Skip to main content
SpringerLink
Log in
Book cover

Annual Meeting of the Bulgarian Section of SIAM

BGSIAM 2018: Advanced Computing in Industrial Mathematics pp 278–290Cite as

Influence of the Temperature on Simulated Annealing Method for Metal Nanoparticle Structures Optimization

  • Conference paper
  • First Online:

  • 270 Accesses

Part of the book series: Studies in Computational Intelligence ((SCI,volume 961))

Abstract

The description of the mechanisms of formation and dynamics of changes in the internal structure of nanoparticles can allow predicting the properties of these nanoparticles. Despite the modern development of the experimental base and theoretical approaches, certain tasks in the study of structural characteristics, including the search for stable configurations, the description of the criteria for thermal stability, etc., are not being solved. The stable configuration is when the potential energy is minimal. In this paper we apply Simulated Annealing method for metal nanoparticle structures optimization developed earlier by the authors. Successful application of the method depends on algorithm parameters. One of the most important parameters is the value of the initial temperature. According to the literature the initial temperature needs to have a high value. The question is which value is high. A fixed value can be high for some initial data and not high for other. We propose several variants of calculation of the value of initial temperature and study their influence on algorithm performance.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Cai, W.S., Shao, X.G.: A fast annealing evolutionary algorithm for global optimization. J. Comput. Chem. 23(4), 427–435 (2002)

    Article  Google Scholar 

  2. Cai, W.S., Feng, Y., Shao, X.G., Pan, Z.X.: Optimization of Lennard-Jones atomic clusters. J. Mol. Struct. (Theochem) 579(1), 229–234 (2002)

    Article  Google Scholar 

  3. Cheng, L.J., Cai, W.S., Shao, X.G.: A connectivity table for cluster similarity checking in the evolutionary optimization method. Chem. Phys. Lett. 389(4), 309–314 (2004)

    Article  Google Scholar 

  4. Cheng, L., Feng, Y., Yang, J., Yang, J.: Funnel hopping: searching the cluster potential energy surface over the funnels. J. Chem. Phys. 130, 214112 (2009)

    Article  Google Scholar 

  5. Cleri, F., Rosato, V.: Tight-binding potentials for transition metals and alloys. Phys. Rev. B. 48(1), 22–33 (1993)

    Article  Google Scholar 

  6. Doye, J.P.K.: Physical perspectives on the global optimization of atomic clusters. In: Pintér, J.D. (ed.) Global Optimization. Nonconvex Optimization and Its Applications, vol. 85, pp. 103–139. Springer, Boston, MA (2006)

    Google Scholar 

  7. Gelfand, S.B., Mitter, S.K.: Metropolis-type annealing algorithms for global optimization in Rd. SIAM J. Control Optim. 31(1), 111–131 (1993)

    Article  MathSciNet  Google Scholar 

  8. Gregurick, S.K., Alexander, M.H., Hartke, B.: Global geometry optimization of (Ar)n and B(Ar)n clusters using a modified genetic algorithm. J. Chem. Phys. 104(7), 2684–2691 (1996)

    Article  Google Scholar 

  9. Hauser, A., Schnedlitz, M., Ernst, W.: A coarse-grained Monte Carlo approach to diffusion processes in metallic nanoparticles. Eur. Phys. J. D. 71, 150 (2017). https://doi.org/10.1140/epjd/e2017-80084-y

    Article  Google Scholar 

  10. Huang, W.Q., Lai, X.J., Xu, R.C.: Structural optimization of silver clusters from Ag141 to Ag310 using a modified dynamic lattice searching method with constructed core. Chem. Phys. Lett. 507(1), 199–202 (2011)

    Article  Google Scholar 

  11. Husic, B.E., Schebarchov, D., Wales, D.J.: Impurity effects on solid–solid transitions in atomic clusters. NANO 8, 18326–18340 (2016)

    Google Scholar 

  12. Iravani, S., Korbekandi, H., Mirmohammadi, S.V., Zolfaghari, B.: Synthesis of silver nanoparticles: chemical, physical and biological methods. Res. Pharm. Sci. 9(6), 385–406 (2014)

    Google Scholar 

  13. Jellinek, J., Krissinel, E.B.: NinAlm alloy clusters: analysis of structural forms and their energy ordering. Chem. Phys. Lett. 258(1–2), 283–292 (1996)

    Article  Google Scholar 

  14. Jiang, H.Y., Cai, W.S., Shao, X.G.: A random tunneling algorithm for the structural optimization problem. Phys. Chem. Chem. Phys. 4(19), 4782–4788 (2002)

