Application of the neural networks for developing new parametrization of the Tersoff potential for carbon

• Autorzy: Nwachukwu Anthony Chukwuemeka , Winczewski Szymon

Identyfikatory

DOI

10.34808/tq2020/24.4/a

• Języki publikacji: EN

Abstrakty

EN

Penta-graphene (PG) is a 2D carbon allotrope composed of a layer of pentagons having sp2- and sp3- bonded carbon atoms. A study carried out in 2018 has shown that the parameterization of the Tersoff potential proposed in 2005 by Ehrhart and Able (T05 potential) performs better than other potentials available for carbon, being able to reproduce structural and mechanical properties of the PG. In this work, we tried to improve the T05 potential by searching for its parameters giving a better reproduction of the structural and mechanical properties of the PG known from the ab initio calculations. We did this using Molecular Statics (MS) simulations and Neural Network (NN). Our test set consisted of the following structural properties: the lattice parameter a; the interlayer spacing h; two lengths of C-C bonds, d1 and d2 respectively; two valence angles, O1 and )2, respectively. We also examined the mechanical properties by calculating three elastic constants, C11, C12 and C66, and two elastic moduli, the Young’s modulus E and the Poisson’s ratio v. We used MS technique to compute the structural and mechanical properties of PG at T =0 K. The Neural Network used is composed of 2 hidden layers, with 20 and 10 nodes for the first and second layer, respectively. We used an Adams optimizer for the NN optimization and the Mean Squared Error as the loss function. We obtained inputs (about 80 000 different sets of potential parameters) for the Molecular Statics simulation by using randomly generated numbers. The outputs from these simulations became the inputs to our Neural Network. The Molecular Statics simulations were done with LAMMPS while the Neural Network and other computations were done with Python, Pytorch, Numpy, Pandas, GNUPLOT and Bash scripts. We obtained a parameterization which has a slightly better accuracy (lower relative errors of the calculated structural and mechanical properties) than the original parameterization.

Słowa kluczowe

EN

penta-graphene; mechanical properties; molecular dynamics

PL

penta-grafen; właściwości mechaniczne; dynamika molekularna

• Wydawca: Politechnika Gdańska
• Czasopismo: TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk
• Rocznik: 2020
• Tom: Vol. 24, No 4
• Strony: 299--333
• Opis fizyczny: Bibliogr. 105. poz., rys., tab.

Twórcy

autor

Nwachukwu Anthony Chukwuemeka

• Faculty of Applied Physics and Mathematics, Gdansk University of Technology, Gabriela Narutowicza 11/12, 80-233 Gdansk, Poland

autor

Winczewski Szymon

• Faculty of Applied Physics and Mathematics, Gdansk University of Technology, Gabriela Narutowicza 11/12, 80-233 Gdansk, Poland

