Point Group D∞h

Character Table of Symmetry Point Group D_∞h

D_∞h E 2C_Φ C₂' i 2iC_Φ iC₂'

A_1g (Σ_g⁺) 1 1 1 1 1 1 (x²+y²); z²

A_1u (Σ_u⁺) 1 1 1 -1 -1 -1 z

A_2g (Σ_g^-) 1 1 -1 1 1 -1 R_z

A_2u (Σ_u^-) 1 1 -1 -1 1 1

E_1g (Π_g) 2 2 cos Φ 0 0 -2 cos Φ 0 (R_x; R_y) (xz ; yz)

E_1u (Π_u) 2 2 cos Φ 0 0 2 cos Φ 0 (x,y)

E_2g (Δ_g) 2 2 cos 2 Φ 0 0 2 cos 2 Φ 0 (x²-y², xy)

E_2u (Δ_u) 2 2 cos 2 Φ 0 0 -2 cos 2 Φ 0

Example: CO₂

Contents

*D_∞h*	E	2C_Φ	C₂'	i	2iC_Φ	iC₂'
A_1g (Σ_g⁺)	1	1	1	1	1	1		(x²+y²); z²
A_1u (Σ_u⁺)	1	1	1	-1	-1	-1		z
A_2g (Σ_g^-)	1	1	-1	1	1	-1	R_z
A_2u (Σ_u^-)	1	1	-1	-1	1	1
E_1g (Π_g)	2	2 cos Φ	0	0	-2 cos Φ	0	(R_x; R_y)	(xz ; yz)
E_1u (Π_u)	2	2 cos Φ	0	0	2 cos Φ	0		(x,y)
E_2g (Δ_g)	2	2 cos 2 Φ	0	0	2 cos 2 Φ	0		(x²-y², xy)
E_2u (Δ_u)	2	2 cos 2 Φ	0	0	-2 cos 2 Φ	0