First-principles study of the structure of RuO$_{2} \cdot x$H$_{2}$O

Hydrous ruthenia, RuO$_{2} \cdot x$H$_{2}$O, is a high-performance electrode material for electrochemical supercapacitors. Two different structural models of hydrous ruthenia had been proposed. In one of them, hydrogen is incorporated in metal vacancies inside the oxide host ( (``bulk model''), while in the other model structural water associated with Ru-O occupies the region between rutile nanograins (``core + grain-boundary model''). We present a theoretical examination of the validity of the bulk model by optimizing hydrogen positions within RuO$_{2}$ with proton-compensated Ru vacancies using a combination of a systematic search algorithm based on electrostatics, database searching and density-functional theory calculations. We find that all the considered bulk model structures are unstable by $\sim 0.3 - 0.4$ eV per H$_{2}$O molecule with respect to phase separation into anhydrous RuO$_{2}$ and water. Structures with hydroxyl groups or aggregate H$_{2}$O are significantly lower in energy (though still unstable with respect to phase separation), demonstrating that the water prefers to agglomerate outside RuO$_{2}$. Our results strongly disfavor the bulk model with hydrogen inside RuO$_{2}$ and support the core+grain-boundary model of hydrous ruthenia.