Actinide-actinide bonding visualized by Hirshfeld atom refinement

The concept of covalency in chemical bonding is well established, but there are few methods to experimentally measure covalency, and none is a panacea. Quantum crystallography X-ray charge density determination could be the most powerful method for experimentally visualizing chemical bonding, but its stringent requirements have prevented routine implementation. Hirshfeld atom refinement (HAR) has begun to emerge as an alternative, potentially more accessible quantum crystallography approach for experimentally visualizing covalency, but its use has remained limited with heavy elements such as actinides due to challenges in partitioning and modeling core and valence electron densities in relativistic regimes. Here, we apply HAR to two extreme test cases of clusters containing three proximate heavy actinides exhibiting multi-center thorium-thorium bonding. We demonstrate exceptional agreement between experimental HAR and purely density functional theory analyses, thus visualizing the thorium-thorium bonding and paving the way to more routine use of experimental HAR visualization of chemical bonding.