A calculation of the crystalline field strength, $\mathrm{Dq}$, is reported for the case of chrome alum, using the same model and crystal field potential employed by Kleiner and recently determined Hartree-Fock wave functions for the ${\mathrm{Cr}}^{+3}$ ion. On this basis, earlier theoretical attempts at determining, within the framework of crystal field theory, accurate $\mathrm{Dq}$ values are reviewed and analyzed. Particular emphasis is placed on a consideration of reported point charge calculations and Phillips' method of including the effects of orthogonalization of ligand to metal ion wave functions. Our results indicate that the point charge model estimates for $\mathrm{Dq}$ gave good results mostly because they were based on the use of improper $3d$ wave functions for the transition metal cation. Kleiner's result is significantly improved---his wrong sign for $\mathrm{Dq}$ is reversed and a small positive $\mathrm{Dq}$ is obtained---but in such a way as to contradict Phillips conclusions. A discussion is given of the various evidence for the inadequacy of the electrostatic potential theory and some of the necessary modifications are indicated.