example 2
 PF_{5}

The vibrational modes associated with the PF bonds in PF_{5} The PF_{5} molecule belongs to the D_{3h} point group. The molecule contains both axial and equatorial bonds, these are calculated separately as they are different. The number of bonds that remain unshifted by the operations are represented by the following:
The reduction is made somewhat easier by considering the two types of F hybrid separately. The representation for the axial hybrids is generated by adding the A_{1}' and A_{2}" rows together. (This is readily seen by noting that the '0' for the s_{h} column requires one row from the single prime and one row from the double prime irreps be used. The '2' for the 3s_{v} column can then only come about from adding the A_{1}' and A_{2}" rows).
The representation for the equatorial hybrids is generated by adding together the A_{1}' and E' rows together. (This is readily seen by noting that the '3' for the s_{h} column means that only only single prime rows have to be considered. The '1' for the 3C_{2} and for the 3s_{v} columns can then only come about from adding the A_{1}' and E' rows).
G_{axial}
= A_{1}' + A_{2}" and G_{equatorial}
= A_{1}' + E' 