Skip to main content
SpringerLink
Log in

Covalent organic frameworks: topological characterizations, spectral patterns and graph entropies

  • Original Paper
  • Published:
Journal of Mathematical Chemistry Aims and scope Submit manuscript

Abstract

Donor–acceptor covalent organic frameworks are porous polymers that are covalently bonded through dative donor–acceptor bonds. These materials have been the subject of several studies because of their unusual properties that render them as candidates for a wide range of applications. We have considered metal phthalocyanine with diimide linkers as donor–acceptor covalent organic frameworks. Owing to their photoinduced charge separations and photoenergy conversions, these frameworks are vital components in the next-generation devices. Since these networks exhibit interesting topologies, and their topological structures are correlated to the underlying connectivity, the study of structure–property relations is of utmost importance. In the present study, we aim to determine the topological characterization and entropy measure of these frameworks through various degree based and scalar self-powered topological descriptors. Furthermore we obtain combinatorially enabled machine generated NMR and ESR spectral patterns.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. Y. Song, Q. Sun, B. Aguila, S. Ma, Opportunities of covalent organic frameworks for advanced applications. Adv. Sci. 6(2), 1801410 (2018)

    Google Scholar 

  2. J.L. Segura, S. Royuela, M.M. Ramos, Post-synthetic modification of covalent organic frameworks. Chem. Soc. Rev. 48(14), 3903–3945 (2019)

    CAS  PubMed  Google Scholar 

  3. A.P. Côté, A.I. Benin, N.W. Ockwig, M. O’Keeffe, A.J. Matzger, O.M. Yaghi, Porous, crystalline, covalent organic frameworks. Science 310(5751), 1166–1170 (2005)

    PubMed  Google Scholar 

  4. M. Wang, M. Ballabio, M. Wang, H.-H. Lin, B.P. Biswal, X. Han, S. Paasch, E. Brunner, P. Liu, M. Chen, M. Bonn, T. Heine, S. Zhou, E. Cánovas, R. Dong, X. Feng, Unveiling electronic properties in metal-phthalocyanine-based pyrazine-linked conjugated two-dimensional covalent organic frameworks. J. Am. Chem. Soc. 141(42), 16810–16816 (2019)

    CAS  PubMed  Google Scholar 

  5. S. Pakhira, K.P. Lucht, J.L. Mendoza-Cortes, Iron intercalation in covalent-organic frameworks: a promising approach for semiconductors. J. Phys. Chem. C 121(39), 21160–21170 (2017)

    CAS  Google Scholar 

  6. L. Wang, Y. Xie, Y. Yang, H. Liang, L. Wang, Y. Song, Electroactive covalent organic frameworks/carbon nanotubes composites for electrochemical sensing. ACS Appl. Nano Mater. 3(2), 1412–1419 (2020)

    CAS  Google Scholar 

  7. K.K. Khaing, D. Yin, Y. Ouyang, S. Xiao, B. Liu, L. Deng, L. Li, X. Guo, J. Wang, J. Liu, Y. Zhang, Fabrication of 2D–2D heterojunction catalyst with covalent organic framework (COF) and MoS\(_2\) for highly efficient photocatalytic degradation of organic pollutants. Inorg. Chem. 59(10), 6942–6952 (2020)

    CAS  PubMed  Google Scholar 

  8. T. Sun, R. Xia, J. Zhou, X. Zheng, S. Liu, Z. Xie, Protein-assisted synthesis of nanoscale covalent organic frameworks for phototherapy of cancer. Mater. Chem. Front. 4(8), 2346–2356 (2020)

    CAS  Google Scholar 

  9. J. Gan, A.R. Bagheri, N. Aramesh, I. Gul, M. Franco, Y.Q. Almulaiky, M. Bilal, Covalent organic frameworks as emerging host platforms for enzyme immobilization and robust biocatalysis—a review. Int. J. Biol. Macromol. 167, 502–515 (2021)

    CAS  PubMed  Google Scholar 

  10. A. Wen, G. Li, D. Wu, Y. Yu, Y. Yang, N. Hu, H. Wang, J. Chen, Y. Wu, Sulphonate functionalized covalent organic framework-based magnetic sorbent for effective solid phase extraction and determination of fluoroquinolones. J. Chromatogr. A 1612, 460651 (2020)

    CAS  PubMed  Google Scholar 

  11. H. Wang, L. Zhao, X. Liu, J. Xu, W. Hou, J. Wang, E. He, R. Zhang, H. Zhang, Novel hydrogen bonding composite based on copper phthalocyanine/perylene diimide derivatives p-n heterojunction with improved photocatalytic activity. Dyes Pigm. 137, 322–328 (2017)

    CAS  Google Scholar 

  12. D. Jiang, Covalent organic frameworks: an amazing chemistry platform for designing polymers. Chem 6(10), 2461–2483 (2020)

