A generalized-Yvon-Born-Green theory for determining coarse-grained interaction potentials

The present work introduces a generalized-Yvon-Born-Green (YBG) theory for calculating coarse-grained (CG) force fields directly from structure ensembles. The method is noniterative and determines the CG potentials from a system of coupled linear integral equations that are expressed in terms of structural correlation functions for the CG sites. The force field obtained by solving these linear equations provides a variationally optimal approximation to the many-body potential of mean force determined by the atomistic model and the CG mapping. The generalized-YBG theory is equivalent to the conventional YBG equation when applied to monatomic liquids but also correctly treats the many-body structural correlations present in more complex molecular systems. Additionally, this work introduces an analogous version of the theory for determining discrete force field parameters. Numerical calculations for a CG model of a propane-propanol mixture illustrate the method.