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

Your representation

E |
C_{3}(z) |
(C_{3})^{2} |
_{h} |
S_{3} |
(S_{3})^{5} |

324 |
0 |
0 |
24 |
0 |
0 |

can be reduced to

A' |
E' |
A'' |
E'' |

58 |
58 |
50 |
50 |

Substraction of translational and rotational contributions results in

A' |
E' |
A'' |
E'' |

57 |
57 |
49 |
49 |

###
Force field analysis

Infrared and Raman activities (harmonic approximation)
Method |
A' |
E' |
A'' |
E'' |

Infrared |
- |
+ |
+ |
- |

Raman |
+ |
+ |
- |
+ |

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

linear |
318 |
318 |
57 |

quadratic |
101124 |
50721 |
8528 |

cubic |
32157432 |
5410240 |
902766 |

quartic |
XXX^{*} | XXX^{*} | XXX^{*} |

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' |
E' |
A'' |
E'' |

linear |
57 |
57 |
49 |
49 |

quadratic |
8528 |
8528 |
8379 |
8379 |

cubic |
902766 |
902709 |
900718 |
900669 |

quartic |
XXX^{*} | XXX^{*} | XXX^{*} | XXX^{*} |

^{*}Not calculated for systems with more than 75 atoms

Number of independant internal coordinates |
57 |

### Literature

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

The Numbers of Structural Parameters and Potential Constants of Molecules