Multiscale Coarse-Graining with Effective Polarizabilities: A Fully Bottom-Up Approach

Coarse-grain (CG) models offer a way to estimate the behavior of larger systems, for longer times than possible in fine-grain calculations by eliminating fine detail. For most atomistic models this often involves eliminating electrostatic interactions, yet, in many calculations, the dielectric properties of a material may be too important to ignore. In this work, we expand upon a previous CG representation which preserves the instantaneous center of mass (CoM), charge, and dipole of clusters of atoms by representing them with charged dimers. We then derive a formal mapping of the microscopic coordinates onto the CG representation allowing for a fully bottom-up construction of the CG force field that statistically matches the CoM, and first two terms of the multipole expansion. In the method presented here, unlike any previous bottom-up mappings, the atomistic particles are fractionally mapped to both sites in the dimer representation. Despite this difference, we show that the corresponding coordinate transformation augmented with a dipole moment mapping can be constructed as a canonical transformation and hence can derive correct ensemble statistics in the associated force mapping. The method is tested on nitromethane at a submolecular resolution, where the nitro group is represented through a charged dimer while the methyl group is a standard CoM projection, next we test a lower resolution of nitromethane where the entire molecule is represented as a single dimer. At the high resolution we showed the method can be mixed with standard CoM projections, and give rise to intramolecular interactions. After nitromethane, we test the method at a supramolecular level using an aggressive scheme of 10 water molecules to one CG dimer. We find in all cases the CoM–CoM radial distribution functions are well matched, and the dipole distributions are matched. For the submolecular nitromethane we find the model is transferable to simulations with external fields, and with the single-dimer nitromethane, we see the dipole–dipole correlation function is matched, but we find the frequency dependent dielectric constant significantly deviates indicating enhanced kinetics as commonly seen in CG molecular dynamics. Lastly, for water we see some discrepancy in the dipole–dipole correlation function that stems from the pairwise decomposition of forces rather than the mapping method presented here.