On coarse projective integration for atomic deposition in amorphous systems

Direct molecular dynamics simulation of atomic deposition under realistic conditions is notoriously challenging because of the wide range of time scales that must be captured. Numerous simulation approaches have been proposed to address the problem, often requiring a compromise between model fidelity, algorithmic complexity, and computational efficiency. Coarse projective integration, an example application of the "equation-free" framework, offers an attractive balance between these constraints. Here, periodically applied, short atomistic simulations are employed to compute time derivatives of slowly evolving coarse variables that are then used to numerically integrate differential equations over relatively large time intervals. A key obstacle to the application of this technique in realistic settings is the "lifting" operation in which a valid atomistic configuration is recreated from knowledge of the coarse variables. Using Ge deposition on amorphous SiO₂ substrates as an example application, we present a scheme for lifting realistic atomistic configurations comprised of collections of Ge islands on amorphous SiO₂ using only a few measures of the island size distribution. The approach is shown to provide accurate initial configurations to restart molecular dynamics simulations at arbitrary points in time, enabling the application of coarse projective integration for this morphologically complex system