Non-crystalographic:D_5d- Products

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Representation Products:

⊗	A1g	A2g	E1g	E2g	A1u	A2u	E1u	E2u
A1g	A1g	A2g	E1g	E2g	A1u	A2u	E1u	E2u
A2g	A2g	A1g	E1g	E2g	A2u	A1u	E1u	E2u
E1g	E1g	E1g	A1g+A2g+E2gg	E1g+E2g	E1u	E1u	A1u+A2u+E2u	E1u+E2u
E2g	E2g	E2g	E1g+E2g	A1g+A2g+E2g	E2u	E2u	E1u+E2u	A1u+A2u+E2u
A1u	A1u	A2u	E1u	E2u	A1g	A2g	E1g	E2g
A2u	A2u	A1u	E1u	E2u	A2g	A1g	E1g	E2g
E1u	E1u	E1u	A1u+A2u+E2u	E1u+E2u	E1g	E1g	A1g+A2g+E2gg	E1g+E2g
E2u	E2u	E2u	E1u+E2u	A1u+A2u+E2u	E2g	E2g	E1g+E2g	A1g+A2g+E2g

Transition Products:

For the D_5d point group, the irreducible representation of the dipole operator is (A_2u+E_1u). Transitions that are dipole forbidden are indicated by parentheses.

⊗(A2u+E1u)⊗	A1g	A2g	E1g	E2g	A1u	A2u	E1u	E2u
A1g	(A2u+E1u)	(A1u+E1u)	(A1u+A2u+E1u+E2u)	(E1u+2E2u)	(A2g+E1g)	A1g+E1g	A1g+A2g+E1g+E2g	(E1g+2E2g)
A2g	(A1u+E1u)	(A2u+E1u)	(A1u+A2u+E1u+E2u	(E1u+2E2u)	A1g+E1g	(A2g+E1g)	A1g+A2g+E1g+E2g	(E1g+2E2g)
E1g	(A1u+A2u+E1u+E2u)	(A1u+A2u+E1u+E2u)	(A1u+A2u+3E1u+2E2u)	(A1u+A2u+2E1u+3E2u)	A1g+A2g+E1g+E2g	A1g+A2g+E1g+E2g	A1g+A2g+3E1g+2E2g	A1g+A2g+2E1g+3E2g
E2g	(E1u+2E2u)	(E1u+2E2u)	(A1u+A2u+2E1u+3E2u)	(A1u+A2u+3E1u+2E2u)	(E1g+2E2g)	(E1g+2E2g)	A1g+A2g+2E1g+3E2g	A1g+A2g+3E1g+2E2g
A1g	(A2g+E1g)	A1g+E1g	A1g+A2g+E1g+E2g	(E1g+2E2g)	(A2u+E1u)	(A1u+E1u)	(A1u+A2u+E1u+E2u)	(E1u+2E2u)
A2g	A1g+E1g	(A2g+E1g)	A1g+A2g+E1g+E2g	(E1g+2E2g)	(A1u+E1u)	(A2u+E1u)	(A1u+A2u+E1u+E2u	(E1u+2E2u)
E1g	A1g+A2g+E1g+E2g	A1g+A2g+E1g+E2g	A1g+A2g+3E1g+2E2g	A1g+A2g+2E1g+3E2g	(A1u+A2u+E1u+E2u)	(A1u+A2u+E1u+E2u)	(A1u+A2u+3E1u+2E2u)	(A1u+A2u+2E1u+3E2u)
E2g	(E1g+2E2g)	(E1g+2E2g)	A1g+A2g+2E1g+3E2g	A1g+A2g+3E1g+2E2g	(E1u+2E2u)	(E1u+2E2u)	(A1u+A2u+2E1u+3E2u)	(A1u+A2u+3E1u+2E2u)

• D_5d character table
• D_5d correlation table