Unraveling water's entropic mysteries: A unified view of nonpolar, polar, and ionic hydration

Most chemical processes on earth are intimately linked to the unique properties of water, relying on the versatility with which water interacts with molecules of varying sizes and polarities. These interactions determine everything from the structure and activity of proteins and living cells to the geological partitioning of water, oil, and minerals in the Earth's crust. The role of hydrophobic hydration in the formation of biological membranes and in protein folding, as well as the importance of electrostatic interactions in the hydration of polar and ionic species, are all well known. However, the underlying molecular mechanisms of hydration are often not as well understood. This Account summarizes and extends emerging understandings of these mechanisms to reveal a newly unified view of hydration and explain previously mystifying observations. For example, rare gas atoms (e.g., Ar) and alkali-halide ions (e.g., K+ and Cl-) have nearly identical experimental hydration entropies, despite the significant charge-induced reorganization of water molecules. Here, we explain how such previously mysterious observations may be understood as arising from Gibbs inequalities, which impose rigorous energetic upper and lower bounds on both hydration free energies and entropies. These fundamental Gibbs bounds depend only on the average interaction energy of a solute with water, thus providing a deep link between solute-water interaction energies and entropies. One of the surprising consequences of the emerging picture is the understanding that the hydration of an ion produces two large but nearly perfectly canceling, entropic contributions: a negative ion-water interaction entropy and a positive water reorganization entropy. Recent work has also clarified the relationship between the strong cohesive energy of water and the free energy required to form an empty hole (cavity) in water. Here, we explain how linear response theory (whose roots may also be traced to Gibbs inequalities) can provide remarkably accurate descriptions of the process of filling aqueous cavities with nonpolar, polar, or charged molecules. The hydration of nonpolar molecules is well-described by first-order perturbation theory, which implies that turning on solute-water van der Waals interactions does not induce a significant change in water structure. The larger changes in water structure that are induced by polar and ionic solutes are well-described by second-order perturbation theory, which is equivalent to linear response theory. Comparisons of the free energies of nonpolar and polar or ionic solutes may be used to experimentally determine electrostatic contributions to water reorganization energies and entropies. The success of this approach implies that water's ability to respond to solutes of various polarities is far from saturated, as illustrated by simulations of acetonitrile (CH3CN) in water, which reveal that even such a strongly dipolar solute only produces subtle changes in the structure of water.