What Coordinate Best Describes the Affinity of the Hydrated Excess Proton for the Air-Water Interface?

: Molecular dynamics simulations and free energy sampling are employed in this work to investigate the surface affinity of the hydrated excess proton with two definitions of the interface: The Gibbs dividing interface (GDI) and the Willard-Chandler interface (WCI). Both the multistate empirical valence bond (MS-EVB) reactive molecular dynamics method and density functional theory-based ab initio molecular dynamics (AIMD) were used to describe the hydrated excess proton specieis, including it "vehicular" (standard diffusion) transport and (Grotthuss) proton hopping transport and associated structures of the hydrated excess proton net positive charge defect. The excess proton is found to exhibit a similar trend and quantitative free energy behavior in terms of its surface affinity as a function of the GDI or WCI. Importantly, the definitions of the two interfaces in terms of the excess proton charge defect are highly correlated and far from independent of one another, thus undermining the argument that one interface is superior to the other when describing the proton interface affinity. Moreover, the hydrated excess proton and its solvation shell significantly influences the location and local curvature of the WCI, making it difficult to disentangle the interfacial thermodynamics of the excess proton from the influence of that species on the instantaneous surface curvature.