The nature of metal–ligand bonding in lanthanide and actinide complexes is generally considered to be mostly ionic owing to the poor orbital overlap between the metal-based orbitals and the ligand-based orbitals. However, there has been a growing number of reports exploring whether covalency is also present, and if so, how much. In essence, this means defining the extent to which metal-based orbitals interact with the surrounding ligand orbitals in f-element complexes and probing its role on their resulting electronic structures and physical properties. A better understanding of this can help researchers address challenges in f-element separation processes, nuclear fuels development, and quantum information science.

Recently, Autschbach, Vitova, Bagus, and co-workers addressed this ambiguity in electron counting in their spectroscopic and theoretical study of PuO2. The authors demonstrate this by distinguishing between two similar metrics used for f-orbital electron counting that have different meanings: nopen, which is defined as the formal 5f electron count, and nf, which is the effective 5f electron count or occupation, which considers electron donating and withdrawing effects on the electron configuration in addition to the number of f-electrons. When covalency is not considered, they can have similar values and the two metrics are sometimes used interchangeably. However, in cases considering some amount of covalency in metal–ligand bonding, the two values can diverge. Therefore, distinguishing between the two is crucial as the two metrics describe different physical properties. When electron donating effects to the metal ion are dominant, nf values tend to be greater than nopen. When electron withdrawing or backbonding effects are important, nf values can be less than nopen. With X-ray spectroscopy techniques and computational methods, their study demonstrates how the presence of covalency and excess electron density donation from the donor oxygen atoms in PuO2 can lead to nf values larger than nopen, which could possibly create differing opinions on the electronic structure of PuO2.