pH in Grand Canonical Statistics of an Electrochemical Interface

We present an atomic-scale model of the electrochemical interface, which unfolds the effects of pH and electrode potential using a generalized computational hydrogen electrode. The liquid structure of the solvent is included with the use of ab initio molecular dynamics to sample thousands of microstates with varying numbers of protons and electrons. The grand canonical probability weight function at constant pH and electrode potential is calculated a posteriori. The only inputs to the model are the fundamental assumptions of an equilibrated solvent, charge neutrality of the interface, and the dimensions of the system. The structures are unbiased outputs, and several atomic-scale quantities are calculated for our model system, water/Au(111), as weighted averages. We present the potentials of zero charge, Gibbs isotherms, and differential capacities as a function of pH. The potential of maximum entropy is also calculated, which to our knowledge has not previously been done with any first-principles method. The model predicts a non-Nernstian pH behavior for the potential of maximum entropy.