Skip to main content
SpringerLink
Log in

A Review of Enhanced Sampling Approaches for Accelerated Molecular Dynamics

  • Chapter
  • First Online:
Multiscale Materials Modeling for Nanomechanics

Part of the book series: Springer Series in Materials Science ((SSMATERIALS,volume 245))

Abstract

Molecular dynamics (MD) simulations have become a tool of immense use and popularity for simulating a variety of systems. With the advent of massively parallel computer resources, one now routinely sees applications of MD to systems as large as hundreds of thousands to even several million atoms, which is almost the size of most nanomaterials. However, it is not yet possible to reach laboratory timescales of milliseconds and beyond with MD simulations. Due to the essentially sequential nature of time, parallel computers have been of limited use in solving this so-called timescale problem. Instead, over the years a large range of statistical mechanics based enhanced sampling approaches have been proposed for accelerating molecular dynamics, and accessing timescales that are well beyond the reach of the fastest computers. In this review we provide an overview of these approaches, including the underlying theory, typical applications, and publicly available software resources to implement them.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. D. Frenkel, B. Smit, Understanding Molecular Simulation: From Algorithms to Applications, vol. 1 (Academic, New York, 2001)

    Google Scholar 

  2. F.F. Abraham, R. Walkup, H. Gao, M. Duchaineau, T.D. De La Rubia, M. Seager, Simulating materials failure by using up to one billion atoms and the world’s fastest computer: Brittle fracture. Proc. Natl. Acad. Sci. 99 (9), 5777–5782 (2002)

    Article  Google Scholar 

  3. M. Tuckerman, B.J. Berne, G.J. Martyna, Reversible multiple time scale molecular dynamics. J. Chem. Phys. 97 (3), 1990–2001 (1992)

    Article  Google Scholar 

  4. A.F. Voter, F. Montalenti, T.C. Germann, Extending the time scale in atomistic simulation of materials. Ann. Rev. Mater. Res. 32 (1), 321–346 (2002)

    Article  Google Scholar 

  5. A. Barducci, M. Bonomi, M. Parrinello, metadynamics. Wiley Interdiscip. Rev. Comput. Mol. Sci. 1 (5), 826–843 (2011)

    Google Scholar 

  6. A. van de Walle, Simulations provide a rare look at real melting. Science 346 (6210), 704–705 (2014)

    Article  Google Scholar 

  7. D. Perez, B.P. Uberuaga, Y. Shim, J.G. Amar, A.F. Voter, Accelerated molecular dynamics methods: introduction and recent developments. Annu. Rep. Comput. Chem. 5, 79–98 (2009)

    Article  Google Scholar 

  8. E. Weinan, Principles of Multiscale Modeling (Cambridge University Press, Cambridge, 2011)

    Google Scholar 

  9. D. Chandler, Introduction to Modern Statistical Mechanics, vol. 1 (Oxford University Press, Oxford, 1987)

    Google Scholar 

  10. D.A. McQuarrie, Statistical Thermodynamics (Harper Collins Publishers, New York, 1973)

    Google Scholar 

  11. B.J. Berne, M. Borkovec, J.E. Straub, Classical and modern methods in reaction rate theory. J. Phys. Chem. 92 (13), 3711–3725 (1988)

    Article  Google Scholar 

  12. B.J. Berne, N. De Leon, R. Rosenberg, Isomerization dynamics and the transition to chaos. J. Phys. Chem. 86 (12), 2166–2177 (1982)

    Article  Google Scholar 

  13. J.-P. Eckmann, D. Ruelle, Ergodic theory of chaos and strange attractors. Rev. Mod. Phys. 57 (3), 617 (1985)

    Google Scholar 

  14. D. Wales, Energy Landscapes: Applications to Clusters, Biomolecules and Glasses (Cambridge University Press, Cambridge, 2003)

    Google Scholar 

  15. D. Sheppard, R. Terrell, G. Henkelman, Optimization methods for finding minimum energy paths. J. Chem. Phys. 128 (13), 134106 (2008)

    Google Scholar 

  16. G. Henkelman, B.P. Uberuaga, H. Jónsson, A climbing image nudged elastic band method for finding saddle points and minimum energy paths. J. Chem. Phys. 113 (22), 9901–9904 (2000)

