Skip to main content
Log in

Accelerating rare events and building kinetic Monte Carlo models using temperature programmed molecular dynamics

  • Review
  • Published:
Journal of Materials Research Aims and scope Submit manuscript

Abstract

The temperature programmed molecular dynamics (TPMD) method is a recent addition to the list of rare-event simulation techniques for materials. Study of thermally-activated events that are rare at molecular dynamics (MD) timescales is possible with TPMD by employing a temperature program that raises the temperature in stages to a point where the transitions happen frequently. Analysis of the observed waiting time distribution yields a wealth of information including kinetic mechanisms in the material, their rate constants and Arrhenius parameters. The first part of this review covers the foundations of the TPMD method. Recent applications of TPMD are discussed to highlight its main advantages. These advantages offer the possibility for rapid construction of kinetic Monte Carlo (KMC) models of a chosen accuracy using TPMD. In this regards, the second part focuses on the latest developments on uncertainty measures for KMC models. The third part focuses on current challenges for the TPMD method and ways of resolving them.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

FIG. 1
FIG. 2
FIG. 3
FIG. 4
FIG. 5
FIG. 6
FIG. 7

Similar content being viewed by others

References

  1. A.B. Bortz, M.H. Kalos, and J.L. Lebowitz: A new algorithm for Monte Carlo simulations of Ising spin systems. J. Comput. Phys. 17, 10 (1975).

    Article  Google Scholar 

  2. D.T. Gillespie: Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem. 81, 2340 (1977).

    Article  CAS  Google Scholar 

  3. K.A. Fichthorn and W.H. Weinberg: Theoretical foundations of dynamical Monte Carlo simulations. J. Chem. Phys. 95, 1090 (1991).

    Article  CAS  Google Scholar 

  4. A. Chatterjee and D.G. Vlachos: An overview of spatial microscopic and accelerated kinetic Monte Carlo methods. J. Comput. Mater. Des. 14, 253 (2007).

    Article  Google Scholar 

  5. P. Haldar and A. Chatterjee: Seeking kinetic pathways relevant to the structural evolution of metal nanoparticles. Modell. Simul. Mater. Sci. Eng. 23, 25002 (2015).

    Article  CAS  Google Scholar 

  6. P. Haldar and A. Chatterjee: Connectivity-list based characterization of 3D nanoporous structures formed via selective dissolution. Acta Mater. 127, 379 (2017).

    Article  CAS  Google Scholar 

  7. M. Jaraiz, E. Rubio, P. Castrillo, L. Pelaz, L. Bailon, J. Barbolla, G.H. Gilmer, and C.S. Rafferty: Kinetic Monte Carlo simulations: An accurate bridge between ab initio calculations and standard process experimental data. Mater. Sci. Semicond. Process. 3, 59 (2000).

    Article  CAS  Google Scholar 

  8. G.R. Bowman and V.S. Pande: Protein folded states are kinetic hubs. Proc. Natl. Acad. Sci. U. S. A. 107, 10890 (2009).

    Article  Google Scholar 

  9. K. Reuter, D. Frenkel, and M. Scheffler: The steady state of heterogeneous catalysis, studied by first-principles statistical mechanics. Phys. Rev. Lett. 93, 116105 (2004).

    Article  CAS  Google Scholar 

  10. R. Pornprasertsuk, P. Ramanarayanan, C.B. Musgrave, and F.B. Prinz: Predicting ionic conductivity of solid oxide fuel cell electrolyte from first principles. J. Appl. Phys. 98, 103513 (2005).

    Article  CAS  Google Scholar 

  11. Y.G. Yang, R.A. Johnson, and H.N.G. Wadley: Kinetic Monte Carlo simulation of heterometal epitaxial deposition. Surf. Sci. 499, 141 (2002).

    Article  CAS  Google Scholar 

  12. C.C. Battaile and D.J. Srolovitz: Kinetic Monte Carlo simulation of chemical vapor deposition. Annu. Rev. Mater. Res. 32, 297 (2002).

    Article  CAS  Google Scholar 

  13. V.S. Pande, K. Beauchamp, and G.R. Bowman: Everything you wanted to know about Markov state models but were afraid to ask. Methods 52, 99 (2010).

