## Reduction formula for point group D_{5h}

Your representation

E |
2C_{5} |
2(C_{5})^{2} |
5C'_{2} |
_{h} |
2S_{5} |
2(S_{5})^{3} |
5_{v} |

30 |
0.0000 |
0.0000 |
-2 |
10 |
0.0000 |
0.0000 |
2 |

can be reduced to

A'_{1} |
A'_{2} |
E'_{1} |
E'_{2} |
A''_{1} |
A''_{2} |
E''_{1} |
E''_{2} |

2 |
2 |
4 |
4 |
0 |
2 |
2 |
2 |

Substraction of translational and rotational contributions results in

A'_{1} |
A'_{2} |
E'_{1} |
E'_{2} |
A''_{1} |
A''_{2} |
E''_{1} |
E''_{2} |

2 |
1 |
3 |
4 |
0 |
1 |
1 |
2 |

###
Force field analysis

Infrared and Raman activities (harmonic approximation)
Method |
A'_{1} |
A'_{2} |
E'_{1} |
E'_{2} |
A''_{1} |
A''_{2} |
E''_{1} |
E''_{2} |

Infrared |
- |
- |
+ |
- |
- |
+ |
- |
- |

Raman |
+ |
- |
- |
+ |
- |
- |
+ |
- |

No. 1 : Total number of force constants .

No. 2 : Total number of force constants k.

No. 3 : Total number of nonvanishing force constants k.

Symmetry properties of force field parameters
Force field |
A'_{1} |
A'_{2} |
E'_{1} |
E'_{2} |
A''_{1} |
A''_{2} |
E''_{1} |
E''_{2} |

linear |
2 |
1 |
3 |
4 |
0 |
1 |
1 |
2 |

quadratic |
25 |
12 |
37 |
35 |
12 |
13 |
24 |
23 |

cubic |
150 |
137 |
289 |
290 |
108 |
121 |
231 |
232 |

quartic |
980 |
889 |
1868 |
1867 |
815 |
828 |
1643 |
1641 |

Number of independant internal coordinates |
2 |

### Literature

- J.K.G. Watson, J. Mol. Spec.
**41** 229 (1972)

The Numbers of Structural Parameters and Potential Constants of Molecules