University of Exeter

Non-crystalographic: C5h - Products

Exeter Symmetry Pages

Irreducible Representation Products:

product A' E1' E2' A'' E1'' E2''
A' A' E1' E2' A'' E1'' E2''
E1' E1' 2A'+E2' E1'+E2' E1'' 2A''+E2'' E1''+E2''
E2' E2' E1'+E2' 2A'+E1' E2'' E1''+E2'' 2A''+E1''
A'' A'' E1'' E2'' A' E1' E2'
E1'' E1'' 2A''+E2'' E1''+E2'' E1' 2A'+E2' E1'+E2'
E2'' E2'' E1''+E2'' 2A''+E1'' E2' E1'+E2' 2A'+E1'

Dipole Transition Products:

For the C5h point group, the irreducible representation of the dipole operator is (A''+E1'). Transitions that are dipole forbidden are indicated by parentheses.

product(A''+E1')product A' E1' E2' A'' E1'' E2''
A' (E1'+A'') 2A'+E2'+E1'' (E1'+E2'+E2'') A'+E1'' (E1'+2A''+E2'') (E2'+E1''+E2'')
E1' 2A'+E2'+E1'' (3E1'+E2'+2A''+E2'') 2A'+E1'+2E2'+E1''+E2'' (E1'+2A''+E2'') 2A'+E2'+3E1''+E2'' (E1'+E2'+2A''+E1''+2E2'')
E2' (E1'+E2'+E2'') 2A'+E1'+2E2'+E1''+E2'' 2A'+2E1'+E2'+2A''+E1'' E2'+E1''+E2'' (E1'+E2'+2A''+E1''+2E2'') 2A'+E1'+2A''+2E1''+E2''
A'' A'+E1'' (E1'+2A''+E2'') (E2'+E1''+E2'') (E1'+A'') 2A'+E2'+E1'' (E1'+E2'+E2'')
E1'' (E1'+2A''+E2'') 2A'+E2'+3E1''+E2'' (E1'+E2'+2A''+E1''+2E2'') 2A'+E2'+E1'' (3E1'+E2'+2A''+E2'') 2A'+E1'+2E2'+E1''+E2''
E2'' E2'+E1''+E2'' (E1'+E2'+2A''+E1''+2E2'') 2A'+E1'+2A''+2E1''+E2'' (E1'+E2'+E2'') 2A'+E1'+2E2'+E1''+E2'' 2A'+2E1'+E2'+2A''+E1''