University of Exeter

Cubic: Th (m3) - Products

Exeter Symmetry Pages

Irreducible Representation Products:

product Ag Eg Tg Au Eu Tu
Ag Ag Eg Tg Au Eu Tu
Eg Eg 2Ag+Eg 2Tg Eu 2Au+Eu 2Tu
Tg Tg 2Tg Ag+Eg+2Tg Tu 2Tu Au+Eu+2Tu
Au Au Eu Tu Ag Eg Tg
Eu Eu 2Au+Eu 2Tu Eg 2Ag+Eg 2Tg
Tu Tu 2Tu Au+Eu+2Tu Tg 2Tg Ag+Eg+2Tg

Dipole Transition Products:

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

productTuproduct Ag Eg Tg Au Eu Tu
Ag (Tu) (2Tu) (Au+Eu+2Tu) (Tg) (2Tg) Ag+Eg+2Tg
Eg (2Tu) (4Tu) (2Au+2Eu+4Tu) (2Tg) (4Tg) 2Ag+2Eg+4Tg
Tg (2Au+2Eu+4Tu) (2Au+2Eu+4Tu) (2Au+2Eu+7Tu) 2Ag+2Eg+4Tg 2Ag+2Eg+4Tg 2Ag+2Eg+7Tg
Au (Tg) (2Tg) Ag+Eg+2Tg (Tu) (2Tu) (Au+Eu+2Tu)
Eu (2Tg) (4Tg) 2Ag+2Eg+4Tg (2Tu) (4Tu) (2Au+2Eu+4Tu)
Tu 2Ag+2Eg+4Tg 2Ag+2Eg+4Tg 2Ag+2Eg+7Tg (2Au+2Eu+4Tu) (2Au+2Eu+4Tu) (2Au+2Eu+7Tu)