Key findings
First direct experimental evidence of thorium–thorium bonding
Demonstrates Hirshfeld atom refinement can visualise bonding in heavy elements
Validates theoretical models and enables more routine experimental study of electron sharing
Researchers have directly visualised a rare type of chemical bond between some of the heaviest elements in the periodic table, providing experimental evidence of how these atoms share electrons in systems where this has been difficult to prove.
In the study published in Chem, researchers applied a method called Hirshfeld atom refinement, or HAR, to two model systems containing three closely spaced thorium atoms. These clusters display what the authors describe as multi‑centre thorium–thorium bonding, meaning electrons are shared across three atoms at once rather than between just two.
By applying HAR the team demonstrated that experimental electron density measurements closely matched theoretical calculations, providing direct evidence of thorium–thorium bonding that had previously been predicted but never observed.
Stephen Liddle , Professor of Inorganic Chemistry at The University of Manchester explains:
"This work shows that we can now experimentally access information that was previously out of reach. It sets the stage for studying bonding across a much wider range of complex systems."
Chemical bonding is often described in terms of covalency, where atoms share electrons. While this concept is well understood, experimentally measuring covalency remains challenging and no single method works reliably in all cases. One of the most direct approaches is X‑ray charge density determination, which maps where electrons sit within a material, but this typically requires exceptionally high‑quality crystals and highly controlled conditions, limiting its use in routine studies.
To address this, the researchers used HAR, a form of quantum crystallography, which combines experimental X‑ray data with theoretical calculations to build a detailed picture of electron density, the distribution of electrons that defines how atoms bond. This method is more accessible than traditional charge density techniques, but until now has been difficult to apply to heavy elements such as actinides, where electron behaviour becomes more complex due to relativistic effects.
To test the method, the team analysed two trithorium clusters, which differ in how many electrons are involved in bonding. In one case, a single electron is shared across all three atoms, while in the other, two electrons are shared. Both systems act as "extreme test cases" because the atoms are heavy and closely spaced, making their electron distributions difficult to resolve.
By analysing the electron density, the researchers identified features such as bond critical points, which mark where bonding interactions occur. The measurements matched closely with theoretical calculations, providing direct evidence for thorium–thorium bonding and helping resolve debate about how electrons are shared in these systems.
The results also revealed clear differences between the two clusters, consistent with their underlying characteristics. These differences reflect how the number of shared electrons changes the nature of the bonding. Importantly, the method achieved this using standard experimental data rather than the specialised conditions typically required for charge density studies. This suggests that HAR could be applied more widely to investigate bonding in other complex materials.
Professor Liddle adds: "Understanding how electrons are distributed in these systems is important because small changes in bonding can affect how materials behave, including their chemical reactivity and physical properties. By providing a way to directly measure electron sharing, the approach offers a more reliable way to connect experimental observations with theoretical predictions."
Journal: Chem
Full title: Actinide‑actinide bonding visualized by Hirshfeld atom refinement
DOI: 10.1016/j.chempr.2026.103107
URL: https://doi.org/10.1016/j.chempr.2026.103107
