University of Exeter

Hexagonal: D6 (622) - Products

Exeter Symmetry Pages

Irreducible Representation Products:

product A1 A2 B1 B2 E1 E2
A1 A1 A2 B1 B2 E1 E2
A2 A2 A1 B2 B1 E1 E2
B1 B1 B2 A1 A2 E2 E1
B2 B2 B1 A2 A1 E2 E1
E1 E1 E1 E2 E2 A1+A2+E2 B1+B2+E1
E2 E2 E2 E1 E1 B1+B2+E1 A1+A2+E2

Dipole Transition Products:

For the D6 point group, the irreducible representation of the dipole operator is (A2+E1). Transitions that are dipole forbidden are indicated by parentheses.

product(A2+E1)product A1 A2 B1 B2 E1 E2
A1 (A2+E1) A1+E1 (B2+E2) (B1+E2) A1+A2+E1+E2 (B1+B2+E1+E2)
A2 A1+E1 (A2+E1) (B1+E2) (B2+E2) A1+A2+E1+E2 (B1+B2+E1+E2)
B1 (B2+E2) (B1+E2) (A2+E1) A1+E1 (B1+B2+E1+E2) A1+A2+E1+E2
B2 (B1+E2) (B2+E2) A1+E1 (A2+E1) (B1+B2+E1+E2) A1+A2+E1+E2
E1 A1+A2+E1+E2 A1+A2+E1+E2 (B1+B2+E1+E2) (B1+B2+E1+E2) A1+A2+B1+B2+3E1+E2 A1+A2+B1+B2+E1+3E2
E2 (B1+B2+E1+E2) (B1+B2+E1+E2) A1+A2+E1+E2 A1+A2+E1+E2 A1+A2+B1+B2+E1+3E2 A1+A2+B1+B2+3E1+E2