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).