Quantum-inspired evolutionary optimization of SLMoS2 two-phase structures

Quantum-inspired evolutionary optimization of SLMoS2 two-phase structures

Wacław Kuś1, Adam Mrozek2

1Silesian University of Technology, Gliwice, Poland.

2AGH University of Science and Technology, Krakow, Poland.




The paper focuses on applying a Quantum Inspired Evolutionary Algorithm to achieve the optimization of 2D material containing two phases, 2H and 1T, of Molybdenum Disulphide (MoS2). The goal of the optimization is to obtain a nanostructure with tailored mechanical properties. The design variables describe the shape of inclusion made from phase 1T in the 2H unit cell. The modification of the size of the inclusions leads to changes in the mechanical properties. The problem is solved with the use of computed mechanical properties on the basis of the Molecular Statics approach with ReaxFF potentials.

Cite as:

Kuś, W., & Mrozek, A. (2022). Quantum-inspired evolutionary optimization of SLMoS2 two-phase structures. Computer Methods in Materials Science, 22(2), 67-78. https://doi.org/10.7494/cmms.2022.2.0777

Article (PDF):


Quantum-inspired evolutionary algorithm, Optimization, Nanostructure, Two-phase SLMoS2, Molecular dynamics, Molecular statics, Atomic potential, ReaxFF, Material properties


Aktulga, H.M., Fogarty, J.C., Pandit, S.A., & Grama, A.Y. (2012). Parallel reactive molecular dynamics: Numerical methods and algorithmic techniques. Parallel Computing, 38(4–5), 245–259. https://doi.org/10.1016/j.parco.2011.08.005.

Burczynski, T., Mrozek, A., Gorski, R., & Kus, W. (2010). Molecular statics coupled with the subregion boundary element method in multiscale analysis. International Journal for Multiscale Computational Engineering, 8(3), 319–330. https://doi.org/10.1615/IntJMultCompEng.v8.i3.70.

Burczyński, T., Kuś, W., Beluch, W., Długosz A., Poteralski, A. & Szczepanik, M. (2020). Intelligent Computing in Optimal Design. Springer Cham, “Solid Mechanics and Its Applications” 261.

Burczyński, T., Pietrzyk, M., Kuś, W., Madej, Ł., Mrozek, A., & Rauch. Ł (2022). Multiscale Modelling and Optimisation of Materials and Structures. Wiley.

Chenoweth, K., Duin, A.C.T. van, & Goddard, W.A. (2008). ReaxFF reactive force field for molecular dynamics simulations of hydrocarbon oxidation. The Journal of Physical Chemistry A, 112, 1040–1053. https://doi.org/10.1021/jp709896w.

Cranford, S.W., Buehler, M.J. (2011). Mechanical properties of graphyne. Carbon, 49(13), 4111–4121. https://doi.org/10.1016/ j.carbon.2011.05.024.

Duin, A.C.T., van, Dasgupta, S., Lorant, F., & Goddard, W.A. (2001). ReaxFF: A Reactive Force Field for Hydrocarbons. The Journal of Physical Chemistry A, 105(41), 9396–9409. https://doi.org/10.1021/jp004368u.

Enyashin, A.N., Ivanovskii, A.L. (2011). Graphene allotropes. Physica Status Solidi B, 248(8), 1879–1883. https://doi.org/10.1002/pssb.201046583.

Han, K.H., & Kim, J.H. (2002). Quantum-inspired evolutionary algorithm for a class of combinatorial optimization. IEEE Transactions on Evolutionary Computation, 6(6), 580–593. https://www.doi.org/10.1109/TEVC.2002.804320.

Jiang, J.W. (2015). Graphene versus MoS2: a short review. Frontiers of Physics, 10, 106801. https://doi.org/10.1007/s11467- 015-0459-z.