Bibliografia

• [1] Berger C, Song Z, Li T, Li X, Ogbazghi A Y, Feng R, Dai Z, Marchenkov A N, Conrad E H, First P N and de Heer W A 2004 Ultrathin Epitaxial Graphite: 2D Electron Gas Properties and a Route toward Graphene-based Nanoelectronics, The Journal of Physical Chemistry, American Chemical Society (ACS), 108 (52) 19912
• [2] Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva I V and Firsov A A 2004 Electric Field Effect in Atomically Thin Carbon Films, American Association for the Advancement of Sciences, 306 (5696) 666
• [3] Iijima S 1991 Helical microtubules of graphitic carbon, Nature, Springer Science and Business Media LLC, 354 (6348) 56
• [4] Ebbesen T W and Ajayan P M 1992 Large-scale synthesis of carbon nanotubes, Nature, Springer Science and Business Media LLC, 358 (6383) 220
• [5] Zhang S, Zhou J, Wang Q, Chen X, Kawazoe Y and Jena P 2015 Penta-graphene: A new carbon allotrope, Proceedings of the National Academy of Sciences, Proceedings of the National Academy of Sciences, 112 (8) 2372
• [6] Zhao Z, Tian F, Dong X, Li Q, Wang Q, Wang H, Zhong X, Xu B, Yu D, He J, Wang H, Ma Y and Tian Y 2012 Tetragonal Allotrope of Group 14 Elements, Journal of the American Chemical Society, American Chemical Society (ACS), 134 (30) 12362
• [7] Sun H, Mukherjee S and Singh C V 2016 Mechanical properties of monolayer penta-graphene and phagraphene: a first-principles study, Physical Chemistry Chemical Physics, Royal Society of Chemistry (RSC), 18 (38) 26736
• [8] Ewels C P, Rocquefelte X, Kroto H W, Rayson M J, Briddon P R and Heggie M I 2015 Predicting experimentally stable allotropes: Instability of penta-graphene, Proceedings of the National Academy of Sciences, Proceedings of the National Academy of Sciences, 112 (51) 15609
• [9] Cranford S W 2016 When is 6 less than 5? Penta- to hexa-graphene transition, Carbon, Elsevier BV, 96 421
• [10] Berdiyorov G R, Dixit G and Madjet M E 2016 Band gap engineering in penta-graphene by substitutional doping: first-principles calculations, Journal of Physics: Condensed Matter, IOP Publishing, 28 (47) 475001
• [11] Li X, Zhang S, Wang F Q, Guo Y, Liu J L and Wang Q 2016 Tuning the electronic and mechanical properties of penta-graphene via hydrogenation and fluorination, Physical Chemistry Chemical Physics, Royal Society of Chemistry (RSC), 18 (21) 14191
• [12] Xu W, Zhang G and Li B 2015 Thermal conductivity of penta-graphene from molecular dynamics study, The Journal of Chemical Physics, AIP Publishing, 143 (15) 154703
• [13] Xufei Wu X, Varshney V, Lee J, Zhang T, Wohlwend J L, Roy A K and Luo T 2016 Hydrogenation of Penta-Graphene Leads to Unexpected Large Improvement in Thermal Conductivity, Nano Letters, American Chemical Society (ACS), 16 (6) 3925
• [14] Yu Z G and Zhang Y 2015 A comparative density functional study on electrical properties of layered penta-graphene, Journal of Applied Physics, AIP Publishing, 118 (16) 165706
• [15] Rajbanshi B, Sarkar S, Mandal B, Sarkar P 2016 Energetic and electronic structure of penta-graphene nanoribbons, Carbon, Elsevier BV, 100 118
• [16] Xiao B, Li Y, Yu X and Cheng J 2016 Penta-graphene: A Promising Anode Material as the Li/Na-Ion Battery with Both Extremely High Theoretical Capacity and Fast Charge/Discharge Rate, ACS Applied Materials & Interfaces, American Chemical Society (ACS), 8 (51) 35342
• [17] Ebrahimi S 2016 Effect of hydrogen coverage on the buckling of penta-graphene by molecular dynamics simulation, Molecular Simulation, Informa UK Limited, 42 (17) 1485
• [18] Avramov P, Demin V, Luo M, Choi C H, Sorokin P B, Yakobson B and Chernozatonskii L 2015 Translation Symmetry Breakdown in Low-Dimensional Lattices of Pentagonal Rings, The Journal of Physical Chemistry Letters, American Chemical Society (ACS), 6 (22) 4525
• [19] Stauber T, Beltrán J I and Schliemann J 2016 Tight-binding approach to penta-graphene, Scientific Reports, Springer Science and Business Media LLC, 6 (1) 2045
