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Representation Products:
⊗ |
A1g |
A2g |
B1g |
B2g |
E1g |
E2g |
A1u |
A2u |
B1u |
B2u |
E1u |
E2u |
A1g |
A1g |
A2g |
B1g |
B2g |
E1g |
E2g |
A1u |
A2u |
B1u |
B2u |
E1u |
E2u |
A2g |
A2g |
A1g |
B2g |
B1g |
E1g |
E2g |
A2u |
A1u |
B2u |
B1u |
E1u |
E2u |
B1g |
B1g |
B2g |
A1g |
A2g |
E2g |
E1g |
B1u |
B2u |
A1u |
A2u |
E2u |
E1u |
B2g |
B2g |
B1g |
A2g |
A1g |
E2g |
E1g |
B2u |
B1u |
A2u |
A1u |
E2u |
E1u |
E1g |
E1g |
E1g |
E2g |
E2g |
A1g+A2g+E2g |
B1g+B2g+E1g |
E1u |
E1u |
E2u |
E2u |
A1u+A2u+E2u |
B1u+B2u+E1u |
E2g |
E2g |
E2g |
E1g |
E1g |
B1g+B2g+E1g |
A1g+A2g+E2g |
E2u |
E2u |
E1u |
E1u |
B1u+B2u+E1u |
A1u+A2u+E2u |
A1u |
A1u |
A2u |
B1u |
B2u |
E1u |
E2u |
A1g |
A2g |
B1g |
B2g |
E1g |
E2g |
A2u |
A2u |
A1u |
B2u |
B1u |
E1u |
E2u |
A2g |
A1g |
B2g |
B1g |
E1g |
E2g |
B1u |
B1u |
B2u |
A1u |
A2u |
E2u |
E1u |
B1g |
B2g |
A1g |
A2g |
E2g |
E1g |
B2u |
B2u |
B1u |
A2u |
A1u |
E2u |
E1u |
B2g |
B1g |
A2g |
A1g |
E2g |
E1g |
E1u |
E1u |
E1u |
E2u |
E2u |
A1u+A2u+E2u |
B1u+B2u+E1u |
E1g |
E1g |
E2g |
E2g |
A1g+A2g+E2g |
B1g+B2g+E1g |
E2u |
E2u |
E2u |
E1u |
E1u |
B1u+B2u+E1u |
A1u+A2u+E2u |
E2g |
E2g |
E1g |
E1g |
B1g+B2g+E1g |
A1g+A2g+E2g |
Transition Products:
For the D6h point group, the irreducible representation of the dipole operator is (A2u+E1u). Transitions that are dipole forbidden are indicated by parentheses.
⊗(A2u+E1u)⊗ |
A1g |
A2g |
B1g |
B2g |
E1g |
E2g |
A1u |
A2u |
B1u |
B2u |
E1u |
E2u |
A1g |
(A2u+E1u) |
(A1u+E1u) |
(B2u+E2u) |
(B1u+E2u) |
(A1u+A2u+E1u+E2u) |
(B1u+B2u+E1u+E2u) |
(A2g+E1g) |
A1g+E1g |
(B2g+E2g) |
(B1g+E2g) |
A1g+A2g+E1g+E2g |
(B1g+B2g+E1g+E2g) |
A2g |
(A1u+E1u) |
(A2u+E1u) |
(B1u+E2u) |
(B2u+E2u) |
(A1u+A2u+E1u+E2u) |
(B1u+B2u+E1u+E2u) |
A1g+E1g |
(A2g+E1g) |
(B1g+E2g) |
(B2g+E2g) |
A1g+A2g+E1g+E2g |
(B1g+B2g+E1g+E2g) |
B1g |
(B2u+E2u) |
(B1u+E2u) |
(A2u+E1u) |
(A1u+E1u) |
(B1u+B2u+E1u+E2u) |
(A1u+A2u+E1u+E2u) |
(B2g+E2g) |
(B1g+E2g) |
(A2g+E1g) |
A1g+E1g |
(B1g+B2g+E1g+E2g) |
A1g+A2g+E1g+E2g |
B2g |
