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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Cai, W.S., Shao, X.G.: A fast annealing evolutionary algorithm for global optimization. J. Comput. Chem. 23(4), 427–435 (2002)
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)
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)
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)
Cleri, F., Rosato, V.: Tight-binding potentials for transition metals and alloys. Phys. Rev. B. 48(1), 22–33 (1993)
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)
Gelfand, S.B., Mitter, S.K.: Metropolis-type annealing algorithms for global optimization in Rd. SIAM J. Control Optim. 31(1), 111–131 (1993)
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)
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
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)
Husic, B.E., Schebarchov, D., Wales, D.J.: Impurity effects on solid–solid transitions in atomic clusters. NANO 8, 18326–18340 (2016)
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)
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)
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)
Kirkpatrick, S., Gellat, C.D., Vecchi, P.M.: Optimization by simulated annealing. Science 220, 671–680 (1983)
Leary, R.H.: Global optimization on funneling landscapes. J. Glob. Optim. 18(4), 367–383 (2000)
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)
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)
Liu, D.C., Nocedal, J.: On the limited memory BFGS method for large scale optimization. Math. Prog. 45(1), 503–528 (1989)
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)
Ma, J.P., Straub, J.E.J.: Simulated annealing using the classical density distribution. Chem. Chem. Phys. 101(1), 533–541 (1994)
Michaelian, K., Rendón, N., Garzón, I.L.: Structure and energetics of Ni, Ag, and Au nanoclusters. Phys. Rev. B. 60, 2000–2010 (1999)
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)
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)
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)
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)
Romero, D., Barrón, C., Gómez, S.: The optimal geometry of Lennard-Jones clusters: 148–309. Comput. Phys. Commun. 123, 87–96 (1999)
Rossi, G., Ferrando, R.: Combining shape-changing with exchange moves in the optimization of nanoalloys. Comput. Theor. Chem. 1107(1), 66–73 (2017)
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)
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)
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)
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)
Takeuchi, H.: Clever and efficient method for searching optimal geometries of Lennard-Jones clusters. J. Chem. Inf. Model. 46(5), 2066–2070 (2006)
Wales, D.J.: Global optimization of clusters, crystals, and biomolecules. Science 285(5432), 1368–1372 (1999)
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)
Wales, D.J., Scheraga, H.A.: Global optimization of clusters, crystals, and biomolecules. Science 285(5432), 1368–1372 (1999)
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)
Wolf, M.D., Landman, U.: Genetic algorithms for structural cluster optimization. J. Phys. Chem. A. 102(30), 6129–6137 (1998)
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)
Xue, G.L.: Improvement on the Northby algorithm for molecular conformation: better solutions. J. Glob. Optim. 4(4), 425–440 (1994)
http://www-wales.ch.cam.ac.uk/CCD.html (The Cambridge Energy Landscape Database)
https://www.azonano.com/article.aspx?ArticleID=3274 (Cobalt (Co) Nanoparticles- Properties, Applications)
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
Corresponding authors
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
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
DOI: https://doi.org/10.1007/978-3-030-71616-5_25
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-71615-8
Online ISBN: 978-3-030-71616-5
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)