Danny Perez

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.

A mathematical formalization of the parallel replica dynamics

Abstract. We propose a mathematical analysis of a well-known numerical approach used in molecular dynamics to efficiently sample a coarse-grained description of the original trajectory (in terms of state-to-state dynamics). This technique is called parallel replica dynamics and has been introduced by Arthur F. Voter. The principle is to introduce many replicas of the original dynamics, and to consider the first transition event observed among all the replicas. The effective physical time is obtained by summing up all the times elapsed for all replicas. Using a parallel implementation, a speed-up of the order of the number of replicas can thus be obtained, allowing longer time scales to be computed. By drawing connections with the theory of Markov processes and, in particular, exploiting the notion of quasi-stationary distribution, we provide a mathematical setting appropriate for assessing theoretically the performance of the approach, and possibly improving it.

Diffusion and transformation kinetics of small helium clusters in bulk tungsten

The production of energy through nuclear fusion poses serious challenges related to the stability and performance of materials in extreme conditions. In particular, the constant bombardment of the walls of the reactor with high doses of He ions is known to lead to deleterous changes in their microstructures. These changes follow from the aggregation of He into bubbles that can grow and blister, potentially leading to the contamination of the plasma, or to the degradation of their mechanical properties. We computationally study the behavior of small clusters of He atoms in W in conditions relevant to fusion energy production. Using a wide range of techniques, we investigate the thermodynamics of the clusters and their kinetics in terms of diffusivity, growth, and breakup, as well as mutation into nano-bubbles. Our study provides the essential ingredients to model the early stages of He exposure leading up to the nucleation of He bubbles.

Molecular Dynamics in the Multicanonical Ensemble: Equivalence of Wang-Landau Sampling, Statistical Temperature Molecular Dynamics, and Metadynamics.

We show a direct formal relationship between the Wang-Landau iteration [PRL 86, 2050 (2001)], metadynamics [PNAS 99, 12562 (2002)], and statistical temperature molecular dynamics (STMD) [PRL 97, 050601 (2006)] that are the major work-horses for sampling from generalized ensembles. We demonstrate that STMD, itself derived from the Wang-Landau method, can be made indistinguishable from metadynamics. We also show that Gaussian kernels significantly improve the performance of STMD, highlighting the practical benefits of this improved formal understanding.

Ablation of molecular solids under nanosecond laser pulses: The role of inertial confinement

The thermal routes to ablation in molecular solids having a long (micron scale) optical penetration depth are investigated under nanosecond laser pulses using a two-dimensional molecular-dynamics model. The authors demonstrate that the mechanisms of matter removal are mainly determined by the local degree of inertial confinement; by increasing level of confinement, these are (trivial) fragmentation, phase explosion, and heterogeneous nucleation of vapor bubbles at solid-liquid boundaries. The thermodynamic pathways to ablation are shown to be different from those predicted by the model of Miotello and Kelly [Appl. Phys. Lett. 67, 3535 (1995); Appl. Phys. A: Mater. Sci. Process. 69, S67 (1999)].

Long-time dynamics through parallel trajectory splicing

Simulating the atomistic evolution of materials over long time scales is a longstanding challenge, especially for complex systems where the distribution of barrier heights is very heterogeneous. Such systems are difficult to investigate using conventional long-time scale techniques, and the fact that they tend to remain trapped in small regions of configuration space for extended periods of time strongly limits the physical insights gained from short simulations. We introduce a novel simulation technique, Parallel Trajectory Splicing (ParSplice), that aims at addressing this problem through the timewise parallelization of long trajectories. The computational efficiency of ParSplice stems from a speculation strategy whereby predictions of the future evolution of the system are leveraged to increase the amount of work that can be concurrently performed at any one time, hence improving the scalability of the method. ParSplice is also able to accurately account for, and potentially reuse, a substantial fraction of the computational work invested in the simulation. We validate the method on a simple Ag surface system and demonstrate substantial increases in efficiency compared to previous methods. We then demonstrate the power of ParSplice through the study of topology changes in Ag42Cu13 core-shell nanoparticles.

Coupled motion of grain boundaries in bcc tungsten as a possible radiation-damage healing mechanism under fusion reactor conditions

As a potential first-wall fusion reactor material, tungsten will be subjected to high radiation flux and extreme mechanical stress. We propose that under these conditions, coupled grain boundary (GB) motion, in some cases enhanced by interstitial loading, can lead to a radiation-damage healing mechanism, in which a large stress activates coupled GB motion, and the GB sweeps up the defects, such as voids and vacancies, as it passes through the material. The stress-induced mobility characteristics of a number of GBs in tungsten are examined to investigate the likelihood of this scenario.

Thermal activation in atomic friction: revisiting the theoretical analysis.

The effect of thermal activation on atomic-scale friction is often described in the framework of the Prandtl-Tomlinson model. Accurate use of this model relies on parameters that describe the shape of the corrugation potential β and the transition attempt frequency f(0). We show that the commonly used form of β for a sinusoidal corrugation potential can lead to underestimation of friction, and that the attempt frequency is not, as is usually assumed, a constant value, but rather varies as the energy landscape evolves. We partially resolve these issues by demonstrating that numerical results can be captured by a model with a fitted β and using harmonic transition state theory to develop a variable form of the attempt frequency. We incorporate these developments into a more accurate and generally applicable expression relating friction to temperature and velocity. Finally, by using a master equation approach, we verify the improved analytical model is accurate in its expected regime of validity.

Influence of point defects on grain boundary mobility in bcc tungsten.

Atomistic computer simulations were performed to study the influence of radiation-induced damage on grain boundary (GB) sliding processes in bcc tungsten (W), the divertor material in the ITER tokamak and the leading candidate for the first wall material in future fusion reactors. In particular, we calculated the average sliding-friction force as a function of the number of point defects introduced into the GB for a number of symmetric tilt GBs. In all cases the average sliding-friction force at fixed shear strain rate depends on the number of point defects introduced into the GB, and in many cases introduction of these defects reduces the average sliding-friction force by roughly an order of magnitude. We have also observed that as the number of interstitials in the GB is varied, the direction of the coupled GB motion sometimes reverses, causing the GB to migrate in the opposite direction under the same applied shear stress. This could be important in the microstructural evolution of polycrystalline W under the harsh radiation environment in a fusion reactor, in which high internal stresses are present and frequent collision cascades generate interstitials and vacancies.

The Modern Temperature-Accelerated Dynamics Approach

Accelerated molecular dynamics (AMD) is a class of MD-based methods used to simulate atomistic systems in which the metastable state-to-state evolution is slow compared with thermal vibrations. Temperature-accelerated dynamics (TAD) is a particularly efficient AMD procedure in which the predicted evolution is hastened by elevating the temperature of the system and then recovering the correct state-to-state dynamics at the temperature of interest. TAD has been used to study various materials applications, often revealing surprising behavior beyond the reach of direct MD. This success has inspired several algorithmic performance enhancements, as well as the analysis of its mathematical framework. Recently, these enhancements have leveraged parallel programming techniques to enhance both the spatial and temporal scaling of the traditional approach. We review the ongoing evolution of the modern TAD method and introduce the latest development: speculatively parallel TAD.