## Reduction formula for point group D_{3h}

Your representation

E |
2C_{3} (z) |
3C'_{2} |
_{h} (xy) |
2S_{3} |
3_{v} |

6 |
0 |
0 |
4 |
-2 |
2 |

can be reduced to

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

1 |
0 |
2 |
0 |
1 |
0 |

###
Force field analysis

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

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

linear |
1 |
0 |
2 |
0 |
1 |
0 |

quadratic |
5 |
1 |
5 |
0 |
1 |
2 |

cubic |
9 |
5 |
13 |
1 |
5 |
5 |

quartic |
19 |
9 |
29 |
5 |
9 |
13 |

Number of independant internal coordinates |
1 |

### Literature

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

The Numbers of Structural Parameters and Potential Constants of Molecules