    CAS  Google Scholar 

  13. R. Liu, K.T. Tan, Y. Gong, Y. Chen, Z. Li, S. Xie, T. He, Z. Lu, H. Yang, D. Jiang, Covalent organic frameworks: an ideal platform for designing ordered materials and advanced applications. Chem. Soc. Rev. 50(1), 120–242 (2021)

    CAS  PubMed  Google Scholar 

  14. S.R. Batten, N.R. Champness, X.-M. Chen, J. Garcia-Martinez, S. Kitagawa, L. Öhrström, M. O’Keeffe, M.P. Suh, J. Reedijk, Terminology of metal-organic frameworks and coordination polymers (IUPAC Recommendations 2013). Pure Appl. Chem. 85(8), 1715–1724 (2013)

    CAS  Google Scholar 

  15. D.K. Susarova, P.A. Troshin, D. Höglinger, R. Koeppe, S.D. Babenko, R.N. Lyubovskaya, V.F. Razumov, N.S. Sariciftci, Donor–acceptor complex formation in evaporated small molecular organic photovoltaic cells. Sol. Energy Mater. Sol. Cells 94(5), 803–811 (2010)

    CAS  Google Scholar 

  16. K. Balasubramanian, Computational and artificial intelligence techniques for drug discovery and administration, in Comprehensive Pharmacology, vol. 2, ed. by T. Kenakin (Elsevier, Amsterdam, 2022), pp.553–616

    Google Scholar 

  17. S. Mondal, N. De, A. Pal, Topological properties of graphene using some novel neighborhood degree-based topological indices. Int. J. Math. Ind. 11(1), 1950006 (2019)

    Google Scholar 

  18. K. Balasubramanian, Relativistic quantum chemical and molecular dynamics techniques for medicinal chemistry of bioinorganic compounds, in Biophysical and Computational Tools in Drug Discovery. Topics in Medicinal Chemistry, vol. 37, ed. by A.K. Saxena (Springer, Cham, 2021), pp.133–193

    Google Scholar 

  19. H. Ali, M.A. Binyamin, M.K. Shafiq, W. Gao, On the degree based topological indices of some derived networks. Mathematics 7(7), 612 (2019)

    Google Scholar 

  20. M. Arockiaraj, J. Jency, J. Abraham, S.R.J. Kavitha, K. Balasubramanian, Two-dimensional coronene fractal structures: topological entropy measures, energetics, NMR and ESR spectroscopic patterns and existence of isentropic structures. Mol. Phys. 120(11), 2079568 (2022)

    Google Scholar 

  21. A. Golbraikh, D. Bonchev, A. Tropsha, Novel chirality descriptors derived from molecular topology. J. Chem. Inf. Comput. Sci. 41(1), 147–158 (2001)

    CAS  PubMed  Google Scholar 

  22. A. Golbraikh, D. Bonchev, A. Tropsha, Novel ZE-isomerism descriptors derived from molecular topology and their application to QSAR analysis. J. Chem. Inf. Comput. Sci. 42(4), 769–787 (2002)

    CAS  PubMed  Google Scholar 

  23. S. Nikolić, I.M. Tolić, N. Trinajstić, I. Baučić, On the Zagreb indices as complexity indices. Croat. Chem. Acta 73(4), 909–921 (2000)

    Google Scholar 

  24. N. Nikolić, N. Trinajstić, I.M. Tolić, G. Rücker, C. Rücker, Shannonś information and complexity, in Complexity in Chemistry: Introduction and Fundamentals. ed. by D. Bonchev, D.H. Rouvray (Taylor & Francis, London, 2003), pp.29–89

    Google Scholar 

  25. P. Ali, S. Ajaz, K. Kirmani, O.A. Rugaie, F. Azam, Degree based topological indices and polynomials of hyaluronic acid-curcumin conjugates. Saudi Pharm. J. 28, 1093–110 (2020)

    CAS  PubMed  PubMed Central  Google Scholar 

  26. G. Zhang, M. Azeem, A. Aslam, S. Yousaf, S. Kanwal, Topological aspects of certain covalent organic frameworks and metal organic frameworks. J. Funct. Spaces 2022, 5426037 (2022)

    Google Scholar 

  27. T. Augustine, S. Roy, Topological study on triazine-based covalent-organic frameworks. Symmetry 14(8), 1590 (2022)

    CAS  Google Scholar 

  28. S. Manzoor, M.K. Siddiqui, S. Ahmad, On entropy measures of molecular graphs using topological indices. Arab. J. Chem. 13(8), 6285–6298 (2020)

    CAS  Google Scholar 

  29. C. Feng, M.H. Muhamad, M.K. Siddiqui, S.A.K. Kirmani, S. Manzoor, M.F. Hanif, On entropy measures for molecular structures of Remdesivir system and their applications. Int. J. Quantum Chem. 122(18), e26957 (2022)

    CAS  Google Scholar 

  30. S.R.J. Kavitha, J. Abraham, M. Arockiaraj, J. Jency, K. Balasubramanian, Topological characterization and graph entropies of tessellations of kekulene structures: existence of isentropic structures and applications to thermochemistry, nuclear magnetic resonance, and electron spin resonance. J. Phys. Chem. A 125(36), 8140–8158 (2021)