Jiang, J.W., Park, H.S., & Rabczuk, T. (2013). Molecular dynamics simulations of single-layer molybdenum disulphide (MoS2): Stillinger–Weber parametrization, mechanical properties, and thermal conductivity. Journal of Applied Physics, 114, 064307. https://doi.org/10.1063/1.4818414.

Kandemir, A., Yapicioglu, H., Kinaci, A., Çağın, T., & Sevik, C. (2016). Thermal transport properties of MoS2 and MoSe2 monolayers. Nanotechnology, 27, 055703. https://www.doi.org/10.1088/0957-4484/27/5/055703.

Kuś, W., Mrozek, A., Burczyński, T. (2016). Memetic optimization of graphene-like materials on Intel PHI coprocessor. In L. Rutkowski, M. Korytkowski, R. Scherer, R. Tadeusiewicz, L.A. Zadeh, J.M. Zurada (Eds.), Artificial Intelligence and Soft Computing. 15th International Conference, ICAISC 2016, Zakopane, Poland, June 12–16, 2016, Proceedings, Part I (pp. 401–410). Springer Cham, “Lecture Notes in Computer Science” 9692. https://doi.org/10.1007/978-3-319-39378-0_35.

Kuś, W., Akhter, M.J., & Burczyński, T. (2022). Optimization of monolayer MoS2 with prescribed mechanical properties. Ma­terials, 15(8), 1–9. https://www.doi.org/10.3390/ma15082812.

Lahoz-Beltra, R. (2016). Quantum genetic algorithms for computer scientists. Computers, 5(24), 1–24. https://doi.org/10.3390/computers5040024.

Li, H., Contryman, A.W., Qian, X., Ardakani, S.M., Gong, Y., Wang, X., Weisse, J.M., Lee, C.H., Zhao, J., Ajayan, P.M., Li, J., Manoharan, H.C., Zheng, X. (2015). Optoelectronic crystal of artificial atoms in strain – textured molybdenum disul­phide. Nature Communications, 6, 1–6. https://www.doi.org/10.1038/ncomms8381.

Liang, T., Phillpot, S.R., & Sinnot, S.R. (2009). Parametrization of a reactive many-body potential for Mo–S systems. Physical Review B, 79(24), 245110. https://doi.org/10.1103/PhysRevB.79.245110.

Liang, T., Phillpot, S.R., & Sinnot, S.R. (2012). Erratum: Parametrization of a reactive many-body potential for Mo–S systems. Physical Review B, 85(19), 199903(E). https://doi.org/10.1103/PhysRevB.85.199903.

Lin, Y.C., Dumcenco, D.O., Huang, Y.S., & Suenaga K. (2014). Atomic mechanism of the semiconducting-to-metallic phase transition in single-layered MoS2. Nature Nanotechnology, 9, 391–396. https://www.doi.org/10.1038/nnano.2014.64.

Maździarz, M., Mrozek, A., Kuś, W., Burczyński, T. (2018). Anisotropic-cyclicgraphene: a new two-dimensional semiconduct­ing carbon allotrope. Materials, 11(3), 1–12. https://doi.org/10.3390/ma11030432.

Mortazavi, B., Ostadhossein, A., Rabczuk, T., & Duin, A.C.T, van (2016). Mechanical response of all-MoS2 single-layer hetero­structures: a ReaxFF investigation. Physical Chemistry Chemical Physics, 18(34), 23695–23701. https://doi.org/10.1039/C6CP03612K.

Mrozek A. (2019). Basic mechanical properties of 2H and 1T single-layer molybdenum disulfide polymorphs. A short com­parison of various atomic potentials. International Journal for Multiscale Computational Engineering, 17(3), 339–359. https://www.doi.org/10.1615/IntJMultCompEng.2019029100.

Mrozek, A., Burczyński, T. (2013). Examination of mechanical properties of graphene allotropes by means of computer simu­lation. Computer Assisted Methods in Engineering and Science, 20(4), 309–323.

