Skip to main content
SpringerLink
Log in

Derivation of a Force Field for Computer Simulations of Multi-Walled Nanotubes Using Genetic Algorithm. I. Tungsten Disulfide

  • THEORETICAL INORGANIC CHEMISTRY
  • Published:
Russian Journal of Inorganic Chemistry Aims and scope Submit manuscript

Abstract

A technique for constructing force fields based on the use of genetic algorithms is proposed, which is aimed at parameterization of potentials intended for computer simulation of polyatomic nanosystems. To illustrate the proposed approach, a force field has been developed for modeling layered modifications of WS2, including multi-walled nanotubes, the dimensions of which are beyond the capabilities of ab initio methods. When determining the potential parameters, layered polytypes of bulk crystals, monolayers, bilayers, and nanotubes of small diameters were used as calibration systems. The parameterization found was successfully tested on double-walled nanotubes, the structure of which was determined using density functional calculations. The obtained force field was used for the first time to model the structure and stability of achiral multi-walled nanotubes based on WS2. The interwall distances obtained from the simulation are in good agreement with the results of recent measurements of these parameters for existing nanotubes.

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.

REFERENCES

  1. J. L. Musfeldt, Y. Iwasa, and R. Tenne, Phys. Today 73, 42 (2020). https://doi.org/10.1063/PT.3.4547

    Article  CAS  Google Scholar 

  2. H. Kawai, M. Sugahara, R. Okada, et al., Appl. Phys. Express 10, 015001 (2017). https://doi.org/10.7567/APEX.10.015001

    Article  Google Scholar 

  3. B. Kim, N. Park, and J. Kim, Nat. Commun. 13, 3237 (2022). https://doi.org/10.1038/s41467-022-31018-8

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  4. K. R. O’Neal, J. G. Cherian, A. Zak, et al., Nano Lett. 16, 993 (2016). https://doi.org/10.1021/acs.nanolett.5b03996

    Article  CAS  PubMed  Google Scholar 

  5. S. S. Sinha, A. Zak, R. Rosentsvieg, et al., Small 16, 1904390 (2020). https://doi.org/10.1002/smll.201904390

    Article  CAS  Google Scholar 

  6. K. S. Nagapriya, O. Goldbart, I. Kaplan-Ashiri, et al., Phys. Rev. Lett. 101, 195501 (2008). https://doi.org/10.1103/PhysRevLett.101.195501

    Article  CAS  PubMed  Google Scholar 

  7. R. Levi, O. Bitton, G. Leitus, et al., Nano Lett. 13, 3736 (2013). https://doi.org/10.1021/nl401675k

    Article  CAS  PubMed  Google Scholar 

  8. M. Sugahara, H. Kawai, Y. Yomogida, et al., Appl. Phys. Express 9, 075001 (2016). https://doi.org/10.7567/APEX.9.075001

    Article  CAS  Google Scholar 

  9. F. Qin, W. Shi, T. Ideue, et al., Nat. Commun. 8, 14465 (2017). https://doi.org/10.1038/ncomms14465

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  10. C. Y. Zhang, S. Wang, L. J. Yang, et al., Appl. Phys. Lett. 100, 243101 (2012). https://doi.org/10.1063/1.4729144

    Article  CAS  Google Scholar 

  11. Y. J. Zhang, M. Onga, F. Qin, et al., 2D Mater. 5, 035002 (2018). https://doi.org/10.1088/2053-1583/aab670

  12. Y. Divon, R. Levi, J. Garel, et al., Nano Lett. 17, 28 (2017). https://doi.org/10.1021/acs.nanolett.6b03012

    Article  CAS  PubMed  Google Scholar 

  13. D. Maharaj and B. Bhushan, Tribol. Lett. 49, 323 (2013). https://doi.org/10.1007/s11249-012-0071-0

    Article  CAS  Google Scholar 

  14. C. S. Reddy, A. Zak, and E. Zussman, J. Mater. Chem. 21, 16086 (2011).

    Article  CAS  Google Scholar 

  15. E. Zohar, S. Baruch, M. H. Shneider, et al., J. Adhes. Sci. Technol. 25, 1603 (2011). https://doi.org/10.1163/016942410X524138

    Article  CAS  Google Scholar 

  16. G. Otorgust, H. Dodiuk, S. Kenig, and R. Tenne, Eur. Polym. J. 89, 281 (2017). https://doi.org/10.1016/j.eurpolymj.2017.02.027

    Article  CAS  Google Scholar 

  17. L. Yadgarov, B. Višić, T. Abir, et al., Phys. Chem. Chem. Phys. 20, 20812 (2018). https://doi.org/10.1039/c8cp02245c

    Article  CAS  PubMed  Google Scholar 

  18. Md. A. Rahman, Y. Yomogida, M. Nagano, et al., Jpn. J. Appl. Phys. 60, 100902 (2021). https://doi.org/10.35848/1347-4065/ac2013

