## Reduction formula for point group C_{s}

**Characters of input representation**
E |
_{h} |

6 |
2 |

**Decomposition into Irreducible representations**
A' |
A'' |
Total |

4 |
2 |
6 |

###
Force field analysis

**Allowed / forbidden vibronational transitions**
Operator |
A' |
A'' |
Total |

Linear (IR) |
4 |
2 |
6 / 0 |

Quadratic (Raman) |
4 |
2 |
6 / 0 |

IR + Raman |
4 |
2 |
6 / 0 |

**Characters of symmetric powers for vibration representation**
Force field |
Tensor Order |
E |
_{h} |

linear |
1 |
6 |
2 |

quadratic |
2 |
21 |
5 |

cubic |
3 |
56 |
8 |

quartic |
4 |
126 |
14 |

quintic |
5 |
252 |
20 |

sextic |
6 |
462 |
30 |

**Decomposition into Irreducible representations**

Number of nonvanshing force constants
Force field |
Tensor Order |
A' |
A'' |

linear |
1 |
4 |
2 |

quadratic |
2 |
13 |
8 |

cubic |
3 |
32 |
24 |

quartic |
4 |
70 |
56 |

quintic |
5 |
136 |
116 |

sextic |
6 |
246 |
216 |

### Literature

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

The Numbers of Structural Parameters and Potential Constants of Molecules

- X.F. Zhou, P. Pulay. J. Comp. Chem.
**10** No. 7, 935-938 (1989)

Characters for Symmetric and Antisymmetric Higher Powers of Representations:

Application to the Number of Anharmonic Force Constants in Symmetrical Molecules

Last update Mai, 23^{rd} 2018 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement