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Absolute ion hydration free energy scale and the surface potential of water via quantum simulation

Significance Establishing an absolute free energy scale for single-ion hydration has been an elusive goal of condensed-phase chemistry for nearly a century. In this paper, a zero for the free energy scale is determined by employing quasi-chemical theory and quantum mechanical simulations of the sodium ion in water. The simulation results produce an accurate estimate of the effective surface potential of water by comparison of the computed “bulk” hydration free energy with experimental values for the “real” hydration free energy. This work provides a firm quantitative footing for studies of interfacial specific ion structure, thermodynamics, and kinetics in fields as diverse as colloid science, electrochemistry, biophysics, and energy storage materials. With a goal of determining an absolute free energy scale for ion hydration, quasi-chemical theory and ab initio quantum mechanical simulations are employed to obtain an accurate value for the bulk hydration free energy of the Na+ ion. The free energy is partitioned into three parts: 1) the inner-shell or chemical contribution that includes direct interactions of the ion with nearby waters, 2) the packing free energy that is the work to produce a cavity of size λ in water, and 3) the long-range contribution that involves all interactions outside the inner shell. The interfacial potential contribution to the free energy resides in the long-range term. By averaging cation and anion data for that contribution, cumulant terms of all odd orders in the electrostatic potential are removed. The computed total is then the bulk hydration free energy. Comparison with the experimentally derived real hydration free energy produces an effective surface potential of water in the range −0.4 to −0.5 V. The result is consistent with a variety of experiments concerning acid–base chemistry, ion distributions near hydrophobic interfaces, and electric fields near the surface of water droplets.