WEB TUTORIAL - Group Theory

[Re₂Cl₈]^2- Worked Example

D4h	E	2C4 (z)	C2	2C'2	2C''2	i	2S4	h	2v	2d	Linear Functions, Rotations	Quadratic Functions	Cubic Functions
A1g	+1	+1	+1	+1	+1	+1	+1	+1	+1	+1	-	x2+y2, z2	-
A2g	+1	+1	+1	-1	-1	+1	+1	+1	-1	-1	Rz	-	-
B1g	+1	-1	+1	+1	-1	+1	-1	+1	+1	-1	-	x2-y2	-
B2g	+1	-1	+1	-1	+1	+1	-1	+1	-1	+1	-	xy	-
Eg	+2	0	-2	0	0	+2	0	-2	0	0	(Rx, Ry)	(xz, yz)	-
A1u	+1	+1	+1	+1	+1	-1	-1	-1	-1	-1	-	-	-
A2u	+1	+1	+1	-1	-1	-1	-1	-1	+1	+1	z	-	z3, z(x2+y2)
B1u	+1	-1	+1	+1	-1	-1	+1	-1	-1	+1	-	-	xyz
B2u	+1	-1	+1	-1	+1	-1	+1	-1	+1	-1	-	-	z(x2-y2)
Eu	+2	0	-2	0	0	-2	0	+2	0	0	(x, y)	-	(xz2, yz2) (xy2, x2y), (x3, y3)

h = 16

Now we have all of the required parts we simply put then together into the Reduction Formula one row at a time. This calculation will be quite long, but it is important that you are able to compute a reduction of this size.

It is worth doing this on a piece of paper rather than trying in your head before checking your answers!

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