## Abstract

We introduce a new mathematical tool for quantifying the symmetry contents of molecular structures: the Symmetry Operation Measures. In this approach, we measure the minimal distance between a given structure and the structure which is obtained after applying a selected symmetry operation on it. If the given operation is a true symmetry operation for the structure, this distance is zero; otherwise it gives an indication of how different the transformed structure is from the original one. Specifically, we provide analytical solutions for measures of all the improper rotations, S_{n}^{p}, including mirror symmetry and inversion, as well as for all pure rotations, C _{n}^{p}. These measures provide information complementary to the Continuous Symmetry Measures (CSM) that evaluate the distance between a given structure and the nearest structure which belongs to a selected symmetry point-group.

Original language | American English |
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Pages (from-to) | 190-197 |

Number of pages | 8 |

Journal | Journal of Computational Chemistry |

Volume | 29 |

Issue number | 2 |

DOIs | |

State | Published - 30 Jan 2008 |

## Keywords

- Improper rotation
- Inversion
- Reflection
- Rotation
- Symmetry
- Symmetry measure
- Symmetry operation