• [20] Rahaman O, Mortazavi B, Dianat A, Cuniberti G and Rabczuk T 2017 Metamorphosis in carbon network: From penta-graphene to biphenylene under uniaxial tension, FlatChem, Elsevier BV, 1 65
• [21] Wei X, Fragneaud B, Marianetti C A and Kysar J W 2009 Nonlinear elastic behavior of graphene: Ab initio calculations to continuum description, Physical Review B, American Physical Society (APS), 80 (20) 205407
• [22] Pop E, Varshney V and Roy A K 2012 Thermal properties of graphene: Fundamentals and applications, MRS Bulletin, Cambridge University Press (CUP), 37 (12) 1273
• [23] Winczewski S, Shaheen M Y and Rybicki J 2018 Interatomic potential suitable for the modeling of penta-graphene: Molecular statics/molecular dynamics studies, Carbon, Elsevier BV, 126 165
• [24] Chenoweth K, van Duin A C T and Goddard W A 2008 ReaxFF Reactive Force Field for Molecular Dynamics Simulations of Hydrocarbon Oxidation, The Journal of Physical Chemistry, American Chemical Society (ACS), 112 (5) 1040
• [25] Brenner D W, Shenderova O A, Harrison J A, Stuart S J, Ni B and Sinnott S B 2002 A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons, Journal of Physics: Condensed Matter, IOP Publishing, 14 (4) 783
• [26] Tersoff J 1989 Modeling solid-state chemistry: Interatomic potentials for multicomponent systems, Physical Review B, American Physical Society (APS), 39 (8) 5566
• [27] Tersoff J 1990 Erratum: Modeling solid-state chemistry: Interatomic potentials for multicomponent systems, Physical Review B, American Physical Society (APS), 41 (5) 3248
• [28] Lindsay L and Broido D A 2010 Optimized Tersoff and Brenner empirical potential parameters for lattice dynamics and phonon thermal transport in carbon nanotubes and graphene, Physical Review B, American Physical Society (APS), 81 (20) 205441
• [29] Lindsay L and Broido D A 2010 Erratum: Optimized Tersoff and Brenner empirical potential parameters for lattice dynamics and phonon thermal transport in carbon nanotubes and graphene, Physical Review B, American Physical Society (APS), 82 (20)
• [30] Marks N 2002 Modelling diamond-like carbon with the environment-dependent interaction potential, Journal of Physics: Condensed Matter, IOP Publishing, 14 (11) 2901
• [31] Erhart P and Albe K 2005 Analytical potential for atomistic simulations of silicon, carbon, and silicon carbide, Physical Review B, American Physical Society (APS), 71 (3) 35211
• [32] P. Mahon P, Pailthorpe B A and Bacskay G B 1991 A quantum mechanical calculation of interatomic interactions in diamond, Philosophical Magazine B, Informa UK Limited, 63 (6) 1419
• [33] Barnard A S and Russo S P 2002 Development of an improved Stillinger-Weber potential for tetrahedral carbon using ab initio (Hartree-Fock and MP2) methods, Molecular Physics, Informa UK Limited, 100 (10) 1517
• [34] Brenner D W 1990 Empirical potential for hydrocarbons for use in simulating the chemical vapor deposition of diamond films, Physical Review B, American Physical Society (APS), 42 (15) 9458
• [35] Brenner D W 1992 Erratum: Empirical potential for hydrocarbons for use in simulating the chemical vapor deposition of diamond films, Physical Review B, American Physical Society (APS), 46 (3) 1948
• [36] Stuart S J, Tutein A B and Harrison J A 2000 A reactive potential for hydrocarbons with intermolecular interactions, The Journal of Chemical Physics, AIP Publishing, 112 (14) 6472
• [37] O’Connor T C, Jan Andzelm J and Robbins M O 2015 AIREBO-M: A reactive model for hydrocarbons at extreme pressures, The Journal of Chemical Physics, AIP Publishing, 142 (2) 24903
• [38] van Duin A C T, Dasgupta S, Lorant F and Goddard W A 2001 ReaxFF: A Reactive Force Field for Hydrocarbons, The Journal of Physical Chemistry, American Chemical Society (ACS), 105 (41) 9396
