## Reduction formula for point group C_{3v}

Your representation

E |
2C_{3} (z) |
3_{v} |

9 |
0 |
3 |

can be reduced to

###
Force field analysis

Infrared and Raman activities (harmonic approximation)
Method |
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 |

linear |
3 |
0 |
3 |

quadratic |
12 |
3 |
15 |

cubic |
38 |
19 |
54 |

quartic |
102 |
63 |
165 |

Number of independant internal coordinates |
3 |

### Literature

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

The Numbers of Structural Parameters and Potential Constants of Molecules