# Ligand-field splitting of an atomic orbital in a point-group field

crystod-group --ligand-field d --point-group m-3m

* Point group *
m-3m

* Orbital *
d

* Reducible representation of the d orbital in the m-3m field *
1E: 5
8C3: -1
6C2: 1
6C4: -1
3C4^2: 1
1i: 5
6S4: -1
8S6: -1
3sgh: 1
6sgd: 1

* Result *
1(Eg) + 1(T2g)


crystod-group --ligand-field f --point-group m-3m

* Point group *
m-3m

* Orbital *
f

* Reducible representation of the f orbital in the m-3m field *
1E: 7
8C3: 1
6C2: -1
6C4: -1
3C4^2: -1
1i: -7
6S4: 1
8S6: -1
3sgh: 1
6sgd: 1

* Result *
1(A2u) + 1(T1u) + 1(T2u)


crystod-group --ligand-field f --point-group 6/mmm

* Point group *
6/mmm

* Orbital *
f

* Reducible representation of the f orbital in the 6/mmm field *
1E: 7
2C6: -1
2C3: 1
1C2: -1
3C2': -1
3C2'': -1
1i: -7
2S3: 1
2S6: -1
1sgh: 1
3sgd: 1
3sgv: 1

* Result *
1(A2u) + 1(B1u) + 1(B2u) + 1(E1u) + 1(E2u)


crystod-group --ligand-field d --point-group -4

* Point group *
-4

* Orbital *
d

* Reducible representation of the d orbital in the -4 field *
1E: 5
2S4: -1
1C2: 1

* Result *
1(A) + 2(B) + 1(E)
