## Reduction formula for point group T_{d}

Your representation

E |
8C_{3} |
3C_{2} |
6S_{4} |
6_{d} |

15 |
0 |
-1 |
-1 |
3 |

can be reduced to

A_{1} |
A_{2} |
E |
T_{1} |
T_{2} |

1 |
0 |
1 |
1 |
3 |

Substraction of translational and rotational contributions results in

A_{1} |
A_{2} |
E |
T_{1} |
T_{2} |

1 |
0 |
1 |
0 |
2 |

###
Force field analysis

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

linear |
1 |
0 |
1 |
0 |
2 |

quadratic |
5 |
0 |
5 |
3 |
7 |

cubic |
13 |
4 |
14 |
15 |
25 |

quartic |
33 |
12 |
45 |
51 |
69 |

Number of independant internal coordinates |
1 |

### Literature

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

The Numbers of Structural Parameters and Potential Constants of Molecules