    CAS  PubMed  Google Scholar 

  31. J. Abraham, M. Arockiaraj, J. Jency, S.R.J. Kavitha, K. Balasubramanian, Graph entropies, enumerations of circuits, walks and topological properties of three classes of isoreticular metal organic frameworks. J. Math. Chem. 60, 695–732 (2022)

    CAS  Google Scholar 

  32. A. Mowshowitz, M. Dehmer, Entropy and the complexity of graphs revisited. Entropy 14(3), 559–570 (2012)

    Google Scholar 

  33. S. Cao, M. Dehmer, Degree-based entropies of networks revisited. Appl. Math. Comput. 261, 141–147 (2015)

    Google Scholar 

  34. P.G. Mezey, Fuzzy electron density fragments in macromolecular quantum chemistry, combinatorial quantum chemistry, functional group analysis, and shape-activity relations. Acc. Chem. Res. 47(9), 2821–2827 (2014)

    CAS  PubMed  Google Scholar 

  35. P.G. Mezey, Similarity analysis in two and three dimensions using lattice animals and polycubes. J. Math. Chem. 11, 27–45 (1992)

    Google Scholar 

  36. P.G. Mezey, Some dimension problems in molecular databases. J. Math. Chem. 45, 1–6 (2009)

    CAS  Google Scholar 

  37. P.G. Mezey, Shape-similarity measures for molecular bodies: a 3D topological approach in quantitative shape-activity relations. J. Chem. Inf. Comput. Sci. 32(6), 650–656 (1992)

    CAS  Google Scholar 

  38. R. Carbó-Dorca, Quantum similarity and QSPR in Euclidean-, and Minkowskian–Banach spaces. J. Math. Chem. (2023). https://doi.org/10.1007/s10910-023-01454-y

    Article  Google Scholar 

  39. Saloni, D. Kumari, H. Tandon, M. Labarca, T. Chakraborty, Computation of atomic electronegativity values using atomic and covalent potential: a FSGO based study. J. Math. Chem. 60, 1505–1520 (2022)

  40. G.S. Bloom, J.W. Kennedy, L.V. Quintas, Some problems concerning distance and path degree sequences, in Graph Theory. Lecture Notes in Mathematics, vol. 1018, ed. by M. Borowiecki, J.W. Kennedy, M.M. Sysło (Springer, Berlin, Heidelberg, 1983), pp.179–190

    Google Scholar 

  41. K. Balasubramanian, Topochemie-2020—a computational package for computing topological indices, spectral polynomials, walks and distance degree sequences and combinatorial generators (2020)

  42. K. Balasubramanian, Operator and algebraic methods for NMR-spectroscopy. I. Generation of NMR spin species. J. Chem. Phys. 78(11), 6358–6368 (1983)

    CAS  Google Scholar 

  43. F.H. Kaatz, A. Bultheel, Informational thermodynamic model for nanostructures. J. Math. Chem. 52(6), 1563–1575 (2014)

    CAS  Google Scholar 

  44. K. Balasubramanian, CASSCF/CI calculations on Si\(_4\) and Si\(_{4}^+\). Chem. Phys. Lett. 135(3), 283–287 (1987)

    CAS  Google Scholar 

  45. K. Balasubramanian, Enumeration of internal-rotation reactions and their reaction graphs. Theor. Chim. Acta 53, 129–146 (1979)

    CAS  Google Scholar 

  46. K. Balasubramanian, Electronic structure of (GaAs)\(_2\) Chem. Phys. Lett. 171(1–2), 58–62 (1990). https://doi.org/10.1016/0009-2614(90)80050-N

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Loyola College, Chennai, 600034, India

    Micheal Arockiaraj, Joseph Jency & Shagufa Mushtaq

  2. Department of Mathematics, Women’s Christian College, Chennai, 600006, India

    Arul Jeya Shalini

  3. School of Molecular Sciences, Arizona State University, Tempe, AZ, 85287-1604, USA

    Krishnan Balasubramanian

Authors
  1. Micheal Arockiaraj
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Joseph Jency
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Shagufa Mushtaq
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Arul Jeya Shalini
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Krishnan Balasubramanian
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

MA: Conceptualization, Supervision, Writing—review & editing. JJ: Writing—original draft, Visualization, Writing—review & editing. SM: Formal analysis, Methodology, Writing—review & editing. AJS: Formal analysis, Methodology, Writing—review & editing. KB: Conceptualization, Validation, Writing—review & editing

Corresponding author

Correspondence to Micheal Arockiaraj.

Ethics declarations

Conflict of interest

The authors declare no competing interests.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Arockiaraj, M., Jency, J., Mushtaq, S. et al. Covalent organic frameworks: topological characterizations, spectral patterns and graph entropies. J Math Chem 61, 1633–1664 (2023). https://doi.org/10.1007/s10910-023-01477-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10910-023-01477-5

Keywords

Search

Navigation