  19. G. Shen, Y. Yan, and K. Hong, Mater. Lett. 319, 132303 (2022). https://doi.org/10.1016/j.matlet.2022.132303

    Article  CAS  Google Scholar 

  20. S. S. Sinha, L. Yadgarov, S. B. Aliev, et al., J. Phys. Chem. 125, 6324 (2021). https://doi.org/10.1021/acs.jpcc.0c10784

  21. Y. Yomogida, Y. Miyata, and K. Yanagi, Appl. Phys. Express 12, 085001 (2019). https://doi.org/10.7567/1882-0786/ab2acb

    Article  CAS  Google Scholar 

  22. Sadan M. Bar, L. Houben, A. N. Enyashin, et al., PNAS 105, 15643 (2008). https://doi.org/10.1073/pnas.0805407105

    Article  PubMed  PubMed Central  Google Scholar 

  23. H. Deniz and L.-C. Qin, Chem. Phys. Lett. 552, 92 (2012). https://doi.org/10.1016/j.cplett.2012.09.041

    Article  CAS  Google Scholar 

  24. Y. Chen, H. Deniz, and L.-C. Qin, Nanoscale 9, 7124 (2017). https://doi.org/10.1039/c7nr01688c

    Article  CAS  PubMed  Google Scholar 

  25. M. Krause, A. Mücklich, A. Zak, et al., Phys. Status Solidi B 248, 2716 (2011). https://doi.org/10.1002/pssb.201100076

    Article  CAS  Google Scholar 

  26. G. Seifert, H. Terrones, M. Terrones, et al., Solid State Commun. 114, 245 (2000). https://doi.org/10.1016/S0038-1098(00)00047-8

    Article  CAS  Google Scholar 

  27. M. Ghorbani-Asl, N. Zibouche, M. Wahiduzzaman, et al., Sci. Rep. 3, 2961 (2013). https://doi.org/10.1038/srep02961

    Article  PubMed  PubMed Central  Google Scholar 

  28. A. V. Bandura, D. D. Kuruch, S. I. Lukyanov, and R. A. Evarestov, Russ. J. Inorg. Chem. 67, 2009 (2022). https://doi.org/10.1134/S0036023622601970

    Article  CAS  Google Scholar 

  29. R. A. Evarestov, A. V. Bandura, V. V. Porsev, and A. V. Kovalenko, J. Comput. Chem. 38, 2581 (2017). https://doi.org/10.1002/jcc.24916

    Article  CAS  PubMed  Google Scholar 

  30. R. A. Evarestov, A. V. Kovalenko, A. V. Bandura, et al., Mater. Res. Express 5, 115028 (2018). https://doi.org/10.1088/2053-1591/aadf00

    Article  CAS  Google Scholar 

  31. A. V. Bandura, S. I. Lukyanov, D. D. Kuruch, and R. A. Evarestov, Physica E 124, 114183 (2020). https://doi.org/10.1016/j.physe.2020.114183

    Article  CAS  Google Scholar 

  32. S. Piskunov, O. Lisovski, Y. F. Zhukovskii, et al., ACS Omega 4, 1434 (2019). https://doi.org/10.1021/acsomega.8b03121

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  33. J. A. Talla, Kh. Al-Khaza’leh, and N. Omar, Russ. J. Inorg. Chem. 67, 1025 (2022). https://doi.org/10.1134/S0036023622070178

    Article  CAS  Google Scholar 

  34. S. I. Lukyanov, A. V. Bandura, R. A. Evarestov, et al., Physica E 133, 114779 (2021). https://doi.org/10.1016/j.physe.2021.114779

