Supervised Machine Learning-Graph Theory Approach For Analyzing the Electronic Properties of Alkanes
Year 2024,
Volume: 11 Issue: 1, 137 - 148, 04.02.2024
Zubainun Mohamed Zabidi
,
Nurul Aimi Zakaria
,
Ahmad Nazib Alias
Abstract
The combination of advanced scientific computing and quantum chemistry improves the existing approach in all chemistry and material science fields. Machine learning has revolutionized numerous disciplines within chemistry and material science. In this study, we present a supervised learning model for predicting the HOMO and LUMO energies of alkanes, which is trained on a database of molecular topological indices. We introduce a new moment topology approach has been introduced as molecular descriptors. Supervised learning utilizes artificial neural networks and support vector machines, taking advantage of the correlation between the molecular descriptors. The result demonstrate that this supervised learning model outperforms other models in predicting the HOMO and LUMO energies of alkanes. Additionally, we emphasize the importance of selecting appropriate descriptors and learning systems, as they play crucial role in accurately modeling molecules with topological orbitals.
Thanks
The authors would like to thank Dr James J. P. Stewart from MOPAC Inc. for his permission to use the MOPAC software.
References
- 1. Takata M, Lin BL, Xue M, Zushi Y, Terada A, Hosomi M. Predicting the acute ecotoxicity of chemical substances by machine learning using graph theory. Chemosphere. 2020 Jan;238:124604. Available from: <URL>.
- 2. Tamilarasi C, others. QSPR analysis of novel indices with priority polycyclic aromatic hydrocarbons (PAHs). Turkish Journal of Computer and Mathematics Education (TURCOMAT). 2021;12(10):3992–9.
- 3. Kirmani SAK, Ali P, Azam F. Topological indices and QSPR / QSAR analysis of some antiviral drugs being investigated for the treatment of COVID ‐19 patients. Int J of Quantum Chemistry. 2021 May 5;121(9):e26594. Available from: <URL>.
- 4. Sporns O. Graph theory methods: applications in brain networks. Dialogues in Clinical Neuroscience. 2018 Jun 30;20(2):111–21. Available from: <URL>.
- 5. Randić M. Novel molecular descriptor for structure—property studies. Chemical Physics Letters. 1993 Aug;211(4–5):478–83. Available from: <URL>.
- 6. Boguñá M, Bonamassa I, De Domenico M, Havlin S, Krioukov D, Serrano MÁ. Network geometry. Nature Reviews Physics. 2021 Jan 29;3(2):114–35. Available from: <URL>.
- 7. Rada J, Rodríguez JM, Sigarreta JM. General properties on Sombor indices. Discrete Applied Mathematics. 2021 Aug;299:87–97. Available from: <URL>.
- 8. Van Engelen JE, Hoos HH. A survey on semi-supervised learning. Machine Learning. 2020 Feb;109(2):373–440. Available from: <URL>.
- 9. Prezhdo OV. Advancing Physical Chemistry with Machine Learning. Journal of Physical Chemistry Letters. 2020 Nov 19;11(22):9656–8. Available from: <URL>.
- 10. Pavithra M, Kumar PP, Divya P, Manjubala P, Jayalakshmi S. The significance of learning in data analytics: Supervised learning techniques. Global Journal of Internet Interventions and IT Fusion. 2021;4(1–2021).
- 11. Dalfó C, Fiol MA, Garriga E. Moments in graphs. Discrete Applied Mathematics. 2013 Apr;161(6):768–77. Available from: <URL>.
- 12. Chang C, Ren H, Deng Z, Deng B. The ρ ‐-moments of vertex‐weighted graphs. Applied Mathematics and Computation. 2021 Jul;400:126070. Available from: <URL>.
- 13. Cao J, Ali U, Javaid M, Huang C. Zagreb connection indices of molecular graphs based on operations. Complexity. 2020 Mar 30;2020:1–15. Available from: <URL>.
- 14. Chu YM, Julietraja K, Venugopal P, Siddiqui MK, Prabhu S. Degree- and irregularity-based molecular descriptors for benzenoid systems. European Physical Journal Plus. 2021 Jan;136(1):78. Available from: <URL>.
- 15. Kumar KA, Basavarajappa N, Shanmukha M. QSPR analysis of alkanes with certain degree based topological indices. Malaya Journal of Mathematik. 2020;8(1):314–30.
