## Reduction formula for point group D_{6}

Your representation

E |
2C_{6} (z) |
2C_{3} (z) |
C_{2} (z) |
3C'_{2} |
3C''_{2} |

36 |
0 |
0 |
0 |
-4 |
0 |

can be reduced to

A_{1} |
A_{2} |
B_{1} |
B_{2} |
E_{1} |
E_{2} |

2 |
4 |
2 |
4 |
6 |
6 |

Substraction of translational and rotational contributions results in

A_{1} |
A_{2} |
B_{1} |
B_{2} |
E_{1} |
E_{2} |

2 |
2 |
2 |
4 |
4 |
6 |

###
Force field analysis

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

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} |
B_{1} |
B_{2} |
E_{1} |
E_{2} |

linear |
2 |
2 |
2 |
4 |
4 |
6 |

quadratic |
50 |
33 |
36 |
36 |
76 |
79 |

cubic |
416 |
416 |
398 |
430 |
818 |
832 |

quartic |
3500 |
3348 |
3396 |
3396 |
6796 |
6844 |

Number of independant internal coordinates |
2 |

### Literature

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

The Numbers of Structural Parameters and Potential Constants of Molecules