    Article  Google Scholar 

  17. G. Henkelman, H. Jónsson, A dimer method for finding saddle points on high dimensional potential surfaces using only first derivatives. J. Chem. Phys. 111 (15), 7010–7022 (1999)

    Article  Google Scholar 

  18. P.G. Bolhuis, D. Chandler, C. Dellago, P.L. Geissler, Transition path sampling: throwing ropes over rough mountain passes, in the dark. Ann. Rev. Phys. Chem. 53 (1), 291–318 (2002)

    Article  Google Scholar 

  19. G.H. Vineyard, Frequency factors and isotope effects in solid state rate processes. J. Phys. Chem. Solids 3 (1), 121–127 (1957)

    Article  Google Scholar 

  20. G.A. Tribello, M. Ceriotti, M. Parrinello, Using sketch-map coordinates to analyze and bias molecular dynamics simulations. Proc. Natl. Acad. Sci. 109 (14), 5196–5201 (2012)

    Article  Google Scholar 

  21. P.G. Bolhuis, C. Dellago, D. Chandler, Reaction coordinates of biomolecular isomerization. Proc. Natl. Acad. Sci. 97 (11), 5877–5882 (2000)

    Article  Google Scholar 

  22. A. Samanta, E. Weinan, Atomistic simulations of rare events using gentlest ascent dynamics. J. Chem. Phys. 136 (12), 124104 (2012)

    Google Scholar 

  23. W. Ren, E. Vanden-Eijnden, Finite temperature string method for the study of rare events. J. Phys. Chem. B 109 (14), 6688–6693 (2005)

    Article  Google Scholar 

  24. P. Hänggi, P. Talkner, M. Borkovec, Reaction-rate theory: fifty years after Kramers. Rev. Mod. Phys. 62 (2), 251 (1990)

    Google Scholar 

  25. H. Eyring, The activated complex in chemical reactions. J. Chem. Phys. 3 (2), 107–115 (1935)

    Article  Google Scholar 

  26. R.G. Mullen, J.-E. Shea, B. Peters, Transmission coefficients, committors, and solvent coordinates in ion-pair dissociation. J. Chem. Theory Comput. 10 (2), 659–667 (2014)

    Article  Google Scholar 

  27. R.F. Grote, J.T. Hynes, The stable states picture of chemical reactions. ii. rate constants for condensed and gas phase reaction models. J. Chem. Phys. 73 (6), 2715–2732 (1980)

    Google Scholar 

  28. A.K. Faradjian, R. Elber, Computing time scales from reaction coordinates by milestoning. J. Chem. Phys. 120 (23), 10880–10889 (2004)

    Article  Google Scholar 

  29. T.T. Lau, A. Kushima, S. Yip, Atomistic simulation of creep in a nanocrystal. Phys. Rev. Lett. 104 (17), 175501 (2010)

    Google Scholar 

  30. J.-H. Prinz, H. Wu, M. Sarich, B. Keller, M. Senne, M. Held, J.D. Chodera, C. Schütte, F. Noé, Markov models of molecular kinetics: Generation and validation. J. Chem. Phys. 134 (17), 174105 (2011)

    Google Scholar 

  31. J.E. Straub, B.J. Berne, A rapid method for determining rate constants by molecular dynamics. J. Chem. Phys. 83 (3), 1138–1139 (1985)

    Article  Google Scholar 

  32. A. Samanta, M.E. Tuckerman, T.-Q. Yu, E. Weinan, Microscopic mechanisms of equilibrium melting of a solid. Science 346 (6210), 729–732 (2014)

    Article  Google Scholar 

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

    Article  Google Scholar 

  34. A.F. Voter, A method for accelerating the molecular dynamics simulation of infrequent events. J. Chem. Phys. 106 (11), 4665–4677 (1997)

    Article  Google Scholar 

  35. R.A. Miron, K.A. Fichthorn, Accelerated molecular dynamics with the bond-boost method. J. Chem. Phys. 119 (12), 6210–6216 (2003)

    Article  Google Scholar 

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

    Article  Google Scholar 

  37. M. Steiner, P.-A. Genilloud, J. Wilkins, Simple bias potential for boosting molecular dynamics with the hyperdynamics scheme. Phys. Rev. B 57 (170, 10236 (1998)

    Google Scholar 

  38. H. Grubmüller, Predicting slow structural transitions in macromolecular systems: conformational flooding. Phys. Rev. E 52, 2893–2906 (1995)

