Yunsic Shim

Chapter 4 Accelerated Molecular Dynamics Methods: Introduction and Recent Developments

Abstract Because of its unrivaled predictive power, the molecular dynamics (MD) method is widely used in theoretical chemistry, physics, biology, materials science, and engineering. However, due to computational cost, MD simulations can only be used to directly simulate dynamical processes over limited timescales (e.g., nanoseconds or at most a few microseconds), even though the simulation of nonequilibrium processes can often require significantly longer timescales, especially when they involve thermal activation. In this paper, we present an introduction to accelerated molecular dynamics, a class of methods aimed at extending the timescale range of molecular dynamics, sometimes up to seconds or more. The theoretical foundations underpinning the different methods (parallel replica dynamics, hyperdynamics, and temperature-accelerated dynamics) are first discussed. We then discuss some applications and recent advances, including super-state parallel replica dynamics, self-learning hyperdynamics, and spatially parallel temperature-accelerated dynamics.

Hybrid asynchronous algorithm for parallel kinetic Monte Carlo simulations of thin film growth

We have generalized and implemented the hybrid asynchronous algorithm, originally proposed for parallel simulations of the spin-flip Ising model, in order to carry out parallel kinetic Monte Carlo (KMC) simulations. The parallel performance has been tested using a simple model of thin-film growth in both 1D and 2D. We also briefly describe how the data collection must be modified as compared to the case of the spin-flip Ising model in order to carry out rigorous data collection. Due to the presence of a wide range of rates in the simulations, this algorithm turns out to be very inefficient. The poor parallel performance results from three factors: (1) the high probability of selecting a Metropolis Monte Carlo (MMC) move, (2) the low acceptance probability of boundary moves and (3) the high cost of communications which is required before every MMC move. We also find that the parallel efficiency in two dimensions is lower than in one-dimension due to the higher probability of selecting an MMC attempt, suggesting that this algorithm may not be suitable for KMC simulations of two-dimensional thin-film growth.

Adaptive temperature-accelerated dynamics.

We present three adaptive methods for optimizing the high temperature T(high) on-the-fly in temperature-accelerated dynamics (TAD) simulations. In all three methods, the high temperature is adjusted periodically in order to maximize the performance. While in the first two methods the adjustment depends on the number of observed events, the third method depends on the minimum activation barrier observed so far and requires an a priori knowledge of the optimal high temperature T(high)(opt)(E(a)) as a function of the activation barrier E(a) for each accepted event. In order to determine the functional form of T(high)(opt)(E(a)), we have carried out extensive simulations of submonolayer annealing on the (100) surface for a variety of metals (Ag, Cu, Ni, Pd, and Au). While the results for all five metals are different, when they are scaled with the melting temperature T(m), we find that they all lie on a single scaling curve. Similar results have also been obtained for (111) surfaces although in this case the scaling function is slightly different. In order to test the performance of all three methods, we have also carried out adaptive TAD simulations of Ag/Ag(100) annealing and growth at T = 80 K and compared with fixed high-temperature TAD simulations for different values of T(high). We find that the performance of all three adaptive methods is typically as good as or better than that obtained in fixed high-temperature TAD simulations carried out using the effective optimal fixed high temperature. In addition, we find that the final high temperatures obtained in our adaptive TAD simulations are very close to our results for T(high)(opt)(E(a)). The applicability of the adaptive methods to a variety of TAD simulations is also briefly discussed.

Localized saddle-point search and application to temperature-accelerated dynamics.

We present a method for speeding up temperature-accelerated dynamics (TAD) simulations by carrying out a localized saddle-point (LSAD) search. In this method, instead of using the entire system to determine the energy barriers of activated processes, the calculation is localized by only including a small chunk of atoms around the atoms directly involved in the transition. Using this method, we have obtained N-independent scaling for the computational cost of the saddle-point search as a function of system size N. The error arising from localization is analyzed using a variety of model systems, including a variety of activated processes on Ag(100) and Cu(100) surfaces, as well as multiatom moves in Cu radiation damage and metal heteroepitaxial growth. Our results show significantly improved performance of TAD with the LSAD method, for the case of Ag/Ag(100) annealing and Cu/Cu(100) growth, while maintaining a negligibly small error in energy barriers.

Grain growth, anomalous scaling, and grain boundary grooving in polycrystalline CdTe thin films

We examine the evolution of the surface morphology as well as the dynamics of grain growth and grain boundary (GB) grooving in polycrystalline CdTe films sputter deposited on CdS/glass substrates. Anomalous scaling behavior is found with local roughness exponent αloc = 1 and global (local) growth exponent β = 0.36 (βloc = 0.14). In good agreement with the scaling relation, βloc = β − nαloc, we obtain the correlation length exponent n=1/z≃0.23. We also find that the grain size coarsening exponent p and GB groove growth exponent βg are both equal to β, while the grain size distribution is well described by a log-normal distribution. These results suggest that GB grooving is responsible for the enhanced anomalous scaling and a deviation from the theoretical prediction of p = 1/2, along with the observed log-normal grain size distribution.