Chapter 12 - Molecular Symmetry

  • Group theory - The systematic discussion of symmetry.

The symmetry elements of objects

  • Symmetry operation - An action that leaves an object looking the same after it has been carried out.
  • Symmetry element - The point, line, or plane with respect to which the symmetry operation is performed.

12.1 Operations and symmetry elements

  • Identity (E) - Consists of doing nothing; the corresponding symmetry element is the entire object.

12.2 The symmetry classification of molecules

  • Schoenflies system - Used for individual molecules.
  • Hermann-Mauguin system (International system) - Used almost exclusively in the discussion of crystal symmetry.
The groups C1, Ci and Cs
  • A molecule belongs to group C1 if it has no element other than the identity.
  • It belongs to Ci if it has the identity and the inversion alone.
  • It belongs to Cs if it has the identity and a mirror plane alone.
The full rotation group
  • The full rotation group, R3 (the 3 refers to the rotation in three dimensions) - Consists of an infinite number of rotation axes with all possible values of n.

12.3 Some immediate consequences of symmetry

Polarity
  • Polar molecule - One with a permanent electric dipole moment.
Chirality
  • Chiral molecule - A molecule that cannot be superimposed on its mirror image.
  • Achiral molecule - A molecule that can be superimposed on its mirror image.
  • Optically active molecules - They rotate the plane of polarized light. Chiral molecules are optically active.

Applications to molecular orbital theory and spectroscopy

12.4 Character tables and symmetry labels

  • Character table - A table that characterizes the different symmetry types possible in the point group.
  • Characters - The entries in a complete character table.
  • Matrix representation (Γ) - The set of matrices that represents all the operations of the group.

12.5 Vanishing integrals and orbital overlap

  • Order - The total number of operations in a group.
  • Basis - A set of atomic orbitals.
  • Symmetry-adapted linear combinations (SALC) - Combinations that adapt to the symmetry of the molecule.

12.6 Vanishing integrals and selection rules

  • Transition dipole moment

   

\