The molecular dynamics (MD) simulation technique, in which the classical equations of motion are integrated for a system of atoms, is commonly used in chemistry, physics, and materials science. However, for processes occurring on time scales longer than about one microsecond, direct MD is computationally unfeasible. If the dynamics are characterized by "infrequent events," in which the system makes an occasional transition from one potential basin to another, rate constants can be determined from transition state theory, without ever performing dynamics, provided that the relevant pathways and saddle points can be found. However, the events that occur in real systems are often complicated and cannot be predicted in advance. How to accurately model these systems, where the events are not known in advance and occur on time scales inaccessible to MD, has been a long-standing problem. In this research, we are developing new methods for treating systems like this.

The key concept underpinning the accelerated molecular dynamics methods is, in a phrase, that trajectories are smarter than we are. While previous approaches for reaching long time scales have involved applying physical or chemical intuition to specify the states the system might evolve to, in fact the system often does something unexpected, something outside our intuition. A way around this problem is to simply let the trajectory find the escape path for us. Each of the three accelerated dynamics methods described here is built on this foundation.

For example, in the "hyperdynamics" approach [1,2], one constructs a bias potential that raises the energy within the potential basins. Evolving dynamically on this biased potential surface, the system makes transitions from state to state with the correct relative probabilities, but at an accelerated rate. Time is no longer an independent variable, but is instead estimated statistically as the simulation evolves, ultimately converging on the correct result with vanishing relative error. In simulations on metal systems using embedded-atom interatomic potentials, we have shown the simulation time can be extended into the microsecond range with no advanced knowledge of the transitions the system will make.

In "parallel replica dynamics" (ParRep)[3], the power of parallel computing is harnessed to extend the MD time scale, rather than the length scale. The ParRep algorithm is surprisingly simple, efficiently parallel, and gives rigorously correct dynamical evolution from state to state in an infrequent-event system. It is also extremely general -- any dynamical process with detectible events and exponentially distributed first-escape times from each "state" can be parallelized with this method. A recent mathematical development by Le Bris et al[4] has shown that the ParRep method is even more general than we originally thought.

The temperature-accelerated dynamics (TAD) method [5] is designed to be easier to implement than hyperdynamics (no bias potential is required) at the cost of an additional approximation: harmonic transition state theory. By evolving the system at high temperature, transitions occur more rapidly, but not necessarily in the correct order. The TAD procedure filters out all the incorrect events, retaining the correct transitions and their transition times at the desired temperature.

To learn more about these methods, see one of our review articles, [6] , [7], [8] , or [9], or one of the links on the main page.

[1] "A Method for Accelerating the Molecular Dynamics Simulation of Infrequent Events," A.F. Voter, J. Chem. Phys. 106, 4665 (1997).

[2] "Hyperdynamics: Accelerated Molecular Dynamics of Infrequent Events," A.F. Voter, Phys. Rev. Lett., 78, 3908 (1997).

[3] "Parallel Replica Method for Dynamics of Infrequent Events," A.F. Voter, Phys. Rev. B, 57, 13985 (1998).

[4] "A mathematical formalization of the parallel replica dynamics," C. Le Bris, T. Lelievre, M. Luskin, D. Perez, Monte Carlo Methods and Applications, 18, 119 (2012).

[5] "Temperature-Accelerated Dynamics for Simulation of Infrequent Events," M.R. Sørensen and A.F. Voter, J. Chem. Phys. 112 9599 (2000).

[6] "Extending the Time Scale in Atomistic Simulation of Materials," A.F. Voter, F. Montalenti and T.C. Germann, Annu. Rev. Mater. Res., 32, 321 (2002). PDF file

[7] "Accelerated Molecular Dynamics Methods," B.P. Uberuaga and A.F. Voter, in Radiation Effects in Solids, edited by K.E. Sickafus, E.A. Kotomin and B.P. Uberuaga (Springer, NATO Publishing Unit, Dordrecht, The Netherlands, 2006) pp. 25-43.

[8] "Accelerated Molecular Dynamics Methods: Introduction and Recent Developments," D. Perez, B.P. Uberuaga, Y. Shim, J.G. Amar, and A.F. Voter, Annual Reports in Comp. Chem. 5, 79 (2009).

[9] "The Parallel Replica Dynamics Method - Coming of Age," D. Perez, B.P. Uberuaga, and A.F. Voter, Comp. Mater. Sci. 100, 90 (2015).

This work is primarily supported by DOE/BES (Department of Energy/Office of Science/Office of Basic Energy Sciences/Materials Sciences and Engineering Division), by the Los Alamos Laboratory Directed Research and Development program, by DOE/ASCR and by DOE/SciDAC.

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