Chapter 12 - Molecular Symmetry

Group theory

The systematic discussion of symmetry

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

Identity (E)

Consists of doing nothing; the corresponding symmetry element is the entire object

Schoenflies system

Used for individual molecules

Hermann-Mauguin system (International system)

Used almost exclusively in the discussion of crystal symmetry

Group C1

A molecule belongs to group C1 if it has no element other than the identity.

Group Ci

A molecule belongs to group Ci if it has the identity and the inversion alone.

Group Cs

A molecule belongs to group Cs if it has the identity and a mirror plane alone.

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

Polar molecule

One with a permanent electric dipole moment

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

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

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

Transition dipole moment