Similar to the case of the spin-lattice coupling coefficients G_ij in cubic symmetry, in this paper the simple correlations between the coupling coefficients F_ij(F₁₁, F₁₂ and F₄₄) in a cubic field and the g-factor in cubic and low symmetries have been established, and hence a simple and uniform method suitable for calculating the coefficients F_ij for all dⁿ ions is given. As an example, the analytic expressions for F_ij for d³ ions in a cubic field are obtained from the high-order perturbation formulae for the g-factor. From these expressions, the coefficients F_ij for MgO:Cr³⁺ crystals have been calculated. The results are close to the experimental values and the errors are, as in the case of G_ij, attributed mainly to the fact that the local elastic constants s_ij in the vicinity of impurity ions are different from the host values. The coefficients F_ij for MgO:V²⁺ crystals, in which the local values are very similar to the bulk values, are also predicted. The results should be, as shown for the coefficients G_ij, closer to the experimental values calculated from the bulk elastic constants. This point remains to be verified.