Hund’s three Rules in Actinide-Containing Superatoms with Spin-Orbit Coupling Calculations

The intriguing and challenge issue in magnetic superatoms is searching for the suitable candidates to validate the Hund’s rules. Here, early actinide elements (An: Ac, Th, Pa, U, Np, Pu, Am) whose 5f electrons may crossover the localization and delocalization characteristics have been chosen to alloy with Al atoms in designing magnetic An@Al12 superatoms. By doing the global minimum structure search and the spin-orbital coupling (SOC) density functional theory (DFT) calculations, we provide an original idea to give theoretical argument that Hund’s three rules are still applicable in superatoms, which can be related to the fillings of highly localized An-5f orbitals into large exchange-splitting 2F superatom orbitals. Specifically, selective 5f sub-orbitals of several An dopants can exhibit a dual nature in superatomic bonding, i.e., partial 5f electrons of Pa and Pu are reactive whereas all 5f electrons of U, Np and Am are highly localized. The molecular orbital analyses, combined with the qualitative interpretation of the phenomenological superatom sub-shell model, address the intricate interplays between the structure symmetry, electronic structure, spin and orbital magnetic moments. These findings have important implications for understanding the bonding and magnetic behaviors of An-containing superatoms and pave the way for designing novel magnetic superatoms.