- 16. Zhou B, Trinajstić N. On a novel connectivity index. Journal of Mathematical Chemistry. 2009 Nov;46(4):1252–70. Available from: <URL>.
- 17. Estrada E, Torres L, Rodriguez L, Gutman I. An atom-bond connectivity index: modelling the enthalpy of formation of alkanes. Indian Journal of Chemistry. 1998;37:849-55. Available from: <URL>.
- 18. Vukičević D, Furtula B. Topological index based on the ratios of geometrical and arithmetical means of end-vertex degrees of edges. Journal of Mathematical Chemistry. 2009 Nov;46(4):1369–76. Available from: <URL>.
- 19. Shahni Karamzadeh N, Darafsheh MR. Topological Indices of Certain Graphs. Iranian Journal of Mathematical Chemistry [Internet]. 2022 Sep [cited 2023 Nov 27];13(3): 167-74. Available from: <URL>.
- 20. Alqesmah A, Alloush KAA, Saleh A, Deepak G. Entire Harary index of graphs. Journal of Discrete Mathematical Sciences and Cryptography. 2022 Nov 17;25(8):2629–43. Available from: <URL>.
- 21. Thomas N, Mathew L, Sriram S, Nagar AK, Subramanian KG. Certain Distance-Based Topological Indices of Parikh Word Representable Graphs. Cangul IN, editor. Journal of Mathematics. 2021 May 25;2021:1–7. <URL>.
- 22. Gutman I. On degree-and-distance-based topological indices. 2021;66(2):119-23.
- 23. Das KC. On the Balaban index of chain graphs. Bulletin of the Malaysian Mathematical Sciences Society. 2021;44:2123–38.
- 24. Ren B. A New Topological Index for QSPR of Alkanes. Journal of Chemical Information and Computer Sciences. 1999 Jan 25;39(1):139–43. Available from: <URL>.
- 25. Zhou B, Cai X, Trinajstić N. On Harary index. Journal of Mathematical Chemistry. 2008 Aug;44(2):611–8. Available from: <URL>.
- 26. Zhou ZH. Support Vector Machine. In: Machine Learning [Internet]. Singapore: Springer Singapore; 2021 [cited 2023 Nov 27]. p. 129–53. Available from: <URL>.
- 27. Alias AN, Zabidi ZM, Zakaria NA, Mahmud ZS, Ali R. Biological Activity Relationship of Cyclic and Noncyclic Alkanes Using Quantum Molecular Descriptors. Open Journal of Applied Sciences. 2021;11(08):966–84. Available from: <URL>.
- 28. Brown RD, Martin YC. The Information Content of 2D and 3D Structural Descriptors Relevant to Ligand-Receptor Binding. Journal of Chemical Information and Computer Sciences. 1997 Jan 1;37(1):1–9. Available from: <URL>.
- 29. Herndon WC, Ellzey ML, Raghuveer KS. Topological orbitals, graph theory, and ionization potentials of saturated hydrocarbons. Journal of the American Chemical Society. 1978 Apr;100(9):2645–50. Available from: <URL>.
- 30. Liu Z, Shao J, Xu W, Meng Y. Prediction of rock burst classification using the technique of cloud models with attribution weight. Natural Hazards. 2013 Sep;68(2):549–68. Available from: <URL>.
- 31. Woon KL, Chong ZX, Ariffin A, Chan CS. Relating molecular descriptors to frontier orbital energy levels, singlet and triplet excited states of fused tricyclics using machine learning. Journal of Molecular Graphics and Modelling. 2021 Jun;105:107891. Available from: <URL>.
- 32. Chou SH, Voss J, Bargatin I, Vojvodic A, Howe RT, Abild-Pedersen F. An orbital-overlap model for minimal work functions of cesiated metal surfaces. Journal of Physics: Condensed Matter. 2012 Nov 7;24(44):445007. Available from: <URL>.
- 33. Dewar MJS. σ‐Conjugation and σ‐Aromaticity. Bulletin des Soc Chimique. 1979 Jan;88(12):957–67. Available from: <URL>.
- 34. Li Z, Omidvar N, Chin WS, Robb E, Morris A, Achenie L, et al. Machine-Learning Energy Gaps of Porphyrins with Molecular Graph Representations. Journal of Physical Chemistry A. 2018 May 10;122(18):4571–8. Available from: <URL>.