    Article  CAS  Google Scholar 

  35. R. Dovesi, A. Erba, R. Orlando, et al., WIREs Comput. Mol. Sci. 8, e1360 (2018). https://doi.org/10.1002/wcms.1360

  36. R. Dovesi, V. R. Saunders, C. Roetti, et al., CRYSTAL17 User’s Manual (University of Turin, Torino, 2018).

    Google Scholar 

  37. L. F. Pacios and P. A. Christiansen, J. Chem. Phys. 82, 2664 (1985). https://doi.org/10.1063/1.448263

    Article  Google Scholar 

  38. R. B. Ross, J. M. Powers, T. Atashroo, et al., J. Chem. Phys. 93, 6654 (1990). https://doi.org/10.1063/1.458934

    Article  CAS  Google Scholar 

  39. J. Heyd, G. E. Scuseria, and M. Ernzerhof, J. Chem. Phys. 118, 8207 (2003). https://doi.org/10.1063/1.1564060

    Article  CAS  Google Scholar 

  40. H. J. Monkhorst and J. D. Pack, Phys. Rev. B 13, 5188 (1976). https://doi.org/10.1103/PhysRevB.13.5188

    Article  Google Scholar 

  41. S. Grimme, J. Comput. Chem. 27, 1787 (2006). https://doi.org/10.1002/jcc.20495

    Article  CAS  PubMed  Google Scholar 

  42. J. D. Gale and A. L. Rohl, Mol. Simul. 29, 291 (2003). https://doi.org/10.1080/0892702031000104887

    Article  CAS  Google Scholar 

  43. S. Shi, L. Yan, Y. Yang, et al., J. Comput. Chem. 24, 1059 (2003). https://doi.org/10.1002/jcc.10171

    Article  CAS  PubMed  Google Scholar 

  44. A. Krishnamoorthy, A. Mishra, D. Kamal, et al., SoftwareX 13, 100663 (2021). https://doi.org/10.1016/j.softx.2021.100663

    Article  Google Scholar 

  45. K. Nomura, R. K. Kalia, A. Nakano, et al., SoftwareX 11, 100389 (2020). https://doi.org/10.1016/j.softx.2019.100389

    Article  Google Scholar 

  46. Platypus. https://github.com/Project-Platypus/Platypus (accessed May 23, 2023).

  47. M. L. Waskom, J. Open Source Soft 6, 3021 (2021). https://doi.org/10.21105/joss.03021

    Article  Google Scholar 

  48. J. D. Hunter, Comput. Sci. Eng. 9, 90 (2007). https://doi.org/10.1109/MCSE.2007.55

    Article  Google Scholar 

  49. The pandas Development Team. Zenodo 2023, pandas-dev/pandas: Pandas (v2.0.1). https://doi.org/10.5281/zenodo.7857418

  50. F. Pedregosa, G. Varoquaux, A. Gramfort, et al., J. Machine Learning Res. 12, 2825 (2011). https://doi.org/10.48550/arXiv.1201.0490

    Article  Google Scholar 

  51. W. J. Schutte, J. L. De Boer, and F. Jellinek, J. Solid State Chem. 70, 207 (1987). https://doi.org/10.1016/0022-4596(87)90057-0

    Article  CAS  Google Scholar 

  52. A. V. Bandura and R. A. Evarestov, Sur. Sci. 641, 6 (2015). https://doi.org/10.1016/j.susc.2015.04.027

    Article  CAS  Google Scholar 

  53. G. Seifert, T. Köhler, and R. Tenne, J. Phys. Chem. B 106, 2497 (2002). https://doi.org/10.1021/jp0131323

    Article  CAS  Google Scholar 

Download references

ACKNOWLEDGMENTS

The authors thank the Resource Center “Computer Center of St. Petersburg State University” for providing the computational facilities and help in the accomplishment of the high performance calculations.

Funding

This work was financially supported by the Russian Science Foundation (RSF) within the framework of research project no. 23-23-00040, https://rscf.ru/project/23-23-00040/.

Author information

Authors and Affiliations

  1. Quantum Chemistry Department, Saint-Petersburg State University, 199034, St. Petersburg, Russia

    A. V. Bandura, S. I. Lukyanov, A. V. Domnin, D. D. Kuruch & R. A. Evarestov

Authors
  1. A. V. Bandura
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. I. Lukyanov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. V. Domnin
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. D. D. Kuruch
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. R. A. Evarestov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. V. Bandura.

Ethics declarations

The authors declare that they have no conflicts of interest.

Additional information

Dedicated to the 300th anniversary of St. Petersburg University

Publisher’s Note.

Pleiades Publishing remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary Information

Supporting information includes:

Table S1. The SWMBL-C force field parameters.

Table S2. Comparison of the properties of WS2 2H and 3R bulk phases, monolayer and nanotubes (12, 12), (6, 6), measured experimentally or calculated by DFT method with the results of modeling by molecular mechanics using the proposed force field.

Table S3. Comparison of the phonon frequencies (cm–1) at the Γ point of the Brillouin zone for the 2H-WS2 crystal, measured experimentally and calculated by DFT method, with the results of modeling by the molecular mechanics using the proposed force field.

Fig. S1. Cross-sectional view of the force-field optimized structure of a WS2 5-walled NT (82, 82)@(89, 89)@(96, 96)@(103, 103)@(110, 110) with armchair chirality.

Fig. S2. Cross-sectional view of the force-field optimized structure of a WS2 5-walled NT (142, 0)@(154, 0)@(166, 0)@(178, 0)@(190, 0) with zigzag chirality.

11502_2023_3148_MOESM1_ESM.pdf

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bandura, A.V., Lukyanov, S.I., Domnin, A.V. et al. Derivation of a Force Field for Computer Simulations of Multi-Walled Nanotubes Using Genetic Algorithm. I. Tungsten Disulfide. Russ. J. Inorg. Chem. 68, 1582–1591 (2023). https://doi.org/10.1134/S003602362360209X

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S003602362360209X

Keywords:

Search

Navigation