Calculation of electrostatic crystal-field parameters including contributions of induced dipoles: Application to ${\mathrm{Nd}}_2$${\mathrm{O}}_3$ and ${\mathrm{Nd}}_2$${\mathrm{O}}_2$S

The method utilized for the calculation of the dipolar contribution to crystal-field parameters (cfp) is outlined and applied to the case of neodymium oxide and neodymium oxysulfide. The slowly converging electric field and electric-field gradients necessary for deriving induced moments are calculated by Ewald's method. The dipole components are then obtained by resolving the linear system linking induced moments and the electric field produced by point charges and dipoles throughout the crystal lattice. The dipole components are introduced in a general correction formula for the cfp. The calculation shows that mainly the second-order parameters are changed by the corrections. The total $B_0^2$ (point charges plus dipoles) exhibits the correct experimental sign for both compounds investigated, whereas the point-charge contribution alone does not: ${\left(B_0^2\right)}_{\mathrm{expt}}=-800\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$(${\mathrm{Nd}}_2$ ${\mathrm{O}}_3$), +194 ${\mathrm{cm}}^{-1\mathrm{}}$(${\mathrm{Nd}}_2$ ${\mathrm{O}}_2$S); ${\left(B_0^2\right)}_{\mathrm{PC}}=-1500\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$(${\mathrm{Nd}}_2$ ${\mathrm{O}}_3$), -653 ${\mathrm{cm}}^{-1\mathrm{}}$(${\mathrm{Nd}}_2$ ${\mathrm{O}}_2$S); ${\left(B_0^2\right)}_{\mathrm{D}}=-478\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$(${\mathrm{Nd}}_2$ ${\mathrm{O}}_3$), +1363 ${\mathrm{cm}}^{-1\mathrm{}}$(${\mathrm{Nd}}_2$ ${\mathrm{O}}_2$S). As usual, the calculated second-order parameters are too large, the fourth- and sixth-order parameters too small (1.4 and 2 times, respectively) when utilizing the theoretical radial integrals $〈r^k〉$.