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Novel Enhanced Sampling Strategies for Transitions Between Ordered and Disordered Structures

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Handbook of Materials Modeling

Abstract

At the atomic scale, condensed matter displays a fascinating variety of structural transformation processes. Examples include phase transitions between ordered and/or disordered structures (crystal to crystal, liquid to crystal, amorphous to crystal, etc.), isomerization of nanoclusters, chemical reactions, protein conformational changes, and many other phenomena. In all these cases, it is necessary to find suitable distance metrics and collective variables in order to analyze atomistic simulations of transformations as well as to accelerate them with enhanced sampling techniques, yielding mechanisms and free-energy landscapes. In this context, the present chapter illustrates approaches stemming from the idea of watching transformations of matter as modifications of the adjacency matrix formed by interatomic connections. The resulting tools have a general formulation and can therefore be applied to a range of different processes in physics, chemistry, and nanoscience.

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References

  • Abascal JL, Vega C (2005) A general purpose model for the condensed phases of water: TIP4P/2005. J Chem Phys 123(23):234505

    Article  ADS  Google Scholar 

  • Amann-Winkel K, Böhmer R, Fujara F, Gainaru C, Geil B, Loerting T (2016) Colloquium: water’s controversial glass transitions. Rev Mod Phys 88(1):011002

    Article  ADS  Google Scholar 

  • Balan E, Pietrucci F, Gervais C, Blanchard M, Schott J, Gaillardet J (2016) First-principles study of boron speciation in calcite and aragonite. Geochim Cosmochim Acta 193:119–131

    Article  ADS  Google Scholar 

  • Baletto F, Ferrando R (2005) Structural properties of nanoclusters: energetic, thermodynamic, and kinetic effects. Rev Mod Phys 77:371–423. https://doi.org/10.1103/RevModPhys.77.371

    Article  ADS  Google Scholar 

  • Ballone P, Andreoni W, Car R, Parrinello M (1988) Equilibrium structures and finite temperature properties of silicon microclusters from ab initio molecular-dynamics calculations. Phys Rev Lett 60:271–274

    Article  ADS  Google Scholar 

  • Bartels-Rausch T, Bergeron V, Cartwright JH, Escribano R, Finney JL, Grothe H, Gutiérrez PJ, Haapala J, Kuhs WF, Pettersson JB et al (2012) Ice structures, patterns, and processes: a view across the icefields. Rev Mod Phys 84(2):885

    Article  ADS  Google Scholar 

  • Barthel S, Alexandrov EV, Proserpio DM, Smit B (2018) Distinguishing metal-organic frameworks. Cryst Growth Des 18(3):1738–1747. https://doi.org/10.1021/acs.cgd.7b01663

    Article  Google Scholar 

  • Baturin V, Lepeshkin S, Magnitskaya M, Matsko N, Uspenskii YA (2014) Structural and electronic properties of small silicon clusters. J Phys Conf Ser 510:012032

    Article  Google Scholar 

  • Berteotti A, Cavalli A, Branduardi D, Gervasio FL, Recanatini M, Parrinello M (2008) Protein conformational transitions: the closure mechanism of a kinase explored by atomistic simulations. J Am Chem Soc 131(1):244–250

    Article  Google Scholar 

  • Best RB, Hummer G (2005) Reaction coordinates and rates from transition paths. Proc Natl Acad Sci USA 102(19):6732–6737

    Article  ADS  Google Scholar 

  • Billinge SJL, Levin I (2007) The problem with determining atomic structure at the nanoscale. Science 316(5824):561–565

    Article  ADS  Google Scholar 

  • Bolhuis P, Chandler D, Dellago C, Geissler P (2002) Transition path sampling: throwing ropes over rough mountain passes, in the dark. Annu Rev Phys Chem 53:291–318

    Article  ADS  Google Scholar 

  • Bonacich P (1987) Power and centrality: a family of measures. Am J Sociol 92(5):1170–1182

    Article  Google Scholar 

  • Branduardi D, Gervasio FL, Parrinello M (2007) From a to b in free energy space. J Chem Phys 126(5):054,103

    Article  Google Scholar 

  • Branduardi D, De Vivo M, Rega N, Barone V, Cavalli A (2011) Methyl phosphate dianion hydrolysis in solution characterized by path collective variables coupled with DFT-based enhanced sampling simulations. J Chem Theory Comput 7(3):539–543

