Analytic Self-Consistent-Field Wave Functions for the(3d)(4s)Configuration of the Transition-Metal Ions

The Roothaan method has been used to calculate analytic self-consistent-field functions for the excited $\mathrm{}\left(3d\right)\mathrm{}\left(4s\right)\mathrm{}$ configuration for the first-row transition-metal ions which normally have a ${\mathrm{}\left(3d\right)\mathrm{}}^2$ ground configuration. Wave functions are calculated for both ${}_{}{}^1{}_{}{}^{}D$ and ${}_{}{}^3{}_{}{}^{}D$ multiplets arising from the excited configuration. The separations of these two multiplet levels from the ground ${\mathrm{}\left(3d\right)\mathrm{}}^2 {}_{}{}^3{}_{}{}^{}F$ level deviate from experiment by 3-8%.