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Stochastic Surface Walking Method and Applications to Real Materials

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Handbook of Materials Modeling

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Abstract

The macroscopic properties of a material are generally governed by its potential energy surface (PES) that determines not only thermodynamics but also kinetics. A thoroughly search of the global PES of material, however, has been a great challenge in theory. Three major hurdles, namely, the high energy barrier in material transformation, the large entropy due to huge structural configurations, and the large atomic degrees of freedom, are often encountered simultaneously in computational simulation of material. Owing to these, the limitation in the timescale of current simulations restricts heavily theoreticians to address many important questions in material science. In this chapter, we introduce a newly developed theoretical method, stochastic surface walking (SSW) method targeting for both global PES exploration and reaction pathway sampling. The SSW PES sampling is automated, unbiased, and taking into account the second derivative information. The algorithm of SSW is summarized here in detail, focusing on its mechanism to follow low energy pathways while being able to overcome high barriers. SSW simulation has recently been applied to different areas in material and reaction systems. Several typical examples of PES exploration by combining SSW with first principles and neural network potential calculations are presented to illustrate the power of SSW for unbiased PES exploration and pathway searching.

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References

  • Amsler M, Goedecker S (2010) Crystal structure prediction using the minima hopping method. J Chem Phys 133:224104

    Article  ADS  Google Scholar 

  • Bakardjieva S, Stengl V, Szatmary L, Subrt J, Lukac J, Murafa N, Niznansky D, Cizek K, Jirkovsky J, Petrova N (2006) Transformation of brookite-type TiO2 nanocrystals to rutile: correlation between microstructure and photoactivity. J Mater Chem 16:1709–1716

    Article  Google Scholar 

  • Bansal GK, Heuer AH (1974) On a martensitic phase transformation in zirconia (ZrO2)—II, crystallographic aspects. Acta Metall 22:409–417

    Article  Google Scholar 

  • Bhattacharya K, Conti S, Zanzotto G, Zimmer J (2004) Crystal symmetry and the reversibility of martensitic transformations. Nature 428:55–59

    Article  ADS  Google Scholar 

  • Britun VF, Kurdyumov AV, Petrusha IA (2004) Diffusionless nucleation of lonsdaleite and diamond in hexagonal graphite under static compression. Powder Metall Met Ceram 43:87–93

    Article  Google Scholar 

  • Bundy FP, Kasper JS (1967) Hexagonal diamond—a new form of carbon. J Chem Phys 46:3437–3446

    Article  ADS  Google Scholar 

  • Carr JM, Trygubenko SA, Wales DJ (2005) Finding pathways between distant local minima. J Chem Phys 122:234903

    Article  ADS  Google Scholar 

  • Cheng S, Wei-Na Z, Zhi-Pan L (2015) Searching for new TiO 2 crystal phases with better photoactivity. J Phys Condens Matter 27:134203

    Article  ADS  Google Scholar 

  • Chien FR, Ubic F, Prakash V, Heuer AH (1998) Stress-induced martensitic transformation and ferroelastic deformation adjacent microhardness indents in the tetragonal zirconia single crystals. Acta Mater 46:2151–2171

    Article  Google Scholar 

  • DeCarli PS, Jamieson JC (1961) Formation of diamond by explosive shock. Science 133:1821–1822

    Article  ADS  Google Scholar 

  • Dijkstra EW (1959) A note on two problems in connexion with graphs. Numer Math 1:269–271

    Article  MathSciNet  MATH  Google Scholar 

  • Fahy S, Louie SG, Cohen ML (1987) Theoretical total-energy study of the transformation of graphite into hexagonal diamond. Phys Rev B 35:7623–7626

    Article  ADS  Google Scholar 

  • Grimme S, Antony J, Ehrlich S, Krieg H (2010) A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. J Chem Phys 132:154104

    Article  ADS  Google Scholar 

  • Guan S-H, Zhang X-J, Liu Z-P (2015) Energy landscape of zirconia phase transitions. J Am Chem Soc 137:8010–8013