    Article  CAS  Google Scholar 

  14. E. Clouet, C. Hin, D. Gendt, M. Nastar, and F. Soisson: Kinetic Monte Carlo simulations of precipitation. Adv. Eng. Mater. 8, 1210 (2006).

    Article  CAS  Google Scholar 

  15. A. Bhoutekar, S. Ghosh, S. Bhattacharya, and A. Chatterjee: A new class of enhanced kinetic sampling methods for building Markov state models. J. Chem. Phys. 147, 152702 (2017).

    Article  CAS  Google Scholar 

  16. V.J. Bhute and A. Chatterjee: Accuracy of a Markov state model generated by searching for basin escape pathways. J. Chem. Phys. 138, 84103 (2013).

    Article  CAS  Google Scholar 

  17. V.J. Bhute and A. Chatterjee: Building a kinetic Monte Carlo model with a chosen accuracy. J. Chem. Phys. 138, 244112 (2013).

    Article  CAS  Google Scholar 

  18. M.P. Allen and D.J. Tildesley: Computer Simulation of Liquids (Oxford Science Publications, Oxford, 1989).

    Google Scholar 

  19. D.E. Shaw, K.J. Bowers, E. Chow, M.P. Eastwood, D.J. Ierardi, J.L. Klepeis, J.S. Kuskin, R.H. Larson, K. Lindorff-Larsen, P. Maragakis, M.A. Moraes, R.O. Dror, S. Piana, Y. Shan, B. Towles, J.K. Salmon, J.P. Grossman, K.M. Mackenzie, J.A. Bank, C. Young, M.M. Deneroff, and B. Batson: Proceedings of the Conference on High Performance Computing Networking, Storage Analysis—SC’09 (ACM Press, New York, New York, USA, 2009); p. 1.

    Book  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  22. M.R. Sorenson and A.F. Voter: Temperature-accelerated dynamics for simulation of infrequent events. J. Chem. Phys. 112, 9599 (2000).

    Article  Google Scholar 

  23. A.F. Voter, F. Montalenti, and T.C. Germann: Extending the time scales in atomistic simulation of materials. Annu. Rev. Mater. Res. 32, 321 (2002).

    Article  CAS  Google Scholar 

  24. R. Miron and K.A. Fichthorn: Accelerated molecular dynamics with the bond-boost method. J. Chem. Phys. 119, 6210 (2003).

    Article  CAS  Google Scholar 

  25. L. Xu and G. Henkelman: Adaptive kinetic Monte Carlo for first-principles accelerated dynamics. J. Chem. Phys. 129, 114104 (2008).

    Article  CAS  Google Scholar 

  26. A. Kara, O. Trushin, H. Yildirim, and T.S. Rahman: Off-lattice self-learning kinetic Monte Carlo: Application to 2D cluster diffusion on the fcc(111) surface. J. Phys.: Condens. Matter 21, 84213 (2009).

    Google Scholar 

  27. P.G. Bolhuis, D. Chandler, C. Dellago, and P.L. Geissler: Transition path sampling: Throwing ropes over rough mountain passes, in the dark. Annu. Rev. Phys. Chem. 53, 291 (2002).

    Article  CAS  Google Scholar 

  28. E. Weinan, W. Ren, and E. Vanden-Eijnden: String method for the study of rare events. Phys. Rev. B 66, 52301 (2002).

    Google Scholar 

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

    Article  CAS  Google Scholar 

  30. A.K. Faradjian and R. Elber: Computing time scales from reaction coordinates by milestoning. J. Chem. Phys. 120, 10880 (2004).

    Article  CAS  Google Scholar 

  31. L.K. Béland, P. Brommer, F. El-Mellouhi, J-F. Joly, and N. Mousseau: Kinetic activation-relaxation technique. Phys. Rev. E 84, 46704 (2011).

    Article  CAS  Google Scholar 

  32. A.F. Voter: Classically exact overlayer dynamics: Diffusion of rhodium clusters on Rh(100). Phys. Rev. B 34, 6819 (1986).