- 35. von Lilienfeld OA. Quantum Machine Learning in Chemical Compound Space. Angewandte Chemie International Edition. 2018 Apr 9;57(16):4164–9. Available from: <URL>.
- 36. Zabidi ZM, Alias AN, Nurul AZ, Zaidatul SM, Rosliza A, Muhamad KY. Machine Learning Predictor Models in the Electronic Properties of Alkanes Based on Degree Topology Indices. Unpublished work. 2021;N/A.
Year 2024,
Volume: 11 Issue: 1, 137 - 148, 04.02.2024
Zubainun Mohamed Zabidi
,
Nurul Aimi Zakaria
,
Ahmad Nazib Alias
References
- 1. Takata M, Lin BL, Xue M, Zushi Y, Terada A, Hosomi M. Predicting the acute ecotoxicity of chemical substances by machine learning using graph theory. Chemosphere. 2020 Jan;238:124604. Available from: <URL>.
- 2. Tamilarasi C, others. QSPR analysis of novel indices with priority polycyclic aromatic hydrocarbons (PAHs). Turkish Journal of Computer and Mathematics Education (TURCOMAT). 2021;12(10):3992–9.
- 3. Kirmani SAK, Ali P, Azam F. Topological indices and QSPR / QSAR analysis of some antiviral drugs being investigated for the treatment of COVID ‐19 patients. Int J of Quantum Chemistry. 2021 May 5;121(9):e26594. Available from: <URL>.
- 4. Sporns O. Graph theory methods: applications in brain networks. Dialogues in Clinical Neuroscience. 2018 Jun 30;20(2):111–21. Available from: <URL>.
- 5. Randić M. Novel molecular descriptor for structure—property studies. Chemical Physics Letters. 1993 Aug;211(4–5):478–83. Available from: <URL>.
- 6. Boguñá M, Bonamassa I, De Domenico M, Havlin S, Krioukov D, Serrano MÁ. Network geometry. Nature Reviews Physics. 2021 Jan 29;3(2):114–35. Available from: <URL>.
- 7. Rada J, Rodríguez JM, Sigarreta JM. General properties on Sombor indices. Discrete Applied Mathematics. 2021 Aug;299:87–97. Available from: <URL>.
- 8. Van Engelen JE, Hoos HH. A survey on semi-supervised learning. Machine Learning. 2020 Feb;109(2):373–440. Available from: <URL>.
- 9. Prezhdo OV. Advancing Physical Chemistry with Machine Learning. Journal of Physical Chemistry Letters. 2020 Nov 19;11(22):9656–8. Available from: <URL>.
- 10. Pavithra M, Kumar PP, Divya P, Manjubala P, Jayalakshmi S. The significance of learning in data analytics: Supervised learning techniques. Global Journal of Internet Interventions and IT Fusion. 2021;4(1–2021).
- 11. Dalfó C, Fiol MA, Garriga E. Moments in graphs. Discrete Applied Mathematics. 2013 Apr;161(6):768–77. Available from: <URL>.
- 12. Chang C, Ren H, Deng Z, Deng B. The ρ ‐-moments of vertex‐weighted graphs. Applied Mathematics and Computation. 2021 Jul;400:126070. Available from: <URL>.
- 13. Cao J, Ali U, Javaid M, Huang C. Zagreb connection indices of molecular graphs based on operations. Complexity. 2020 Mar 30;2020:1–15. Available from: <URL>.
- 14. Chu YM, Julietraja K, Venugopal P, Siddiqui MK, Prabhu S. Degree- and irregularity-based molecular descriptors for benzenoid systems. European Physical Journal Plus. 2021 Jan;136(1):78. Available from: <URL>.
- 15. Kumar KA, Basavarajappa N, Shanmukha M. QSPR analysis of alkanes with certain degree based topological indices. Malaya Journal of Mathematik. 2020;8(1):314–30.
- 16. Zhou B, Trinajstić N. On a novel connectivity index. Journal of Mathematical Chemistry. 2009 Nov;46(4):1252–70. Available from: <URL>.
- 17. Estrada E, Torres L, Rodriguez L, Gutman I. An atom-bond connectivity index: modelling the enthalpy of formation of alkanes. Indian Journal of Chemistry. 1998;37:849-55. Available from: <URL>.
