C_{s} |
E | _{h} |
rotations |
functions |
functions |
---|---|---|---|---|---|

A' | +1 | +1 | x, y, R_{z} |
x^{2}, y^{2}, z^{2}, xy |
xz^{2}, yz^{2}, x^{2}y, xy^{2}, x^{3}, y^{3} |

A'' | +1 | -1 | z, R_{x}, R_{y} |
yz, xz | x^{3}, xyz, y^{2}z, x^{2}z |

Number of symmetry elements | h = 2 |

Number of irreducible representations | n = 2 |

Abelian group | yes |

Optical Isomerism (Chirality) | no |

dipole (p) | 2A'+A'' |
---|---|

quadrupole (d) | 3A'+2A'' |

octopole (f) | 4A'+3A'' |

hexadecapole (g) | 5A'+4A'' |

32-pole (h) | 6A'+5A'' |

64-pole (i) | 7A'+6A'' |

128-pole (j) | 8A'+7A'' |

256-pole(k) | 9A'+8A'' |

512-pole (l) | 10A'+9A'' |

- A. Gelessus, W. Thiel and W. Weber, J. Chem. Educ.
**72**, 505 (1995)

Multipoles and Symmetry