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Symmetry and group
            theory
The symmetry of molecules and solids is a very
powerful tool for developing an understanding of
bonding and physical properties
– Used to predict the nature of molecular orbitals
– Used to predict if electronic and vibration
spectroscopic transitions can be Observed
We will cover the following material:
 Identification/classification of symmetry
elements and symmetry operations
 Assignment of point groups
 Identifying polarity and chirality using point
groups
Polar Molecules
A molecule cannot be polar if it has
1. a center of inversion
    –any group with i
2. an electric dipole moment
perpendicular to any mirror planes
   –any of the groups D and their
derivatives
3. an electric dipole moment
perpendicular to any axis of rotation
   –the cubic groups T, O, the
icosahedral I, and
   their modifications
Chiral Molecules
A molecule is not chiral if
1. it posses an improper rotation
   axis Sn
      (this includes mirror planes an
inversion
      centers)
2. it belongs to the group Dnh or
Dnd
3. it belongs to Td or Oh

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Symmetry and group theory

  • 2. The symmetry of molecules and solids is a very powerful tool for developing an understanding of bonding and physical properties – Used to predict the nature of molecular orbitals – Used to predict if electronic and vibration spectroscopic transitions can be Observed We will cover the following material:  Identification/classification of symmetry elements and symmetry operations  Assignment of point groups  Identifying polarity and chirality using point groups
  • 3. Polar Molecules A molecule cannot be polar if it has 1. a center of inversion –any group with i 2. an electric dipole moment perpendicular to any mirror planes –any of the groups D and their derivatives 3. an electric dipole moment perpendicular to any axis of rotation –the cubic groups T, O, the icosahedral I, and their modifications
  • 4. Chiral Molecules A molecule is not chiral if 1. it posses an improper rotation axis Sn (this includes mirror planes an inversion centers) 2. it belongs to the group Dnh or Dnd 3. it belongs to Td or Oh