(B1u+E2u) |
(B2u+E2u) |
(A1u+E1u) |
(A2u+E1u) |
(B1u+B2u+E1u+E2u) |
(A1u+A2u+E1u+E2u) |
(B1g+E2g) |
(B2g+E2g) |
A1g+E1g |
(A2g+E1g) |
(B1g+B2g+E1g+E2g) |
A1g+A2g+E1g+E2g |
E1g |
(A1u+A2u+E1u+E2u) |
(A1u+A2u+E1u+E2u) |
(B1u+B2u+E1u+E2u) |
(B1u+B2u+E1u+E2u) |
(A1u+A2u+B1u+B2u+3E1u+E2u) |
(A1u+A2u+B1u+B2u+E1u+3E2u) |
A1g+A2g+E1g+E2g |
A1g+A2g+E1g+E2g |
(B1g+B2g+E1g+E2g) |
(B1g+B2g+E1g+E2g) |
A1g+A2g+B1g+B2g+3E1g+E2g |
A1g+A2g+B1g+B2g+E1g+3E2g |
E2g |
(A1u+A2u+E1u+E2u) |
(A1u+A2u+E1u+E2u) |
(B1u+B2u+E1u+E2u) |
(B1u+B2u+E1u+E2u) |
(A1u+A2u+B1u+B2u+E1u+3E2u) |
(A1u+A2u+B1u+B2u+3E1u+E2u) |
A1g+A2g+E1g+E2g |
A1g+A2g+E1g+E2g |
(B1g+B2g+E1g+E2g) |
(B1g+B2g+E1g+E2g) |
A1g+A2g+B1g+B2g+E1g+3E2g |
A1g+A2g+B1g+B2g+3E1g+E2g |
A1u |
(A2g+E1g) |
A1g+E1g |
(B2g+E2g) |
(B1g+E2g) |
A1g+A2g+E1g+E2g |
(B1g+B2g+E1g+E2g) |
(A2u+E1u) |
(A1u+E1u) |
(B2u+E2u) |
(B1u+E2u) |
(A1u+A2u+E1u+E2u) |
(B1u+B2u+E1u+E2u) |
A2u |
A1g+E1g |
(A2g+E1g) |
(B1g+E2g) |
(B2g+E2g) |
A1g+A2g+E1g+E2g |
(B1g+B2g+E1g+E2g) |
(A1u+E1u) |
(A2u+E1u) |
(B1u+E2u) |
(B2u+E2u) |
(A1u+A2u+E1u+E2u) |
(B1u+B2u+E1u+E2u) |
B1u |
(B2g+E2g) |
(B1g+E2g) |
(A2g+E1g) |
A1g+E1g |
(B1g+B2g+E1g+E2g) |
A1g+A2g+E1g+E2g |
(B2u+E2u) |
(B1u+E2u) |
(A2u+E1u) |
(A1u+E1u) |
(B1u+B2u+E1u+E2u) |
(A1u+A2u+E1u+E2u) |
B2u |
(B1g+E2g) |
(B2g+E2g) |
A1g+E1g |
(A2g+E1g) |
(B1g+B2g+E1g+E2g) |
A1g+A2g+E1g+E2g |
(B1u+E2u) |
(B2u+E2u) |
(A1u+E1u) |
(A2u+E1u) |
(B1u+B2u+E1u+E2u) |
(A1u+A2u+E1u+E2u) |
E1u |
A1g+A2g+E1g+E2g |
A1g+A2g+E1g+E2g |
(B1g+B2g+E1g+E2g) |
(B1g+B2g+E1g+E2g) |
A1g+A2g+B1g+B2g+3E1g+E2g |
A1g+A2g+B1g+B2g+E1g+3E2g |
(A1u+A2u+E1u+E2u) |
(A1u+A2u+E1u+E2u) |
(B1u+B2u+E1u+E2u) |
(B1u+B2u+E1u+E2u) |
(A1u+A2u+B1u+B2u+3E1u+E2u) |
(A1u+A2u+B1u+B2u+E1u+3E2u) |
E2u |
(B1g+B2g+E1g+E2g) |
(B1g+B2g+E1g+E2g) |
A1g+A2g+E1g+E2g |
A1g+A2g+E1g+E2g |
A1g+A2g+B1g+B2g+E1g+3E2g |
A1g+A2g+B1g+B2g+3E1g+E2g |
(A1u+A2u+E1u+E2u) |
(A1u+A2u+E1u+E2u) |
(B1u+B2u+E1u+E2u) |
(B1u+B2u+E1u+E2u) |
(A1u+A2u+B1u+B2u+E1u+3E2u) |
(A1u+A2u+B1u+B2u+3E1u+E2u) |
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