Predicting energetic and entropic driving forces with coarse-grained models

Low resolution coarse-grained (CG) models provide exceptional computational efficiency for simulating soft materials. Consequently, many studies employ CG models to determine free energy surfaces along order parameters or reaction coordinates of interest. However, because CG models average over atomic details, it is challenging to determine the energetic and entropic contributions to the resulting free energy surfaces. In this work, we present a rigorous and predictive CG framework for computing these energetic and entropic driving forces based upon simulations at a single temperature. This dual approach employs distinct variational principles to independently approximate the exact CG interaction potential, W(R), and its energetic component, EW(R). This dual approach determines the free energy surface, aφ(x), along an order parameter, φ(x), via simulations with W(R). The dual approach then determines the energetic driving force, ūφ(x), by evaluating EW(R) for the sampled configurations. The entropic driving force, s̄φ(x), is indirectly inferred, s̄φ(x)=ūφ(x)-aφ(x)/T. Importantly, this entropic contribution reflects both the CG configuration distribution and the atomic details that have been eliminated from the CG model. We demonstrate that the dual approach reasonably describes the energetic and entropic driving forces between a pair of nonpolar solutes in a polar solvent. In contrast, naïvely estimating energetics with the CG interaction potential provides a qualitatively incorrect description for these driving forces.