Mrozek, A., Kuś, W., Burczyński, T. (2010). Searching of stable configurations of nanostructures using computational intelli­gence methods. Czasopismo Techniczne. Mechanika – Technical Transactions. Mechanics, 107(20), 85–97.

Mrozek, A., Kuś, W., Burczyński, T. (2015). Nano level optimization of graphene allotropes by means of a hybrid par­allel evolutionary algorithm. Computational Materials Science, 106, 161–169. https://doi.org/10.1016/j.commatsci.2015.05.002.

Nakano, A. (1997). Parallel multilevel preconditioned conjugate-gradient approach to variable-charge molecular dynamics. Computer Physics Communications, 104(1–3), 59–69. https://doi.org/10.1016/S0010-4655(97)00041-6.

Narita, N., Nagai, S., Suzuki, S., & Nakao, K. (2000). Electronic structure of three-dimensional graphyne. Physical Review B, 62(16), 11146. https://doi.org/10.1103/PhysRevB.62.11146.

Ostadhossein, A., Rahnamoun, A., Wang, Y., Zhao, P., Zhang, S., Crespi, V.H, & Duin, A.C.T., van (2017). ReaxFF reactive force-field study of molybdenum disulfide (MoS2). The Journal of Physical Chemistry Letters, 8(3), 631–640. https://doi.org/10.1021/acs.jpclett.6b02902.

Park, H., Fellinger, M.R., Lenosky, T.J., Tipton, W.W., Trinkle, D.R., Rudin, S.P., Woodward, Ch., Wilkins, J.W., Hennig, R.G. (2012). Ab initio based empirical potential used to study the mechanical properties of molybdenum. Physical Review B, 85(21), 214121. https://doi.org/10.1103/PhysRevB.85.214121.

Peng, Q., Ji, W., De, S. (2012). Mechanical properties of graphyne monolayers: a first-principles study. Physical Chemistry Chemical Physics, 14(38), 13385–13391. https://doi.org/10.1039/C2CP42387A.

Shen, S., & Atluri, S.N. (2004). Atomic-level stress calculation and continuum-molecular system equivalence. CMES – Com­puter Modeling in Engineering & Sciences, 6(1), 91–104. https://doi.org/10.3970/cmes.2004.006.091.

Silveira, L.R., da, Transcheit, R., & Vellasco, M.M.B.R. (2017). Quantum inspired evolutionary algorithm for ordering prob­lems. Expert Systems with Applications, 67, 71–83. https://doi.org/10.1016/j.eswa.2016.08.067.

Thompson, A.P., Aktulga, H.M., Berger, R., Bolintineanu, D.S., Brown, W.M., Crozier, P.S., Veld, P.J., in ‘t, Kohlmeyer, A., Moore, S.G., Nguyen, T.D., Shan, R., Stevens, M.J., Tranchida, J., Trott, C., & Plimpton, S.J. (2022). LAMMPS – a flex­ible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales. Computer Physics Communications, 271, 108171. https://doi.org/10.1016/j.cpc.2021.108171.

Wang, Y., Lv, J., Zhu, L., Ma, Y. (2010). Crystal structure prediction via particle-swarm optimization. Physical Review B, 82(9), 094116. https://doi.org/10.1103/PhysRevB.82.094116.

Xiong, S., & Cao, G. (2015). Molecular dynamics simulations of mnechanical properties of monolayer MoS2. Nanotechnology, 26(18), 185705. https://doi.org/10.1088/0957-4484/26/18/185705.

Zhang, G. (2011). Quantum-inspired evolutionary algorithms: A survey and empirical study. Journal of Heuristics, 17(3), 303–351. https://doi.org/10.1007/s10732-010-9136-0.

Zhou, M. (2003). A new look at the atomic level virial stress: on continuum-molecular system equivalence. Proceedings of the Royal Society A, 459(2037), 2347–2392. https://doi.org/10.1098/rspa.2003.1127.