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Representation Products:
⊗ |
A1g |
A2g |
B1g |
B2g |
Eg |
A1u |
A2u |
B1u |
B2u |
Eu |
A1g |
A1g |
A2g |
B1g |
B2g |
Eg |
A1u |
A2u |
B1u |
B2u |
Eu |
A2g |
A2g |
A1g |
B2g |
B1g |
Eg |
A2u |
A1u |
B2u |
B1u |
Eu |
B1g |
B1g |
B2g |
A1g |
A2g |
Eg |
B1u |
B2u |
A1u |
A2u |
Eu |
B2g |
B2g |
B1g |
A2g |
A1g |
Eg |
B2u |
B1u |
A2u |
A1u |
Eu |
Eg |
Eg |
Eg |
Eg |
Eg |
A1g+A2g+B1g+B2g |
Eu |
Eu |
Eu |
Eu |
A1u+A2u+B1u+B2u |
A1u |
A1u |
A2u |
B1u |
B2u |
Eu |
A1g |
A2g |
B1g |
B2g |
Eg |
A2u |
A2u |
A1u |
B2u |
B1u |
Eu |
A2g |
A1g |
B2g |
B1g |
Eg |
B1u |
B1u |
B2u |
A1u |
A2u |
Eu |
B1g |
B2g |
A1g |
A2g |
Eg |
B2u |
B2u |
B1u |
A2u |
A1u |
Eu |
B2g |
B1g |
A2g |
A1g |
Eg |
Eu |
Eu |
Eu |
Eu |
Eu |
A1u+A2u+B1u+B2u |
Eg |
Eg |
Eg |
Eg |
A1g+A2g+B1g+B2g |
Transition Products:
For the D4h point group, the irreducible representation of the dipole operator is (A2u+Eu). Transitions that are dipole forbidden are indicated by parentheses.
⊗(A2u+Eu)⊗ |
A1g |
A2g |
B1g |
B2g |
Eg |
A1u |
A2u |
B1u |
B2u |
Eu |
A1g |
(A2u+Eu) |
(A1u+Eu) |
(B2u+Eu) |
(B1u+Eu) |
(A1u+A2u+B1u+B2u+Eu) |
(A2g+Eg) |
A1g+Eg |
(B2g+Eg) |
(B1g+Eg) |
A1g+A2g+B1g+B2g+Eg |
A2g |
(A1u+Eu) |
(A2u+Eu) |
(B1u+Eu) |
(B2u+Eu) |
(A1u+A2u+B1u+B2u+Eu) |
A1g+Eg |
(A2g+Eg) |
(B1g+Eg) |
(B2g+Eg) |
A1g+A2g+B1g+B2g+Eg |
B1g |
(B2u+Eu) |
(B1u+Eu) |
(A2u+Eu) |
(A1u+Eu) |
(A1u+A2u+B1u+B2u+Eu) |
(B2g+Eg) |
(B1g+Eg) |
(A2g+Eg) |
A1g+Eg |
A1g+A2g+B1g+B2g+Eg |
B2g |
(B1u+Eu) |
(B2u+Eu) |
(A1u+Eu) |
(A2u+Eu) |
(A1u+A2u+B1u+B2u+Eu) |
(B1g+Eg) |
(B2g+Eg) |
A1g+Eg |
(A2g+Eg) |
A1g+A2g+B1g+B2g+Eg |
Eg |
(A1u+A2u+B1u+B2u+Eu) |
(A1u+A2u+B1u+B2u+Eu) |
(A1u+A2u+B1u+B2u+Eu) |
(A1u+A2u+B1u+B2u+Eu) |
(A1u+A2u+B1u+B2u+4Eu) |
A1g+A2g+B1g+B2g+Eg |
A1g+A2g+B1g+B2g+Eg |
A1g+A2g+B1g+B2g+Eg |
A1g+A2g+B1g+B2g+Eg |
A1g+A2g+B1g+B2g+4Eg |
A1u |
(A2g+Eg) |
A1g+Eg |
(B2g+Eg) |
(B1g+Eg) |
A1g+A2g+B1g+B2g+Eg |
(A2u+Eu) |
(A1u+Eu) |
(B2u+Eu) |
(B1u+Eu) |
(A1u+A2u+B1u+B2u+Eu) |
A2u |
A1g+Eg |
(A2g+Eg) |
(B1g+Eg) |
(B2g+Eg) |
A1g+A2g+B1g+B2g+Eg |
(A1u+Eu) |
(A2u+Eu) |
(B1u+Eu) |
(B2u+Eu) |
(A1u+A2u+B1u+B2u+Eu) |
B1u |
(B2g+Eg) |
(B1g+Eg) |
(A2g+Eg) |
A1g+Eg |
A1g+A2g+B1g+B2g+Eg |
(B2u+Eu) |
(B1u+Eu) |
(A2u+Eu) |
(A1u+Eu) |
(A1u+A2u+B1u+B2u+Eu) |
B2u |
(B1g+Eg) |
(B2g+Eg) |
A1g+Eg |
(A2g+Eg) |
A1g+A2g+B1g+B2g+Eg |
(B1u+Eu) |
(B2u+Eu) |
(A1u+Eu) |
(A2u+Eu) |
(A1u+A2u+B1u+B2u+Eu) |
Eu |
A1g+A2g+B1g+B2g+Eg |
A1g+A2g+B1g+B2g+Eg |
A1g+A2g+B1g+B2g+Eg |
A1g+A2g+B1g+B2g+Eg |
A1g+A2g+B1g+B2g+4Eg |
(A1u+A2u+B1u+B2u+Eu) |
(A1u+A2u+B1u+B2u+Eu) |
(A1u+A2u+B1u+B2u+Eu) |
(A1u+A2u+B1u+B2u+Eu) |
(A1u+A2u+B1u+B2u+4Eu) |
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