The moderate disparity between the free energy values for H⁺ and H₂ reflects a balanced adsorption-desorption process, a hallmark of an efficient HER catalyst. This balance minimizes the overpotential required for the reaction, enhancing the thermodynamic efficiency of hydrogen evolution. The synergy between the platinum dopant and the phenalene matrix likely optimizes the electronic structure and active site distribution, ensuring that the Gibbs free energy aligns closely with the thermoneutral value (ideal ΔG ≈ 0 eV) for hydrogen adsorption. These properties underscore the material's promise as a highly effective electrocatalyst for hydrogen evolution, combining favorable thermodynamics with robust catalytic activity.