Parameterization of coarse-grained molecular interactions through potential of mean force calculations and cluster expansion techniques

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. In this way, the suggested model becomes computationally tractable, since no information from long n-body (bulk) simulations is required in order to develop it, while retaining the fluctuations at the coarse-grained level. 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 the pair potential of mean force. The comparison of the coarse-grained simulations is done on the basis of the structural properties, against detailed all-atom data. On the other hand, by construction, the approximate coarse-grained models retain, in principle, the thermodynamic properties of the atomistic model without the need for any further parameter fitting. We give specific examples for methane and ethane molecules in which the coarse-grained variable is the centre of mass of the molecule. We investigate different temperature (T) and density (r) 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 ρ 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.