We calculate the electronic structures of La halides and oxides from a first-principles calculation by the spin-unrestricted DV-$X\ensuremath{\alpha}$ molecular-orbital method of model clusters. The model clusters we use are $[{\mathrm{LaO}}_{6}{]}^{9\ensuremath{-}},$ $[{\mathrm{LaF}}_{6}{]}^{3\ensuremath{-}},$ $[{\mathrm{LaCl}}_{6}{]}^{3\ensuremath{-}},$ and $[{\mathrm{LaBr}}_{6}{]}^{3\ensuremath{-}},$ 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 ${3d}^{\ensuremath{-}1}$ core-hole states. The ${3d}^{\ensuremath{-}1}$ core-hole states can be regarded as the final states of La $3d$ x-ray photoemission spectroscopy (XPS), and the creation of ${3d}^{\ensuremath{-}1}$ 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 ${3d}^{\ensuremath{-}1}$ core-hole states of $[{\mathrm{LaCl}}_{6}{]}^{3\ensuremath{-}},$ $[{\mathrm{LaBr}}_{6}{]}^{3\ensuremath{-}},$ $[{\mathrm{LaF}}_{6}{]}^{3\ensuremath{-}},$ and $[{\mathrm{LaO}}_{6}{]}^{9\ensuremath{-}}$ 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 ${[\mathrm{LaBr}}_{6}{]}^{3\mathrm{\ensuremath{-}}}{=[\mathrm{LaCl}}_{6}{]}^{3\mathrm{\ensuremath{-}}}{g[\mathrm{LaO}}_{6}{]}^{9\mathrm{\ensuremath{-}}}{g[\mathrm{LaF}}_{6}{]}^{3\mathrm{\ensuremath{-}}}.$ $\mathrm{La} 3d$ 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 al., Phys. Rev. Lett. 45, 1597 (1980)], and the intensity ratios of the high- to low-binding-energy peaks of $\mathrm{La} 3d$ XPS for ${\mathrm{LaCl}}_{3},$ ${\mathrm{LaBr}}_{3},$ ${\mathrm{LaF}}_{3},$ and ${\mathrm{La}}_{2}{\mathrm{O}}_{3}$ are 1.4, 1.4, 0.3, and 0.8 in case of both ${3d}_{5/2}$ and ${3d}_{3/2}$ XPS, which means that the core-hole screening ordering is ${\mathrm{LaBr}}_{3}{=\mathrm{L}\mathrm{a}\mathrm{C}\mathrm{l}}_{3}{g\mathrm{La}}_{2}{\mathrm{O}}_{3}{g\mathrm{LaF}}_{3}.$ From these results, it is found that the intensity ratio of the high- to low-binding-energy peak of $\mathrm{La} 3d$ XPS among La compounds corresponds to the charge-transfer effect.
Read full abstract