    Article  Google Scholar 

  • Hanneman RE, Strong HM, Bundy FP (1967) Hexagonal diamonds in meteorites: implications. Science 155:995–997

    Article  ADS  Google Scholar 

  • Henkelman G, Jonsson H (1999) A dimer method for finding saddle points on high dimensional potential surfaces using only first derivatives. J Chem Phys 111:7010–7022

    Article  ADS  Google Scholar 

  • Huang S-D, Shang C, Zhang X-J, Liu Z-P (2017) Material discovery by combining stochastic surface walking global optimization with a neural network. Chem Sci 8:6327–6337

    Article  Google Scholar 

  • Huber T, Torda A, Gunsteren W (1994) Local elevation: a method for improving the searching properties of molecular dynamics simulation. J Comput Aided Mol Des 8:695–708

    Article  ADS  Google Scholar 

  • Iannuzzi M, Laio A, Parrinello M (2003) Efficient exploration of reactive potential energy surfaces using Car-Parrinello molecular dynamics. Phys Rev Lett 90:238302

    Article  ADS  Google Scholar 

  • Jin X-J (2005) Martensitic transformation in zirconia containing ceramics and its applications. Curr Opin Solid State Mater Sci 9:313–318

    Article  ADS  Google Scholar 

  • Kelly PM, Rose LRF (2002) The martensitic transformation in ceramics-its role in transformation toughening. Prog Mater Sci 47:463–557

    Article  Google Scholar 

  • Khaliullin RZ, Eshet H, Kühne TD, Behler J, Parrinello M (2011) Nucleation mechanism for the direct graphite-to-diamond phase transition. Nat Mater 10:693–697

    Article  ADS  Google Scholar 

  • Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220:671–680

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Kresse G, Joubert D (1999) From ultrasoft pseudopotentials to the projector augmented-wave method. Phys Rev B 59:1758–1775

    Article  ADS  Google Scholar 

  • Laio A, Parrinello M (2002) Escaping free-energy minima. Proc Natl Acad Sci U S A 99:12562–12566

    Article  ADS  Google Scholar 

  • Li Y-F, Liu Z-P (2011) Particle size, shape and activity for photocatalysis on titania anatase nanoparticles in aqueous surroundings. J Am Chem Soc 133:15743–15752

    Article  Google Scholar 

  • Li Y-F, Liu Z-P, Liu L, Gao W (2010) Mechanism and activity of photocatalytic oxygen evolution on titania anatase in aqueous surroundings. J Am Chem Soc 132:13008–13015

    Article  Google Scholar 

  • Lonie DC, Zurek E (2011) XtalOpt: an open-source evolutionary algorithm for crystal structure prediction. Comput Phys Commun 182:372–387

    Article  ADS  MATH  Google Scholar 

  • Ma S, Huang S-D, Fang Y-H, Liu Z-P (2017) Microporous titania crystals with penta-oxygen coordination. ACS Appl Energy Mater 1:22–26

    Article  Google Scholar 

  • Maeda S, Ohno K, Morokuma K (2009) Automated global mapping of minimal energy points on seams of crossing by the anharmonic downward distortion following method: a case study of H2CO. J Phys Chem A 113:1704–1710

    Article  Google Scholar 

  • Maeda S, Taketsugu T, Morokuma K (2014) Exploring transition state structures for intramolecular pathways by the artificial force induced reaction method. J Comput Chem 35:166–173

    Article  Google Scholar 

  • Maragliano L, Vanden-Eijnden E (2006) A temperature accelerated method for sampling free energy and determining reaction pathways in rare events simulations. Chem Phys Lett 426:168–175

    Article  ADS  Google Scholar 

  • Marks NA (2000) Generalizing the environment-dependent interaction potential for carbon. Phys Rev B 63:035401

    Article  ADS  Google Scholar 

  • Martonak R, Donadio D, Oganov AR, Parrinello M (2006) Crystal structure transformations in SiO2 from classical and ab initio metadynamics. Nat Mater 5:623–626

