NH3-symmetry1.ppt Rotational and Translational Motion operation

Rotational and Translational Motion operation

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

2. Dr. S. M. Condren

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

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

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

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

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

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

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

10. Dr. S. M. Condren
Mirrors

v 
v
Cl Cl

h
I 
d

d
Cl Cl

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

12. Dr. S. M. Condren
Benzene Ring

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

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

15. Dr. S. M. Condren
Inversion vs. C
2

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

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

18. Dr. S. M. Condren
S
1
and S
2
Improper Rotations

19. Dr. S. M. Condren
Successive C
3
Rotations on
Trigonal Pyramidal Molecule

20. Dr. S. M. Condren
Linear Molecules

21. Dr. S. M. Condren
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

22. Dr. S. M. Condren

23. Dr. S. M. Condren
Decision Tree

24. Dr. S. M. Condren
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

25. Dr. S. M. Condren
H
2
O and NH
3

26. Dr. S. M. Condren

27. Dr. S. M. Condren

28. Dr. S. M. Condren
Geometric Shapes

29. Dr. S. M. Condren
Orbital Symmetry, p
z
C
2v
z E + X(E) = +1
-+
+ C
2
(z)
x
- +- X(C
2(z)) = +1
y 
v(xz)

- X(
v(xz)
) = +1

v(yz) +
- X(
v(xz)
) = +1

30. Dr. S. M. Condren
Orbital Symmetry, p
y
C
2v

+
-
+
-
-
+
-
+
+
-
z
E
x
y
X(E) = +1
C2(z)
X(C
2(z)
) = -1

v(xz)
X(
v(xz)
) = -1
X(
v(xz)
) = +1

v(yz)

31. Dr. S. M. Condren
Orbital Symmetry, p
x
C
2v

- +
-+
+ -
- +
+ -
z
x
y
E
X(E) = +1
C
2(z)
X(C
2(z)
) = -1

v(xz)

v(yz)
X(
(xz)) = +1
X(
v(xz)) = -1

32. Dr. S. M. Condren
Water, C
2v
Point Group
Translational motion in y
z
yo o
H H H H
x 
v(xz)
“asymmetric” => -1

33. Dr. S. M. Condren
Water, C
2v
Point Group
Translational motion in y
z
o
y H H
x o
H H

v(yz)
“symmetric” => +1

34. Dr. S. M. Condren
Water, C
2v
Point Group
Translational motion in y
z
y C
2(z)
x
O
H H
“asymmetric” = - 1

35. Dr. S. M. Condren
Water, C
2v
Point Group
Translational motion in y
Representation:


E C
2(z)

v(xz) 
v(yz)

3 +1 -1 -1 +1

36. Dr. S. M. Condren
Water, C
2v
Point Group
Rotation about z axis
z
O



H
a H
b

 - movement out of plane towards observer
 - movement out of plane away from observer
a,b - labeling to distinguish hydrogens before and after
symmetry operations

37. Dr. S. M. Condren
Water, C
2v
Point Group
Rotation about z axis
z
O E O



H
a H
b


H
a H
b



+1

38. Dr. S. M. Condren
Water, C
2v
Point Group
Rotation about z axis
z
O C
2z O



H
a
H
b


H
b
H
a



+1

39. Dr. S. M. Condren
Water, C
2v
Point Group
Rotation about z axis
z
O 
v(xz) O



H
a H
b


H
b H
a



x -1

40. Dr. S. M. Condren
Water, C
2v
Point Group
Rotation about z axis
z
O 
v(yz) O



H
a H
b


H
a H
b



-1

41. Dr. S. M. Condren
Water, C
2v
Point Group
Rotation about z axis
Representation


E C
2(z)

v(xz) 
v(yz)

4 +1 +1 -1 -1

42. Dr. S. M. Condren
Water, C
2v
Point Group
Representations:
Rotation


E C
2(z)

v(xz) 
v(yz)

4 +1 +1 -1 -1

43. Dr. S. M. Condren
Water, C
2v
Point Group
Representation:
Translation


EC
2(z)

v(xz)

v(yz)

1 +1+1+1+1 T
z

2 +1-1+1-1 T
x

3
+1-1-1+1 T
y

44. Dr. S. M. Condren
Water, C
2v
Point Group
Representation:
Rotation


EC
2(z)

v(xz)

v(yz)

4 +1+1-1-1 R
z

5 +1-1+1-1 R
y

6
+1-1-1+1 R
x

45. Dr. S. M. Condren
Water, C
2v
Point Group
Character Table


EC
2(z)
v(xz) 
v(yz)
A
1+1+1+1+1 T
z 
1
A
2+1+1-1-1 R
z
4
B
1 +1-1+1-1 R
y, T
x 
2 , 
5
B
2 +1-1-1+1 R
x,T
y 
3, 
6

46. Dr. S. M. Condren

47. Dr. S. M. Condren
Vibrational Modes in CO
2
For linear molecules: 3N - 5 IR fundamentals

48. Dr. S. M. Condren
Vibrational Modes in SO
2
For non-linear molecules: 3N - 6 IR fundamentals

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

50. Dr. S. M. Condren
Vibrational Modes for CH
4
For non-linear molecules: 3N - 6 IR fundamentals

51. Dr. S. M. Condren
Vibrational Modes for [PtCl
4
]
-2
For non-linear molecules: 3N - 6 IR fundamentals

52. Dr. S. M. Condren
Enantiomer Pairs

53. Dr. S. M. Condren
Enantiomer Pairs

54. Dr. S. M. Condren
Polarimeter