Tetragonal: D_2d (−42m) - Products

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Representation Products:

⊗	A1	A2	B1	B2	E
A1	A1	A2	B1	B2	E
A2	A2	A1	B2	B1	E
B1	B1	B2	A1	A2	E
B2	B2	B1	A2	A1	E
E	E	E	E	E	A1+A2+B1+B2

Transition Products:

For the D_2d point group, the irreducible representation of the dipole operator is B₂+E. Transitions that are dipole forbidden are indicated by parentheses.

⊗(B2+E)⊗	A1	A2	B1	B2	E
A1	(B2+E)	(B1+E)	(A2+E)	A1+E	A1+A2+B1+B2+E
A2	(B1+E)	(B2+E)	A1+E	(A2+E)	A1+A2+B1+B2+E
B1	(A2+E)	A1+E	(B2+E)	(B1+E)	A1+A2+B1+B2+E
B2	A1+E	(A2+E)	(B1+E)	(B2+E)	A1+A2+B1+B2+E
E	A1+A2+B1+B2+E	A1+A2+B1+B2+E	A1+A2+B1+B2+E	A1+A2+B1+B2+E	A1+A2+B1+B2+4E

• D_2d character table
• D_2d correlation table