Improved algorithms for symmetry analysis: structure preserving permutations

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We propose an improved algorithm for calculating Avnir’s continuous symmetry and chirality measures of molecules. These measures evaluate the deviation of a given structure from symmetry by calculating the distance between the structure and its nearest symmetric counterpart. Our new algorithm utilizes structural properties of the given molecule to increase the accuracy of the calculation and dramatically reduce the running time by up to tens orders of magnitude. Consequently, a wide variety of molecules of medium size with ca. 100 atoms and even more can be analyzed within seconds. Numerical evidence of the algorithm’s efficiency is presented for several families of molecules such as helicenes, porphyrins, dendrimers building blocks, fullerene and more. The ease and efficiency of the calculation make the continuous symmetry and chirality measures promising descriptors for integration in quantitative structure–activity relationship tools, as well as chemical databases and molecular visualization software.

Original languageEnglish
Pages (from-to)193-212
Number of pages20
JournalJournal of Mathematical Chemistry
Issue number1
StatePublished - 1 Jan 2018

Bibliographical note

Funding Information:
Supported by the Israel Science Foundation (Grant 411/15). We are sincerely grateful for fruitful discussions with Prof. David Avnir (The Hebrew University of Jerusalem). The programming of the new code was done by Itay Zandbank and Devora Witty (The scientific software company, Israel). We are thankful to Sagiv Barhoom (The Open University) for his help in programming and Yaffa Shalit (The Open University) for her help in testing the code. Researchers interested in using the CSM code are welcome to contact Dr. Tuvi-Arad. The authors declare that they have no conflict of interest. This study was funded by the Israel Science Foundation (Grant Number 411/15).

Publisher Copyright:
© 2017, Springer International Publishing AG.


  • Chirality
  • Continuous symmetry measures
  • Graph automorphism
  • Permutations
  • QSAR descriptors


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