1s2p RIXS Calculations for 3d Transition Metal Ions in Octahedral Symmetry

Table 2

Branching of the , , and atomic terms in an octahedral crystal field () [28] (p.262). The first columns can be either the orbital momentum, the total spin , or the total angular momentum . The g for gerade and the u for ungerade must be added to indicate the parity.

O3	→	Oh
, , or	→	Term symbol
0 (S)	→	A1
1 (P)	→	T1
2 (D)	→	E ⊕ T2
3 (F)	→	T1 ⊕ T2 ⊕ A2
4 (G)	→	A1 ⊕ E ⊕ T1 ⊕ T2
5 (H)	→	E ⊕ 2 T2 ⊕ T2
6 (I)	→	A1 ⊕ T1 ⊕ E ⊕ 2 T2 ⊕ A2
7	→	2T2 ⊕ E ⊕ 2 T2 ⊕ A2
8	→	A1 ⊕ 2 T1 ⊕ 2E ⊕ 2 T2
1/2	→	E1/2
3/4	→	F3/2
5/2	→	F3/2 ⊕ E5/2
7/2	→	E1/2 ⊕ F3/2 ⊕ E5/2
9/2	→	E1/2 ⊕ 2F3/2
11/2	→	E1/2 ⊕ 2F3/2 ⊕ E5/2
13/2	→	E1/2 ⊕ 2F3/2 ⊕ 2E5/2
15/2	→	E1/2 ⊕ 3F3/2 ⊕ E5/2