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Combining molecular dynamics with Monte Carlo simulations: implementations and applications

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Abstract

In this contribution, we present an overview of the various techniques for combining atomistic molecular dynamics with Monte Carlo simulations, mainly in the context of condensed matter systems, as well as a brief summary of the main accelerated dynamics techniques. Special attention is given to the force bias Monte Carlo technique and its combination with molecular dynamics, in view of promising recent developments, including a definable timescale. Various examples of the application of combined molecular dynamics / Monte Carlo simulations are given, in order to demonstrate the enhanced simulation efficiency with respect to either pure molecular dynamics or Monte Carlo.

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References

  1. Frenkel D, Smit B (2001) Understanding molecular simulation: from algorithms to applications. Academic Press, London

    Google Scholar 

  2. Cooke DJ, Elliott JA (2007) Atomistic simulations of calcite nanoparticles and their interaction with water. J Chem Phys 127(10). Art no 104706

  3. Khalilov U, Pourtois G, van Duin ACT, Neyts EC (2012) self-limiting oxidation in small-diameter Si nanowires. Chem Mater 24(11):2141–2147

    Article  CAS  Google Scholar 

  4. Lu Y, Cheng H, Chen M (2012) A molecular dynamics examination of the relationship between self-diffusion and viscosity in liquid metals. J Chem Phys 136(21). Art no 214505

  5. Matsukuma M, Hamaguchi S (2008) Molecular dynamics simulation of microcrystalline Si deposition processes by silane plasmas. Thin Solid Films 516(11):3443–3448

    Article  CAS  Google Scholar 

  6. Neyts E, Bogaerts A, Gijbels R, Benedikt J, Van De Sanden M (2004) Molecular dynamics simulations for the growth of diamond-like carbon films from low kinetic energy species. Diam Relat Mater13(10):1873–1881

    Article  CAS  Google Scholar 

  7. Faccioli P, Lonardi A, Orland H (2010) Dominant reaction pathways in protein folding: a direct validation against molecular dynamics simulations. J Chem Phys 133(4). Art no 045104

  8. Rauf S, Sparks T, Ventzek PLG, Smirnov VV, Stengach AV, Gaynullin KG, Pavlovsky VA (2007) A molecular dynamics investigation of fluorocarbon based layer-by-layer etching of silicon and SiO2. J Appl Phys 101(3). Art no 033308

  9. Gou F, Neyts E, Eckert M, Tinck S, Bogaerts A (2010) Molecular dynamics simulations of Cl+ etching on a Si(100) surface. J Appl Phys 107(11):113305

    Article  Google Scholar 

  10. Postawa Z, Czerwinski B, Szewczyk M, Smiley E, Winograd N, Garrison B (2003) Enhancement of sputtering yields due to C-60 versus Ga bombardment of Ag{111} as explored by molecular dynamics simulations. Anal Chem 75(17):4402–4407

    Article  CAS  Google Scholar 

  11. Shen XJ, Xiao Y, Dong W, Yan XH, Busnengo HF (2012) Molecular dynamics simulations based on reactive force-fields for surface chemical reactions. Comput Theor Chem 990: 152–158

    Article  CAS  Google Scholar 

  12. Servantie J, Gaspard P (2003) Methods of calculation of a friction coefficient: application to nanotubes. Phys Rev Lett 91(18). Art no 185503

  13. Thaulow C, Sen D, Buehler MJ (2011) Atomistic study of the effect of crack tip ledges on the nucleation of dislocations in silicon single crystals at elevated temperature. Mater Sci Eng A Struct Mater Prop Microstruct Process 528(13–14):4357–4364

    Article  Google Scholar 

  14. Shibuta Y (2012) Phase transition of metal nanowires confined in a low-dimensional nanospace. Chem Phys Lett 532:84–89

    Article  CAS  Google Scholar 

  15. Neyts EC, Bogaerts A (2009) Numerical study of the size-dependent melting mechanisms of nickel nanoclusters. J Phys Chem C 113(7):2771–2776

