On the equivalence of the hybrid particle-field and Gaussian core models

TL;DR

This paper demonstrates that hybrid particle-field molecular dynamics can accurately replicate the Gaussian Core model's properties, establishing a formal equivalence and exploring the effects of grid spacing and filtering scales.

Contribution

It generalizes the connection between hybrid particle-field methods and pair potentials, showing their equivalence to the Gaussian Core model under certain conditions.

Findings

Hybrid particle-field methods can recover Gaussian Core model properties.

The mean-field regime depends on system specifics, not the model itself.

Structural and dynamical properties are preserved across methods.

Abstract

Hybrid particle-field molecular dynamics is a molecular simulation strategy wherein particles couple to a density field instead of through ordinary pair potentials. Traditionally considered a mean-field theory, a momentum and energy-conserving hybrid particle-field formalism has recently been introduced, which was demonstrated to approach the Gaussian Core model potential in the grid-converged limit. Here, we expand on and generalize the correspondence between the Hamiltonian hybrid particle-field method and particle-particle pair potentials. Using the spectral procedure suggested by Bore and Cascella, we establish compatibility to any local soft pair potential in the limit of infinitesimal grid spacing. Furthermore, we document how the mean-field regime often observed in hybrid particle-field simulations is due to the systems under consideration, and not an inherent property of the model. Considering the Gaussian filter form in particular, we demonstrate the ability of the Hamiltonian hybrid particle-field model of recovering all structural and dynamical properties of the Gaussian Core model, including solid phases, a first-order phase transition, and anomalous transport properties. We quantify the impact of the grid spacing on the correspondence, as well as the effect of the particle-field filtering length scale on the emergent particle-particle correlations.