In a water-electrolysis system for hydrogen production, the kinetics of hydrogen evolution reaction (HER) critically depend on the exchange current density (J(0)) of the electrode. Noble metals, e.g., Pt, Ir, Rh, and Au, offer a significant J(0) when used as electrodes, assisting faster HER. However, instead of using expensive noble metals as electrodes, a thin layer on conventional electrodes, e.g., Ni, Cu, Ag, and Mo, also increases J(0). An electrode's J(0) during HER is calculated from the free energy of hydrogen adsorption (Delta G(H)), which is determined from hydrogen adsorption energy (E-ad) on the electrode surface. This work considered an Ir atomic monolayer as an electrocatalyst on the (111) plane of conventional Ni, Cu, Ag, and Mo electrodes, producing modified Ir/Ni(111), Ir/Cu(111), Ir/Ag(111), and Ir/Mo(111) electrodes. This work calculated E-ad of the modified electrodes using the density functional theory (DFT). In addition, this work develops an advanced kinetic model for the exchange current density considering the concentration of hydrogen ions (CH+) and partial pressure of hydrogen gas (P-H2). The dependence of activation overpotential (eta(a)) vs. J(0) relationship on CH+ and P-H2 in HER is investigated. For the modified electrodes, J(0) increases by 10(2)-10(3) times compared to the conventional electrodes, resulting in efficient H-2 production with low losses.