${4\mathrm{f}}^2$/4f6p configuration interaction in ${\mathrm{LiYF}}_4$ :${\mathrm{Pr}}^{3+}$s

In two other papers [M. D. Faucher, O. K. Moune, D. Garcia, and P. Tanner, Phys. Rev. B 53, 9501 (1996); M. D. Faucher and O. K. Moune, J. Alloys Compounds (to be published)], it was shown that the introduction of the ${5\mathrm{f}}^{\mathrm{n}}$/${5\mathrm{f}}^{\mathrm{n}\mathrm{-}1}$7p (or ${4\mathrm{f}}^{\mathrm{n}}$/${4\mathrm{f}}^{\mathrm{n}\mathrm{-}1}$6p) configuration interaction eliminated large discrepancies in the crystal-field analysis of (i) ${\mathrm{U}}^{4+}$ (${5\mathrm{f}}^2$) in ${\mathrm{Cs}}_2$ ${\mathrm{UBr}}_6$ and ${\mathrm{Cs}}_2$ ${\mathrm{ZrBr}}_6$, for which the least root-mean-square deviation between experimental and calculated energy levels falls down from 241 to 56 ${\mathrm{cm}}^{\mathrm{-}1}$, and (ii) ${\mathrm{Nd}}^{3+}$ in ${\mathrm{Nd}}_2$ ${\mathrm{O}}_2$S, for which the discrepancy of the ${}_{}{}^2{}_{}{}^{}\mathrm{H}$(2${)}_{11\mathrm{/}2}$ level is eliminated by the configuration interaction with the excited ${4\mathrm{f}}^2$6p configuration. The demonstration is now extended to ${\mathrm{Pr}}^{3+}$ and seems to be of general application. For ${\mathrm{LiYF}}_4$:${\mathrm{Pr}}^{3+}$ the mean deviation is divided by more than 2 by utilizing an interaction matrix including 4f6p in addition to the ground configuration ${4\mathrm{f}}^2$.