oh - Point Group Symmetry Character Tables

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oh - Point Group Symmetry Character Tables

O_h grupa punktowa

nieabelowe, nieredukowalne reprezentacje 10(20)

Tabela charakterów dla grupy punktowej O_h

	E	8C₃	6C₂	6C₄	3C₂ =(C₄)²	i	6S₄	8S₆	3σ_h	6σ_d	linear, rotations	quadratic
A_1g	1	1	1	1	1	1	1	1	1	1		x²+y²+z²
A_2g	1	1	-1	-1	1	1	-1	1	1	-1
E_g	2	-1	0	0	2	2	0	-1	2	0		(2z²-x²-y², x²-y²)
T_1g	3	0	-1	1	-1	3	1	0	-1	-1	(R_x, R_y, R_z)
T_2g	3	0	1	-1	-1	3	-1	0	-1	1		(xz, yz, xy)
A_1u	1	1	1	1	1	-1	-1	-1	-1	-1
A_2u	1	1	-1	-1	1	-1	1	-1	-1	1
E_u	2	-1	0	0	2	-2	0	1	-2	0
T_1u	3	0	-1	1	-1	-3	-1	0	1	1	(x, y, z)
T_2u	3	0	1	-1	-1	-3	1	0	1	-1

Tabela mnożenia grupy punktowej O_h

	A_1g	A_2g	E_g	T_1g	T_2g	A_1u	A_2u	E_u	T_1u	T_2u
A_1g	A_1g	A_2g	E_g	T_1g	T_2g	A_1u	A_2u	E_u	T_1u	T_2u
A_2g	A_2g	A_1g	E_g	T_2g	T_1g	A_2u	A_1u	E_u	T_2u	T_1u
E_g	E_g	E_g	A_1g+A_2g+E_g	T_1g+T_2g	T_1g+T_2g	E_u	E_u	A_1u+A_2u+E_u	T_1u+T_2u	T_1u+T_2u
T_1g	T_1g	T_2g	T_1g+T_2g	A_1g+E_g+T_1g+T_2g	A_2g+E_g+T_1g+T_2g	T_1u	T_2u	T_1u+T_2u	A_1u+E_u+T_1u+T_2u	A_2u+E_u+T_1u+T_2u
T_2g	T_2g	T_1g	T_1g+T_2g	A_2g+E_g+T_1g+T_2g	A_1g+E_g+T_1g+T_2g	T_2u	T_1u	T_1u+T_2u	A_2u+E_u+T_1u+T_2u	A_1u+E_u+T_1u+T_2u
A_1u	A_1u	A_2u	E_u	T_1u	T_2u	A_1g	A_2g	E_g	T_1g	T_2g
A_2u	A_2u	A_1u	E_u	T_2u	T_1u	A_2g	A_1g	E_g	T_2g	T_1g
E_u	E_u	E_u	A_1u+A_2u+E_u	T_1u+T_2u	T_1u+T_2u	E_g	E_g	A_1g+A_2g+E_g	T_1g+T_2g	T_1g+T_2g
T_1u	T_1u	T_2u	T_1u+T_2u	A_1u+E_u+T_1u+T_2u	A_2u+E_u+T_1u+T_2u	T_1g	T_2g	T_1g+T_2g	A_1g+E_g+T_1g+T_2g	A_2g+E_g+T_1g+T_2g
T_2u	T_2u	T_1u	T_1u+T_2u	A_2u+E_u+T_1u+T_2u	A_1u+E_u+T_1u+T_2u	T_2g	T_1g	T_1g+T_2g	A_2g+E_g+T_1g+T_2g	A_1g+E_g+T_1g+T_2g

C₁	C_s	C_i
C₂	C₃	C₄	C₅	C₆
C_2v	C_3v	C_4v	C_5v	C_6v
C_2h	C_3h	C_4h	C_5h	C_6h
D₂	D₃	D₄	D₅	D₆
D_2h	D_3h	D_4h	D_5h	D_6h
D_2d	D_3d	D_4d	D_5d	D_6d
S₄	S₆	S₈	S₁₀
T_d	O_h	I_h
C_∞v	D_∞h

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