    Article  Google Scholar 

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

    Article  Google Scholar 

  40. S.Y. Kim, D. Perez, A.F. Voter, Local hyperdynamics. J. Chem. Phys. 139 (14), 144110 (2013)

    Google Scholar 

  41. W.K. Kim, M. Luskin, D. Perez, A. Voter, E. Tadmor, Hyper-qc: an accelerated finite-temperature quasicontinuum method using hyperdynamics. JJ. Mech. Phys. Solids 63, 94–112 (2014)

    Article  Google Scholar 

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

    Article  Google Scholar 

  43. A. Barducci, G. Bussi, M. Parrinello, Well-tempered metadynamics: a smoothly converging and tunable free-energy method. Phys. Rev. Lett. 100 (2), 020603–020606 (2008)

    Article  Google Scholar 

  44. Y. Lin, K.A. Fichthorn, Accelerated molecular dynamics study of the GaAs (001) β 2 (2× 4)/c (2× 8) surface. Phys. Rev. B 86 (16), 165303 (2012)

    Google Scholar 

  45. K.E. Becker, M.H. Mignogna, K.A. Fichthorn, Accelerated molecular dynamics of temperature-programed desorption. Phys. Rev. lett. 102 (4), 046101 (2009)

    Google Scholar 

  46. S. Hara, J. Li, Adaptive strain-boost hyperdynamics simulations of stress-driven atomic processes. Phys. Rev. B 82 (18), 184114 (2010)

    Google Scholar 

  47. R.A. Miron, K.A. Fichthorn, Heteroepitaxial growth of co/ cu (001): an accelerated molecular dynamics simulation study. Phys. Rev. B 72 (3), 035415 (2005)

    Google Scholar 

  48. S.T. Chill, M. Welborn, R. Terrell, L. Zhang, J.-C. Berthet, A. Pedersen, H. Jonsson, G. Henkelman, Eon: software for long time simulations of atomic scale systems. Model. Simul. Mater. Sci. Eng. 22 (5), 055002 (2014)

    Google Scholar 

  49. M. Bonomi, D. Branduardi, G. Bussi, C. Camilloni, D. Provasi, P. Raiteri, D. Donadio, F. Marinelli, F. Pietrucci, R.A. Broglia et al., Plumed: a portable plugin for free-energy calculations with molecular dynamics. Comp. Phys. Comm. 180 (10), 1961–1972 (2009)

    Article  Google Scholar 

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

    Article  Google Scholar 

  51. M.R. So, A.F. Voter et al., Temperature-accelerated dynamics for simulation of infrequent events. J. Chem. Phys. 112 (21), 9599–9606 (2000)

    Article  Google Scholar 

  52. Y. Shim, J.G. Amar, B.P. Uberuaga, A.F. Voter, Reaching extended length scales and time scales in atomistic simulations via spatially parallel temperature-accelerated dynamics. Phys. Rev. B 76, 205439 (2007)

    Article  Google Scholar 

  53. V. Bochenkov, N. Suetin, S. Shankar, Extended temperature-accelerated dynamics: enabling long-time full-scale modeling of large rare-event systems. J. Chem. Phys. 141 (9), 094105 (2014)

    Google Scholar 

  54. X.-M. Bai, A.F. Voter, R.G. Hoagland, M. Nastasi, B.P. Uberuaga, Efficient annealing of radiation damage near grain boundaries via interstitial emission. Science 327 (5973), 1631–1634 (2010)

    Article  Google Scholar 

  55. J.A. Sprague, F. Montalenti, B.P. Uberuaga, J.D. Kress, A.F. Voter, Simulation of growth of cu on ag(001) at experimental deposition rates. Phys. Rev. B 66, 205415 (2002)

    Article  Google Scholar 

  56. F. Montalenti, M. Sørensen, A. Voter, Closing the gap between experiment and theory: crystal growth by temperature accelerated dynamics. Phys. Rev. Lett. 87 (12), 126101 (2001)

    Google Scholar 

  57. B. Uberuaga, R. Smith, A. Cleave, F. Montalenti, G. Henkelman, R. Grimes, A. Voter, K. Sickafus, Structure and mobility of defects formed from collision cascades in MgO. Phys. Rev. Lett. 92 (11), 115505 (2004)

