Table 2. Analytical Expressions for the Kβ Mainline Splittings for Octahedral 3d Metal Complexesa.
| metal d count | initial state | intermediate state | final state | ΔE/(4G1 + 42G3) |
|---|---|---|---|---|
| 3d0 | 1A1g | 2A1g | 2T1u | 0 |
| 3d1 | 2T2g | 1,3T2g | 1,3(A2,E,T1,T2)u | t2 |
| 3d2 | 3T1g | 2,4T1g | 2,4(A1,E,T1,T2)u | (3/2)t2 |
| 3d3 | 4A2g | 3,5A2g | 3,5T2u | 2t2 |
| 3d4 | h.s. 5Eg | 4,6Eg | 4,6(T1,T2)u | (5/2)(3t2+e2)/4 |
| l.s. 3T1g | 2,4T1g | 2,4(A1,E,T1,T2)u | (3/2)t2 | |
| 3d5 | h.s. 6A1g | 5,7A1g | 5,7T1u | 3(3t2+2e2)/5 |
| l.s. 2T2g | 1,3T2g | 1,3(A2,E,T1,T2)u | t2 | |
| 3d6 | h.s. 5T2g | 4,6T2g | 4,6(T1,T2)u | (5/2)(t2+e2)/2 |
| l.s. 1A1g | 2A1g | 2T1u | 0 | |
| 3d7 | h.s. 4T1g | 3,5T1g | 3,5(A1,E,T1,T2)u | 2(t2+2e2)/3 |
| l.s. 2Eg | 1,3Eg | 1,3(T1,T2)u | e2 | |
| 3d8 | 3A2g | 2,4A2g | 2,4T2u | (3/2) e2 |
| 3d9 | 2Eg | 1,3Eg | 1,3(T1,T2)u | e2 |
| 3d10 | 1A1g | 2A1g | 2T1u | 0 |
a
For dn configurations where both high and low spin ground states are available they have been indicated with h.s. and l.s., respectively; except for the low spin ground states, these expressions are also valid for tetrahedral complexes after removal of the indices “g” and “u”.