Rare-earth-boron bonding and 4f state trends in RB4 tetraborides

The B-B bonding, boron-rare earth coupling, and the changes in 4f states across the lanthanide series in RB4 (R=rare earth) compounds are studied using the correlated band theory LDA+U method. A set of boron bonding bands that are well separated from the antibonding bands can be identified. Separately, the dimer B 2p(z) orbital is nonbonding (viz., graphite and MgB2), but mixes strongly with the metal 4d or 5d states that form the conduction states. The bonding bands are not entirely filled even for the trivalent compounds (thus the cation d bands have some filling), which accounts for the lack of stability of this structure when the cations are divalent (with more bonding states unfilled). The trends in the mean 4f level for both majority and minority, and occupied and unoccupied, states are presented and interpreted.