Question

The C2V point group is Abelian. What does this mean? List some of the special properties of such a group? [4 marks]

(ii) Given that the C2V point group contains 4 symmetry operations, how many irreducible representations are in its character table? Explain your reasoning.

Answer 1

1. C2V point group is Abelian. Abelian point groups are such point groups as those for which character table only contains numbers like 1, -1 . Such kind of character tabale does not contain numbers like 0, 2, -2 ,3 and -3. The centre of this group is equal to itself. Eg. H2O etc.
2. Character table representattion of C2v point group

   C2v	E	C2	σv (x,z)	σv' (y,z)
   A1	1	1	1	1
   A2	1	1	-1	-1
   B1	1	-1	1	-1
   B2	1	-1	-1	1

There are 4 irreducible representtation of C2v pointt group containing 4 symmetry operations i.e. A1 ,A2 ,B1 ,B2 as given above .