Rough interfaces, accurate predictions: The necessity of capillary modes in a minimal model of nanoscale hydrophobic solvation

Modern theories of the hydrophobic effect highlight its dependence on length scale, emphasizing in particular the importance of interfaces that emerge in the vicinity of sizable hydrophobes. We recently showed that a faithful treatment of such nanoscale interfaces requires careful attention to the statistics of capillary waves, with significant quantitative implications for the calculation of solvation thermodynamics. Here we show that a coarse-grained lattice model in the spirit of those pioneered by Chandler and coworkers, when informed by this understanding, can capture a broad range of hydrophobic behaviors with striking accuracy. Specifically, we calculate probability distributions for microscopic density fluctuations that agree very well with results of atomistic simulations, even many standard deviations from the mean, and even for probe volumes in highly heterogeneous environments. This accuracy is achieved without adjustment of free parameters, as the model is fully specified by well-known properties of liquid water. As illustrative examples of its utility, we characterize the free energy profile for a solute crossing the air-water interface, and compute the thermodynamic cost of evacuating the space between extended nanoscale surfaces. Together, these calculations suggest that a highly reduced model for aqueous solvation can serve as the basis for efficient multiscale modeling of spatial organization driven by hydrophobic and interfacial forces.