Solving the equations of motion for mixed atomistic and coarse-grained systems

A mixed-resolution molecular dynamics technique is presented that permits simulation of large and complex systems that critically depend on a subtle interplay between energy and entropy and, therefore, require both an accurate energy evaluation and an extensive sampling of a large and complex phase space. The computational approach is based upon the idea that many complex systems can be spatially divided into a relatively small active zone (that requires an accurate energy evaluation but, due to its relatively small size, only a limited sampling of phase space) and a relatively large inactive zone (that requires a less accurate energy description but the sampling of a very large phase space). Mixed-resolution models that use an accurate atomistic model for the active zone and an efficient coarse-grained model (that lumps groups of atoms into pseudo-atoms) for the inactive zone are ideally suited for these systems. One challenge in mixed-resolution simulations is creating a seamless connection between low-and high-resolution zones that exchange groups of atoms. We derive a mixed-resolution Hamiltonian and present a microcanonical simulation protocol that conserves energy and momentum and allows for a change in resolution of selected groups of atoms during a simulation. The method is applicable to simulations in other ensembles and for systems with multiple high-resolution zones. To illustrate the numerical stability of our technique, we present simulation results for a system of mixed-resolution methane molecules.