    Article  ADS  Google Scholar 

  • Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AH, Teller E (1953) Equation of state calculations by fast computing machines. J Chem Phys 21:1087–1092

    Article  ADS  Google Scholar 

  • Mujica A, Rubio A, Muñoz A, Needs RJ (2003) High-pressure phases of group-IV, III-V, and II-VI compounds. Rev Mod Phys 75:863–912

    Article  ADS  Google Scholar 

  • Naka S, Horii K, Takeda Y, Hanawa T (1976) Direct conversion of graphite to diamond under static pressure. Nature 259:38–39

    Article  ADS  Google Scholar 

  • Németh P, Garvie LAJ, Aoki T, Dubrovinskaia N, Dubrovinsky L, Buseck PR (2014) Lonsdaleite is faulted and twinned cubic diamond and does not exist as a discrete material. Nat Commun 5:5447

    Article  ADS  Google Scholar 

  • Oganov AR, Glass CW (2006) Crystal structure prediction using ab initio evolutionary techniques: principles and applications. J Chem Phys 124:244704

    Article  ADS  Google Scholar 

  • Oganov AR, Lyakhov AO, Valle M (2011) How evolutionary crystal structure prediction works-and why. Acc Chem Res 44:227–237

    Article  Google Scholar 

  • Pannetier J, Bassas-Alsina J, Rodriguez-Carvajal J, Caignaert V (1990) Prediction of crystal structures from crystal chemistry rules by simulated annealing. Nature 346:343–345

    Article  ADS  Google Scholar 

  • Penn RL, Banfield JF (1999) Formation of rutile nuclei at anatase {112} twin interfaces and the phase transformation mechanism in nanocrystalline titania. Am Mineral 84:871–876

    Article  ADS  Google Scholar 

  • Perdew JP, Burke K, Ernzerhof M (1996) Generalized gradient approximation made simple. Phys Rev Lett 77:3865–3868

    Article  ADS  Google Scholar 

  • Raiteri P, Martoňák R, Parrinello M (2005) Exploring polymorphism: the case of benzene. Angew Chem Int Ed 44:3769–3773

    Article  Google Scholar 

  • Rosso L, Minary P, Zhu ZW, Tuckerman ME (2002) On the use of the adiabatic molecular dynamics technique in the calculation of free energy profiles. J Chem Phys 116:4389–4402

    Article  ADS  Google Scholar 

  • Scandolo S, Bernasconi M, Chiarotti GL, Focher P, Tosatti E (1995) Pressure-induced transformation path of graphite to diamond. Phys Rev Lett 74:4015–4018

    Article  ADS  Google Scholar 

  • Schaefer B, Mohr S, Amsler M, Goedecker S (2014) Minima hopping guided path search: an efficient method for finding complex chemical reaction pathways. J Chem Phys 140:214102–214113

    Article  ADS  Google Scholar 

  • Schön JC, Jansen M (1996) First step towards planning of syntheses in solid-state chemistry: determination of promising structure candidates by global optimization. Angew Chem Int Ed Eng 35:1286–1304

    Article  Google Scholar 

  • Schön JC, Jansen M (2001) Determination, prediction, and understanding of structures, using the energy landscapes of chemical systems – part III. Z Kristallogr 216:361–383

    Google Scholar 

  • Shang C, Liu Z-P (2010) Constrained Broyden minimization combined with the dimer method for locating transition state of complex reactions. J Chem Theory Comput 6:1136–1144

    Article  Google Scholar 

  • Shang C, Liu ZP (2012) Constrained Broyden dimer method with bias potential for exploring potential energy surface of multistep reaction process. J Chem Theory Comput 8:2215–2222

    Article  Google Scholar 

  • Shang C, Liu ZP (2013) Stochastic surface walking method for structure prediction and pathway searching. J Chem Theory Comput 9:1838–1845

