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As air pollution and energy crises threaten the survival of mankind, various ways to efficiently obtain clean and renewable energies have been discussed in academia and industry. Amongst them, Power-to-X (P2X) conversions have been considered as important chemical reactions for future renewable energy generation. Hydrogen gas is one of the highly focused next-generation fuels in terms of the stability in supply as well as the suitability to buffer the fluctuation of energy supply from green power sources. Although water electrolysis is the most promising sustainable way to produce hydrogen, natural gas reforming techniques, which use fossil gases such as methane, still dominate the entire industry due to their economic efficiency. To overcome this, proton exchange membrane (PEM) water electrolyzers have been extensively studied due to their essential advantages. To date, a major drawback of PEM electrolysis is the sluggish kinetics of the oxygen evolution reaction (OER) at the anode and indispensable precious transition metal-based OER catalysts, which need to be durable under harsh acidic reaction conditions. Iridium oxide (IrO<sub>2</<sub>) has been known as the only active and stable catalyst under such conditions. However, the low abundance of iridium constrains the generalization of PEM techniques. A significant reduction of Ir mass<br>loading on catalysts is thus required. Utilizing ruthenium oxide (RuO<sub>2</<sub>) is one promising way since it is more cost-efficient compared to IrO<sub>2</<sub>. The only obstacle is the relatively poor stability of RuO<sub>2</<sub> at OER operation conditions.<br>Morphology control via nanostructuring is an often used experimental approach to enhance<br>stability. In predictive-quality computational science, many highly efficient morphologies have been proposed, however, long-term stability in industrial operating conditions and a possible subsequent transformation of the morphology have been rarely discussed. Consequently, there are still many longstanding questions on catalysts under working conditions. In this dissertation, structure-function and structure-stability relationships of RuO<sub>2</<sub> based catalyst are mainly discussed by using first-principles density functional theory calculations. Two different types of structural modification in RuO<sub>2</<sub> were discovered that promise better thermodynamic stability and enhanced OER activity. Furthermore, by combining state-of-the-art machine-learning methods with computational chemistry, the complex potential energy surface of rutile oxide materials was explored and hitherto unknown surface reconstructions of rutile RuO<sub>2</<sub> were determined. The theoretical concepts and approaches developed throughout the dissertation may lay the platform for future works to design novel catalysts for PEM OER and other electrocatalytic reactions.