(321k) Coarse-Graining and Soft Matter Systems: Bridging the Atomistic-Meso Scales

With atomistic simulations alone it is not yet possible to
access the wide range of length and time scales needed to understand soft matter
systems (e.g. colloidal and micellar solutions,
solutions of proteins, polymers, etc.). 
A current challenge is to coarse grain such systems by developing
definitions of effective potentials that can be determined in atomistic
simulations (e.g. molecular dynamics), and then used in meso-scale simulations which can access these long time and
length scales.  A variety of
methods, ranging from the use of purely empirical ad hoc potentials, to use of effective
potentials that rigorously match the partition function, have been
proposed.  In this work we test
three of the most promising of these approaches against simulation data for
Lennard-Jones binary mixtures for molecules A (solute)
and B (solvent) having a range of size ratios, σ_AA/σ_BB.  The smaller component,B, is fully
coarse-grained out, creating an implicit solvent for the larger component,
A.  In the limit of infinite
dilution of the larger component, the effective one-component potential is rigorously equivalent to the 2-body
potential of mean force.  However,
at higher concentrations of A this is no longer the
case.  We use atomistic molecular
dynamics to determine effective potentials for A by three routes.  The first is the well known iterative
Boltzmann route proposed by Soper [1].  This
method involves iteratively fitting an effective 2-body potential by requiring
that the AA radial distribution function in the coarse grained system matches
that in the fully atomistic system. The second method is based upon the
force-matching approach first proposed by Ercolessi
and Adams [2] for fitting atomistic force fields from ab initio data and later
reformulated for atomistic to meso-scale
coarse-graining by Izvekov et al. [3].  The force matching method directly gives
an effective 2-body potential from atomistic molecular dynamics trajectories
without iteration.  In the third
method an effective potential is defined by matching the partition function in
the coarse grained system to that in the fully atomistic system.  This is the most desirable method, since
if the partition functions are matched the coarse grained system should give all
of the equilibrium properties correctly. 
However, this method is computationally demanding, and the effective
potential has the form of a sum of 0-body, 1-body, 2-body, etc. terms, and so is
only tractable if this series converges rapidly.  A comparison of the accuracy and
computational expense of all three methods will be discussed.    

[1] 
Soper, A.K, Chem. Phys., 202, 295(1996).

[2] 
Ercolessi, F. and J.B. Adams., Europhys. Lett., 26, 583 (1994).

[3] 
Izvekov, S., Parrinello, M., Burnham, C.J., and G.A. Voth, J. Chem.
Phys., 120, 10896
(2004).