Symmetry in Chemistry: An Introduction 1
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Symmetry in Chemistry: An Introduction
1
Symmetry element and operation
Symmetry Operation Symmetry element
Something done to a molecule that leaves it in an equivalent configuration
Point: Inversion (i) Line: Simple rotation (Cn) Complex Rotation (Sn) Plane: Reflection
A geometrical entity with respect to which the operation is performed
Principal axis of symmetry: The axis with the largest n value Horizontal plane: Plane of reflection to which the principal axis is perpendicular Vertical Plane: Contains the principal axis Dihedral plane: Vertical plane which bisects the angle between C2 axes 2
Symmetry point groups: Classification by Symmetry Operations
https://www2.chemistry.msu.edu/faculty/reusch/virttxtjml/symmetry/symmtry.htm 3
Symmetry point groups: Classification by Symmetry Operations
https://www2.chemistry.msu.edu/faculty/reusch/virttxtjml/symmetry/symmtry.htm 4
O
H H
C2
sv
sv’
Equivalent and non-equivalent operations
5
O
H H
C2 sv
sv’
H
N
H
H
C3 sv
sv
sv
• sv : No atom moves
sv ‘: H atoms interchange
• sv : Two atoms move
Other two don’t
• sv and sv ‘ do not interchange by C2 • The three sv planes interchange by C3
Non-equivalent planes (Different classes)
Equivalent planes (Same class)
Ferrocene, eclipsed and staggered
6
C5, 5 C2, 5 sd, sh C5, 5 C2, 5 sd S10,
Tetrahedron
7
8 C3, 3 C2, 6 S4 6 sd E
Allene
8
S4, 3 C2, 2 sd E,
C C C
H
H
H
H
Disubstituted Allene
9
C2 E,
C C C
Cl
H
H
Cl
Octahedron
10
6 C4, E,
A X X
X
X
X
X
C4, C2 (C42)
6 C2,
C2
3 C42 (C2), i, 6 S4, 8 S6, 3 sh, 8 C3, 6 sd
C3
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