University of Exeter

Non-crystalographic: Ih - Products

Exeter Symmetry Pages

Irreducible Representation Products:

product A g T1g T2g G g H g A u T1u T2u G u H u
Ag Ag T1g T2g Gg Hg Au T1u T2u Gu Hu
T1g T1g Ag+T1g+Hg Gg+Hg T2g+Gg+Hg T1g+T2g+Gg+Hg T1u Au+T1u+Hu Gu+Hu T2u+Gu+Hu T1u+T2u+Gu+Hu
T2g T2g Gg+Hg Ag+T2g+Hg T1g+Gg+Hg T1g+T2g+Gg+Hg T2u Gu+Hu Au+T2u+Hu T1u+Gu+Hu T1u+T2u+Gu+Hu
Gg Gg T2g+Gg+Hg T1g+Gg+Hg Ag+T1g+T2g+Gg+Hg T1g+T2g+Gg+2Hg Gu T2u+Gu+Hu T1u+Gu+Hu Au+T1u+T2u+Gu+Hu T1u+T2u+Gu+2Hu
Hg Hg T1g+T2g+Gg+Hg T1g+T2g+Gg+Hg T1g+T2g+Gg+2Hg Ag+T1g+T2g+2Gg+2Hg Hu T1u+T2u+Gu+Hu T1u+T2u+Gu+Hu T1u+T2u+Gu+2Hu Au+T1u+T2u+2Gu+2Hu
Au Au T1u T2u Gu Hu Ag T1g T2g Gg Hg
T1u T1u Au+T1u+Hu Gu+Hu T2u+Gu+Hu T1u+T2u+Gu+Hu T1g Ag+T1g+Hg Gg+Hg T2g+Gg+Hg T1g+T2g+Gg+Hg
T2u T2u Gu+Hu Au+T2u+Hu T1u+Gu+Hu T1u+T2u+Gu+Hu T2g Gg+Hg Ag+T2g+Hg T1g+Gg+Hg T1g+T2g+Gg+Hg
Gu Gu T2u+Gu+Hu T1u+Gu+Hu Au+T1u+T2u+Gu+Hu T1u+T2u+Gu+2Hu Gg T2g+Gg+Hg T1g+Gg+Hg Ag+T1g+T2g+Gg+Hg T1g+T2g+Gg+2Hg
Hu Hu T1u+T2u+Gu+Hu T1u+T2u+Gu+Hu T1u+T2u+Gu+2Hu Au+T1u+T2u+2Gu+2Hu Hg T1g+T2g+Gg+Hg T1g+T2g+Gg+Hg T1g+T2g+Gg+2Hg Ag+T1g+T2g+2Gg+2Hg


Dipole Transition Products:

For the Ih point group, the irreducible representation of the dipole operator is T1u. Transitions that are dipole forbidden are indicated by parentheses.

productT1uproduct Ag T1g T2g Gg Hg Au T1u T2u Gu Hu
Ag (T1u) (Au+T1u+Hu) (Gu+Hu) (T2u+Gu+Hu) (T1u+T2u+Gu+Hu) (T1g) Ag+T1g+Hg (Gg+Hg) (T2g+Gg+Hg) (T1g+T2g+Gg+Hg)
T1g (Au+T1u+Hu) (Au+3T1u+T2u+Gu+2Hu) (T1u+2T2u+2Gu+2Hu) (T1u+2T2u+3Gu+3Hu) (Au+2T1u+2T2u+3Gu+4Hu Ag+T1g+Hg Ag+3T1g+T2g+Gg+2Hg (T1g+2T2g+2Gg+2Hg) (T1g+2T2g+3Gg+3Hg) Ag+2T1g+2T2g+3Gg+4Hg
T2g (Gu+Hu) (T1u+2T2u+2Gu+2Hu) (2T1u+T2u+2Gu+2Hu) (Au+2T1u+2T2u+2Gu+3Hu) (Au+2T1u+2T2u+3Gu+4Hu) (Gg+Hg) (T1g+2T2g+2Gg+2Hg) (2T1g+T2g+2Gg+2Hg) Ag+2T1g+2T2g+2Gg+3Hg Ag+2T1g+2T2g+3Gg+4Hg
Gg (T2u+Gu+Hu) (T1u+2T2u+3Gu+3Hu) (Au+2T1u+2T2u+2Gu+3Hu) (Au+3T1u+2T2u+3Gu+4Hu) (Au+3T1u+3T2u+4Gu+5Hu) (T2g+Gg+Hg) (T1g+2T2g+3Gg+3Hg) Ag+2T1g+2T2g+2Gg+3Hg Ag+3T1g+2T2g+3Gg+4Hg Ag+3T1g+3T2g+4Gg+5Hg
Hg (T1u+T2u+Gu+Hu) (Au+2T1u+2T2u+3Gu+4Hu) (Au+2T1u+2T2u+3Gu+4Hu) (Au+3T1u+3T2u+4Gu+5Hu) (Au+4T1u+4T2u+5Gu+6Hu) (T1g+T2g+Gg+Hg) Ag+2T1g+2T2g+3Gg+4Hg Ag+2T1g+2T2g+3Gg+4Hg Ag+3T1g+3T2g+4Gg+5Hg Ag+4T1g+4T2g+5Gg+6Hg
Au (T1g) Ag+T1g+Hg (Gg+Hg) (T2g+Gg+Hg) (T1g+T2g+Gg+Hg) (T1u) (Au+T1u+Hu) (Gu+Hu) (T2u+Gu+Hu) (T1u+T2u+Gu+Hu)
T1u Ag+T1g+Hg Ag+3T1g+T2g+Gg+2Hg (T1g+2T2g+2Gg+2Hg) (T1g+2T2g+3Gg+3Hg) Ag+2T1g+2T2g+3Gg+4Hg (Au+T1u+Hu) (Au+3T1u+T2u+Gu+2Hu) (T1u+2T2u+2Gu+2Hu) (T1u+2T2u+3Gu+3Hu) (Au+2T1u+2T2u+3Gu+4Hu
T2u (Gg+Hg) (T1g+2T2g+2Gg+2Hg) (2T1g+T2g+2Gg+2Hg) Ag+2T1g+2T2g+2Gg+3Hg Ag+2T1g+2T2g+3Gg+4Hg (Gu+Hu) (T1u+2T2u+2Gu+2Hu) (2T1u+T2u+2Gu+2Hu) (Au+2T1u+2T2u+2Gu+3Hu) (Au+2T1u+2T2u+3Gu+4Hu)
Gu (T2g+Gg+Hg) (T1g+2T2g+3Gg+3Hg) Ag+2T1g+2T2g+2Gg+3Hg Ag+3T1g+2T2g+3Gg+4Hg Ag+3T1g+3T2g+4Gg+5Hg (T2u+Gu+Hu) (T1u+2T2u+3Gu+3Hu) (Au+2T1u+2T2u+2Gu+3Hu) (Au+3T1u+2T2u+3Gu+4Hu) (Au+3T1u+3T2u+4Gu+5Hu)
Hu (T1g+T2g+Gg+Hg) Ag+2T1g+2T2g+3Gg+4Hg Ag+2T1g+2T2g+3Gg+4Hg Ag+3T1g+3T2g+4Gg+5Hg Ag+4T1g+4T2g+5Gg+6Hg (T1u+T2u+Gu+Hu) (Au+2T1u+2T2u+3Gu+4Hu) (Au+2T1u+2T2u+3Gu+4Hu) (Au+3T1u+3T2u+4Gu+5Hu) (Au+4T1u+4T2u+5Gu+6Hu)