Energy Conservation in Adaptive Hybrid Atomistic/Coarse-Grain Molecular Dynamics.

Multiscale computer simulation algorithms are required to describe complex molecular systems with events occurring over a range of time and length scales. True multiscale simulations must solve the interface, or hand-shaking, problem of coupling together different levels of description in different spatial regions of the system. If the spatial regions of different resolution move over time, or if material is allowed to flow over the inter-region boundaries, a mechanism must be introduced into the multiscale algorithm to allow material to dynamically change its representation. While such a mechanism is highly desirable in many instances, it is fraught with technical difficulties. Here, we present a molecular dynamics simulation algorithm which is multiscale in both time and space. We supplement the potential and kinetic energy expressions with auxiliary terms in order to recover the total energy as a conserved quantity, even when the total number of degrees of freedom changes during the simulation. This is crucial for a proper assessment of the quality of adaptive hybrid algorithms, and in particular, it allows us to tune the hierarchy of RESPA levels to optimize the integration scheme.