Solution (source code)

= Solution

The <octahedral splitting> $\Delta_o$ separates the metal $t_{2g}$ and $e_g$ orbital sets. The <Racah parameter> $B$ characterizes interelectronic repulsion and hence the spacing of many-electron d-shell terms; it is not another name for $\Delta_o$. A <Tanabe-Sugano diagram> plots term excitation energies $E/B$ against $\Delta_o/B$, for specified values of the other repulsion-parameter ratios. Each ordinate is measured relative to whichever term is the <ground state> at that field strength. The original many-electron treatment diagonalizes the relevant d-shell energy <matrices> rather than identifying every <absorption> with a one-electron $t_{2g}\to e_g$ gap.<On the Absorption Spectra of Complex Ions. I by Yukito Tanabe and Satoru Sugano>[1954, pp. 753–766, d-shell energy matrices in a cubic field]{ref}