University of Exeter

Non-crystalographic: D5d - Products

Exeter Symmetry Pages

Irreducible Representation Products:

product A1g A2g E1g E2g A1u A2u E1u E2u
A1g A1g A2g E1g E2g A1u A2u E1u E2u
A2g A2g A1g E1g E2g A2u A1u E1u E2u
E1g E1g E1g A1g+A2g+E2gg E1g+E2g E1u E1u A1u+A2u+E2u E1u+E2u
E2g E2g E2g E1g+E2g A1g+A2g+E2g E2u E2u E1u+E2u A1u+A2u+E2u
A1u A1u A2u E1u E2u A1g A2g E1g E2g
A2u A2u A1u E1u E2u A2g A1g E1g E2g
E1u E1u E1u A1u+A2u+E2u E1u+E2u E1g E1g A1g+A2g+E2gg E1g+E2g
E2u E2u E2u E1u+E2u A1u+A2u+E2u E2g E2g E1g+E2g A1g+A2g+E2g

Dipole Transition Products:

For the D5d 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 E1g E2g A1u A2u E1u E2u
A1g (A2u+E1u) (A1u+E1u) (A1u+A2u+E1u+E2u) (E1u+2E2u) (A2g+E1g) A1g+E1g A1g+A2g+E1g+E2g (E1g+2E2g)
A2g (A1u+E1u) (A2u+E1u) (A1u+A2u+E1u+E2u (E1u+2E2u) A1g+E1g (A2g+E1g) A1g+A2g+E1g+E2g (E1g+2E2g)
E1g (A1u+A2u+E1u+E2u) (A1u+A2u+E1u+E2u) (A1u+A2u+3E1u+2E2u) (A1u+A2u+2E1u+3E2u) A1g+A2g+E1g+E2g A1g+A2g+E1g+E2g A1g+A2g+3E1g+2E2g A1g+A2g+2E1g+3E2g
E2g (E1u+2E2u) (E1u+2E2u) (A1u+A2u+2E1u+3E2u) (A1u+A2u+3E1u+2E2u) (E1g+2E2g) (E1g+2E2g) A1g+A2g+2E1g+3E2g A1g+A2g+3E1g+2E2g
A1g (A2g+E1g) A1g+E1g A1g+A2g+E1g+E2g (E1g+2E2g) (A2u+E1u) (A1u+E1u) (A1u+A2u+E1u+E2u) (E1u+2E2u)
A2g A1g+E1g (A2g+E1g) A1g+A2g+E1g+E2g (E1g+2E2g) (A1u+E1u) (A2u+E1u) (A1u+A2u+E1u+E2u (E1u+2E2u)
E1g A1g+A2g+E1g+E2g A1g+A2g+E1g+E2g A1g+A2g+3E1g+2E2g A1g+A2g+2E1g+3E2g (A1u+A2u+E1u+E2u) (A1u+A2u+E1u+E2u) (A1u+A2u+3E1u+2E2u) (A1u+A2u+2E1u+3E2u)
E2g (E1g+2E2g) (E1g+2E2g) A1g+A2g+2E1g+3E2g A1g+A2g+3E1g+2E2g (E1u+2E2u) (E1u+2E2u) (A1u+A2u+2E1u+3E2u) (A1u+A2u+3E1u+2E2u)

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