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Statistical analyses of hydrophobic interactions: A mini-review

This review focuses on the striking recent progress in solving for hydrophobic interactions between small inert molecules. We discuss several new understandings. Firstly, the _inverse _temperature phenomenology of hydrophobic interactions, _i.e., strengthening of hydrophobic bonds with increasing temperature, is decisively exhibited by hydrophobic interactions between atomic-scale hard sphere solutes in water. Secondly, inclusion of attractive interactions associated with atomic-size hydrophobic reference cases leads to substantial, non-trivial corrections to reference results for purely repulsive solutes. Hydrophobic bonds are _weakened by adding solute dispersion forces to treatment of reference cases. The classic statistical mechanical theory for those corrections is not accurate in this application, but molecular quasi-chemical theory shows promise. Finally, because of the masking roles of excluded volume and attractive interactions, comparisons that do not discriminate the different possibilities face an interpretive danger.