On the Energy Levels of Chrome Alum

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Abstract
The energy levels for the configuration d3 of the chrome ion in chrome alum are calculated by starting with the empirical spectroscopic data on the free Cr+++ ion, and then making the assumption that the interatomic forces in the solid state can be represented by a crystalline potential of cubic symmetry, whose magnitude is taken from Schlapp and Penney's theory of the magnetic susceptibility. The particular point to be tested is whether in the solid there is a doublet level only 15,000 cm—1 above the basic quartet state, as predicted in the preceding paper from the study of Spedding and Nutting's data on the Zeeman effect. The computed deepest doublet is about 18,200 cm—1 higher than the ground level, but the discrepancy is not excessive in view of uncertainties in the parameters of the crystalline field and the fact that any ``one‐atom'' model is only an approximation in the solid state. As already suggested by Spedding and Nutting, it is very essential in computing the positions of excited levels, to include elements of the crystalline potential which are nondiagonal in the quantum number L, for without them the lowest doublet is much too high, viz. 30,000 cm—1 above the ground term. On the other hand, the effect of these nondiagonal members is shown to be unimportant for the ground level of greatest multiplicity, not merely for Cr+++ but also for other salts of the iron group, so that previous calculations by various writers on magnetic susceptibilities are not appreciably impaired by their assumption of Russell‐Saunders coupling.