Continuous symmetry measures of molecules and crystals.

10^th March 2026, 14:00
Gil Alon
Open University of Israel

Abstract

The CSM (Continuous Symmetry Measure) was developed in the 1990s by Avnir, Peleg and Zabrodsky as a measure for the symmetry level of molecules ([1]). For a given molecular structure, the calculation of the CSM is a nontrivial task. Over the past 8 years, we have developed exact and approximate algorithms for the calculation of the CSM in various conditions, depending on the size and type of the molecules ([2]-[5]).
It is natural to try to extend these methods to the symmetry analysis of crystals, where we could have a continuous scale on which the fit of a given crystal to a given space symmetry group will be measured.
In this talk I will focus on the algorithmic side of our work, and describe the methods we developed for molecules, and our recent work on measuring the centrosymmetry of crystal structures ([6]).
Joint work with Inbal Tuvi-Arad.
[1] Hagit Zebrowski, Shnuel Peleg and David Avnir, Continuous Symmetry Measures, Journal of The American Chemical Society, 114, 7843–7851 (1992).
[2] Gil Alon and Inbal Tuvi Arad, Improved Algorithms for Symmetry Analysis: Structure Preserving Permutations, Journal of Mathematical Chemistry, 56, 193-212 (2018).
[3] Inbal Tuvi-Arad and Gil Alon, Improved Algorithms for Quantifying the Near Symmetry of Proteins: Complete Side Chains Analysis, Journal of Cheminformatics, 11:39, 1-11 (2019).
[4] Gil Alon, Yuval Ben-Haim and Inbal Tuvi-Arad, Continuous symmetry and chirality measures: approximate algorithms for large molecular structures, Journal of Cheminformatics, 5, 106 (2023).
[5] Inbal Tuvi-Arad, Yaffa Shalit and Gil Alon, CSM Software: Continuous Symmetry and Chirality Measures for Quantitative Structural Analysis, Journal of Chemical Information and Modeling, 64, 14 (2024).
[6] Inbal Tuvi-Arad and Gil Alon, Quantitative determination of approximate centrosymmetry in P1 organic crystals, CrystEngComm, advance article, DOI: https://doi.org/10.1039/D5CE01181G