Review Article

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

Table 5

Direct products of representations (cont.) in Oh symmetry (SOC). Note that in this table, the parity (g: gerade; u: ungerade) was omitted here as the table can be used for either case. For accurate labelling, the parity has to be added to the term symbol, where gerade times gerade equals gerade and gerade times ungerade equals an ungerade term symbol.

OhE1/2E5/2F3/2

A1E1/2E5/2F3/2
A2E5/2E1/2F3/2
EF3/2F3/2E1/2 ⊕ E5/2 ⊕ F3/2
T1E1/2 ⊕ F3/2E1/2 ⊕ F3/2E1/2 ⊕ E5/2 ⊕ 2F3/2
T2E5/2 ⊕ F3/2E1/2 ⊕ F3/2E1/2 ⊕ E5/2 ⊕ 2F3/2

E1/2A1 ⊕ T1A2 ⊕ T2E ⊕ T1 ⊕ T2
E5/2A1 ⊕ T1E ⊕ T1 ⊕ T2
F3/2A1 ⊕ A2 ⊕ E ⊕ 2 T1 ⊕ T2 ⊕ T2