    Article  Google Scholar 

  • Bryan K, Leise T (2006) The $25,000,000,000 eigenvector: the linear algebra behind google. SIAM Rev 48(3):569–581

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Chuvilin A, Kaiser U, Bichoutskaia E, Besley NA, Khlobystov AN (2010) Direct transformation of graphene to fullerene. Nat Chem 2(6):450–453

    Article  Google Scholar 

  • De S, Bartók AP, Csányi G, Ceriotti M (2016) Comparing molecules and solids across structural and alchemical space. Phys Chem Chem Phys 18(20):13754–13769

    Article  Google Scholar 

  • Deaven D, Ho K (1995) Molecular geometry optimization with a genetic algorithm. Phys Rev Lett 75:288

    Article  ADS  Google Scholar 

  • De Corato M, Bernasconi M, D’Alessio L, Ori O, Putz MV, Benedek G (2013) Topological versus physical and chemical properties of negatively curved carbon surfaces. In: Ashrafi AR, Cataldo F, Iranmanesh A, Ori O (eds) Topological modelling of nanostructures and extended systems. Springer, Dordrecht, pp 105–136

    Chapter  Google Scholar 

  • Fitzner M, Sosso GC, Pietrucci F, Pipolo S, Michaelides A (2017) Pre-critical fluctuations and what they disclose about heterogeneous crystal nucleation. Nat Commun 8(1):2257

    Article  ADS  Google Scholar 

  • Fu CD, Oliveira LF, Pfaendtner J (2017) Assessing generic collective variables for determining reaction rates in metadynamics simulations. J Chem Theory Comput 13(3):968–973

    Article  Google Scholar 

  • Gallet GA, Pietrucci F (2013) Structural cluster analysis of chemical reactions in solution. J Chem Phys 139(7):074,101

    Article  Google Scholar 

  • Gallet G, Pietrucci F, Andreoni W (2012) Bridging static and dynamical descriptions of chemical reactions: an ab initio study of CO2 interacting with water molecules. J Chem Theory Comput 8(11):4029–4039. https://doi.org/10.1021/ct300581n

    Article  Google Scholar 

  • García-Domenech R, Gálvez J, de Julián-Ortiz JV, Pogliani L (2008) Some new trends in chemical graph theory. Chem Rev 108(3):1127–1169

    Article  Google Scholar 

  • Giberti F, Salvalaglio M, Parrinello M (2015) Metadynamics studies of crystal nucleation. IUCrJ 2(2):256–266

    Article  Google Scholar 

  • Giuliani A, Krishnan A, Zbilut JP, Tomita M (2008) Proteins as networks: usefulness of graph theory in protein science. Curr Protein Pept Sci 9(1):28–38

    Article  Google Scholar 

  • Glass CW, Oganov AR, Hansen N (2006) Uspex an evolutionary crystal structure prediction. Comput Phys Commun 175(11):713–720

    Article  ADS  MATH  Google Scholar 

  • Goedecker S (2004) Minima hopping: an efficient search method for the global minimum of the potential energy surface of complex molecular systems. J Chem Phys 120:9911–9917

    Article  ADS  Google Scholar 

  • Goedecker S, Hellmann W, Lenosky T (2005) Global minimum determination of the Born-Oppenheimer surface within density functional theory. Phys Rev Lett 95(5):055501

    Article  ADS  Google Scholar 

  • Haji-Akbari A, Debenedetti PG (2015) Direct calculation of ice homogeneous nucleation rate for a molecular model of water. Proc Natl Acad Sci USA 112(34):10582–10588

    Article  ADS  Google Scholar 

  • Himoto K, Matsumoto M, Tanaka H (2014) Yet another criticality of water. Phys Chem Chem Phys 16(11):5081–5087

    Article  Google Scholar 

  • Ho K, Shvartsburg A, Pan B, Lu Z, Wang C, Wacker J, Fye J, Jarrold M (1998) Structures of medium-sized silicon clusters. Nature 392:582

    Article  ADS  Google Scholar 

  • Huber T, Torda AE, van Gunsteren WF (1994) Local elevation: a method for improving the searching properties of molecular dynamics simulation. J Comput Aid Mol Des 8(6):695–708

