactions, much of which is also likely to occur out in the cold depths of space, getting a precise grip on the factors at play gives us a more solid grounding to base our predictions on.


Tunneling measured in a very slow ion-molecule reaction. Robert Wild, Markus Nötzold, Malcolm Simpson, Thuy Dung Tran, and Roland Wester. Nature 2023 DOI: 10.1038/s41586-023-05727-z