    Google Scholar 

  58. M. Cogoni, B. Uberuaga, A. Voter, L. Colombo, Diffusion of small self-interstitial clusters in silicon: temperature-accelerated tight-binding molecular dynamics simulations. Phys. Rev. B 71 (12), 121203 (2005)

    Google Scholar 

  59. B.P. Uberuaga, S.M. Valone, M. Baskes, Accelerated dynamics study of vacancy mobility in-plutonium. J. Alloys Compd. 444, 314–319 (2007)

    Article  Google Scholar 

  60. S. Plimpton, P. Crozier, A. Thompson, Lammps-Large-Scale Atomic/Molecular Massively Parallel Simulator, vol. 18 (Sandia National Laboratories, Albuquerque, 2007)

    Google Scholar 

  61. W. Smith, C. Yong, P. Rodger, Dl_poly: application to molecular simulation. Mol. Simul. 28 (5), 385–471 (2002)

    Article  Google Scholar 

  62. A.F. Voter, Introduction to the kinetic monte carlo method, in Radiation Effects in Solids (Springer, Berlin, 2007), pp. 1–23

    Google Scholar 

  63. L.K. Béland, P. Brommer, F. El-Mellouhi, J.-F. Joly, N. Mousseau, Kinetic activation-relaxation technique. Phys. Rev. E 84 (4), 046704 (2011)

    Google Scholar 

  64. N. Mousseau, G. Barkema, Traveling through potential energy landscapes of disordered materials: the activation-relaxation technique. Phys. Rev. E 57 (2), 2419 (1998)

    Google Scholar 

  65. H. Xu, Y.N. Osetsky, R.E. Stoller, Self-evolving atomistic kinetic monte carlo: fundamentals and applications. J. Phys. Condens. Matter 24 (37), 375402 (2012)

    Google Scholar 

  66. J.-F. Joly, L.K. Béland, P. Brommer, N. Mousseau, Contribution of vacancies to relaxation in amorphous materials: a kinetic activation-relaxation technique study. Phys. Rev. B 87 (14), 144204 (2013)

    Google Scholar 

  67. L.K. Béland, N. Mousseau, Long-time relaxation of ion-bombarded silicon studied with the kinetic activation-relaxation technique: microscopic description of slow aging in a disordered system. Phys. Rev. B 88 (21), 214201 (2013)

    Google Scholar 

  68. P. Brommer, L.K. Béland, J.-F. Joly, N. Mousseau, Understanding long-time vacancy aggregation in iron: a kinetic activation-relaxation technique study. Phys. Rev. B 90 (13), 134109 (2014)

    Google Scholar 

  69. H. Kallel, N. Mousseau, F. Schiettekatte, Evolution of the potential-energy surface of amorphous silicon. Phys. Rev. letters 105 (4), 045503 (2010)

    Google Scholar 

  70. L. Xu, G. Henkelman, Adaptive kinetic monte carlo for first-principles accelerated dynamics. J. Chem. Phys. 129 (11), 114104 (2008)

    Google Scholar 

  71. C.-Y. Lu, D.E. Makarov, G. Henkelman, Communication: κ-dynamics—an exact method for accelerating rare event classical molecular dynamics. J. Chem. Phys. 133 (20), 201101 (2010)

    Google Scholar 

  72. P. Tiwary, A. van de Walle, Hybrid deterministic and stochastic approach for efficient atomistic simulations at long time scale s. Phys. Rev. B 84, 100301–100304 (2011)

    Article  Google Scholar 

  73. P. Tiwary, A. van de Walle, Accelerated molecular dynamics through stochastic iterations and collective variable based basin identification. Phys. Rev. B 87, 094304–094307 (2013)

    Article  Google Scholar 

  74. A.F. Voter, Parallel replica method for dynamics of infrequent events. Phys. Rev. B 57 (22), R13985 (1998)

    Google Scholar 

  75. G.M. Torrie, J.P. Valleau, Nonphysical sampling distributions in monte carlo free-energy estimation: umbrella sampling. J. Comput. Phys. 23 (2), 187–199 (1977)

    Article  Google Scholar 

  76. D.P. Landau, K. Binder, A Guide to Monte Carlo Simulations in Statistical Physics (Cambridge University Press, Cambridge, 2014)

    Book  Google Scholar 

  77. J.M. Rosenbergl, The weighted histogram analysis method for free-energy calculations on biomolecules. i. the method. J. Comput. Chem. 13 (8), 1011–1021 (1992)

