University of Exeter

Hexagonal: D3h (-6m2) - Products

Exeter Symmetry Pages

Irreducible Representation Products:

product A1' A2' E' A1'' A2'' E''
A1' A1' A2' E' A1'' A2'' E''
A2' A2' A1' E' A2'' A1'' E''
E' E' E' A1'+A2'+E' E'' E'' A1''+A2''+E''
A1'' A1'' A2'' E'' A1' A2' E'
A2'' A2'' A1'' E'' A2' A1' E'
E'' E'' E'' A1''+A2''+E'' E' E' A1'+A2'+E'


Dipole Transition Products:

For the D3h point group, the irreducible representation of the dipole operator is (A2''+E'). Transitions that are dipole forbidden are indicated by parentheses.

product(A2''+E')product A1' A2' E' A1'' A2'' E''
A1' (A2''+E') (A1''+E') A1'+A2'+E'+E'' (A2'+E'') A1'+E'' (A1''+A2''+E'+E'')
A2' (A1''+E') (A2''+E') A1'+A2'+E'+E'' A1'+E'' (A2'+E'') (A1''+A2''+E'+E'')
E' A1'+A2'+E'+E'' A1'+A2'+E'+E'' A1'+A2'+3E'+A1''+A2''+E'' (A1''+A2''+E'+E'') (A1''+A2''+E'+E'') A1'+A2'+E'+A1''+A2''+3E''
A1;' (A2'+E'') A1'+E'' (A1''+A2''+E'+E'') (A2''+E') (A1''+E') A1'+A2'+E'+E''
A2'' A1'+E'' (A2'+E'') (A1''+A2''+E'+E'') (A1''+E') (A2''+E') A1'+A2'+E'+E''
E'' (A1''+A2''+E'+E'') (A1''+A2''+E'+E'') A1'+A2'+E'+A1''+A2''+3E'' A1'+A2'+E'+E'' A1'+A2'+E'+E'' A1'+A2'+3E'+A1''+A2''+E''