# Non-crystalographic: D5d - Products

## Irreducible Representation Products:

 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.

 (A2u+E1u) 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)