An empirical formulation of accelerated molecular dynamics for simulating and predicting microstructure evolution in materials

Despite its widespread use in materials science, conventional molecular dynamics (MD) simulations are severely constrained by timescale limitations. To address this shortcoming, we propose an empirical formulation of accelerated MD method, adapted from a collective-variable-based extended system dynamics framework. While this framework is originally developed for efficient free energy sampling and reaction pathway determination of specific rare events in condensed matter, we have modified it to enable accelerated MD simulation and prediction of microstructure evolution of materials across a broad range of scenarios. In essence, the nearest neighbor off-centering absolute displacement (NNOAD), which quantifies the deviation of an atom from the geometric center of its nearest neighbors in materials, is introduced. We propose that the collection of NNOADs of all atoms can serve as a generalized reaction coordinate for various structural transitions in materials. The NNOAD of each atom, represented by its three components, is coupled with three additional dynamic variables assigned to the atom. Time evolution of the additional dynamic variables follows Langevin equation, while Nos\'e-Hoover dynamics is employed to thermostat the system. Through careful analysis and benchmark simulations, we established appropriate parameter ranges for the equations in our method. Application of this method to several test cases demonstrates its capability to accelerate MD simulations by several orders of magnitude while maintaining kinetic consistency and good accuracy in predicting long timescale microstructure evolutions of materials. We also provide some preliminary thoughts on theoretical justification of the method, offering insights into its underlying principles.