    Article  CAS  Google Scholar 

  16. Dongare AM, Rajendran AM, LaMattina B, Zikry MA, Brenner DW (2009) Atomic scale studies of spall behavior in nanocrystalline Cu. J Appl Phys 108(11):113518

    Article  Google Scholar 

  17. Shaw DE, Maragakis P, Lindorff-Larsen K, Piana S, Dror RO, Eastwood MP, Bank JA, Jumper JM, Salmon JK, Shan Y, Wriggers W (2010) Atomic-level characterization of the structural dynamics of proteins. Science 330(6002):341–346

    Article  CAS  Google Scholar 

  18. Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AH, Teller E (1953) Equation of state calculations by fast computing machines. J Chem Phys 21(6):1087

    Article  CAS  Google Scholar 

  19. Kikuchi K, Yoshida M, Maekawa T, Watanabe H (1991) Metropolis Monte–Carlo method as a numerical technique to solve the Fokker-Planck equation. Chem Phys Lett 185(3–4): 335–338

    Article  CAS  Google Scholar 

  20. Kikuchi K, Yoshida M, Maekawa T, Watanabe H (1992) Metropolis Monte-Carlo method for Brownian dynamics simulation generalized to include hydrodynamic interactions. Chem Phys Lett 196(1–2):57–61

    Article  CAS  Google Scholar 

  21. Bortz AB, Kalos MH, Leibowitz JL (1975) A new algorithm for Monte Carlo simulation of Ising spin systems. J Comput Phys 17:10–18

    Article  Google Scholar 

  22. Netto A, Frenklach M (2005) Kinetic Monte Carlo simulations of CVD diamond growth—interlay among growth, etching, and migration. Diam Relat Mater 14(10):1630–1646

    Article  CAS  Google Scholar 

  23. Henkelman G, Jonsson H (2001) Long time scale kinetic Monte Carlo simulations without lattice approximation and predefined event table. J Chem Phys 115(21):9657–9666

    Article  CAS  Google Scholar 

  24. Liu YH, Neyts E, Bogaerts A (2006) Monte Carlo method for simulations of adsorbed atom diffusion on a surface. Diam Relat Mater 15(10):1629–1635

    Article  CAS  Google Scholar 

  25. Voter A, Montalenti F, Germann T (2002) Extending the time scale in atomistic simulation of materials. Ann Rev Mater Res 32:321–346

    Article  CAS  Google Scholar 

  26. Jonsson H, Mills G, Jacobsen KW (1998) Nudged elastic band method for finding minimum energy paths of transitions. In: Berne BJ, Ciccotti G, Coker DF (ed) Classical and quantum dynamics in condensed phase simulations. World Scientific, Singapore

  27. 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  CAS  Google Scholar 

  28. Dellago C, Bolhuis PG, Csajka FS, Chandler D (1998) Transition path sampling and the calculation of rate constants. J Chem Phys 108(5):1964–1977

    Article  CAS  Google Scholar 

  29. Barkema GT, Mousseau N (1996) Event-based relaxation of continuous disordered systems. Phys Rev Lett 77(21): 4358–4361

    Article  CAS  Google Scholar 

  30. Allen RJ, Warren PB, ten Wolde PR (2005) Sampling rare switching events in biochemical networks. Phys Rev Lett 94: 018104

    Article  Google Scholar 

  31. Ren WE, Vanden-Eijnden E (2005) Finite temperature string method for the study of rare events. J Phys Chem B 109:6668

    Google Scholar 

  32. Faradijan AK, Elber R (2004) Computing time scales from reaction coordinates by milestoning. J Chem Phys 120:10880–10889

    Article  Google Scholar 

  33. Tironi IG, van Gunsteren WF (1994) A molecular-dynamics simulation study of chloroform. Mol Phys 83(2): 381–403

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  35. Zwanzig RW (1954) High temperature equation of state by a perturbation method. I. Nonpolar gases. J Chem Phys 22:1420–1426

