Systematic study of temperature and density variations in effective potentials for coarse-grained models of molecular liquids.

Due to their computational efficiency, coarse-grained (CG) models are widely adopted for modeling soft materials. As a consequence of averaging over atomistic details, the effective potentials that govern the CG degrees of freedom vary with temperature and density. This state-point dependence not only limits their range of validity but also presents difficulties when modeling thermodynamic properties. In this work, we systematically examine the temperature- and density-dependence of effective potentials for 1-site CG models of liquid ethane and liquid methanol. We employ force-matching and self-consistent pressure-matching to determine pair potentials and volume potentials, respectively, that accurately approximate the many-body potential of mean force (PMF) at a range of temperatures and densities. The resulting CG models quite accurately reproduce the pair structure, pressure, and compressibility of the corresponding all-atom models at each state point for which they have been parameterized. The calculated pair potentials vary quite linearly with temperature and density over the range of liquid state points near atmospheric pressure. These pair potentials become increasingly repulsive both with increasing temperature at constant density and also with increasing density at constant temperature. Interestingly, the density-dependence appears to dominate, as the pair potentials become increasingly attractive with increasing temperature at constant pressure. The calculated volume potentials determine an average pressure correction that also varies linearly with temperature, although the associated compressibility correction does not. The observed linearity allows for predictions of pair and volume potentials that quite accurately model these liquids in both the constant NVT and constant NPT ensembles across a fairly wide range of temperatures and densities. More generally, for a given CG configuration and density, the PMF will vary linearly with temperature over the temperature range for which the entropy associated with the conditioned distribution of atomic configurations remains constant.