Grand-Canonical Adaptive Resolution Centroid Molecular Dynamics: Implementation and application

We have implemented the Centroid Molecular Dynamics scheme (CMD) into the Grand Canonical-like version of the Adaptive Resolution SimulationMolecular Dynamics (GC-AdResS) method. We have tested the implementation on twodifferent systems, liquid parahydrogen at extreme thermodynamic conditions and liquid water at ambient conditions; the reproduction of structural as well as dynamical results of reference systems are highly satisfactory. The capability of performing GC-AdResS CMD simulations allows for the treatment of a system characterized by some quantum features and open boundaries. This latter characteristic not only is of computational convenience, allowing for equivalent results of much larger and computationally more expensive systems, but also suggests a tool of analysis so far not explored, that is the unambiguous identification of the essential degrees of freedom required for a given