An accurate prediction of the surface potential (φ) at the air-water interface is critical to calculating ion hydration free energies and electrochemical half-cell potentials. Using Density Functional Theory (DFT), model interfacial configurations, and a theoretical definition of φ, we report a value of +3.63 volt at 0.92 g/cc water density. A maximally localized Wannier function analysis confirms that φ is dominated by molecular quadrupole (or "spherical second moment") contributions. We find that the predicted surface potential depends on computational details, and conclude that standard DFT codes and the existing definition of φ may not yield surface potentials directly comparable to existing experiments."Surface potentials" (or "potentials of the phase") are invoked when a charged particle moves from one phase to another through their mutual interface. One of the simplest and most important examples pertains to the surface between air and water.1-16 ("Air," "vacuum," and "vapor" will be used interchangeably in this work.) The electrostatic potential difference (φ) between an ion in vacuum at infinity and that ion in pure liquid water contributes a term qφ to the absolute hydration free energy (∆G hyd ), where q is the ionic charge. φ thus contributes to all aqueous media electrochemical half-cell potentials, 17,18 which consist of ∆G hyd plus the pertinent ionization potentials. Recent Density Functional Theory (DFT) calculations have yielded φ estimates for the air-water interface 19-23 substantially larger in magnitude than classical force field predictions 5-9 and experimental values, [12][13][14][15][16] suggesting that the methodology and physical basis of such calculations should be re-examined.We first focus on molecular simulation perspectives, [5][6][7][8][9] deferring the question of what is measured in experiments to the concluding discussions. For this purpose, we consider a charge-neutral slab of salt-free liquid water. Using this kind of simulation cell, force field-based simulations (i.e., those not based on electronic structure calculations) have reported that φ depends on the water model used, [8][9][10] but that the widely applied SPC/E model 24 yields φ=-0.55 volt, 8 similar to related threepoint point-charge water models, including polarizable ones.
9DFT takes into account electronic structure and molecular polarizabilites, and might be considered an improvement over non-polarizable water models. As will be shown, however, care must be exercised when interpreting the results based on the existing theoretical definition of the surface potential (see below).5-9 A DFT work that extrapolates the highest occupied molecular orbital in gas phase ion/water-clusters to infinite cluster size has estimated that φ ∼ 4 volt 19 (in our notation). Using the VASP code, 25 the Perdew-Burke-Ernzerhof (PBE) functional, 26 a bulk liquid simulation cell, and approximations for surface dipoles, we have deduced that φ = +4.05 volt.21 By considering pK a and proton hydration free energies in DFT simulations, Che...