# Tetragonal: D4h (4/mmm) - Products

## Irreducible 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

## Dipole 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+E (B2g+Eg) (B1g+Eg) A1g+A2g+B1g+B2g+Eg A2g (A1u+Eu) (A2u+Eu) (B1u+Eu) (B2u+Eu) (A1u+A2u+B1u+B2u+Eu) A1g+E (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+E A1g+A2g+B1g+B2g+Eg B2g (B1u+Eu) (B2u+Eu) (A1u+Eu) (A2u+Eu) (A1u+A2u+B1u+B2u+Eu) (B1g+Eg) (B2g+Eg) A1g+E (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+E (B2g+Eg) (B1g+Eg) A1g+A2g+B1g+B2g+Eg (A2u+Eu) (A1u+Eu) (B2u+Eu) (B1u+Eu) (A1u+A2u+B1u+B2u+Eu) A2u A1g+E (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+E A1g+A2g+B1g+B2g+Eg (B2u+Eu) (B1u+Eu) (A2u+Eu) (A1u+Eu) (A1u+A2u+B1u+B2u+Eu) B2u (B1g+Eg) (B2g+Eg) A1g+E (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)