  We present a systematic coarse-graining (CG) strategy for many particle
molecular systems based on cluster expansion techniques. We construct a
hierarchy of coarse-grained Hamiltonians with interaction potentials consisting
of two, three and higher body interactions. The accuracy of the derived cluster
expansion based on interatomic potentials is examined over a range of various
temperatures and densities and compared to direct computation of pair potential
of mean force. The comparison of the coarse-grained simulations is done on the
basis of the structural properties, against the detailed all-atom data. We give
specific examples for methane and ethane molecules in which the coarse-grained
variable is the center of mass of the molecule. We investigate different
temperature and density regimes, and we examine differences between the methane
and ethane systems. Results show that the cluster expansion formalism can be
used in order to provide accurate effective pair and three-body CG potentials
at high $T$ and low $\rho$ regimes. In the liquid regime the three-body
effective CG potentials give a small improvement, over the typical pair CG
ones; however in order to get significantly better results one needs to
consider even higher order terms.