    Google Scholar 

  78. S.H. Northrup, M.R. Pear, C.-Y. Lee, J.A. McCammon, M. Karplus, Dynamical theory of activated processes in globular proteins. Proc. Natl. Acad. Sci. 79 (13), 4035–4039 (1982)

    Article  Google Scholar 

  79. S. Ryu, K. Kang, W. Cai, Entropic effect on the rate of dislocation nucleation. Proc. Natl. Acad. Sci. 108 (13), 5174–5178 (2011)

    Article  Google Scholar 

  80. J.A. Morrone, J. Li, B.J. Berne, Interplay between hydrodynamics and the free energy surface in the assembly of nanoscale hydrophobes. J. Phys. Chem. B 116 (1), 378–389 (2011)

    Article  Google Scholar 

  81. J.E. Straub, B.J. Berne, B. Roux, Spatial dependence of time-dependent friction for pair diffusion in a simple fluid. J. Chem. Phys. 93 (9), 6804–6812 (1990)

    Article  Google Scholar 

  82. G. Hummer, Position-dependent diffusion coefficients and free energies from Bayesian analysis of equilibrium and replica molecular dynamics simulations. New J. Phys. 7 (1), 34 (2005)

    Google Scholar 

  83. S. Keten, C.-C. Chou, A.C. van Duin, M.J. Buehler, Tunable nanomechanics of protein disulfide bonds in redox microenvironments. J. Mech. Behav. Biomed. Mater. 5 (1), 32–40 (2012)

    Article  Google Scholar 

  84. R. Vijayaraj, S. Van Damme, P. Bultinck, V. Subramanian, Molecular dynamics and umbrella sampling study of stabilizing factors in cyclic peptide-based nanotubes. J. Phys. Chem. B 116 (33), 9922–9933 (2012)

    Article  Google Scholar 

  85. J.F. Dama, M. Parrinello, G.A. Voth, Well-tempered metadynamics converges asymptotically. Phys. Rev. Lett. 112 (24), 240602–240605 (2014)

    Article  Google Scholar 

  86. P. Tiwary, M. Parrinello, A time-independent free energy estimator for metadynamics. J. Phys. Chem. B 119 (3), 736–742 (2015). doi:10.1021/jp504920s

    Article  Google Scholar 

  87. P. Tiwary, M. Parrinello, From metadynamics to dynamics. Phys. Rev. Lett. 111, 230602–230606 (2013)

    Article  Google Scholar 

  88. R.B. Best, G. Hummer, Reaction coordinates and rates from transition paths. Proc. Natl. Acad. Sci. U. S. A. 102 (19), 6732–6737 (2005)

    Article  Google Scholar 

  89. M. Salvalaglio, P. Tiwary, M. Parrinello, Assessing the reliability of the dynamics reconstructed from metadynamics. J. Chem. Theory Comput. 10 (4), 1420–1425 (2014)

    Article  Google Scholar 

  90. T. Lelièvre, Two Mathematical Tools to Analyze Metastable Stochastic Processes (Springer, Berlin, 2013), pp. 791–810

    Google Scholar 

  91. G. Gronau, Z. Qin, M.J. Buehler, Effect of sodium chloride on the structure and stability of spider silk’s n-terminal protein domain. Biomater. Sci. 1 (3), 276–284 (2013)

    Article  Google Scholar 

  92. D. Lau, K. Broderick, M.J. Buehler, O. Büyüköztürk, A robust nanoscale experimental quantification of fracture energy in a bilayer material system. Proc. Natl. Acad. Sci. 111 (33), 11990–11995 (2014)

    Article  Google Scholar 

  93. F. Sicard, N. Destainville, M. Manghi, DNA denaturation bubbles: free-energy landscape and nucleation/closure rates. J. Chem. Phys. 142 (3), 034903 (2015)

    Google Scholar 

  94. P. Tiwary, V. Limongelli, M. Salvalaglio, M. Parrinello, Kinetics of protein-ligand unbinding: predicting pathways, rates, and rate-limiting steps. Proc. Natl. Acad. Sci. 112 (5), E386–E391 (2015)

    Article  Google Scholar 

  95. P. Tiwary, J. Mondal, J. Morrone, B. Berne, Understanding the influence of water and steric effects on the kinetics of cavity-ligand unbinding (2015). Proc. Natl. Acad. Sci. 112 (39), 12015–12019 (2015). doi:10.1073/pnas.1516652112

