C_{3} |
E | C_{3} |
(C_{3})^{2} |
rotations |
functions |
functions |
---|---|---|---|---|---|---|

A | +1 | +1 | +1 | z, R_{z} |
x^{2}+y^{2}, z^{2} |
z^{3}, y(3x^{2}-y^{2}), x(x^{2}-3y^{2}), z(x^{2}+y^{2}) |

E | +1 +1 |
+ + ^{*} |
+^{*}+ |
x+iy; R_{x}+iR_{y}x-iy; R _{x}-iR_{y} |
(x^{2}-y^{2}, xy) (yz, xz) |
(xz^{2}, yz^{2}) [xyz, z(x^{2}-y^{2})] [x(x^{2}+y^{2}), y(x^{2}+y^{2})] |

Number of symmetry elements | h = 3 |

Number of irreducible representations | n = 3 |

Number of real irreducible representations | n = 2 |

Abelian group | yes |

Optical Isomerism (Chirality) | yes |

dipole (p) | A+E |
---|---|

quadrupole (d) | A+2E |

octopole (f) | 3A+2E |

hexadecapole (g) | 3A+3E |

32-pole (h) | 3A+4E |

64-pole (i) | 5A+4E |

128-pole (j) | 5A+5E |

256-pole(k) | 5A+6E |

512-pole (l) | 7A+6E |

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

Multipoles and Symmetry