## Reduction formula for point group S_{4}

Your representation

E |
S_{4} |
C_{2} |
(S_{4})^{3} |

15 |
-1 |
-1 |
-1 |

can be reduced to

Substraction of translational and rotational contributions results in

###
Force field analysis

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

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 |
B |
E |

linear |
2 |
3 |
2 |

quadratic |
13 |
12 |
10 |

cubic |
42 |
43 |
40 |

quartic |
129 |
126 |
120 |

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