University of Exeter

Cubic: Td (-43m) - Products

Exeter Symmetry Pages

Irreducible Representation Products:

product A1 A2 E T1 T2
A1 A1 A2 E T1 T2
A2 A2 A1 E T2 T1
E E E A1+A2+E T1+T2 T1+T2
T1 T1 T2 T1+T2 A1+E+T1+T2 A2+E+T1+T2
T2 T2 T1 T1+T2 A2+E+T1+T2 A1+E+T1+T2

Dipole Transition Products:

For the Td point group, the irreducible representation of the dipole operator is T2. Transitions that are dipole forbidden are indicated by parentheses.

productT2product A1 A2 E T1 T2
A1 (T2) (T1) (T1+T2) (A2+E+T1+T2) A1+E+T1+T2
A2 (T1) (T2) (T1+T2) A1+E+T1+T2 (A2+E+T1+T2)
E (T1+T2) (T1+T2) (2T1+2T2) A1+A2+2E+2T1+2T2 A1+A2+2E+2T1+2T2
T1 (A2+E+T1+T2) A1+E+T1+T2 A1+A2+2E+2T1+2T2 A1+A2+2E+3T1+4T2 A1+A2+2E+4T1+3T2
T2 A1+E+T1+T2 (A2+E+T1+T2) A1+A2+2E+2T1+2T2 A1+A2+2E+4T1+3T2 A1+A2+2E+3T1+4T2