The molecular dynamics (MD) simulation technique, in which the classical equations of motion are integrated for a system of atoms, is a commonly used tool in chemistry, physics, and materials science. However, for processes occurring on time scales longer than nanoseconds, 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 saddle points can be found. However, the events that occur in real systems are often complicated and cannot be predicted in advance. How to treat these realistic 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 project, we are developing new approaches for treating infrequent events in solids.
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. 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, and without ever finding the saddle points.
In the "parallel replica" method [3], the power of parallel processing is harnessed to extend the MD time scale, rather than the length scale. The algorithm is surprisingly simple, efficiently parallel, and gives rigorously correct dynamical evolution from state to state in an infrequent-event system. Recently, we have demonstrated that the hyperdynamics method can be combined with the parallel replica method to obtain a multiplicative boost in the simulation time [4].
The newest addition to the suite of methods is temperature-accelerated dynamics (TAD) [5,6]. This approach is designed to be easier to implement than hyperdynamics (no bias potential is required) at the cost of one 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.
These methods are described in more detail in the following 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] "Accelerating Atomistic Simulations of Defect Dynamics: Hyperdynamics, Parallel Replica Dynamics, and Temperature-Accelerated Dynamics," A.F. Voter and M.R. Sørensen, Mat. Res. Soc. Symp. Proc., 538, 427 (1999).
[6] "Temperature-Accelerated Dynamics for Simulation of Infrequent Events," M.R. Sørensen and A.F. Voter, submitted for publication, 1999.
There is also a brief description of the hyperdynamics work in PDF format with two figures.
People in T-12 working on this project include: