The lanthanide ions doped hexagon (β)-NaYF4 nanocrystals exhibit photoluminescence outputs, where β-NaYF4 with a strong cation disorder serve as host substance. The ab initio computation of β-NaYF4 with different atomic sizes NamYmF4m, for m = 3, 6, 12, 24, 48, or 96 in periodic boundary conditions is simulated based on density functional theory with the generalized gradient approximation. With the increase of unit sizes, the energy of highest occupied molecular orbital (HOMO), lowest unoccupied molecular orbital (LUMO), energy gap, and energy per atom exhibit asymptotic convergence as well as the interatomic distances. The calculation of first ionization energy appreciates the prediction of the Koopmans' theorem. The investigation of orbital's spatial distribution proves the ligand (F− −1e → F) to metal (Y3+ +1e → Y2+) transition during the excitations mainly through the p → d path. Two families of lifetimes are observed in the simulated results from the optical absorption spectrum, which indicates that transitions can be divided by two categories. © 2012 Wiley Periodicals, Inc.