Local Refinements in Classical Molecular Dynamics Simulations

Quantum mechanics provide a detailed description of the physical and chemical behavior of molecules. However, with increasing size of the system the complexity rises exponentially, which is prohibitive for efficient dynamical simulation. In contrast, classical molecular dynamics procure a coarser description by using less degrees of freedom. Thus, it seems natural to seek for an adequate trade-off between accurateness and computational feasibility in the simulation of molecules. Here, we propose a novel method, which combines classical molecular simulations with quantum mechanics for molecular systems. For this we decompose the state space of the respective molecule into subsets, by employing a meshfree partition of unity. We show, that this partition allows us to localize an empirical force field and to run locally constrained classical trajectories. Within each subset, we compute the energy on the quantum level for a fixed number of spatial states (ab initio points). With these energy values from the ab initio points we have a local scattered data problem, which can be solved by the moving least squares method.