Cubic: O_h (m3m) - Products

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Representation Products:

⊗	A1g	A2g	Eg	T1g	T2g	A1u	A2u	Eu	T1u	T2u
A1g	A1g	A2g	Eg	T1g	T2g	A1u	A2u	Eu	T1u	T2u
A2g	A2g	A1g	Eg	T2g	T1g	A2u	A1u	Eu	T2u	T1u
Eg	Eg	Eg	A1g+A2g+Eg	T1g+T2g	T1g+T2g	Eu	Eu	A1u+A2u+Eu	T1u+T2u	T1u+T2u
T1g	T1g	T2g	T1g+T2g	A1g+Eg+T1g+T2g	A2g+Eg+T1g+T2g	T1u	T2u	T1u+T2u)	A1u+Eu+T1u+T2u	A2u+Eu+T1u+T2u
T2g	T2g	T1g	T1g+T2g	A2g+Eg+T1g+T2g	A1g+Eg+T1g+T2g	T2u	T1u	T1u+T2u)	A2u+Eu+T1u+T2u	A1u+Eu+T1u+T2u
A1u	A1u	A2u	Eu	T1u	T2u	A1g	A2g	Eg	T1g	T2g
A2u	A2u	A1u	Eu	T2u	T1u	A2g	A1g	Eg	T2g	T1g
Eu	Eu	Eu	A1u+A2u+Eu	T1u+T2u	T1u+T2u	Eg	Eg	A1g+A2g+Eg	T1g+T2g	T1g+T2g
T1u	T1u	T2u	T1u+T2u)	A1u+Eu+T1u+T2u	A2u+Eu+T1u+T2u	T1g	T2g	T1g+T2g	A1g+Eg+T1g+T2g	A2g+Eg+T1g+T2g
T2u	T2u	T1u	T1u+T2u)	A2u+Eu+T1u+T2u	A1u+Eu+T1u+T2u	T2g	T1g	T1g+T2g	A2g+Eg+T1g+T2g	A1g+Eg+T1g+T2g

Transition Products:

For the O_h point group, the irreducible representation of the dipole operator is T_1u. Transitions that are dipole forbidden are indicated by parentheses.

⊗T1u⊗	A1g	A2g	Eg	T1g	T2g	A1u	A2u	Eu	T1u	T2u
A1g	(T1u)	(T2u)	(T1u+T2u)	(A1u+Eu+T1u+T2u)	(A2u+Eu+T1u+T2u)	(T1g)	(T2g)	(T1g+T2g)	A1g+Eg+T1g+T2g	(A2g+Eg+T1g+T2g)
A2g	(T2u)	(T1u)	(T1u+T2u)	(A2u+Eu+T1u+T2u)	(A1u+Eg+T1g+T2g)	(T2g)	(T1g)	(T1g+T2g)	(A2g+Eg+T1g+T2g)	A1g+Eg+T1g+T2g
Eg	(T1u+T2u)	(T1u+T2u)	(2T1u+2T2u)	(A1u+A2u+2Eu+2T1u+2T2u)	(A1u+A2u+2Eu+2T1u+2T2u)	(T1g+T2g)	(T1g+T2g)	(2T1g+2T2g)	A1g+A2g+2Eg+2T1g+2T2g	A1g+A2g+2Eg+2T1g+2T2g
T1g	(A1u+Eu+T1u+T2u)	(A2u+Eu+T1u+T2u)	(A1u+A2u+2Eu+2T1u+2T2u)	(A1u+A2u+2Eu+4T1u+3T2u)	(A1u+A2u+2Eu+3T1u+4T2u)	A1g+Eg+T1g+T2g	(A2g+Eg+T1g+T2g)	A1g+A2g+2Eg+2T1g+2T2g	A1g+A2g+2Eg+4T1g+3T2g	A1g+A2g+2Eg+3T1g+4T2g
T2g	(A2u+Eu+T1u+T2u)	(A1u+Eu+T1u+T2u)	(A1u+A2u+2Eu+2T1u+2T2u)	(A1u+A2u+2Eu+4T1u+3T2u)	(A1u+A2u+2Eu+3T1u+4T2u)	(A2g+Eg+T1g+T2g)	A1g+Eg+T1g+T2g	A1g+A2g+2Eg+2T1g+2T2g	A1g+A2g+2Eg+4T1g+3T2g	A1g+A2g+2Eg+3T1g+4T2g
A1u	(T1g)	(T2g)	(T1g+T2g)	A1g+Eg+T1g+T2g	(A2g+Eg+T1g+T2g)	(T1u)	(T2u)	(T1u+T2u)	(A1u+Eu+T1u+T2u)	(A2u+Eu+T1u+T2u)
A2u	(T2g)	(T1g)	(T1g+T2g)	(A2g+Eg+T1g+T2g)	A1g+Eg+T1g+T2g	(T2u)	(T1u)	(T1u+T2u)	(A2u+Eu+T1u+T2u)	(A1u+Eg+T1g+T2g)
Eu	(T1g+T2g)	(T1g+T2g)	(2T1g+2T2g)	A1g+A2g+2Eg+2T1g+2T2g	A1g+A2g+2Eg+2T1g+2T2g	(T1u+T2u)	(T1u+T2u)	(2T1u+2T2u)	(A1u+A2u+2Eu+2T1u+2T2u)	(A1u+A2u+2Eu+2T1u+2T2u)
T1u	A1g+Eg+T1g+T2g	(A2g+Eg+T1g+T2g)	A1g+A2g+2Eg+2T1g+2T2g	A1g+A2g+2Eg+4T1g+3T2g	A1g+A2g+2Eg+3T1g+4T2g	(A1u+Eu+T1u+T2u)	(A2u+Eu+T1u+T2u)	(A1u+A2u+2Eu+2T1u+2T2u)	(A1u+A2u+2Eu+4T1u+3T2u)	(A1u+A2u+2Eu+3T1u+4T2u)
T2u	(A2g+Eg+T1g+T2g)	A1g+Eg+T1g+T2g	A1g+A2g+2Eg+2T1g+2T2g	A1g+A2g+2Eg+4T1g+3T2g	A1g+A2g+2Eg+3T1g+4T2g	(A2u+Eu+T1u+T2u)	(A1u+Eu+T1u+T2u)	(A1u+A2u+2Eu+2T1u+2T2u)	(A1u+A2u+2Eu+4T1u+3T2u)	(A1u+A2u+2Eu+3T1u+4T2u)

• O_h character table
• O_h correlation table