A quickly converging method for computing electrostatic crystal field parameters

Abstract

Ewald’s method is utilized to obtain quickly convergent second and fourth order crystal field parameters in the point charge hypothesis. The procedure consists first in expressing crystal field parameters following Racah’s formalism Bkq as functions of partial derivatives of 1/R in Cartesian coordinates, then in differentiating correspondingly Ewald’s expression of 1/R. Electrostatic parameters of Nd2O3 are computed by this method. Perfect convergence is met by performing the summation within a 12 Å sphere in the direct space and a 8 Å−1 sphere in the reciprocal space.