University of Exeter

Non-crystalographic: I - Products

Exeter Symmetry Pages

Irreducible Representation Products:

product A T1 T2 G H
A A T1 T2 G H
T1 T1 A+T1+H G+H T2+G+H T1+T2+G+H
T2 T2 G+H A+T2+H T1+G+H T1+T2+G+H
G G T2+G+H T1+G+H A+T1+T2+G+H T1+T2+G+2H
H H T1+T2+G+H T1+T2+G+H T1+T2+G+2H A+T1+T2+2G+2H

Dipole Transition Products:

For the I point group, the irreducible representation of the dipole operator is T1. Transitions that are dipole forbidden are indicated by parentheses.

productT1product A T1 T2 G H
A (T1) A+T1+H (G+H) (T2+G+H) (T1+T2+G+H)
T1 A+T1+H A+3T1+T2+G+2H (T1+2T2+2G+2H) (T1+2T2+3G+3H) A+2T1+2T2+3G+4H
T2 (G+H) (T1+2T2+2G+2H) (2T1+T2+2G+2H) A+2T1+2T2+2G+3H A+2T1+2T2+3G+4H
G (T2+G+H) (T1+2T2+3G+3H) A+2T1+2T2+2G+3H A+3T1+2T2+3G+4H A+3T1+3T2+4G+5H
H (T1+T2+G+H) A+2T1+2T2+3G+4H A+2T1+2T2+3G+4H A+3T1+3T2+4G+5H A+4T1+4T2+5G+6H