Chemical Bonding of Crystalline LnB6 (Ln = La–Lu) and Its Relationship with Ln2B8 Gas-Phase Complexes

Solid-state lanthanide (Ln) borides of the simple LnB6 composition not only exhibit exciting physical behavior, in particular magnetic properties, but their electronic structure and chemical bonding are particularly intriguing as well. To shed more light on the latter, we have performed quantum-chemical (DFT+ U) electronic-structure calculations and bonding analyses of the entire LnB6 series with Ln from La to Lu. Trivially, the boron framework is held together by the B 2sp orbitals, and this framework bonds to the Ln atoms via covalent-ionic interactions. The Ln 4f electrons, however, are decisive for the magnetic properties. In more detail, the effective charges of the Ln atoms as calculated by (Mulliken or Löwdin) occupation numbers of the 6s/5d/4f orbitals are compatible with experimentally assigned oxidation numbers. The shorter inter-octahedral B-B bonds, dominated by 2s-2p interactions, turn out to be stronger than the intra-octahedral B-B bonding with a more 2p-2p-like character. Interestingly, there are strong structural similarities between the LnB6 motif studied here and gas-phase Ln2B8 species showing inverse sandwich structures, and these similarities are also reflected in the electronic structure. In particular, Ln2B8 is predicted to have a large electron affinity. Hence, this work aims at providing an intrinsic link between gas-phase complexes and solid-state crystal structures in order to better understand the former species.