Question

Example2: XeF4 1. Determine point group of the molecule • D4h 2. Generate the reducible representation for translation (x, y, z) El 26 (2zcze i zsa Gn 20, Z6d 3. Write down the number of atoms which do not change their location during each symmetry operation 31153 4. Multiply together the characters that have been generated in steps 2 and 3. The result is the reducible representation for total degree of freedom.

#2 and 3 I'm confused on how to get the answers for

Answer 1

Question 3.

(i) During the identical (E) operation, no atom will be changed, so 5 atoms do not change the position.

(ii) During the 4-fold axis of rotation (C₄) operation, i.e. 90^o rotation, four atoms change their position, so 1 atom does not change the position.

(iii) During the 2-fold axis of rotation (C₂) operation, i.e. 180^o rotation, four atoms (4 F's along vertical XY-plane) change their position, so 1 atom does not change the position.

(iv) During the 2-fold axis of rotation (ZC₂') operation, the two atoms (2 F's) change their position, so 3 atom does not change the position.

(v) During the 4-fold axis of rotation (ZC₂'') operation, the four atoms (4F's along horizontal XY-plane) change their position, so 1 atom does not change the position.

(vi) During the inversion (i) operation, i.e. the four F's change their position, so 1 atom does not change the position.

(vii) During the rotation followed reflection (S₄) operation, four F's change their position, so 1 atom does not change the position.

(viii) During the horizontal plane of rotation ($\sigma$h) operation, no atom will be changed, hence all the 5 atoms do not change the position.

(ix) During the vertical plane of rotation ($\sigma$v) operation, 2 F's change the position, hence 3 atoms do not change the position.

(x) During the diagonal plane of rotation ($\sigma$d) operation, 4 F's will be changed, hence 1 atom does not change the position.