Question

Mulliken symbol for the following E=1,
Cn= -1, nC2= -1, i= 1, oh= 1*​

Answer 1

Answer:

B'2g-Mulliken symbol for the following E=1,

Cn= -1, nC2= -1, i= 1, oh= 1*

Answer 2

Answer:

Mulliken symbol for the given representation is $B^{'} _{2g}$

Explanation:

Every Irreducible representation in a character table is represented by a particular symbol called Mulliken symbol.

Mulliken symbol notation is found with the help of following rules:

1. All one dimensional representations are designated either A or B.Two dimensional representations are designated E and Three dimensional representation by T.
2. One dimensional representation that are symmetric with respect to the principle axis are designated A while that are antisymmetric w.r.t. principle axis is given by B.
3. Subscripts 1 and 2 are given when it is symmetric or antisymmetric respectively w.r.t $C_2$ axis perpendicular to principle axis. If $C_2$ is absent consider vertical plane of symmetry.
4. Superscript '  is attached when representation is symmetric w.r.t $\sigma_h$ and " when representation is antisymmetric w.r.t $\sigma_h$.
5. Subscript g is attached when representations are symmetric w.r.t inversion and u is used when it is antisymmetric to inversion i.

In the given example :

• It is a one dimensional representation and is antisymmetric w.r.t principle axis. Therefore symbol is B.
• It is antisymmetric w.r.t perpendicular $C_2$ axis, therefore subscript 2 is attached. $B_2$
• There is inversion which is symmetric therefore subscript g is attached.$B_2_g$
• The superscipt ' is added since it is symmetric w.r.t. $\sigma_h$.(since both i and $\sigma_h$ are present, i supercades. Thus ' is not necessarily used in representation)