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Abstract The versatile Bell-Evans-Polanyi (BEP) relation stipulates the kinetics of a reaction in terms of thermodynamics. Herein, we establish the BEP relation for the hydrogen evolution reaction (HER) from fundamental electrochemical principles leveraging the Butler-Volmer relation for a one-step, one-electron process and the transition state theory. Based on first-principles investigations of HER mechanisms on fourteen metal electrodes, we firmly justify the BEP relation solely using an easy-to compute hydrogen adsorption free energy and universal electrochemical constants. 

Nørskov and collaborators proposed a simple kinetic model to explain the volcano relation for the hydrogen evolution reaction on transition metal surfaces such that j 0 = k 0 f (Δ G H ) where j 0 is the exchange current density, f (Δ G H ) is a function of the hydrogen adsorption free energy Δ G H as computed from density functional theory, and k 0 is a universal rate constant. Herein, focusing on the hydrogen evolution reaction in acidic medium, we revisit the original experimental data and find that the fidelity of this kinetic model can be significantly improved by invoking metal-dependence on k 0 such that the logarithm of k 0 linearly depends on the absolute value of Δ G H . We further confirm this relationship using additional experimental data points obtained from a critical review of the available literature. Our analyses show that the new model decreases the discrepancy between calculated and experimental exchange current density values by up to four orders of magnitude. Furthermore, we show the model can be further improved using machine learning and statistical inference methods that integrate additional material properties.