Symmetry Pages

Hexagonal:C6v(6mm) - Products

Symmetry Pages

Representation Products:

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

Transition Products:

For the C6v point group, the irreducible representation of the dipole operator is (A1+E1). Transitions that are dipole forbidden are indicated by parentheses.

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

Revised: © University of Newcastle upon Tyne, UK