From classical to quantum and back: Hamiltonian coupling of classical and Path Integral models of atoms

In computer simulations, quantum delocalization of atomic nuclei can be modeled making use of the Path Integral (PI) formulation of quantum statistical mechanics. This approach, however, comes with a large computational cost. By restricting the PI modeling to a small region of space, this cost can be significantly reduced. In the present work we derive a Hamiltonian formulation for a bottom-up, theoretically solid simulation protocol that allows molecules to change their resolution from quantum-mechanical to classical and vice versa on the fly, while freely diffusing across the system. This approach renders possible simulations of quantum systems at constant chemical potential. The validity of the proposed scheme is demonstrated by means of simulations of low temperature parahydrogen. Potential future applications include simulations of biomolecules, membranes, and interfaces.