## Reduction formula for point group D_{7h}

Your representation

E |
2C_{7} |
2(C_{7})^{2} |
2(C_{7})^{3} |
7C'_{2} |
_{h} |
2S_{7} |
2(S_{7})^{5} |
2(S_{7})^{3} |
7_{v} |

42 |
0.0000 |
0.0000 |
-0.0000 |
-2 |
14 |
0.0000 |
-0.0000 |
-0.0000 |
2 |

can be reduced to

A'_{1} |
A'_{2} |
E'_{1} |
E'_{2} |
E'_{3} |
A''_{1} |
A''_{2} |
E''_{1} |
E''_{2} |
E''_{3} |

2 |
2 |
4 |
4 |
4 |
0 |
2 |
2 |
2 |
2 |

Substraction of translational and rotational contributions results in

A'_{1} |
A'_{2} |
E'_{1} |
E'_{2} |
E'_{3} |
A''_{1} |
A''_{2} |
E''_{1} |
E''_{2} |
E''_{3} |

2 |
1 |
3 |
4 |
4 |
0 |
1 |
1 |
2 |
2 |

###
Force field analysis

Infrared and Raman activities (harmonic approximation)
Method |
A'_{1} |
A'_{2} |
E'_{1} |
E'_{2} |
E'_{3} |
A''_{1} |
A''_{2} |
E''_{1} |
E''_{2} |
E''_{3} |

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'_{1} |
E'_{2} |
E'_{3} |
A''_{1} |
A''_{2} |
E''_{1} |
E''_{2} |
E''_{3} |

linear |
2 |
1 |
3 |
4 |
4 |
0 |
1 |
1 |
2 |
2 |

quadratic |
38 |
19 |
57 |
55 |
55 |
20 |
21 |
40 |
39 |
38 |

cubic |
335 |
316 |
653 |
654 |
655 |
265 |
284 |
551 |
552 |
553 |

quartic |
3162 |
2972 |
6133 |
6132 |
6131 |
2800 |
2819 |
5619 |
5617 |
5617 |

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