## Reduction formula for point group C_{2v}

Your representation

E |
C_{2} (z) |
_{v}(xz) |
_{v}(yz) |

324 |
0 |
24 |
8 |

can be reduced to

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

89 |
73 |
85 |
77 |

Substraction of translational and rotational contributions results in

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

88 |
72 |
83 |
75 |

###
Force field analysis

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

Infrared |
+ |
- |
+ |
+ |

Raman |
+ |
+ |
+ |
+ |

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

linear |
318 |
318 |
88 |

quadratic |
101124 |
50721 |
12880 |

cubic |
32157432 |
5410240 |
1354512 |

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_{1} |
A_{2} |
B_{1} |
B_{2} |

linear |
88 |
72 |
83 |
75 |

quadratic |
12880 |
12561 |
12704 |
12576 |

cubic |
1354512 |
1350768 |
1353672 |
1351288 |

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

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

Number of independant internal coordinates |
88 |

### Literature

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

The Numbers of Structural Parameters and Potential Constants of Molecules