Symmetry Pages

Trigonal:D3d(-3m) - Products

Symmetry Pages

Representation Products:

A1g A2g Eg A1u A2u Eu
A1g A1g A2g Eg A1u A2u Eu
A2g A2g A1g Eg A2u A1u Eu
Eg Eg Eg A1g+A2g+Eg Eu Eu A1u+A2u+Eu
A1u A1u A2u Eu A1g A2g Eg
A2u A2u A1u Eu A2g A1g Eg
Eu Eu Eu A1u+A2u+Eu Eg Eg A1g+A2g+Eg

Transition Products:

For the D3d 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 Eg A1u A2u Eu
A1g (A2u+Eu) (A1u+Eu) (A1u+A2u+2Eu) (A2g+Eg) A1g+Eg A1g+A2g+2Eg
A2g (A1u+Eu) (A2u+Eu) (A1u+A2u+2Eu) A1g+Eg (A2g+Eg) A1g+A2g+2Eg
Eg (A1u+A2u+Eu) (A1u+A2u+Eu) (2A1u+2A2u+4Eu) A1g+A2g+Eg A1g+A2g+Eg 2A1g+2A2g+4Eg
A1u (A2g+Eg) A1g+Eg A1g+A2g+2Eg (A2u+Eu) (A1u+Eu) (A1u+A2u+2Eu)
A2u A1g+Eg (A2g+Eg) A1g+A2g+2Eg (A1u+Eu) (A2u+Eu) (A1u+A2u+2Eu)
Eu A1g+A2g+Eg A1g+A2g+Eg 2A1g+2A2g+4Eg (A1u+A2u+Eu) (A1u+A2u+Eu) (2A1u+2A2u+4Eu)

Revised: © University of Newcastle upon Tyne, UK