Non-crystalographic: Ih - Products |
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 |
For the Ih point group, the irreducible representation of the dipole operator is T1u. Transitions that are dipole forbidden are indicated by parentheses.
T1u | 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) |