- 18. Vukičević D, Furtula B. Topological index based on the ratios of geometrical and arithmetical means of end-vertex degrees of edges. Journal of Mathematical Chemistry. 2009 Nov;46(4):1369–76. Available from: <URL>.
- 19. Shahni Karamzadeh N, Darafsheh MR. Topological Indices of Certain Graphs. Iranian Journal of Mathematical Chemistry [Internet]. 2022 Sep [cited 2023 Nov 27];13(3): 167-74. Available from: <URL>.
- 20. Alqesmah A, Alloush KAA, Saleh A, Deepak G. Entire Harary index of graphs. Journal of Discrete Mathematical Sciences and Cryptography. 2022 Nov 17;25(8):2629–43. Available from: <URL>.
- 21. Thomas N, Mathew L, Sriram S, Nagar AK, Subramanian KG. Certain Distance-Based Topological Indices of Parikh Word Representable Graphs. Cangul IN, editor. Journal of Mathematics. 2021 May 25;2021:1–7. <URL>.
- 22. Gutman I. On degree-and-distance-based topological indices. 2021;66(2):119-23.
- 23. Das KC. On the Balaban index of chain graphs. Bulletin of the Malaysian Mathematical Sciences Society. 2021;44:2123–38.
- 24. Ren B. A New Topological Index for QSPR of Alkanes. Journal of Chemical Information and Computer Sciences. 1999 Jan 25;39(1):139–43. Available from: <URL>.
- 25. Zhou B, Cai X, Trinajstić N. On Harary index. Journal of Mathematical Chemistry. 2008 Aug;44(2):611–8. Available from: <URL>.
- 26. Zhou ZH. Support Vector Machine. In: Machine Learning [Internet]. Singapore: Springer Singapore; 2021 [cited 2023 Nov 27]. p. 129–53. Available from: <URL>.
- 27. Alias AN, Zabidi ZM, Zakaria NA, Mahmud ZS, Ali R. Biological Activity Relationship of Cyclic and Noncyclic Alkanes Using Quantum Molecular Descriptors. Open Journal of Applied Sciences. 2021;11(08):966–84. Available from: <URL>.
- 28. Brown RD, Martin YC. The Information Content of 2D and 3D Structural Descriptors Relevant to Ligand-Receptor Binding. Journal of Chemical Information and Computer Sciences. 1997 Jan 1;37(1):1–9. Available from: <URL>.
- 29. Herndon WC, Ellzey ML, Raghuveer KS. Topological orbitals, graph theory, and ionization potentials of saturated hydrocarbons. Journal of the American Chemical Society. 1978 Apr;100(9):2645–50. Available from: <URL>.
- 30. Liu Z, Shao J, Xu W, Meng Y. Prediction of rock burst classification using the technique of cloud models with attribution weight. Natural Hazards. 2013 Sep;68(2):549–68. Available from: <URL>.
- 31. Woon KL, Chong ZX, Ariffin A, Chan CS. Relating molecular descriptors to frontier orbital energy levels, singlet and triplet excited states of fused tricyclics using machine learning. Journal of Molecular Graphics and Modelling. 2021 Jun;105:107891. Available from: <URL>.
- 32. Chou SH, Voss J, Bargatin I, Vojvodic A, Howe RT, Abild-Pedersen F. An orbital-overlap model for minimal work functions of cesiated metal surfaces. Journal of Physics: Condensed Matter. 2012 Nov 7;24(44):445007. Available from: <URL>.
- 33. Dewar MJS. σ‐Conjugation and σ‐Aromaticity. Bulletin des Soc Chimique. 1979 Jan;88(12):957–67. Available from: <URL>.
- 34. Li Z, Omidvar N, Chin WS, Robb E, Morris A, Achenie L, et al. Machine-Learning Energy Gaps of Porphyrins with Molecular Graph Representations. Journal of Physical Chemistry A. 2018 May 10;122(18):4571–8. Available from: <URL>.
- 35. von Lilienfeld OA. Quantum Machine Learning in Chemical Compound Space. Angewandte Chemie International Edition. 2018 Apr 9;57(16):4164–9. Available from: <URL>.
- 36. Zabidi ZM, Alias AN, Nurul AZ, Zaidatul SM, Rosliza A, Muhamad KY. Machine Learning Predictor Models in the Electronic Properties of Alkanes Based on Degree Topology Indices. Unpublished work. 2021;N/A.