1. Chapter 4 Molecular Symmetry
Dr. S. M. Condren

2. Dr. S. M. Condren

3. Symmetry Elements and Symmetry Operations
Identity
Proper axis of rotation
Mirror planes
Center of symmetry
Improper axis of rotation
Dr. S. M. Condren

4. Symmetry Elements and Symmetry Operations
Identity => E
Dr. S. M. Condren

5. Symmetry Elements and Symmetry Operations
Proper axis of rotation => Cn
where n = 2, 180o rotation
n = 3, 120o rotation
n = 4, 90o rotation
n = 6, 60o rotation
n = , (1/ )o rotation
principal axis of rotation, Cn
Dr. S. M. Condren

6. 2-Fold Axis of Rotation
Dr. S. M. Condren

7. 3-Fold Axis of Rotation
Dr. S. M. Condren

8. Rotations for a Trigonal Planar Molecule
Dr. S. M. Condren

9. Symmetry Elements and Symmetry Operations
Mirror planes =>
sh => mirror plane perpendicular to a
principal axis of rotation
sv => mirror plane containing principal
axis of rotation
sd => mirror plane bisects dihedral angle made
by the principal axis of rotation and two
adjacent C2 axes perpendicular to principal
rotation axis
Dr. S. M. Condren

10. Mirrors
sv sv
Cl Cl sh
I sd sd
Dr. S. M. Condren

11. Rotations and Mirrors in a Bent Molecule
Dr. S. M. Condren

12. Benzene Ring
Dr. S. M. Condren

13. Symmetry Elements and Symmetry Operations
Center of symmetry => i
Dr. S. M. Condren

14. Center of Inversion
Dr. S. M. Condren

15. Inversion vs. C2
Dr. S. M. Condren

16. Symmetry Elements and Symmetry Operations
Improper axis of rotation => Sn
rotation about n axis followed by inversion through center of symmetry
Dr. S. M. Condren

17. Improper Rotation in a Tetrahedral Molecule
Dr. S. M. Condren

18. S1 and S2 Improper Rotations
Dr. S. M. Condren

19. Successive C3 Rotations on Trigonal Pyramidal Molecule
Dr. S. M. Condren

20. Linear Molecules
Dr. S. M. Condren

21. Selection of Point Group from Shape
first determine shape using Lewis Structure and VSEPR Theory
next use models to determine which symmetry operations are present
then use the flow chart Figure 3.9, Pg. 81 text to determine the point group
Dr. S. M. Condren

22. Dr. S. M. Condren

23. Decision Tree
Dr. S. M. Condren

24. Selection of Point Group from Shape
1. determine the highest axis of rotation
2. check for other non-coincident axis of rotation
3. check for mirror planes
Dr. S. M. Condren

25. H2O and NH3
Dr. S. M. Condren

26. Dr. S. M. Condren

27. Dr. S. M. Condren

28. Geometric Shapes
Dr. S. M. Condren

29. Orbital Symmetry, pz C2v z E + X(E) = +1 - + + C2(z) x
- +
+ C2(z) x
X(C2(z)) = +1
y sv(xz)
- X(sv(xz)) = +1
sv(yz)
- X(sv(xz)) = +1
Dr. S. M. Condren

30. Orbital Symmetry, py C2v - X(E) = +1 z + E + - C2(z) x - X(C2(z)) = -1
sv(xz) y +
X(sv(xz)) = -1 -
sv(yz) - +
X(sv(xz)) = +1
Dr. S. M. Condren

31. Orbital Symmetry, px C2v z X(E) = +1 - + E C2(z) x + - - +
X(C2(z)) = -1 y
sv(xz) - +
X(s(xz)) = +1
sv(yz) + -
X(sv(xz)) = -1
Dr. S. M. Condren

32. Water, C2v Point Group Translational motion in yz
y o o
H H H H
x sv(xz)
“asymmetric” => -1
Dr. S. M. Condren

33. Water, C2v Point Group Translational motion in yz o
y H H
x o
H H
sv(yz)
“symmetric” => +1
Dr. S. M. Condren

34. Water, C2v Point Group Translational motion in yz
y C2(z) x O
H H
“asymmetric” = - 1
Dr. S. M. Condren

35. Water, C2v Point Group Translational motion in y
Representation:
E C2(z) sv(xz) sv(yz) G
Dr. S. M. Condren

36. Water, C2v Point Group Rotation about z axis
rHa Hbs
r - movement out of plane towards observer
s - movement out of plane away from observer
a,b - labeling to distinguish hydrogens before and after symmetry operations
Dr. S. M. Condren

37. Water, C2v Point Group Rotation about z axis
O E O
rHa Hbs rHa Hbs +1
Dr. S. M. Condren

38. Water, C2v Point Group Rotation about z axis
O C2z O
rHa Hbs rHb Has +1
Dr. S. M. Condren

39. Water, C2v Point Group Rotation about z axis
O sv(xz) O
rHa Hbs sHb Har
x -1
Dr. S. M. Condren

40. Water, C2v Point Group Rotation about z axis
O sv(yz) O
rHa Hbs sHa Hbr -1
Dr. S. M. Condren

41. Water, C2v Point Group Rotation about z axis
Representation
E C2(z) sv(xz) sv(yz) G
Dr. S. M. Condren

42. Water, C2v Point Group Representations: Rotation E C2(z) sv(xz) sv(yz)
Dr. S. M. Condren

43. Water, C2v Point Group E C2(z) sv(xz) sv(yz) G1 +1 +1 +1 +1 Tz
Representation:
Translation
E C2(z) sv(xz) sv(yz)
G Tz
G Tx
G Ty
Dr. S. M. Condren

44. Water, C2v Point Group E C2(z) sv(xz) sv(yz) G4 +1 +1 -1 -1 Rz
Representation:
Rotation
E C2(z) sv(xz) sv(yz)
G Rz
G Ry
G Rx
Dr. S. M. Condren

45. Water, C2v Point Group E C2(z) sv(xz) sv(yz) A1 +1 +1 +1 +1 Tz G1
Character Table
E C2(z) sv(xz) sv(yz)
A Tz G1
A Rz G4
B Ry, Tx G2 , G5
B Rx,Ty G3, G6
Dr. S. M. Condren

46. Dr. S. M. Condren

47. Vibrational Modes in CO2
For linear molecules: 3N - 5 IR fundamentals
Dr. S. M. Condren

48. Vibrational Modes in SO2
For non-linear molecules: 3N - 6 IR fundamentals
Dr. S. M. Condren

49. Vibration Modes for SO3
For non-linear molecules: 3N - 6 IR fundamentals
Dr. S. M. Condren

50. Vibrational Modes for CH4
For non-linear molecules: 3N - 6 IR fundamentals
Dr. S. M. Condren

51. Vibrational Modes for [PtCl4]-2
For non-linear molecules: 3N - 6 IR fundamentals
Dr. S. M. Condren

52. Enantiomer Pairs
Dr. S. M. Condren

53. Enantiomer Pairs
Dr. S. M. Condren

54. Polarimeter
Dr. S. M. Condren