Understanding three-body contributions to coarse-grained force-fields

Coarse-graining (CG) is a systematic reduction of the number of degrees of freedom (DOF) used to describe a system of interest. CG can be thought of as a projection on coarse-grained DOF and is therefore dependent on the functions used to represent the CG force field. In this work, we show that naive extensions of the coarse-grained force-field can result in unphysical parametrizations of the CG potential energy surface (PES). This issue can be elevated by coarse-graining the two- and three-body forces separately, which also helps to evaluate the importance of many-body interactions for a given system. The approach is illustrated on liquid water, where three-body interactions are essential to reproduce the structural properties, and liquid methanol, where two-body interactions are sufficient to reproduce the main features of the atomistic system.