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

Your representation

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

120 |
0 |
8 |

can be reduced to

Substraction of translational and rotational contributions results in

###
Force field analysis

Infrared and Raman activities (harmonic approximation)
Method |
A_{1} |
A_{2} |
E |

Infrared |
+ |
- |
+ |

Raman |
+ |
- |
+ |

Number of force field parameters
Force field |
No. 1 |
No. 2 |
No. 3 |

linear |
114 |
114 |
23 |

quadratic |
12996 |
6555 |
1137 |

cubic |
1481544 |
253460 |
42528 |

quartic |
168896016 |
7413705 |
1237452 |

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 |
23 |
15 |
38 |

quadratic |
1137 |
1048 |
2185 |

cubic |
42528 |
41984 |
84474 |

quartic |
1237452 |
1233783 |
2471235 |

Number of independant internal coordinates |
23 |

### Literature

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

The Numbers of Structural Parameters and Potential Constants of Molecules