Despite promising developments of experimental techniques the molecular processes on the surface of catalysts are still not fully understood. Hydrogen atoms binding to the surface atoms are hard to detect with modern techniques because of the nature of hydrogen. In this work we will first gain insight into the hydrogen coverage and the atomic configuration on the surface of iridium oxide and ruthenium oxide by computing surface phase diagrams with ab-initio methods. With these findings we will move on towards explaining the improvement of catalytic reactions on the iridium surface when mixing in titanium to enhance the activity which is experimentally evident and will be elucidated by ab-initio methods. The computation of a cyclic voltammogram measurement by means of a cluster expansion in combination with machine learning will be presented in the last chapter which is also compared to experimental data. Finally a discussion about the results from this work, the context of their validity and also the shortcomings of the currently available methods is summarized with an outlook in the final paragraph.