    Article  Google Scholar 

  • Ivanciuc O, Balaban AT (1998) Graph theory in chemistry. In: Schleyer PVR, Allinger NL, Clark T, Gasteiger J, Kollman PA, Schaefer III HF, Schreiner PR (eds) The encyclopedia of computational chemistry. John Wiley & Sons, Chichester, pp 1169–1190

    Google Scholar 

  • Johansson KO, Dillstrom T, Monti M, El Gabaly F, Campbell MF, Schrader PE, Popolan-Vaida DM, Richards-Henderson NK, Wilson KR, Violi A et al (2016) Formation and emission of large furans and oxygenated hydrocarbons from flames. Proc Natl Acad Sci USA 113:8374–8379

    Article  Google Scholar 

  • Klotz S, Strassle T, Nelmes R, Loveday J, Hamel G, Rousse G, Canny B, Chervin J, Saitta A (2005) Nature of the polyamorphic transition in ice under pressure. Phys Rev Lett 94:025506

    Article  ADS  Google Scholar 

  • Lai JY, Elvati P, Violi A (2014) Stochastic atomistic simulation of polycyclic aromatic hydrocarbon growth in combustion. Phys Chem Chem Phys 16(17):7969–7979

    Article  Google Scholar 

  • Laio A, Gervasio FL (2008) Metadynamics: a method to simulate rare events and reconstruct the free energy in biophysics, chemistry and material science. Rep Prog Phys 71(12):126601

    Article  ADS  Google Scholar 

  • Laio A, Parrinello M (2002) Escaping free-energy minima. Proc Natl Acad Sci USA 99(20):12562–12566

    Article  ADS  Google Scholar 

  • Lechner W, Dellago C (2008) Accurate determination of crystal structures based on averaged local bond order parameters. J Chem Phys 129(11):114707

    Article  ADS  Google Scholar 

  • Lloyd L, Johnston RL (1998) Modelling aluminium clusters with an empirical many-body potential. Chem Phys 236:107

    Article  Google Scholar 

  • Lyon JT, Gruene P, Fielicke A, Meijer G, Janssens E, Claes P, Lievens P (2009) Structures of silicon cluster cations in the gas phase. J Am Chem Soc 131(3):1115–1121

    Article  Google Scholar 

  • Malkin TL, Murray BJ, Brukhno AV, Anwar J, Salzmann CG (2012) Structure of ice crystallized from supercooled water. Proc Natl Acad Sci USA 109(4):1041–1045

    Article  ADS  Google Scholar 

  • Manolopoulos DE, Fowler PW (1992) Molecular graphs, point groups, and fullerenes. J Chem Phys 96(10):7603–7614

    Article  ADS  Google Scholar 

  • Maragliano L, Fischer A, Vanden-Eijnden E, Ciccotti G (2006) String method in collective variables: minimum free energy paths and isocommittor surfaces. J Chem Phys 125(2):024106

    Article  ADS  Google Scholar 

  • Martelli F, Ko HY, Oğuz EC, Car R (2018) Local-order metric for condensed-phase environments. Phys Rev B 97(6):064105

    Article  ADS  Google Scholar 

  • Martínez-Núñez E (2015) An automated transition state search using classical trajectories initialized at multiple minima. Phys Chem Chem Phys 17(22):14912–14921

    Article  Google Scholar 

  • Martoňák R, Laio A, Parrinello M (2003) Predicting crystal structures: the Parrinello-Rahman method revisited. Phys Rev Lett 90(7):075503

    Article  ADS  Google Scholar 

  • Mishima O, Stanley HE (1998) The relationship between liquid, supercooled and glassy water. Nature 396(6709):329–335

    Article  ADS  Google Scholar 

  • Mishima O, Calvert L, Whalley E (1984) Melting ice I at 77 K and 10 kbar: a new method of making amorphous solids. Nature 310(5976):393–395

    Article  ADS  Google Scholar 

  • Molinero V, Moore EB (2009) Water modeled as an intermediate element between carbon and silicon. J Phys Chem B 113(13):4008–4016. https://doi.org/10.1021/jp805227c