    Article  CAS  Google Scholar 

  36. Torrie GM, Valleau JP (1977) Nonphysical sampling distributions in Monte Carlo free-energy estimation: umbrella sampling. J Comput Phys 22(2):187–199

    Article  Google Scholar 

  37. Darve E, Pohorille A (2001) Calculating free energies using average force. J Chem Phys 115: 9169–9183

    Article  CAS  Google Scholar 

  38. Leech J, Prins J, Hermans J (1996) SMD: Visual steering of molecular dynamics for protein design. IEEE Comput Sci Eng 3:38–45

    Article  CAS  Google Scholar 

  39. Sorensen M, Voter A (2000) Temperature-accelerated dynamics for simulation of infrequent events. J Chem Phys 112(21):9599–9606

    Article  CAS  Google Scholar 

  40. Voter A (1997) Hyperdynamics: accelerated molecular dynamics of infrequent events. Phys Rev Lett 78(20):3908–3911

    Article  CAS  Google Scholar 

  41. Voter A (1998) Parallel replica method for dynamics of infrequent events. Phys Rev B Condens Matter 57(22): 13985–13988

    Article  Google Scholar 

  42. Egelhoff WF, Jacob I (1998) Reflection high-energy electron-diffraction (RHEED) oscillations at 77 K. Phys Rev Lett 62(8): 921–924

    Article  Google Scholar 

  43. Georgieva V, Voter AF, Bogaerts A (2011) Understanding the surface diffusion processes during magnetron sputter-deposition of complex oxide Mg-Al-O thin films. Cryst Growth Des 11(6): 2553–2558

    Article  CAS  Google Scholar 

  44. Fichthorn KA, Miron RA, Wang YS, Tiwary Y (2009) Accelerated molecular dynamics simulation of thin-film growth with the bond-boost method. J Phys Condens Matter 21(8):084212

    Article  Google Scholar 

  45. Hamelberg D, Mongan J, McCammon JA (2004) Accelerated molecular dynamics: a promising and efficient simulation method for biomolecules. J Chem Phys 120(24): 11919–11929

    Article  CAS  Google Scholar 

  46. Uberuaga BP, Stuart SJ, Windl W, Masquelier MP, Voter AF (2012) Fullerene and graphene formation from carbon nanotube fragments. Comput Theor Chem 987(SI):115–121

    Article  CAS  Google Scholar 

  47. Mees MJ, Pourtois G, Neyts EC, Thijsse BJ, Stesmans A (2012) Uniform-acceptance force-bias Monte Carlo method with time scale to study solid-state diffusion. Phys Rev B 85(13):134301

    Article  Google Scholar 

  48. Laberge L, Tully J (2000) A rigorous procedure for combining molecular dynamics and Monte Carlo simulation algorithms. Chem Phys 260(1-2):183–191

    Article  CAS  Google Scholar 

  49. Ribeiro AAST, de Alencastro RB (2012) Mixed Monte Carlo/molecular dynamics simulations in explicit solvent. J Comput Chem 33(8):901–905

    Article  CAS  Google Scholar 

  50. Ulmschneider JP, Jorgensen WL (2003) Monte Carlo backbone sampling for polypeptides with variable bond angles and dihedral angles using concerted rotations and a Gaussian bias. J Chem Phys 118(9):4261–4271

    Article  CAS  Google Scholar 

  51. Leach AR (2001) Molecular modelling: principles and applications. Prentice Hall, Essex

    Google Scholar 

  52. Bussi G, Donadio D, Parrinello M (2007) Canonical sampling through velocity rescaling. J Chem Phys 126(1):014101

    Article  Google Scholar 

  53. Forray C, Muthukumar M (2006) Langevin dynamics simulations of genome packing in bacteriophage. Biophys J 91:25–41

    Article  Google Scholar 

  54. Duane S, Kennedy A, Pendleton B, Roweth D (1987) Hybrid Monte-Carlo. Phys Lett B 195(2):216–222

    Article  CAS  Google Scholar 

  55. Mehlig B, Heermann D, Forrest B (1992) Hybrid Monte-Carlo method for condensed-matter systems. Phys Rev B 45(2):679–685

