University of Exeter

Hexagonal: D6h (6/mmm) - Products

Exeter Symmetry Pages

Irreducible Representation Products:

product 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

Dipole 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.

product(A2u+E1u)product 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)

Last modified: Fri Oct 6 16:30:53 BST 2000 by JPG (goss@excc.ex.ac.uk)
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