• [39] Nielson K D, van Duin A C T, Oxgaard J, Deng W and Goddard W A 2005 Development of the ReaxFF Reactive Force Field for Describing Transition Metal Catalyzed Reactions, with Application to the Initial Stages of the Catalytic Formation of Carbon Nanotubes, The Journal of Physical Chemistry, American Chemical Society (ACS), 109 (3) 493
• [40] Srinivasan S G, van Duin A C T and Ganesh P 2015 Development of a ReaxFF Potential for Carbon Condensed Phases and Its Application to the Thermal Fragmentation of a Large Fullerene, The Journal of Physical Chemistry, American Chemical Society (ACS), 119 (4) 571
• [41] M. I. Baskes 1992 Modified embedded-atom potentials for cubic materials and impurities, Physical Review B, American Physical Society (APS), 46 (5) 2727
• [42] Los J H and Fasolino A 2003 Intrinsic long-range bond-order potential for carbon: Performance in Monte Carlo simulations of graphitization, Physical Review B, American Physical Society (APS), 68 (2) 24107
• [43] Zhou X W, Ward D K and Foster M E 2015 An analytical bond-order potential for carbon, Journal of Computational Chemistry, Wiley, 36 (23) 1719
• [44] Marks N A 2000 Generalizing the environment-dependent interaction potential for carbon, Physical Review B, American Physical Society (APS), 63 (3) 35401
• [45] Yin M T and Cohen M L 1980 Microscopic Theory of the Phase Transformation and Lattice Dynamics of Si, Physical Review Letters, American Physical Society (APS), 45 (12) 1004
• [46] Yin M T and Cohen M L 1982 Theory of static structural properties, crystal stability, and phase transformations: Application to Si and Ge, Physical Review B, American Physical Society (APS), 26 (10) 5668
• [47] Pandey K C 1981 NewΠ-Bonded Chain Model for Si(111)-(2×1) Surface, Physical Review Letters, American Physical Society (APS), 47 (26) 1913
• [48] Northrup J E 1986 Origin of surface states on Si(111)(7×7), Physical Review Letters, American Physical Society (APS), 57 (1) 154
• [49] Car R, Kelly P J, Oshiyama A and Pantelides S T 1984 Microscopic Theory of Atomic Diffusion Mechanisms in Silicon, Physical Review Letters, American Physical Society (APS), 52 (20) 1814
• [50] Dodson B W 1987 Development of a many-body Tersoff-type potential for silicon, Physical Review B, American Physical Society (APS), 35 (6) 2795
• [51] Abell G C 1985 Empirical chemical pseudopotential theory of molecular and metallic bonding, Physical Review B, American Physical Society (APS), 31 (10) 6184
• [52] Kane E O 1985 Phonon spectra of diamond and zinc-blende semiconductors, Physical Review B, American Physical Society (APS), 31 (12) 7865
• [53] Keating P N 1966 Effect of Invariance Requirements on the Elastic Strain Energy of Crystals with Application to the Diamond Structure, Physical Review B, American Physical Society (APS), 145 (2) 637
• [54] Stillinger F H and Weber t A 1985 Computer simulation of local order in condensed phases of silicon, Phys. Rev. B, American Physical Society, 31 5262
• [55] Biswas R and Hamann D R 1987 New classical models for silicon structural energies, Phys. Rev. B, American Physical Society, 36 6434
• [56] Tersoff J 1988 Empirical interatomic potential for silicon with improved elastic properties, Phys. Rev. B, American Physical Society, 38 9902
• [57] Tersoff J 1988 Empirical Interatomic Potential for Carbon, with Applications to Amorphous Carbon, Phys. Rev. Lett., American Physical Society, 61 2879
• [58] Zhang S, Zhou J, Wang Q, Chen X, Kawazoe Y and Jena P 2015 Penta-graphene: A new carbon allotrope, Proceedings of the National Academy of Sciences, Proceedings of the National Academy of Sciences, 112 (8) 2372
• [59] Ewels C P, Rocquefelte X, Kroto H W, Rayson M J, Briddon P R and Heggie M I 2015 Predicting experimentally stable allotropes: Instability of penta-graphene, Proceedings of the National Academy of Sciences, Proceedings of the National Academy of Sciences, 112 (51) 15609
• [60] Einollahzadeh H, Fazeli S M and Dariani R S 2016 Studying the electronic and phononic structure of penta-graphane, Science and Technology of Advanced Materials, Informa UK Limited, 17 (1) 610