    Article  Google Scholar 

  56. Clamp ME, Baker PG, Stirling CJ, Brass A (1994) Hybrid Monte-Carlo—an efficient algorithm for condensed matter simulation. J Comput Chem 15(8):838–846

    Article  CAS  Google Scholar 

  57. Brotz FA, Depablo JJ (1994) Hybrid Monte-Carlo simulation of silica. Chem Eng Sci 49(17):3015–3031

    Article  CAS  Google Scholar 

  58. Pangali C, Rao M, Berne B (1978) Novel Monte-Carlo scheme for simulating water and aqueous-solutions. Chem Phys Lett 55(3):413–417

    Article  CAS  Google Scholar 

  59. Rao M, Pangali C, Berne B (1979) Force bias Monte-Carlo simulation of water—methodology, optimization and comparison with molecular-dynamics. Mol Phys 37(6):1773–1798

    Article  CAS  Google Scholar 

  60. Dereli G (1992) Stillinger-Weber type potentials in Monte-Carlo simulation of amorphous-silicon. Mol Simul 8(6):351–360

    Article  Google Scholar 

  61. Mezei M (1991) Distance-scaled force biased Monte Carlo simulation for solutions containing a strongly interacting solute. Mol Simul 5:405–408

    Article  Google Scholar 

  62. Timonova M, Groenewegen J, Thijsse BJ (2010) Modeling diffusion and phase transitions by a uniform-acceptance force-bias Monte Carlo method. Phys Rev B 81(14):144107

    Article  Google Scholar 

  63. Neyts EC, Thijsse BJ, Mees MJ, Bal KM, Pourtois G (2012) Establishing uniform acceptance in force biased Monte Carlo simulations. J Chem Theory Comput 8: 1865–1869

    Article  CAS  Google Scholar 

  64. Rossky P, Doll J, Friedman H (1978) Brownian dynamics as smart Monte-Carlo simulation. J Chem Phys 69(10): 4628–4633

    Article  CAS  Google Scholar 

  65. Chiu S, Jakobsson E, Scott H (2001) Combined Monte Carlo and molecular dynamics simulation of hydrated lipid-cholesterol lipid bilayers at low cholesterol concentration. Biophys J 80(3): 1104–1114

    Article  CAS  Google Scholar 

  66. Chiu S, Jakobsson E, Subramaniam S, Scott H (1999) Combined Monte Carlo and molecular dynamics simulation of fully hydrated dioleyl and palmitoyl-oleyl phosphatidylcholine lipid bilayers. Biophys J 77(5):2462–2469

    Article  CAS  Google Scholar 

  67. Jager HU, Belov AY (2003) ta-C deposition simulations: film properties and time-resolved dynamics of film formation. Phys Rev B 68(2):024201

    Article  Google Scholar 

  68. Taguchi M, Hamaguchi S (2006) Molecular dynamics study on Ar ion bombardment effects in amorphous Sio2 deposition processes. J Appl Phys 100(12):123305

    Article  Google Scholar 

  69. Taguchi M, Hamaguchi S (2007) Md simulations of amorphous Sio2 thin film formation in reactive sputtering deposition processes. Thin Solid Films 515(12):4879–4882

    Article  CAS  Google Scholar 

  70. Tavazza F, Nurminen L, Landau D, Kuronen A, Kaski K (2004) Hybrid Monte Carlo-molecular dynamics algorithm for the study of islands and step edges on semiconductor surfaces: application to Si/Si(001). Phys Rev E 70(3, Part 2): 036701

