C_{7} |
E | C_{7} |
(C_{7})^{2} |
(C_{7})^{3} |
(C_{7})^{4} |
(C_{7})^{5} |
(C_{7})^{6} |
rotations |
functions |
functions |
---|---|---|---|---|---|---|---|---|---|---|

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

E_{1} |
+1 +1 |
+ + ^{*} | +^{2}+ ^{2*} | +^{3}+ ^{3*} | +^{3*}+ ^{3} | +^{2*}+ ^{2} | +^{*}+ | x+iy, R_{x}+iR_{y} x-iy, R _{x}-iR_{y} |
(xz, yz) | (xz^{2}, yz^{2}) [x(x^{2}+y^{2}), y(x^{2}+y^{2})] |

E_{2} |
+1 +1 |
+^{2}+ ^{2*} | +^{3*}+ ^{3} | +^{*}+ | + + ^{*} | +^{3}+ ^{3*} | +^{2*}+ ^{2} | - | (x^{2}-y^{2}, xy) |
[xyz, z(x^{2}-y^{2})] |

E_{3} |
+1 +1 |
+^{3}+ ^{3*} | +^{*}+ | +^{2}+ ^{2*} | +^{2*}+ ^{2} | + + ^{*} | +^{3*}+ ^{3} | - | - | [y(3x^{2}-y^{2}), x(x^{2}-3y^{2})] |

Number of symmetry elements | h = 7 |

Number of irreducible representations | n = 7 |

Number of real irreducible representations | n = 4 |

Abelian group | yes |

Optical Isomerism (Chirality) | yes |

Polar | yes |

dipole (p) | A+E_{1} |
---|---|

quadrupole (d) | A+E_{1}+E_{2} |

octopole (f) | A+E_{1}+E_{2}+E_{3} |

hexadecapole (g) | A+E_{1}+E_{2}+2E_{3} |

32-pole (h) | A+E_{1}+2E_{2}+2E_{3} |

64-pole (i) | A+2E_{1}+2E_{2}+2E_{3} |

128-pole (j) | 3A+2E_{1}+2E_{2}+2E_{3} |

256-pole(k) | 3A+3E_{1}+2E_{2}+2E_{3} |

512-pole (l) | 3A+3E_{1}+3E_{2}+2E_{3} |

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

Multipoles and Symmetry

Last update Mai, 23