    Article  CAS  Google Scholar 

  33. S. Divi and A. Chatterjee: Accelerating rare events while overcoming the low-barrier problem using a temperature program. J. Chem. Phys. 140, 184115 (2014).

    Article  CAS  Google Scholar 

  34. V. Imandi and A. Chatterjee: Estimating Arrhenius parameters using temperature programmed molecular dynamics. J. Chem. Phys. 145, 34104 (2016).

    Article  CAS  Google Scholar 

  35. D.J. Wales: Energy landscapes: Calculating pathways and rates. Int. Rev. Phys. Chem. 25, 237 (2006).

    Article  CAS  Google Scholar 

  36. A. Chatterjee and S. Bhattacharya: Uncertainty in a Markov state model with missing states and rates: Application to a room temperature kinetic model obtained using high temperature molecular. J. Chem. Phys. 143, 114109 (2015).

    Article  CAS  Google Scholar 

  37. S. Ghosh, A. Chatterjee, and S. Bhattacharya: Time-dependent markov state models for single molecule force spectroscopy. J. Chem. Theory Comput. 13, 957 (2017).

    Article  CAS  Google Scholar 

  38. A. Chatterjee and S. Bhattacharya: Probing the energy landscape of alanine dipeptide and decalanine using temperature as a tunable parameter in molecular dynamics. J. Phys.: Conf. Ser. 759, 12024 (2016).

    Google Scholar 

  39. P. Haldar and A. Chatterjee: Nudged-elastic band study of lithium diffusion in bulk silicon in the presence of strain. Energy Procedia 54, 310 (2014).

    Article  CAS  Google Scholar 

  40. M. Jaipal and A. Chatterjee: Relative occurrence of oxygen-vacancy pairs in yttrium-containing environments of Y2O3-doped ZrO2 can be crucial to ionic conductivity. J. Phys. Chem. C 121, 14534 (2017).

    Article  CAS  Google Scholar 

  41. D. Konwar, V.J. Bhute, and A. Chatterjee: An off-lattice, self-learning kinetic Monte Carlo method using local environments. J. Chem. Phys. 135, 174103 (2011).

    Article  CAS  Google Scholar 

  42. A. Chatterjee and A.F. Voter: Accurate acceleration of kinetic Monte Carlo simulations through the modification of rate constants. J. Chem. Phys. 132, 194101 (2010).

    Article  CAS  Google Scholar 

  43. N.G. Van Kampen: Stochastic Processes in Physics and Chemistry (North-Holland Personal Library, Amsterdam, the Netherlands, 2007).

    Google Scholar 

  44. G. Deng and L.W. Cahill: 1993 IEEE Conference Rec. Nuclear Science Symposium and Medical Imaging Conference (IEEE, San Francisco, California, 1993); pp. 1615–1619.

    Book  Google Scholar 

  45. A.J. Bard and L.R. Faulkner: Electrochemical Methods: Fundamentals and Applications (Wiley, New York, 1980).

    Google Scholar 

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

    Article  CAS  Google Scholar 

  47. S. Verma, T. Rehman, and A. Chatterjee: A cluster expansion model for rate constants of surface diffusion processes on Ag, Al, Cu, Ni, Pd, and Pt (100) surfaces. Surf. Sci. 613, 114 (2013).

    Article  CAS  Google Scholar 

  48. T. Rehman, M. Jaipal, and A. Chatterjee: A cluster expansion model for predicting the activation barrier of atomic processes. J. Comp. Physiol. 243, 244 (2013).

    Article  CAS  Google Scholar 

Download references

ACKNOWLEDGMENTS

The author acknowledges support from Science and Engineering Research Board, Department of Science and Technology Grant No. SB/S3/CE/022/2014 and Indian National Science Academy Grant No. SP/YSP/120/2015/307.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Abhijit Chatterjee.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chatterjee, A. Accelerating rare events and building kinetic Monte Carlo models using temperature programmed molecular dynamics. Journal of Materials Research 33, 835–846 (2018). https://doi.org/10.1557/jmr.2017.460

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1557/jmr.2017.460

Navigation