• [61] Bataineh M H 2012 Artificial neural network for studying human performance, The University of Iowa
• [62] Shimamura K, Fukushima S, Koura A, Shimojo F, Misawa M, Kalia R K, Nakano A, Vashishta P, Matsubara T and Tanaka S 2019 Guidelines for creating artificial neural network empirical interatomic potential from first-principles molecular dynamics data under specific conditions and its application to -Ag2Se, The Journal of Chemical Physics, AIP Publishing, 151 (12) 124303
• [63] Hobday S, Smith R and Belbruno J 1999 Applications of neural networks to fitting interatomic potential functions, Modelling and Simulation in Materials Science and Engineering, IOP Publishing, 7 (3) 397
• [64] Lee K, Yoo D, Jeong W and Han S 2019 SIMPLE-NN: An efficient package for training and executing neural-network interatomic potentials, Computer Physics Communications, Elsevier BV, 242 95
• [65] Purja Pun G P, Batra R, Ramprasad R and Mishin Y 2019 Physically informed artificial neural networks for atomistic modeling of materials, Nature Communications, Springer Science and Business Media LLC, 10 (1) 2339
• [66] Bukkapatnam S, Malshe M, Agrawal P M, Raff L M and Komanduri R 2006 Parametrization of interatomic potential functions using a genetic algorithm accelerated with a neural network, Physical Review B, American Physical Society (APS), 74 (22) 224102
• [67] McCulloch W S and Pitts W 1943 A logical calculus of the ideas immanent in nervous activity, The Bulletin of Mathematical Biophysics, Springer Science and Business Media LLC, 5 (4) 115
• [68] Kleene S C 1956 Representation of events in nerve nets and finite automata, Princeton University Press
• [69] Morris R G M 1999 D.O. Hebb: The Organization of Behavior, Wiley: New York; 1949, Brain Research Bulletin, Elsevier BV, 50 (5-6) 437
• [70] Farley B and Clark W 1954 Simulation of self-organizing systems by digital computer, Transactions of the IRE Professional Group on Information Theory, Institute of Electrical and Electronics Engineers (IEEE), 4 (4) 76
• [71] Rochester N, Holland J, Haibt L and Duda W 1956 Tests on a cell assembly theory of the action of the brain, using a large digital computer, IEEE Transactions on Information Theory, Institute of Electrical and Electronics Engineers (IEEE), 2 (3) 80
• [72] Rosenblatt F 1958 The perceptron: A probabilistic model for information storage and organization in the brain, Psychological Review, American Psychological Association (APA), 65 (6) 386
• [73] Werbos P J 1974 Beyond Regression: New Tools for Prediction and Analysis in the Behavioral Sciences
• [74] Hubel D H and Wiesel T N 2004 Brain and Visual Perception, Oxford University Press
• [75] Schmidhuber J 2015 Deep learning in neural networks: An overview, Neural Networks, Elsevier BV, 61 85
• [76] Ivakhnenko A G and Lapa V G 1973 Cybernetic Predicting Devices, CCM Information Corporation
• [77] Ivakhnenko A G, Lapa V G and McDonough R N 1967 Cybernetics and Forecasting Techniques, American Elsevier Publishing Company
• [78] Minsky M and Seymour P 1969 Perceptrons: An introduction to computational geometry, MIT Press
• [79] Schmidhuber J 2015 Deep learning in neural networks: An overview, Neural Networks, Elsevier BV, 61 85
• [80] Rosenblatt F 1958 The perceptron: A probabilistic model for information storage and organization in the brain, Psychological Review, American Psychological Association (APA), 65 (6) 386
• [81] Polak E and Ribiere G 1969 Note sur la convergence de methodes de directions conjuguees, ESAIM: Mathematical Modelling and Numerical Analysis - Modelisation Mathematique et Analyse Numerique, Dunod, 3 (R1) 35
• [82] Plimpton S 1995 Fast Parallel Algorithms for Short-Range Molecular Dynamics, Journal of Computational PhysicS, Elsevier BV, 117 (1) 1
• [83] Stukowski A Visualization and analysis of atomistic simulation data with OVITO - the Open Visualization Tool
