Cooperative hydrophobic/hydrophilic interactions in the hydration of dimethyl ether

Cooperative interactions in the hydration of dimethyl ether (DME) relative to its purely hydrophobic analog, propane, are analyzed by expressing the free energy of hydration in terms of an "inner-shell" contribution from water molecular packing and chemical association, and an "outer-shell" contribution described by the mean binding energy of the solute to the solution and fluctuations in this binding energy. We find that nonadditive, cooperative interactions associated with strong correlations in the binding energy fluctuations of the methyl groups and ether oxygen play a dominant role in the hydration of DME relative to propane. The electrostatic nature of these interactions is revealed in a multi-Gaussian analysis of hydration substates, which shows that the formation of favorable ether oxygen-water hydrogen bonds is correlated with less favorable methyl group-water interactions, and vice versa. We conclude that the group additive distinction between the hydrophobic hydration of the DME methyl groups and hydrophilic hydration of the ether oxygen is lost in the context of these cooperative interactions. Our results also suggest that the binding energy fluctuations of constituent hydrophobic/hydrophilic groups are more sensitive than local water density fluctuations for characterizing the hydration of heterogeneous interfaces.