Past exam of the chemistry course of the year 3 of the natural sciences course of the University of Cambridge / 2022 / Paper 2A / Section A / 15 / a

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.^[ref]