Atomistic understanding of hydrogen coverage on RuO2(110) surface under electrochemical conditions from ab initio statistical thermodynamics

Understanding the dehydrogenation of transition metal oxide surfaces under electrochemical potential is critical to the control of important chemical processes such as the oxygen evolution reaction (OER). Using first principles computations, we model the thermodynamic dehydrogenation process on RuO$_2$(110) and compare the results to experimental cyclic voltammetry (CV) on single crystal. We use a cluster expansion model trained on *ab initio* energy data coupled with Monte Carlo (MC) sampling to derive the macroscopic electrochemical observables, i.e., experimental CV, from the energetics of different hydrogen coverage microstates on well-defined RuO$_2$(110). Our model reproduces the unique "two-peaks" cyclic voltammogram observed experimentally with current density peak positions and shapes in good qualitative agreement. We show that RuO$_2$(110) starts as a water-covered surface with hydrogen on bridge (BRG) and coordination-unsaturated sites (CUS) at low potential (less than 0.4 V vs. reversible hydrogen electrode, RHE). As the potential increases, the hydrogens on BRG desorb, becoming the main contributor to the first CV peak with smaller contributions from CUS. When all BRG hydrogens are desorbed (before 1.2 V vs. RHE), the remaining CUS hydrogens desorb abruptly in a very small potential window leading to the sharp second peak observed during CV. Our work shows that above 1.23 V, the OER proceeds on a fully dehydrogenated RuO$_2$(110) surface.