  The free energetics of water density fluctuations in bulk water, at
interfaces, and in hydrophobic confinement inform the hydration of hydrophobic
solutes as well as their interactions and assembly. The characterization of
such free energetics is typically performed using enhanced sampling techniques
such as umbrella sampling. In umbrella sampling, order parameter distributions
obtained from adjacent biased simulations must overlap in order to estimate
free energy differences between biased ensembles. Many biased simulations are
typically required to ensure such overlap, which exacts a steep computational
cost. We recently introduced a sparse sampling method, which circumvents the
overlap requirement by using thermodynamic integration to estimate free energy
differences between biased ensembles. Here we build upon and generalize sparse
sampling for characterizing the free energetics of water density fluctuations
in systems near liquid-vapor coexistence. We also introduce sensible heuristics
for choosing the biasing potential parameters and strategies for adaptively
refining them, which facilitate the estimation of such free energetics
accurately and efficiently. We illustrate the method by characterizing the free
energetics of cavitation in a large volume in bulk water. We also use sparse
sampling to characterize the free energetics of capillary evaporation for water
confined between two hydrophobic plates. In both cases, sparse sampling is
nearly two orders of magnitude faster than umbrella sampling. Given its
efficiency, the sparse sampling method is particularly well suited for
characterizing free energy landscapes for systems wherein umbrella sampling is
prohibitively expensive.