    Article  Google Scholar 

  • Oganov AR, Valle M (2009) How to quantify energy landscapes of solids. J Chem Phys 130(10):104504

    Article  ADS  Google Scholar 

  • Palmer JC, Martelli F, Liu Y, Car R, Panagiotopoulos AZ, Debenedetti PG (2014) Metastable liquid-liquid transition in a molecular model of water. Nature 510(7505):385–388

    Article  ADS  Google Scholar 

  • Pfaendtner J, Branduardi D, Parrinello M, Pollard TD, Voth GA (2009) Nucleotide-dependent conformational states of actin. Proc Natl Acad Sci USA 106(31):12723–12728

    Article  ADS  Google Scholar 

  • Piaggi PM, Parrinello M (2017) Entropy based fingerprint for local crystalline order. J Chem Phys 147(11):114112

    Article  ADS  Google Scholar 

  • Pickard CJ, Needs R (2011) Ab initio random structure searching. J Phys Condens Matt 23(5):053201

    Article  ADS  Google Scholar 

  • Pietrucci F (2017) Strategies for the exploration of free energy landscapes: unity in diversity and challenges ahead. Rev Phys 2:32–45

    Article  Google Scholar 

  • Pietrucci F, Andreoni W (2011) Graph theory meets ab initio molecular dynamics: atomic structures and transformations at the nanoscale. Phys Rev Lett 107:085504. https://doi.org/10.1103/PhysRevLett.107.085504

    Article  ADS  Google Scholar 

  • Pietrucci F, Andreoni W (2014) Fate of a graphene flake: a new route toward fullerenes disclosed with ab initio simulations. J Chem Theory Comput 10(3):913–917

    Article  Google Scholar 

  • Pietrucci F, Martoňák R (2015) Systematic comparison of crystalline and amorphous phases: charting the landscape of water structures and transformations. J Chem Phys 142(10):104704

    Article  ADS  Google Scholar 

  • Pietrucci F, Saitta AM (2015) Formamide reaction network in gas phase and solution via a unified theoretical approach: toward a reconciliation of different prebiotic scenarios. Proc Natl Acad Sci USA 112(49):15030–15035

    Article  ADS  Google Scholar 

  • Pipolo S, Salanne M, Ferlat G, Klotz S, Saitta AM, Pietrucci F (2017) Navigating at will on the water phase diagram. Phys Rev Lett 119(24):245701

    Article  ADS  Google Scholar 

  • Porto M, Bastolla U, Roman H, Vendruscolo M (2004) Reconstruction of protein structures from a vectorial representation. Phys Rev Lett 92(21):218101

    Article  ADS  Google Scholar 

  • Qian W, Chuang SC, Amador RB, Jarrosson T, Sander M, Pieniazek S, Khan SI, Rubin Y (2003) Synthesis of stable derivatives of C62: the first nonclassical fullerene incorporating a four-membered ring. J Am Chem Soc 125(8):2066–2067. https://doi.org/10.1021/ja029679s

    Article  Google Scholar 

  • Radha A, Lander L, Rousse G, Tarascon J, Navrotsky A (2015) Thermodynamic stability and correlation with synthesis conditions, structure and phase transformations in orthorhombic and monoclinic Li2M(SO4)2 (M = Mn,Fe,Co,Ni) polymorphs. J Mater Chem A 3(6): 2601–2608

    Article  Google Scholar 

  • Roethlisberger U, Andreoni W (1991) Structural and electronic-properties of sodium microclusters (n = 2−20) at low and high temperatures: New insights from ab initio molecular-dynamics studies. J Chem Phys 94(12):8129–8151

    Article  ADS  Google Scholar 

  • Roethlisberger U, Andreoni W, Parrinello M (1994) Structure of nanoscale silicon clusters. Phys Rev Lett 72:665–668

    Article  ADS  Google Scholar 

  • Rossi K, Baletto F (2017) The effect of chemical ordering and lattice mismatch on structural transitions in phase segregating nanoalloys. Phys Chem Chem Phys 19(18):11057–11063

    Article  Google Scholar 

  • Rossi G, Ferrando R (2009) Searching for low-energy structures of nanoparticles: a comparison of different methods and algorithms. J Phys Condens Matter 21(8):084208

