Electronic structure and metal-metal bonding in early lanthanide dimers La2, Ce2, and Pr2

Understanding whether 4f electrons participate directly in lanthanide-lanthanide bonding remains a long-standing question in f-element chemistry. Lanthanide dimers provide the simplest molecular platform for isolating intrinsic metal-metal bonding interactions without ligand-field or oxidation-state complications. Here, we present a fully relativistic multireference investigation of La2, Ce2, and Pr2 to resolve their ground electronic states and elucidate the evolution of bonding across the early lanthanide series. The ground states under spin-orbit coupling are determined to be 0g, 1g, and 2u for La2, Ce2, and Pr2, respectively, with spectroscopic constants in improved agreement with available experimental data. Molecular orbital analysis reveals a common σ2π4 inner-core framework, while Ce2 exhibits the highest bond order, consistent with partial multiple-bonding character. Importantly, the results demonstrate that 4f orbitals contribute to metal-metal bonding only through cooperative interaction with energetically accessible 5d orbitals; in the absence of such mixing, the 4f electrons remain essentially nonbonding. These findings provide a unified chemical picture for the onset of f-electron participation in lanthanide bonding and clarify the electronic origin of metal-metal interactions in early lanthanide dimers.