    Article  Google Scholar 

  • Shang C, Zhang X-J, Liu Z-P (2014) Stochastic surface walking method for crystal structure and phase transition pathway prediction. Phys Chem Chem Phys 16:17845–17856

    Article  Google Scholar 

  • Sheppard D, Xiao P, Chemelewski W, Johnson DD, Henkelman G (2012) A generalized solid-state nudged elastic band method. J Chem Phys 136:074103

    Article  ADS  Google Scholar 

  • Siepmann JI, Frenkel D (1992) Configurational bias Monte-Carlo – a new sampling scheme for flexible chains. Mol Phys 75:59–70

    Article  ADS  Google Scholar 

  • Tateyama Y, Ogitsu T, Kusakabe K, Tsuneyuki S (1996) Constant-pressure first-principles studies on the transition states of the graphite-diamond transformation. Phys Rev B 54:14994–15001

    Article  ADS  Google Scholar 

  • Trimarchi G, Zunger A (2007) Global space-group optimization problem: finding the stablest crystal structure without constraints. Phys Rev B 75:104113

    Article  ADS  Google Scholar 

  • van Beest BWH, Kramer GJ, van Santen RA (1990) Force fields for silicas and aluminophosphates based on ab initio calculations. Phys Rev Lett 64:1955–1958

    Article  ADS  Google Scholar 

  • Voter AF (1997) Hyperdynamics: accelerated molecular dynamics of infrequent events. Phys Rev Lett 78:3908–3911

    Article  ADS  Google Scholar 

  • Wales DJ (2002) Discrete path sampling. Mol Phys 100:3285–3305

    Article  ADS  Google Scholar 

  • Wales DJ, Doye JPK (1997) Global optimization by basin-hopping and the lowest energy structures of Lennard-Jones clusters containing up to 110 atoms. J Phys Chem A 101:5111–5116

    Article  Google Scholar 

  • Wang CM, Fan KN, Liu ZP (2007) Origin of oxide sensitivity in gold-based catalysts: a first principle study of CO oxidation over Au supported on monoclinic and tetragonal ZrO. J Am Ceram Soc 129:2642–2647

    Google Scholar 

  • Wang Y, Lv J, Zhu L, Ma Y (2012) CALYPSO: a method for crystal structure prediction. Comput Phys Commun 183:2063–2070

    Article  ADS  Google Scholar 

  • Wei Z-Y, Shang C, Zhang X-J, Liu Z-P (2017) Glassy nature and glass-to-crystal transition in the binary metallic glass CuZr. Phys Rev B 95:214111

    Article  ADS  Google Scholar 

  • Wolten GM (1963) Diffusionless phase transformations in zirconia and hafnia. J Am Ceram Soc 46:418–422

    Article  Google Scholar 

  • Wolten GM (1964) Direct high-temperature single-crystal observation of orientation relationship in zirconia phase transformation. Acta Cryst 17:763–765

    Article  Google Scholar 

  • Woods CJ, Essex JW, King MA (2003) The development of replica-exchange-based free-energy methods. J Phys Chem B 107:13703–13710

    Article  Google Scholar 

  • Wu Y-C, Chiang Y-T (2011) The m-t transformation and twinning analysis of hot-pressed sintered 3YSZ ceramics. J Am Ceram Soc 94:2200–2212

    Article  Google Scholar 

  • Xiao P, Henkelman G (2012) Communication: from graphite to diamond: reaction pathways of the phase transition. J Chem Phys 137:101101

    Article  ADS  Google Scholar 

  • Xie Y-P, Zhang X-J, Liu Z-P (2017) Graphite to diamond: origin for kinetics selectivity. J Am Chem Soc 139:2545–2548

    Article  Google Scholar 

  • Yagi T, Utsumi W, M-a Y, Kikegawa T, Shimomura O (1992) High-pressure \textit{in situ} x-ray-diffraction study of the phase transformation from graphite to hexagonal diamond at room temperature. Phys Rev B 46:6031–6039

