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

journal contribution

posted on 2018-02-27, 00:00 authored by Patrick G. Lafond, Sergei IzvekovCoarse-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.