## DFT Calculation of Russell–Saunders Splitting
for Lanthanide Ions Doped in Hexagonal (β)-NaYF_{4} Nanocrystals

journal contribution

posted on 22.08.2013, 00:00 by Ge Yao, Mary T. Berry, P. Stanley May, Dmitri KilinA systematic
investigation is reported of the optimized geometry
and electronic structure of trivalent lanthanide ions (Ln

^{3+}) doped in hexagonal (β)-NaYF_{4}nanocrystals in the basis of density functional theory with a spin polarization approach. A model Na_{24}Y_{23}Ln_{1}F_{96}nanocrystal with a single central lanthanide dopant (Ln^{3+}) is used. Electron spins couple to give a total spin, S, and electron orbital angular momenta couple to give total orbital angular momentum, L. Spin–orbit coupling is neglected in this initial study. Several key observables are found to be strongly related to the number of unpaired f-electrons in the model. After geometry optimization, the phenomenon of the lanthanide contraction is observed, and the configurations of 4f-electron-like orbitals satisfy Hund’s Rule under the orbital decomposition. Spin-polarized density functional theory is applied to generate the Russell–Saunders terms (^{2S+1}L) terms of lanthanide ions. The energy differences between the first and the second terms are calculated and show good agreement with experimental measurements. The free-ion-like behavior of Ln^{3+}ions in the nanocrystal is observed as well.