The search for efficient and durable cathodes for the Hydrogen Evolution Reaction (HER) is critical for advancing renewable energy technologies. In this study, we employ Density Functional Theory (DFT) to explore and identify novel cathode material that can enhance HER performance. By systematically evaluating a modified transition metal-based cathode and its catalytic properties, we aim to discover material that exhibit low overpotentials and preferentially activities close to that of platinum. Our DFT calculations focus on key parameters such as hydrogen adsorption free energy (ΔG_H), electronic structure, and reaction pathways to HER. Activation energies for proton recombination and evolution as H₂ is also investigated. We identify a promising material, hafnium-based, that demonstrate optimal ΔG_H value close to zero, indicating favorable hydrogen adsorption and desorption kinetics. Our findings also highlight the importance of electronic structure tuning through surface modifications, which can significantly enhance catalytic activity. Overall, this study provides a comprehensive theoretical framework for the discovery and optimization of high-performance cathodes for HER, paving the way for more efficient and sustainable hydrogen production technologies.