    Article  Google Scholar 

  96. G. Kresse, J. Furthmüller, Software VASP, Vienna (1999). Phys. Rev. B 54 (11), 169 (1996)

    Google Scholar 

  97. B.P. Uberuaga, A.F. Voter, K.K. Sieber, D.S. Sholl, Mechanisms and rates of interstitial h 2 diffusion in crystalline c 60. Phys. Rev. Lett. 91 (10), 105901 (2003)

    Google Scholar 

  98. O. Kum, B.M. Dickson, S.J. Stuart, B.P. Uberuaga, A.F. Voter, Parallel replica dynamics with a heterogeneous distribution of barriers: application to n-hexadecane pyrolysis. J. Chem. Phys. 121 (20), 9808–9819 (2004)

    Article  Google Scholar 

  99. B.P.Uberuaga, S.M. Valone, M. Baskes, Accelerated dynamics study of vacancy mobility in-plutonium. J. Alloys Compd. 444, 314–319 (2007)

    Google Scholar 

  100. B. Uberuaga, R. Hoagland, A. Voter, S. Valone, Direct transformation of vacancy voids to stacking fault tetrahedra. Phys. Rev. Lett. 99 (13), 135501 (2007)

    Google Scholar 

  101. B.P. Uberuaga, S.J. Stuart, A.F. Voter, Parallel replica dynamics for driven systems: derivation and application to strained nanotubes. Phys. Rev. B 75 (1), 014301 (2007)

    Google Scholar 

  102. Y. Mishin, A. Suzuki, B. Uberuaga, A. Voter, Stick-slip behavior of grain boundaries studied by accelerated molecular dynamics. Phys. Rev. B 75 (22), 224101 (2007)

    Google Scholar 

  103. K. Baker, D. Warner, Extended timescale atomistic modeling of crack tip behavior in aluminum. Model. Simul. Mater. Sci. Eng. 20 (6), 065005 (2012)

    Google Scholar 

  104. T. Dumitrica, Trends in Computational Nanomechanics: Transcending Length and Time Scales, vol. 9 (Springer Science & Business Media, New York, 2010)

    Book  Google Scholar 

  105. T.S. Van Erp, P.G. Bolhuis, Elaborating transition interface sampling methods. J. Comput. Phys. 205 (1), 157–181 (2005)

    Article  Google Scholar 

  106. M. Grünwald, E. Rabani, C. Dellago, Mechanisms of the wurtzite to rocksalt transformation in CdSe nanocrystals. Phys. Rev. lett. 96 (25), 255701 (2006)

    Google Scholar 

  107. M. Gruünwald, C. Dellago, Nucleation and growth in structural transformations of nanocrystals. Nano lett. 9 (5), 2099–2102 (2009)

    Article  Google Scholar 

  108. D. Moroni, P.R. Ten Wolde, P.G. Bolhuis, Interplay between structure and size in a critical crystal nucleus. Phys. Rev. Lett. 94 (23), 235703 (2005)

    Google Scholar 

Download references

Acknowledgements

The authors thank Pablo Piaggi for a careful reading of the manuscript. PT would like to acknowledge numerous discussions and arguments on the subject over the years with Bruce Berne, Michele Parrinello, and Art Voter.

Author information

Authors and Affiliations

  1. Department of Chemistry, Columbia University, New York, NY, USA

    Pratyush Tiwary

  2. School of Engineering, Brown University, Providence, RI, USA

    Axel van de Walle

Authors
  1. Pratyush Tiwary
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Axel van de Walle
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Pratyush Tiwary .

Editor information

Editors and Affiliations

  1. Drexel University, Philadelphia, Pennsylvania, USA

    Christopher R. Weinberger

  2. Drexel University, Philadelphia, Pennsylvania, USA

    Garritt J. Tucker

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Tiwary, P., van de Walle, A. (2016). A Review of Enhanced Sampling Approaches for Accelerated Molecular Dynamics. In: Weinberger, C., Tucker, G. (eds) Multiscale Materials Modeling for Nanomechanics. Springer Series in Materials Science, vol 245. Springer, Cham. https://doi.org/10.1007/978-3-319-33480-6_6

Download citation

Publish with us

Policies and ethics

Search

Navigation