    Article  CAS  Google Scholar 

  71. Tiwary P, van de Walle A (2011) Hybrid deterministic and stochastic approach for efficient atomistic simulations at long time scales. Phys Rev B 84(10):100301

    Article  Google Scholar 

  72. Grein C, Benedek R, Delarubia T (1996) Epitaxial growth simulation employing a combined molecular dynamics and Monte Carlo approach. Comput Mater Sci 6(2):123–126

    Article  CAS  Google Scholar 

  73. Eckert M, Mortet V, Zhang L, Neyts E, Verbeeck J, Haenen K, Bogaerts A (2011) Theoretical investigation of grain size tuning during prolonged bias-enhanced nucleation. Chem Mater 23(6):1414–1423

    Article  CAS  Google Scholar 

  74. Eckert M, Neyts E, Bogaerts A (2009) Modeling adatom surface processes during crystal growth: a new implementation of the metropolis Monte Carlo algorithm. CrystEngComm 11(8):1597–1608

    Article  CAS  Google Scholar 

  75. Eckert M, Neyts E, Bogaerts A (2010) Insights into the growth of (ultra) nanocrystalline diamond by combined molecular dynamics and Monte Carlo simulations. Cryst Growth Design 10(7): 3005–3021

    Article  CAS  Google Scholar 

  76. Neyts EC, Khalilov U, Pourtois G, Van Duin ACT (2011) Hyperthermal oxygen interacting with silicon surfaces: adsorption, implantation, and damage creation. J Phys Chem C 115(11):4818–4823

    Article  CAS  Google Scholar 

  77. Buffat P, Borel J (1976) Size effect on melting temperature of gold particles. Phys Rev A 13(6):2287–2298

    Article  CAS  Google Scholar 

  78. Jiang A, Awasthi N, Kolmogorov AN, Setyawan W, Borjesson A, Bolton K, Harutyunyan AR, Curtarolo S (2007) Theoretical study of the thermal behavior of free and alumina-supported Fe-C nanoparticles. Phys Rev B 75(20):205426

    Article  Google Scholar 

  79. Shibuta Y, Suzuki T (2010) Melting and solidification point of fcc-metal nanoparticles with respect to particle size: a molecular dynamics study. Chem Phys Lett 498(4–6): 323–327

    Article  CAS  Google Scholar 

  80. Neyts EC, Shibuta Y, Van Duin ACT, Bogaerts A (2010) Catalyzed growth of carbon nanotube with definable chirality by hybrid molecular dynamics-force biased Monte Carlo simulations. ACS Nano 4(11): 6665–6672

    Article  CAS  Google Scholar 

  81. Neyts EC, Van Duin ACT, Bogaerts A (2011) Changing chirality during single-walled carbon nanotube growth: a reactive molecular dynamics/Monte Carlo study. J Am Chem Soc 133(43):17225–17231

    Article  CAS  Google Scholar 

  82. Neyts EC, Van Duin ACT, Bogaerts A (2012) Insights in the plasma-assisted growth of carbon nanotubes through atomic scale simulations: effect of electric field. J Am Chem Soc 134(2):1256–1260

    Article  CAS  Google Scholar 

  83. Hatakeyama R, Kaneko T, Kato T, Li YF (2011) Plasma-synthesized single-walled carbon nanotubes and their applications. J Phys D Appl Phys 44(17):174004

    Article  Google Scholar 

  84. Kato T, Hatakeyama R (2006) Formation of freestanding single-walled carbon nanotubes by plasma-enhanced CVD. Chem Vap Depos 12(6):345–352

    Article  CAS  Google Scholar 

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Correspondence to Erik C. Neyts.

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Published as part of the special collection of articles celebrating theoretical and computational chemistry in Belgium.

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Neyts, E.C., Bogaerts, A. Combining molecular dynamics with Monte Carlo simulations: implementations and applications. Theor Chem Acc 132, 1320 (2013). https://doi.org/10.1007/s00214-012-1320-x

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