• [84] Van Rossum G and Drake F 2009 Python 3 Reference Manual, Scotts Valley, CA: CreateSpace
• [85] Williams T and Kelley C Gnuplot 4.6: an interactive plotting program
• [86] Kingma D P and Ba J 2014 Adam: A Method for Stochastic Optimization
• [87] Hinton G 2012 Lecture 6e rmsprop: Divide the gradient by a running average of its recent magnitude, University of Toronto
• [88] Golda A 2004 Principles of training multi-layer neural network using backpropagation, http://galaxy.agh.edu.pl/∼vlsi/AI/backp t en/backprop.html, AGH University of Science and Technology
• [89] Car R and Parrinello M 1985 Unified Approach for Molecular Dynamics and Density-Functional Theory, Physical Review Letters, American Physical Society (APS), 55 (22) 2471
• [90] Payne M C, Bristowe P D and Joannopoulos J D 1987 Ab initio determination of the structure of a grain boundary by simulated quenching, Physical Review Letters, American Physical Society (APS), 58 (13) 1348
• [91] Quijano-Briones J J, Fernández-Escamilla H N and Tlahuice-Flores A 2017 Chiral penta-graphene nanotubes: Structure, bonding and electronic properties, Computational and Theoretical Chemistry, Elsevier BV, 1108 70
• [92] Avramov P, Demin V, Luo M, Choi C H, Sorokin P B, Yakobson B and Chernozatonskii L 2015 Translation Symmetry Breakdown in Low-Dimensional Lattices of Pentagonal Rings, The Journal of Physical Chemistry Letters, American Chemical Society (ACS), 6 (22) 4525
• [93] Su C, Jiang H and Feng J 2013 Two-dimensional carbon allotrope with strong electronic anisotropy, Physical Review B, American Physical Society (APS), 87 (7) 75453
• [94] Yin W, Xie Y, Liu L, Wang R, Wei X, Lau L, Zhong J and Chen Y 2013 R-graphyne: a new two-dimensional carbon allotrope with versatile Dirac-like point in nanoribbons, Journal of Materials Chemistry, Royal Society of Chemistry (RSC), 1 (17) 5341
• [95] Sharma B R, Manjanath A and Singh A K 2014 pentahexoctite: A new two-dimensional allotrope of carbon, Scientific Reports, Springer Science and Business Media LLC, 4 (1)
• [96] Wang Z, Zhou X F, Zhang X, Zhu Q, Dong H, Zhao M and Oganov A R 2015 Phagraphene: A Low-Energy Graphene Allotrope Composed of 5–6–7 Carbon Rings with Distorted Dirac Cones, Nano Letters, American Chemical Society (ACS), 15 (9) 6182
• [97] Zhang X, Wei L, Tan J and Zhao M 2016 Prediction of an ultrasoft graphene allotrope with Dirac cones, Carbon, Elsevier BV, 105 323
• [98] Jiang X, Arhammar C, Liu P, Zhao J and Ahuja R 2013 The R3-carbon allotrope: a pathway towards glassy carbon under high pressure, Scientific Reports, Springer Science and Business Media LLC, 3 (1) 1877
• [99] Zhanpeisov N U 2012 Theoretical DFT study on structure and chemical activity of new carbon K4 clusters, Research on Chemical Intermediates, Springer Science and Business Media LLC, 39 (5) 2141
• [100] Zhang S, Wang Q, Chen X and Jena P 2013 Stable three-dimensional metallic carbon with interlocking hexagons, Proceedings of the National Academy of Sciences, Proceedings of the National Academy of Sciences, 110 (47) 18809
• [101] Burchfield L A, Al Fahim M, Wittman R S, Delodovici F and Manini N 2017 Novamene: A new class of carbon allotropes, Heliyon, Elsevier BV, 3 (2) 242
• [102] Stukowski A 2009 Visualization and analysis of atomistic simulation data with OVITO — the Open Visualization Tool, Modelling and Simulation in Materials Science and Engineering, IOP Publishing, 18 (1) 15012
• [103] Tersoff J 1988 Empirical interatomic potential for silicon with improved elastic properties, Physical Review B, American Physical Society (APS), 38 (14) 9902
• [104] Murani A P, Mattens W C M, de Boer F R and Lander G H 1985 Neutron-inelastic-scattering study of the compound YbCuAl, Physical Review B, American Physical Society (APS), 31 (1) 52
• [105] Plimpton S 1995 Fast parallel algorithms for short-range molecular dynamics, J. Comput. Phys. 11 1

Uwagi

PL

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).