This thesis contains a theoretical approach to rational catalyst design for water electrolysis. Water splitting process consists of two reactions: Hydrogen Evolution Reaction (HER) and Oxygen Evolution reaction (OER). Efficiency of overall process is highly associated with kinetically sluggish OER at the anode side. Therefore, our challenge is to investigate stable, active and low-cost catalyst for OER process. In this thesis, Density Functional Theory (DFT) tool is used to investigate the catalyst activity with reaction intermediates using thermodynamic model. In the first part of results, review for Oxygen Evolution Reaction is presented. This review involves the scaling relation on metal oxides for OER over the last decade. Doped semi-conductor metal oxides is the centre of our findings. Using single dopant in semiconductors result in finite size effect. The robust scaling relation between HO* and HOO* is observed with large data set obtained from the literature as consistent in earlier studies. Scaling between HO* and O* intermediates is deviated due to the finite size effect on doped semiconductor metal oxides. We propose a way to circumvent a computational challenge which can be applied in simulations in general. TiO2 (110) is used as a model system throughout the study. Various different dopants involving p-type and n-type are applied to demonstrate the scaling relation with single and double dopants on TiO2. In the second part of results, co-doping strategy is applied on TiO2 (110) for OER electrochemical study. Improvement of overall activity is observed on co-doped TiO2. Based on our hypothesis, different co-doping candidates are proposed. Vanadium (V) as a n-type and Rhodium (Rh) as a p-type are investigated broadly as a model system. At the end, we performed the experimental study to demonstrate the effect of co-doped on TiO2. The results from these studies lead us to design active OER catalyst using semiconductor metal oxides. The motivation is that they are highly stable in acidic media. Improving the activity of these stable oxides makes cheaper alternative to Ruthenium (Ru) and Iridium (Ir) based catalysts for OER applications. In the last part, challenges on RuO2 and IrO2 are discussed comparing the experimental and computational studies. RuO2 and IrO2 are important benchmark catalysts for OER application for PEM electrolyser. Even though they are the most studied materials, challenges remain to improve RuO2 and IrO2 for practical utilization.