Hamiltonian and alias-free hybrid particle–field molecular dynamics

Hybrid particle–field molecular dynamics combines standard molecular potentials with density-field models into a computationally efficient methodology that is well-adapted for the study of mesoscale soft matter systems. Here, we introduce a new formulation based on filtered densities and a particle–mesh formalism that allows for Hamiltonian dynamics and alias-free force computation. This is achieved by introducing a length scale for the particle–field interactions independent of the numerical grid used to represent the density fields, enabling systematic convergence of the forces upon grid refinement. Our scheme generalizes the original particle–field molecular dynamics implementations presented in the literature, finding them as limit conditions. The accuracy of this new formulation is benchmarked by considering simple monoatomic systems described by the standard hybrid particle–field potentials. We find that by controlling the time step and grid size, conservation of energy and momenta, as well as disappearance of alias, is obtained. Increasing the particle–field interaction length scale permits the use of larger time steps and coarser grids. This promotes the use of multiple time step strategies over the quasi-instantaneous approximation, which is found to not conserve energy and momenta equally well. Finally, our investigations of the structural and dynamic properties of simple monoatomic systems show a consistent behavior between the present formulation and Gaussian core models.