Transcript Symmetry Elements and Symmetry Operations

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
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Symmetry Elements and
Symmetry Operations
•
Identity => E
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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
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2-Fold Axis of Rotation
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3-Fold Axis of Rotation
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Rotations for a Trigonal Planar Molecule
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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
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Mirrors
sv
sv
Cl
Cl
sh
I
sd
Cl
sd
Cl
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Rotations and Mirrors in a Bent
Molecule
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Benzene Ring
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Symmetry Elements and
Symmetry Operations
• Center of symmetry => i
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Center of Inversion
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Inversion vs. C2
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Symmetry Elements and
Symmetry Operations
• Improper axis of rotation => Sn
– rotation about n axis followed by inversion
through center of symmetry
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Improper Rotation in a Tetrahedral
Molecule
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S1 and S2 Improper Rotations
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Successive C3 Rotations on
Trigonal Pyramidal Molecule
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Linear Molecules
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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
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Decision Tree
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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
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H2O and NH3
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Geometric Shapes
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Orbital Symmetry, pz
z
E +
C2v
X(E) = +1
-
+
+
C2(z)
x
y
+
-
X(C2(z)) = +1
-
X(sv(xz)) = +1
sv(xz)
sv(yz)
+
-
X(sv(xz)) = +1
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Orbital Symmetry, py
-
z
E
X(E) = +1
+
-
C2(z)
-
x
+
sv(xz)
y
C2v
+
-
sv(yz)
X(sv(xz)) = -1
+
+
X(C2(z)) = -1
X(sv(xz)) = +1
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Orbital Symmetry, px
z
-
E
-
y
+
+
X(E) = +1
C2(z)
x
C2v
+
sv(xz)
-
sv(yz)
+
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-
+
X(C2(z)) = -1
X(s(xz)) = +1
X(sv(xz)) = -1
Water, C2v Point Group
Translational motion in y
z
y
x
o
o
H H
H H
sv(xz)
“asymmetric” => -1
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Water, C2v Point Group
Translational motion in y
z
o
H H
y
x
o
H H
sv(yz)
“symmetric” => +1
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Water, C2v Point Group
Translational motion in y
z
y
C2(z)
x
O
H H
“asymmetric” = - 1
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Water, C2v Point Group
Translational motion in y
Representation:
E
C2(z)
G3 +1
-1
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sv(xz)
sv(yz)
-1
+1
Water, C2v Point Group
Rotation about z axis
z
O
rH
a
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
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Water, C2v Point Group
Rotation about z axis
z
O
rH
a
E
Hbs
O
rH
+1
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a
Hbs
Water, C2v Point Group
Rotation about z axis
z
O
rH
a
C2z
Hbs
O
rH
+1
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b
Has
Water, C2v Point Group
Rotation about z axis
z
sv(xz)
O
rH
a
O
Hbs
sH
x
-1
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b
Har
Water, C2v Point Group
Rotation about z axis
z
sv(yz)
O
rH
a
Hbs
O
sH
-1
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a
Hbr
Water, C2v Point Group
Rotation about z axis
Representation
E
C2(z)
G4 +1
+1
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sv(xz)
sv(yz)
-1
-1
Water, C2v Point Group
Representations:
Rotation
E
C2(z)
G4 +1
+1
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sv(xz)
sv(yz)
-1
-1
Water, C2v Point Group
Representation:
Translation
E
C2(z)
G1 +1 +1
G2 +1 -1
G3 +1 -1
sv(xz) sv(yz)
+1 +1
Tz
+1 -1
Tx
-1 +1
Ty
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Water, C2v Point Group
Representation:
Rotation
E
C2(z)
G4 +1 +1
G5 +1 -1
G6 +1 -1
sv(xz) sv(yz)
-1 -1
Rz
+1 -1
Ry
-1 +1
Rx
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Water, C2v Point Group
Character Table
E
C2(z)
A1 +1 +1
A2 +1 +1
B1 +1 -1
B2 +1 -1
sv(xz) sv(yz)
+1 +1
-1 -1
+1 -1
-1 +1
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Tz
Rz
Ry, Tx
Rx,Ty
G1
G4
G2 , G5
G3 , G6
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Vibrational Modes in CO2
For linear molecules: 3N - 5 IR fundamentals
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Vibrational Modes in SO2
For non-linear molecules: 3N - 6 IR fundamentals
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Vibration Modes for SO3
For non-linear molecules: 3N - 6 IR fundamentals
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Vibrational Modes for CH4
For non-linear molecules: 3N - 6 IR fundamentals
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Vibrational Modes for [PtCl4]-2
For non-linear molecules: 3N - 6 IR fundamentals
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Enantiomer Pairs
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Enantiomer Pairs
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Polarimeter
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