University of Exeter

Cubic: Oh (m3m) - Products

Exeter Symmetry Pages

Irreducible Representation Products:

product A1g A2g Eg T1g T2g A1u A2u Eu T1u T2u
A1g A1g A2g Eg T1g T2g A1u A2u Eu T1u T2u
A2g A2g A1g Eg T2g T1g A2u A1u Eu T2u T1u
Eg Eg Eg A1g+A2g+Eg T1g+T2g T1g+T2g Eu Eu A1u+A2u+Eu T1u+T2u T1u+T2u
T1g T1g T2g T1g+T2g A1g+Eg+T1g+T2g A2g+Eg+T1g+T2g T1u T2u T1u+T2u) A1u+Eu+T1u+T2u A2u+Eu+T1u+T2u
T2g T2g T1g T1g+T2g A2g+Eg+T1g+T2g A1g+Eg+T1g+T2g T2u T1u T1u+T2u) A2u+Eu+T1u+T2u A1u+Eu+T1u+T2u
A1u A1u A2u Eu T1u T2u A1g A2g Eg T1g T2g
A2u A2u A1u Eu T2u T1u A2g A1g Eg T2g T1g
Eu Eu Eu A1u+A2u+Eu T1u+T2u T1u+T2u Eg Eg A1g+A2g+Eg T1g+T2g T1g+T2g
T1u T1u T2u T1u+T2u) A1u+Eu+T1u+T2u A2u+Eu+T1u+T2u T1g T2g T1g+T2g A1g+Eg+T1g+T2g A2g+Eg+T1g+T2g
T2u T2u T1u T1u+T2u) A2u+Eu+T1u+T2u A1u+Eu+T1u+T2u T2g T1g T1g+T2g A2g+Eg+T1g+T2g A1g+Eg+T1g+T2g


Dipole Transition Products:

For the Oh point group, the irreducible representation of the dipole operator is T1u. Transitions that are dipole forbidden are indicated by parentheses.

productT1uproduct A1g A2g Eg T1g T2g A1u A2u Eu T1u T2u
A1g (T1u) (T2u) (T1u+T2u) (A1u+Eu+T1u+T2u) (A2u+Eu+T1u+T2u) (T1g) (T2g) (T1g+T2g) A1g+Eg+T1g+T2g (A2g+Eg+T1g+T2g)
A2g (T2u) (T1u) (T1u+T2u) (A2u+Eu+T1u+T2u) (A1u+Eg+T1g+T2g) (T2g) (T1g) (T1g+T2g) (A2g+Eg+T1g+T2g) A1g+Eg+T1g+T2g
Eg (T1u+T2u) (T1u+T2u) (2T1u+2T2u) (A1u+A2u+2Eu+2T1u+2T2u) (A1u+A2u+2Eu+2T1u+2T2u) (T1g+T2g) (T1g+T2g) (2T1g+2T2g) A1g+A2g+2Eg+2T1g+2T2g A1g+A2g+2Eg+2T1g+2T2g
T1g (A1u+Eu+T1u+T2u) (A2u+Eu+T1u+T2u) (A1u+A2u+2Eu+2T1u+2T2u) (A1u+A2u+2Eu+4T1u+3T2u) (A1u+A2u+2Eu+3T1u+4T2u) A1g+Eg+T1g+T2g (A2g+Eg+T1g+T2g) A1g+A2g+2Eg+2T1g+2T2g A1g+A2g+2Eg+4T1g+3T2g A1g+A2g+2Eg+3T1g+4T2g
T2g (A2u+Eu+T1u+T2u) (A1u+Eu+T1u+T2u) (A1u+A2u+2Eu+2T1u+2T2u) (A1u+A2u+2Eu+4T1u+3T2u) (A1u+A2u+2Eu+3T1u+4T2u) (A2g+Eg+T1g+T2g) A1g+Eg+T1g+T2g A1g+A2g+2Eg+2T1g+2T2g A1g+A2g+2Eg+4T1g+3T2g A1g+A2g+2Eg+3T1g+4T2g
A1u (T1g) (T2g) (T1g+T2g) A1g+Eg+T1g+T2g (A2g+Eg+T1g+T2g) (T1u) (T2u) (T1u+T2u) (A1u+Eu+T1u+T2u) (A2u+Eu+T1u+T2u)
A2u (T2g) (T1g) (T1g+T2g) (A2g+Eg+T1g+T2g) A1g+Eg+T1g+T2g (T2u) (T1u) (T1u+T2u) (A2u+Eu+T1u+T2u) (A1u+Eg+T1g+T2g)
Eu (T1g+T2g) (T1g+T2g) (2T1g+2T2g) A1g+A2g+2Eg+2T1g+2T2g A1g+A2g+2Eg+2T1g+2T2g (T1u+T2u) (T1u+T2u) (2T1u+2T2u) (A1u+A2u+2Eu+2T1u+2T2u) (A1u+A2u+2Eu+2T1u+2T2u)
T1u A1g+Eg+T1g+T2g (A2g+Eg+T1g+T2g) A1g+A2g+2Eg+2T1g+2T2g A1g+A2g+2Eg+4T1g+3T2g A1g+A2g+2Eg+3T1g+4T2g (A1u+Eu+T1u+T2u) (A2u+Eu+T1u+T2u) (A1u+A2u+2Eu+2T1u+2T2u) (A1u+A2u+2Eu+4T1u+3T2u) (A1u+A2u+2Eu+3T1u+4T2u)
T2u (A2g+Eg+T1g+T2g) A1g+Eg+T1g+T2g A1g+A2g+2Eg+2T1g+2T2g A1g+A2g+2Eg+4T1g+3T2g A1g+A2g+2Eg+3T1g+4T2g (A2u+Eu+T1u+T2u) (A1u+Eu+T1u+T2u) (A1u+A2u+2Eu+2T1u+2T2u) (A1u+A2u+2Eu+4T1u+3T2u) (A1u+A2u+2Eu+3T1u+4T2u)