Calculation for the charge-transfer effect of La compounds in the3d−1core-hole state

We calculate the electronic structures of La halides and oxides from a first-principles calculation by the spin-unrestricted DV-$X\alpha$ molecular-orbital method of model clusters. The model clusters we use are $[{\mathrm{LaO}}_6{]}^{9-},$ $[{\mathrm{LaF}}_6{]}^{3-},$ $[{\mathrm{LaCl}}_6{]}^{3-},$ and $[{\mathrm{LaBr}}_6{]}^{3-},$ as model clusters of ${\mathrm{La}}_2{\mathrm{O}}_3,$ ${\mathrm{LaF}}_3,$ ${\mathrm{LaCl}}_3,$ and ${\mathrm{LaBr}}_3,$ respectively. The electronic structures of these clusters are calculated for the ground state and the ${3d}^{-1}$ core-hole states. The ${3d}^{-1}$ core-hole states can be regarded as the final states of La $3d$ x-ray photoemission spectroscopy (XPS), and the creation of ${3d}^{-1}$ core-hole states induces the charge-transfer effect. It is found from these calculations that, due to the charge-transfer effect, the numbers of unpaired $4f$ electrons in the ${3d}^{-1}$ core-hole states of $[{\mathrm{LaCl}}_6{]}^{3-},$ $[{\mathrm{LaBr}}_6{]}^{3-},$ $[{\mathrm{LaF}}_6{]}^{3-},$ and $[{\mathrm{LaO}}_6{]}^{9-}$ increase by 1.10, 1.15, 0.37, and 0.58, respectively, from the ground state. From this result, it is found that charge-transfer effect ordering is ${[\mathrm{LaBr}}_6{]}^{3\mathrm{-}}{=[\mathrm{LaCl}}_6{]}^{3\mathrm{-}}{>[\mathrm{LaO}}_6{]}^{9\mathrm{-}}{>[\mathrm{LaF}}_6{]}^{3\mathrm{-}}.$ $\mathrm{La}\hspace{0.5em}3d$ XPS of La halides and oxides was reported [S. Suzuki, T. Ishii, and T. Sagawa, J. Phys. Soc. Jpn. 37, 1334 (1974); J. C. Fuggle et...