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Methods for Extending the Time of Molecular Dynamics Simulations of Diffusive Events in Materials

Arthur F. Voter and Mads R. Sørensen

Theoretical Division, Los Alamos National Laboratory

Obtaining a good atomistic description of diffusion dynamics in materials remains a daunting task due to the time-scale limitations of the molecular dynamics (MD) method. For some processes of interest, a direct transition state theory approach suffices to circumvent this problem. One identifies the saddle point for the event and then computes directly the rate constant for the process, without ever running a dynamical simulation. However, in many realistic systems (surface diffusion during film growth, vacancy diffusion near a dislocation core,...), this approach fails because the microscopic events are so complicated they cannot be predicted in advance.

I discuss and compare three new methods, derived from transition state theory, for accelerating moleular dynamics simulations of these infrequent-event processes. The theme these methods have in common is that they operate without any advanced knowledge of the reaction paths available to the system. Two of these methods (hyperdynamics [1,2] and parallel replica dynamics [3]) have been presented recently, and are briefly reviewed. The third, temperature-extrapolated dynamics [5,6], is presented for the first time.

In the hyperdynamics method [1,2], the potential energy of the system is modified with a bias potential that raises the energy within each basin, so that the trajectory spends less time near the minimum and finds an escape path sooner. The accelerated simulation time, which becomes a statistical property of the system, is estimated as the trajectory proceeds. At each integration step, the time advances by the integrator time step (e.g., 2.d-15 s)) multiplied by the inverse Boltzmann factor for the instantaneous strength of the bias potential. Simulation times in the microseconds have been achieved for surface and bulk diffusion in metallic systems using embedded atom interatomic potentials.

In the parallel replica method [3], the power of parallel processing is applied to extend the MD simulation time. This is in contrast to the usual parallel MD algorithms, which extend the length scale. A replica of the entire system is placed on each processor. After assigning momenta independently on each processor, independent trajectories are evolved. When a transition occurs on any processor, all trajectories are interrupted, and the accumulated times are summed. The procedure is then repeated starting in the new state. This gives the exact dynamical evolution of the system from state to state [3]. Moreover, this approach can be combined with hyperdynamics to achieve a multiplicative boost [4].

In the temperature-extrapolated dynamics [5,6], the system temperature is raised to stimulate more rapid escape out of each potential basin, but attempted transitions are filtered to allow only those that would have occurred at the normal temperature. By detecting attempted escapes and reflecting the trajectory back into the current potential basin, a set of high-temperature attempted-first-escape times is collected. After finding the saddle point for each event (but not the preexponetial), an extrapolation procedure gives the exact time the escape would have occurred at low temperature. Assuming that all preexponentials in the system are greater than a certain value allows a determination of when the high temperature trajectory can be terminated. The event with the shortest low-temperature time is then selected, the system is moved to the new state, and the procedure begins again. This method gives boost factors not unlike those observed for hyperdynamics, and the method can be combined with parallel replica dynamics. Extensions of the basic procedure improve the performance when the system is dominated by low barriers [6]. Preliminary results will be presented for surface diffusion processes.

References:

[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] "Accelerating the Dynamics of Infrequent Events: Combining Hyperdynamics and Parallel Replica Dynamics to Treat Epitaxial Layer Growth," A.F. Voter and T.C. Germann, Mat. Res. Soc. Symp. Proc. 528, 221 (1998).

[5] "Methods for Accelerating Atomistic Simulations of Defect Dynamics" A.F. Voter and M. R. Sørensen, 1998 MRS Fall Meeting Symposium Proceedings, Symposium J: Multiscale Modeling of Materials.

[6] M. R. Sørensen and A.F. Voter (to be published).


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