Write characters of the representation of the direct

Question

Assignment

Q1. Classify the following molecules into appropriate point gaps. Justify your answer.

a) CO₃^2-   b) N₃^-      c) SO₄^2-  d) SCN

e) Cio₃     f) B₆H₆^2-  g) Ethane (eclipsed)  h) [Pt(en)₂]²⁺

Q2. Give total number of operations generated by C₅ and S₅ axis.

Q3. Using similarity transformation and GMT for group C₂h, divide symmetry operations into appropriate classes.

Q4. By schematic representations, give the product of the following symmetry operations in NF₃ molecules

i) C₃ x C₃^-1 ii) C₃ x 6v iii) 6v x 6v'

Q5. Using great orthogonality theorem, derive the character table for D₂ point group, given D2 elements are E, C₂(Z), C₂(y), C₂(x).

Q6. Give the properties of irreducible representation for C₂v point group and label the IRs with appropriate mullipen symbols.

Q7. Which IRs of C₃v point group from the basis of following RR?

C3V	E	2C3	36v
A1	1	1	1
A2	1	1	-1
E	2	-1	0
Trr	15	0	3

Q8. Write characters of the representation of the direct product E x E and determine the IRs which compromise them for the grp C₄v

C4V	E	2C4	C2	26v	26d
A1	1	1	1	1	1
A2	1	1	1	-1	-1
B1	1	-1	1	1	-1
B2	1	-1	1	-1	1
E	2	0	-2	0	0

Q9. Which operation has the same effect as following operations?

S₄², S₄³, S₄⁴, C₄², i², 6², C₃³, C₃².