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Topological data analysis for the energy and stability of endohedral metallofullerenes

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Abstract

Topological data analysis is a useful data analysis method that combines the mathematical theory of topology with computational methods to study the valuable relationships hidden in data. Persistent homology is an effective tool in computational topology, used to measure the topological characteristics of data. In this paper, we make the quantitative predictions of the energy and stability of endohedral metallofullerenes molecules, based on topological features computed by the persistent homology. The features indicate topological properties such as Betti numbers, i.e. the number of n-dimensional holes in the molecule data space, and associate them with the structure of endohedral metallofullerenes. Using the barcode informations, we analyse the energy and stability of endohedral metallofullerenes molecules Ni@C\(_{n}\) (even n = 20, 24 \(\sim\) 52, 60, 70), and get excellent correlation coefficients 99.97\(\%\).

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Acknowledgements

This research was supported by the National Natural Science Foundation of China (No.11771116).

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Authors and Affiliations

  1. School of Mathematical Sciences, Hebei Normal University, Shijiazhuang, 050024, People’s Republic of China

    Yan Zhao, Yanying Wang & Yanhong Ding

  2. College of Hui Hua, Hebei Normal University, Shijiazhuang, 050091, People’s Republic of China

    Yan Zhao

  3. School of Sciences, Hebei University of Science and Technology, Shijiazhuang, 050018, People’s Republic of China

    Huiyun Han

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Zhao, Y., Wang, Y., Ding, Y. et al. Topological data analysis for the energy and stability of endohedral metallofullerenes. J Math Chem 60, 337–352 (2022). https://doi.org/10.1007/s10910-021-01309-4

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