    Article  ADS  Google Scholar 

  • Yu T-Q, Tuckerman ME (2011) Temperature-accelerated method for exploring polymorphism in molecular crystals based on free energy. Phys Rev Lett 107:015701

    Article  ADS  Google Scholar 

  • Zhang H, Banfield JF (1999) New kinetic model for the nanocrystalline anatase-to-rutile transformation revealing rate dependence on number of particles. Am Mineral 84:528–535

    Article  ADS  Google Scholar 

  • Zhang X-J, Liu Z-P (2015a) Variable-cell double-ended surface walking method for fast transition state location of solid phase transitions. J Chem Theory Comput 11:4885–4894

    Article  Google Scholar 

  • Zhang X-J, Liu Z-P (2015b) Reaction sampling and reactivity prediction using the stochastic surface walking method. Phys Chem Chem Phys 17:2757–2769

    Article  Google Scholar 

  • Zhang X-J, Shang C, Liu Z-P (2013) Double-ended surface walking method for pathway building and transition state location of complex reactions. J Chem Theory Comput 9:5745–5753

    Article  Google Scholar 

  • Zhang X-J, Shang C, Liu Z-P (2017a) Stochastic surface walking reaction sampling for resolving heterogeneous catalytic reaction network: a revisit to the mechanism of water-gas shift reaction on Cu. J Chem Phys 147:152706

    Article  ADS  Google Scholar 

  • Zhang X-J, Shang C, Liu Z-P (2017b) Pressure-induced silica quartz amorphization studied by iterative stochastic surface walking reaction sampling. Phys Chem Chem Phys 19:4725–4733

    Article  Google Scholar 

  • Zhao W-N, Liu Z-P (2014) Mechanism and active site of photocatalytic water splitting on titania in aqueous surroundings. Chem Sci 5:2256–2264

    Article  Google Scholar 

  • Zhao W-N, Zhu S-C, Li Y-F, Liu Z-P (2015) Three-phase junction for modulating electron–hole migration in anatase–rutile photocatalysts. Chem Sci 6:3483–3494

    Article  Google Scholar 

  • Zhu S-C, Xie S-H, Liu Z-P (2014) Design and observation of biphase TiO2 crystal with perfect junction. J Phys Chem Lett 5:3162–3168

    Article  Google Scholar 

  • Zhu S-C, Xie S-H, Liu Z-P (2015) Nature of rutile nuclei in anatase-to-rutile phase transition. J Am Chem Soc 137:11532–11539

    Article  Google Scholar 

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Acknowledgments

This authors acknowledge National Science Foundation of China (21603035, 21533001), Science and Technology Commission of Shanghai Municipality (08DZ2270500), Shanghai Pujiang Program (16PJ1401200) for financial supports.

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Authors and Affiliations

  1. Collaborative Innovation Center of Chemistry for Energy Material, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, Key Laboratory of Computational Physical Science (Ministry of Education), Department of Chemistry, Fudan University, Shanghai, China

    Cheng Shang & Zhi-Pan Liu

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  1. Cheng Shang
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  2. Zhi-Pan Liu
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Correspondence to Zhi-Pan Liu .

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Editors and Affiliations

  1. Institute of Physics, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Wanda Andreoni

  2. Department of Nuclear Science & Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA

    Sidney Yip

Section Editor information

  1. Ames Laboratory and Department of Physics and Astronomy, Iowa State University, Ames, USA

    Cai-Zhuang Wang

  2. Northwestern University, Evanston, IL, USA

    Christopher M. Wolverton

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Shang, C., Liu, ZP. (2019). Stochastic Surface Walking Method and Applications to Real Materials. In: Andreoni, W., Yip, S. (eds) Handbook of Materials Modeling. Springer, Cham. https://doi.org/10.1007/978-3-319-50257-1_75-1

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  • DOI: https://doi.org/10.1007/978-3-319-50257-1_75-1

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  • Print ISBN: 978-3-319-50257-1

  • Online ISBN: 978-3-319-50257-1

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