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Representation Products:
⊗ |
Ag |
T1g |
T2g |
Gg |
Hg |
Au |
T1u |
T2u |
Gu |
Hu |
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 |
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.
⊗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) |
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