    Article  Google Scholar 

  15. Kirkpatrick, S., Gellat, C.D., Vecchi, P.M.: Optimization by simulated annealing. Science 220, 671–680 (1983)

    Article  MathSciNet  Google Scholar 

  16. Leary, R.H.: Global optimization on funneling landscapes. J. Glob. Optim. 18(4), 367–383 (2000)

    Article  MathSciNet  Google Scholar 

  17. Leary, R.H., Doye, J.P.K.: Tetrahedral global minimum for the 98-atom Lennard-Jones cluster. Phys. Rev. E. 60(6), R6320–R6322 (1999)

    Article  Google Scholar 

  18. Li, X.J., Fu, J., Qin, Y., Hao, S.Z., Zhao, J.J.: Gupta potentials for five HCP rare earth metals. Comput. Mater. Sci. 112, 75–79 (2016)

    Article  Google Scholar 

  19. Liu, D.C., Nocedal, J.: On the limited memory BFGS method for large scale optimization. Math. Prog. 45(1), 503–528 (1989)

    Article  MathSciNet  Google Scholar 

  20. Lloyd, L.D., Johnston, R.L., Salhi, S., Wilson, N.T.: Theoretical investigation of isomer stability in platinum-palladium nanoalloy clusters. J. Mater. Chem. 14(11), 1691–1704 (2004)

    Article  Google Scholar 

  21. Ma, J.P., Straub, J.E.J.: Simulated annealing using the classical density distribution. Chem. Chem. Phys. 101(1), 533–541 (1994)

    Google Scholar 

  22. Michaelian, K., Rendón, N., Garzón, I.L.: Structure and energetics of Ni, Ag, and Au nanoclusters. Phys. Rev. B. 60, 2000–2010 (1999)

    Article  Google Scholar 

  23. Myasnichenko, V., Kirilov, L., Mikhov, R., Fidanova, S., Sdobnyakov, N.: Simulated annealing method for metal nanoparticle structures optimization. In: Georgiev, K., Todorov, M., Georgiev, I. (eds.) Advanced Computing in Industrial Mathematics. Studies in Computational Intelligence, vol. 793, pp. 277–288. Sprigner (2019)

    Google Scholar 

  24. Myasnichenko, V., Sdobnyakov, N., Kirilov, L., Mikhov, R., Fidanova, S.: Monte Carlo approach for modeling and optimization of one-dimensional bimetallic nanostructures. In: Nikolov, G., Kolkovska, N., Georgiev, K. (eds.) Numerical Methods and Applications. NMA 2018. Lecture Notes in Computer Science, vol. 11189, pp. 133–141. Springer (2019)

    Google Scholar 

  25. Myshlyavtsev, A.V., Stishenko, P.V., Svalova, A.I.: A systematic computational study of the structure crossover and coordination number distribution of metallic nanoparticles. Phys. Chem. Chem. Phys. 19(27), 17895–17903 (2017)

    Article  Google Scholar 

  26. Pillardy, J., Liwo, A., Scheraga, H.A.: An efficient deformation-based global optimization method (self-consistent basin-to-deformed-basin mapping (SCBDBM)). Application to Lennard-Jones atomic clusters. J. Phys. Chem. A. 103(46), 9370–9377 (1999)

    Google Scholar 

  27. Romero, D., Barrón, C., Gómez, S.: The optimal geometry of Lennard-Jones clusters: 148–309. Comput. Phys. Commun. 123, 87–96 (1999)

    Article  Google Scholar 

  28. Rossi, G., Ferrando, R.: Combining shape-changing with exchange moves in the optimization of nanoalloys. Comput. Theor. Chem. 1107(1), 66–73 (2017)

    Article  Google Scholar 

  29. Schelstraete, S., Verschelde, H.J.: Finding minimum-energy configurations of Lennard-Jones clusters using an effective potential. Phys. Chem. A. 101(3), 310–315 (1997)

    Article  Google Scholar 

  30. Sebetci, A., Güvenç, Z.B.: Global minima for free Pt_N clusters (N = 22–56): a comparison between the searches with a molecular dynamics approach and a basin-hopping algorithm. Eur. Phys. J. D. 30(1), 71–79 (2004)

    Article  Google Scholar 

  31. Shao, X.G., Cheng, L.J., Cai, W.S.: A dynamic lattice searching method for fast optimization of Lennard-Jones clusters. J. Comput. Chem. 25(14), 1693–1698 (2004)

    Article  Google Scholar 

  32. Shao, X.G., Jiang, H.Y., Cai, W.S.: Parallel random tunneling algorithm for structural optimization of Lennard-Jones clusters up to N = 330. J. Chem. Inf. Comput. Sci. 44(1), 193–199 (2004)

