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We present a systematic coarse-graining (CG) strategy for many particlemolecular systems based on cluster expansion techniques. We construct ahierarchy of coarse-grained Hamiltonians with interaction potentials consistingof two, three and higher body interactions. The accuracy of the derived clusterexpansion based on interatomic potentials is examined over a range of varioustemperatures and densities and compared to direct computation of pair potentialof mean force. The comparison of the coarse-grained simulations is done on thebasis of the structural properties, against the detailed all-atom data. We givespecific examples for methane and ethane molecules in which the coarse-grainedvariable is the center of mass of the molecule. We investigate differenttemperature and density regimes, and we examine differences between the methaneand ethane systems. Results show that the cluster expansion formalism can beused in order to provide accurate effective pair and three-body CG potentialsat high $T$ and low $\rho$ regimes. In the liquid regime the three-bodyeffective CG potentials give a small improvement, over the typical pair CGones; however in order to get significantly better results one needs toconsider even higher order terms.

Parameterization of Coarse-grained Molecular Interactions through Potential of Mean Force Calculations and Cluster Expansions Techniques