    Article  ADS  Google Scholar 

  • Russo J, Romano F, Tanaka H (2014) New metastable form of ice and its role in the homogeneous crystallization of water. Nat Mater 13(7):733–739

    Article  ADS  Google Scholar 

  • Saunders M (2004) Stochastic search for isomers on a quantum mechanical surface. J Comput Chem 25(5):621–626

    Article  Google Scholar 

  • Schoenborn SE, Goedecker S, Roy S, Oganov AR (2009) The performance of minima hopping and evolutionary algorithms for cluster structure prediction. J Chem Phys 130:144108

    Article  ADS  Google Scholar 

  • Schreiber RE, Houben L, Wolf SG, Leitus G, Lang ZL, Carbó JJ, Poblet JM, Neumann R (2017) Real-time molecular scale observation of crystal formation. Nat Chem 9:369–373

    Article  Google Scholar 

  • Tribello GA, Cuny J, Eshet H, Parrinello M (2011) Exploring the free energy surfaces of clusters using reconnaissance metadynamics. J Chem Phys 135(11):114109

    Article  ADS  Google Scholar 

  • Tribello GA, Bonomi M, Branduardi D, Camilloni C, Bussi G (2014) Plumed 2: new feathers for an old bird. Comput Phys Commun 185(2):604–613

    Article  ADS  Google Scholar 

  • Valle M, Oganov AR (2010) Crystal fingerprint space–a novel paradigm for studying crystal-structure sets. Acta Cryst Sect A 66(5):507–517

    Article  ADS  Google Scholar 

  • Wales D, Doye J (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 LP, Titov A, McGibbon R, Liu F, Pande VS, Martínez TJ (2014) Discovering chemistry with an ab initio nanoreactor. Nat Chem 6(12):1044–1048

    Article  Google Scholar 

  • Wang Y, Lv J, Zhu L, Ma Y (2012) Calypso: a method for crystal structure prediction. Comput Phys Commun 183(10):2063–2070

    Article  ADS  Google Scholar 

  • Wang Y, Huang Y, Gu B, Xiao X, Liang D, Rao W (2016) Formation of the H2SO4 ⋅ HSO\(_4^{-}\) dimer in the atmosphere as a function of conditions: a simulation study. Mol Phys 114(23):3475–3482

    Google Scholar 

  • Weinan E, Vanden-Eijnden E (2010) Transition-path theory and path-finding algorithms for the study of rare events. Ann Rev Phys Chem 61:391–420

    Article  Google Scholar 

  • Weinan E, Ren W, Vanden-Eijnden E (2005) Finite temperature string method for the study of rare events. J Phys Chem B 109(14):6688–6693. https://doi.org/10.1021/jp0455430

    Article  Google Scholar 

  • Wilmer CE, Leaf M, Lee CY, Farha OK, Hauser BG, Hupp JT, Snurr RQ (2012) Large-scale screening of hypothetical metal–organic frameworks. Nat Chem 4(2):83–89

    Article  Google Scholar 

  • Woodley S, Catlow R (2008) Crystal structure prediction from first principles. Nat Mater 7: 937–946

    Article  ADS  Google Scholar 

  • Yoo S, Zeng XC (2005) Structures and stability of medium-sized silicon clusters. III. Reexamination of motif transition in growth pattern from Si15 to Si20. J Chem Phys 123(16):164303

    Google Scholar 

  • Zheng S, Pfaendtner J (2014) Car–Parrinello molecular dynamics+ metadynamics study of high-temperature methanol oxidation reactions using generic collective variables. J Phys Chem C 118(20):10764–10770

    Article  Google Scholar 

  • Zhu L, Amsler M, Fuhrer T, Schaefer B, Faraji S, Rostami S, Ghasemi SA, Sadeghi A, Grauzinyte M, Wolverton C, Goedecker S (2016) A fingerprint based metric for measuring similarities of crystalline structures. J Chem Phys 144(3):034203

    Article  ADS  Google Scholar 

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Correspondence to Fabio Pietrucci .

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Pietrucci, F. (2020). Novel Enhanced Sampling Strategies for Transitions Between Ordered and Disordered Structures. In: Andreoni, W., Yip, S. (eds) Handbook of Materials Modeling. Springer, Cham. https://doi.org/10.1007/978-3-319-44677-6_51

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