  Accurate electronic structures of the technologically important
lanthanide/rare earth sesquioxides (Ln2O3, with Ln=La,...,Lu) and CeO2 have
been calculated using hybrid density functionals HSE03, HSE06 and
screened-exchange (sX-LDA). We find that these density functional methods
describe the strongly correlated Ln f-electrons as well as the recent
G0W0@LDA+U results, generally yielding the correct band gaps and trends across
the Ln-period. For HSE, the band gap between O 2p states and lanthanide 5d
states is nearly independent of the lanthanide, while the minimum gap varies as
filled or empty Ln 4f states come into this gap. sX-LDA predicts the unoccupied
4f levels at higher energies, which leads to a better agreement with
experiments for Sm2O3, Eu2O3 and Yb2O3.