    Article  Google Scholar 

  33. Takeuchi, H.: Clever and efficient method for searching optimal geometries of Lennard-Jones clusters. J. Chem. Inf. Model. 46(5), 2066–2070 (2006)

    Article  Google Scholar 

  34. Wales, D.J.: Global optimization of clusters, crystals, and biomolecules. Science 285(5432), 1368–1372 (1999)

    Article  Google Scholar 

  35. Wales, D.J., Doye, J.P.K.: Global optimization by basin-hopping and the lowest energy structures of lennard-jones clusters containing up to 110 atoms: condensed matter; atomic and molecular clusters. J. Phys. Chem. A. 101(28), 5111–5116 (1997)

    Article  Google Scholar 

  36. Wales, D.J., Scheraga, H.A.: Global optimization of clusters, crystals, and biomolecules. Science 285(5432), 1368–1372 (1999)

    Article  Google Scholar 

  37. White, R.P., Mayne, H.R.: An investigation of two approaches to basin hopping minimization for atomic and molecular clusters. Chem. Phys. Lett. 289(5–6), 463–468 (1998)

    Article  Google Scholar 

  38. Wolf, M.D., Landman, U.: Genetic algorithms for structural cluster optimization. J. Phys. Chem. A. 102(30), 6129–6137 (1998)

    Article  Google Scholar 

  39. Wu, X., Sun, Y.: Stable structures and potential energy surface of the metallic clusters: Ni, Cu, Ag, Au, Pd, and Pt. J. Nanopart. Res. 19, 201 (2017)

    Article  Google Scholar 

  40. Xue, G.L.: Improvement on the Northby algorithm for molecular conformation: better solutions. J. Glob. Optim. 4(4), 425–440 (1994)

    Article  MathSciNet  Google Scholar 

  41. http://www-wales.ch.cam.ac.uk/CCD.html (The Cambridge Energy Landscape Database)

  42. https://www.azonano.com/article.aspx?ArticleID=3274 (Cobalt (Co) Nanoparticles- Properties, Applications)

Download references

Acknowledgments

Work presented here is partially supported by the Russian Foundation for Basic Research (project No. 20-37-70007), by the Ministry of Science and Higher Education of the Russian Federation in the framework of the State Program in the Field of the Research Activity (project no. 0817-2020-0007); Stefka Fidanova was supported by the Bulgarian NSF under the grant DFNI-DN 12/5 and by the Grant No BG05M2OP001-1.001-0003, financed by the Science and Education for Smart Growth Operational Program and co-financed by the European Union through the European structural and Investment funds. Leoneed Kirilov and Rossen Mikhov were supported by the National Scientific Program “Information and Communication Technologies for a Single Digital Market in Science, Education and Security (ICTinSES)”, Ministry of Education and Science – Bulgaria, and by the Grant No BG05M2OP001-1.001-0003, financed by the Science and Education for Smart Growth Operational Program and co-financed by the European Union through the European structural and Investment funds.

Author information

Authors and Affiliations

  1. Institute of Information and Communication Technologies—Bulgarian Academy of Sciences, Sofia, Bulgaria

    Rossen Mikhov, Stefka Fidanova & Leoneed Kirilov

  2. Tver State University, Tver, Russia

    Vladimir Myasnichenko & Nickolay Sdobnyakov

Authors
  1. Rossen Mikhov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vladimir Myasnichenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Stefka Fidanova
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Leoneed Kirilov
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Nickolay Sdobnyakov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Vladimir Myasnichenko or Leoneed Kirilov .

Editor information

Editors and Affiliations

  1. Institute of Information and Communication Technologies and Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivan Georgiev

  2. Institute of Mathematics and Informatics, Bulgarian Academy of Science, Sofia, Bulgaria

    Hristo Kostadinov

  3. Institute of Information and Communication Technologies, Bulgarian Academy of Science, Sofia, Bulgaria

    Elena Lilkova

Rights and permissions

Reprints and permissions

Copyright information

© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Mikhov, R., Myasnichenko, V., Fidanova, S., Kirilov, L., Sdobnyakov, N. (2021). Influence of the Temperature on Simulated Annealing Method for Metal Nanoparticle Structures Optimization. In: Georgiev, I., Kostadinov, H., Lilkova, E. (eds) Advanced Computing in Industrial Mathematics. BGSIAM 2018. Studies in Computational Intelligence, vol 961. Springer, Cham. https://doi.org/10.1007/978-3-030-71616-5_25

Download citation

Publish with us

Policies and ethics

Search

Navigation