Revisiting what we lose by coarse-graining: Modeling cooperative hydrophobic phenomena with short-ranged, pair-additive forces

Water and, in particular, hydrophobic phenomena play a central role in science and technology. Unfortunately, the cooperative, many-body interactions that govern hydrophobic phenomena severely challenge coarse-grained (CG) models. Accordingly, we examine current methods for coarse-graining water. We demonstrate that pair potentials determined via force-matching and iterative Boltzmann inversion provide very similar descriptions of hydrophobic phenomena. By modifying these potentials with relatively long-ranged attractive tails, the corresponding models reasonably stabilize the liquid phase under ambient conditions. However, they significantly overestimate solvation free energies, the width of liquid interfaces, and the magnitude of global and local density fluctuations. These models also fail to capture the cooperativity of hydrophobic phenomena. More surprisingly, while the local compressibility, χR, of water decreases with length-scale, R, eχR actually increases with R in these CG models. This qualitative failure stems from the attractive tails that are commonly used to stabilize liquids. Conversely, by supplementing pair potentials with a globaldensity (GD) potential, CG models accurately reproduce global and local density fluctuations. Nevertheless, this GD model dramatically overestimates solvation free energies and fails to stabilize liquid-vapor coexistence. In contrast, local density (LD) potentials that generate pair-additive, environment-dependent forces describe water much more accurately. Although it slightly underestimates the surface tension, this LD model reasonably reproduces the structural and thermodynamic signatures of cooperative hydrophobic phenomena across a wide range of length scales. Our results emphasize the importance of reproducing the local coordination, surface tension, and density fluctuations, while detailed structural correlations appear less important for modeling hydrophobic phenomena.