d5d - Point Group Symmetry Character Tables

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d5d - Point Group Symmetry Character Tables

D_5d 점군

비가환군, 8(12) 기약 표현
D_5d 점군의 하위 군: C_s, C_i, C₂, C₅, D₅, C_5v, S₁₀

D_5d 점군에 대한 지표표

	E	2C₅	2(C₅)²	5C'₂	i	2(S₁₀)³	2S₁₀	5σ_d	linear, rotations	quadratic
A_1g	1	1	1	1	1	1	1	1		x²+y², z²
A_2g	1	1	1	-1	1	1	1	-1	R_z
E_1g	2	2cos(2π/5)	2cos(4π/5)	0	2	2cos(2π/5)	2cos(4π/5)	0	(R_x, R_y)	(xz, yz)
E_2g	2	2cos(4π/5)	2cos(2π/5)	0	2	2cos(4π/5)	2cos(2π/5)	0		(x²-y², xy)
A_1u	1	1	1	1	-1	-1	-1	-1
A_2u	1	1	1	-1	-1	-1	-1	1	z
E_1u	2	2cos(2π/5)	2cos(4π/5)	0	-2	-2cos(2π/5)	-2cos(4π/5)	0	(x, y)
E_2u	2	2cos(4π/5)	2cos(2π/5)	0	-2	-2cos(4π/5)	-2cos(2π/5)	0

D_5d 점군의 곱셈표

	A_1g	A_2g	E_1g	E_2g	A_1u	A_2u	E_1u	E_2u
A_1g	A_1g	A_2g	E_1g	E_2g	A_1u	A_2u	E_1u	E_2u
A_2g	A_2g	A_1g	E_1g	E_2g	A_2u	A_1u	E_1u	E_2u
E_1g	E_1g	E_1g	A_1g+A_2g+E_2g	E_1g+E_2g	E_1u	E_1u	A_1u+A_2u+E_2u	E_1u+E_2u
E_2g	E_2g	E_2g	E_1g+E_2g	A_1g+A_2g+E_2g	E_2u	E_2u	E_1u+E_2u	A_1u+A_2u+E_2u
A_1u	A_1u	A_2u	E_1u	E_2u	A_1g	A_2g	E_1g	E_2g
A_2u	A_2u	A_1u	E_1u	E_2u	A_2g	A_1g	E_1g	E_2g
E_1u	E_1u	E_1u	A_1u+A_2u+E_2u	E_1u+E_2u	E_1g	E_1g	A_1g+A_2g+E_2g	E_1g+E_2g
E_2u	E_2u	E_2u	E_1u+E_2u	A_1u+A_2u+E_2u	E_2g	E_2g	E_1g+E_2g	A_1g+A_2g+E_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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