c, J. Peräjoki, R. Nieminen
Laboratory of Physics, Helsinki University of Technology, P.O. Box 1100, FIN-02015, Finland
G. Jungnickel, T. Frauenheim
Universität/Gesamthochschule Paderborn, 33095 Paderborn, Germany
We present a technique for the structural optimization of atom models to study long time relaxation processes involving different time scales. The method takes advantage of the benefits of both the kinetic Monte-Carlo (KMC) and the molecular dynamics (MD) simulation techniques. In contrast to ordinary KMC, our method allows for an estimation of a true lower limit for the time scale of a relaxation process. The scheme is fairly general in that neither the typical pathways nor the typical metastable states need to be known prior to the simulation. It is independent of the lattice type and the potential which describes the atomic interactions. It is adopted to study systems with structural and/or chemical inhomogeneity which makes it particularly useful for studying growth and diffusion processes in a variety of physical systems, including crystalline bulk, amorphous systems, surfaces with adsorbates, fluids, and interfaces.
The technique attempts to sample the realistic distribution of escape rates from local minima of the model potential for all atoms of interest. We apply our projected conjugate gradient method  to efficiently scan the neighborhood of a given atom for its closeby barriers which determine the escape rates according to transition state theory. The total structure evolves by drawing most likely transition pathways. The distribution of escape rates is simultaneously updated. The largest benefit of the scheme comes from the fact that the escape rates are directly related to a true time scale. Relaxation times associated with atomic movements over larger barriers are not accessible by ordinary molecular dynamics (MD) especially when working with sophisticated model potentials. The ability to extract the true time scale of relaxation events considered allows to access rare and slow events in ordinary MD programs.
A preprint describing the method in more detail can be found at the APS E-print server under:
We demonstrate the method for the very simple case of hydrogen diffusion in a diamond lattice which takes place on a timescale of ms. We find the possible metastable states for H in diamond to be the bond-centered, the tetrahedral and a distorted tetrahedral position. We present diffusion paths for H in diamond and energy barriers for the different pathways. Finally, we give an estimate for the diffusion constant for H inside diamond.
 M. Kaukonen, P. Sitch, G. Jungnickel, R. Nieminen, S. Pöykkö, D. Porezag, T. Frauenheim: Phys. Rev. B 57 (1998) 9965.