Embed Size (px)
Citation preview
Dr. S. M. Condren
Chapter 4
Molecular Symmetry
Dr. S. M. Condren
Dr. S. M. Condren
Symmetry Elements and Symmetry Operations
• Identity
• Proper axis of rotation
• Mirror planes
• Center of symmetry
• Improper axis of rotation
Dr. S. M. Condren
Symmetry Elements and Symmetry Operations
• Identity => E
Dr. S. M. Condren
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
2-Fold Axis of Rotation
Dr. S. M. Condren
3-Fold Axis of Rotation
Dr. S. M. Condren
Rotations for a Trigonal Planar Molecule
Dr. S. M. Condren
Symmetry Elements and Symmetry Operations
Mirror planes =>h => mirror plane perpendicular to a
principal axis of rotationv => mirror plane containing principal
axis of rotationd => 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
Mirrors
v v
Cl Cl
h
I d
d
Cl Cl
Dr. S. M. Condren
Rotations and Mirrors in a Bent Molecule
Dr. S. M. Condren
Benzene Ring
Dr. S. M. Condren
Symmetry Elements and Symmetry Operations
• Center of symmetry => i
Dr. S. M. Condren
Center of Inversion
Dr. S. M. Condren
Inversion vs. C2
Dr. S. M. Condren
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
Improper Rotation in a Tetrahedral Molecule
Dr. S. M. Condren
S1 and S2 Improper Rotations
Dr. S. M. Condren
Successive C3 Rotations onTrigonal Pyramidal Molecule
Dr. S. M. Condren
Linear Molecules
Dr. S. M. Condren
Selection ofPoint 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
Dr. S. M. Condren
Decision Tree
Dr. S. M. Condren
Selection ofPoint 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
H2O and NH3
Dr. S. M. Condren
Dr. S. M. Condren
Dr. S. M. Condren
Geometric Shapes
Dr. S. M. Condren
Orbital Symmetry, pz C2v
z E + X(E) = +1
- +
+ C2(z)
x
- + - X(C2(z)) = +1
y v(xz)
- X(v(xz)) = +1
v(yz) +
- X(v(xz)) = +1
Dr. S. M. Condren
Orbital Symmetry, py C2v
+
-
+-
-+
-
+
+-
zE
x
y
X(E) = +1
C2(z)X(C2(z)) = -1
v(xz)
X(v(xz)) = -1
X(v(xz)) = +1
v(yz)
Dr. S. M. Condren
Orbital Symmetry, px C2v
- +
- +
+ -
- +
+ -
z
x
y
EX(E) = +1
C2(z)
X(C2(z)) = -1v(xz)
v(yz)X((xz)) = +1
X(v(xz)) = -1
Dr. S. M. Condren
Water, C2v Point GroupTranslational motion in y
z
y o o
H H H H
x v(xz)
“asymmetric” => -1
Dr. S. M. Condren
Water, C2v Point GroupTranslational motion in y
z
o
y H H
x o
H H v(yz)
“symmetric” => +1
Dr. S. M. Condren
Water, C2v Point GroupTranslational motion in y
z
y C2(z)
x
O
H H
“asymmetric” = - 1
Dr. S. M. Condren
Water, C2v Point GroupTranslational motion in y
Representation:
E C2(z) v(xz) v(yz)
3 +1 -1 -1 +1
Dr. S. M. Condren
Water, C2v Point GroupRotation about z axis
z
O
Ha Hb
- movement out of plane towards observer
- movement out of plane away from observer
a,b - labeling to distinguish hydrogens before and after symmetry operations
Dr. S. M. Condren
Water, C2v Point GroupRotation about z axis
z
O E O
Ha HbHa Hb
+1
Dr. S. M. Condren
Water, C2v Point GroupRotation about z axis
z
O C2z O
Ha HbHb Ha
+1
Dr. S. M. Condren
Water, C2v Point GroupRotation about z axis
z
O v(xz) O
Ha HbHb Ha
x -1
Dr. S. M. Condren
Water, C2v Point GroupRotation about z axis
z
O v(yz) O
Ha HbHa Hb
-1
Dr. S. M. Condren
Water, C2v Point GroupRotation about z axis
Representation
E C2(z) v(xz) v(yz)
4 +1 +1 -1 -1
Dr. S. M. Condren
Water, C2v Point Group
Representations:
Rotation
E C2(z) v(xz) v(yz)
4 +1 +1 -1 -1
Dr. S. M. Condren
Water, C2v Point Group
Representation:
Translation
E C2(z) v(xz) v(yz)
1 +1 +1 +1 +1 Tz
2 +1 -1 +1 -1 Tx
3 +1 -1 -1 +1 Ty
Dr. S. M. Condren
Water, C2v Point Group
Representation:
Rotation
E C2(z) v(xz) v(yz)
4 +1 +1 -1 -1 Rz
5 +1 -1 +1 -1 Ry
6 +1 -1 -1 +1 Rx
Dr. S. M. Condren
Water, C2v Point Group
Character Table
E C2(z) v(xz) v(yz)
A1 +1 +1 +1 +1 Tz 1
A2 +1 +1 -1 -1 Rz 4
B1 +1 -1 +1 -1 Ry, Tx 2 , 5
B2 +1 -1 -1 +1 Rx,Ty 3, 6
Dr. S. M. Condren
Dr. S. M. Condren
Vibrational Modes in CO2
For linear molecules: 3N - 5 IR fundamentals
Dr. S. M. Condren
Vibrational Modes in SO2
For non-linear molecules: 3N - 6 IR fundamentals
Dr. S. M. Condren
Vibration Modes for SO3
For non-linear molecules: 3N - 6 IR fundamentals
Dr. S. M. Condren
Vibrational Modes for CH4
For non-linear molecules: 3N - 6 IR fundamentals
Dr. S. M. Condren
Vibrational Modes for [PtCl4]-2
For non-linear molecules: 3N - 6 IR fundamentals
Dr. S. M. Condren
Enantiomer Pairs
Dr. S. M. Condren
Enantiomer Pairs
Dr. S. M. Condren
Polarimeter
