Quantum confinement-driven negative Gibbs free energy in Pt-rare Earth alloys: breaking the thermodynamic equilibrium paradigm

Abstract The Gibbs free energy $(\Delta {G})$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>(</mml:mo> <mml:mi>Δ</mml:mi> <mml:mi>G</mml:mi> <mml:mo>)</mml:mo> </mml:math> of key intermediates has long served as the gold standard descriptor for evaluating catalytic activity in energy conversion reactions such as the hydrogen evolution reaction (HER). However, this thermodynamic criterion cannot explain why certain catalysts display exceptional activity at high overpotentials, far from equilibrium, despite possessing highly negative Gibbs free energies. Here, we demonstrate that for Pt-rare earth alloys with quantum confinement effects, negative adsorption energies can enhance surface hydrogen coverage and sustain rapid hydrogen evolution under large current densities through the Volmer-Heyrovsky (VH) mechanism. In the PtGd 3 alloys, quantum confinement effects emerge due to the large atomic radius and low electronegativity of Gd, which expand the Pt-Pt bond length and reduce d - d orbital overlap. This weak hybridization narrows the Pt d-band and shifts its center upward toward the Fermi level. The resulting redistribution of electronic density produces a more negative Δ G value compared with pure Pt. As a result, PtGd 3 exhibits lower HER activity near equilibrium but surpasses Pt under high overpotentials when kinetic factors dominate. These findings reveal how quantum confinement-induced electronic reconstruction can break the conventional thermodynamic equilibrium paradigm and offer a new design strategy for industrial-scale electrocatalysis.