A first-principles investigation of goldene for enhanced hydrogen evolution reaction

The recent synthesis of goldene, a freestanding two-dimensional (2D) sheet of gold exfoliated from Ti₃AuC₂, offers a high specific surface area (∼260 m² g^-1), roughly twice that of fine Au nanodots (∼100 m² g^-1), together with unique electronic properties arising from its densely populated d-orbitals. In this work, we use first-principles density functional theory (DFT) to investigate hydrogen adsorption on pristine goldene (pG), mono-vacant goldene (vG), and their thiolate-functionalized variants (thiolate-pG and thiolate-vG), in which a single S atom is bonded to the sheet. The hydrogen adsorption free energy, ΔG_H, is the central descriptor governing the Volmer step of the hydrogen evolution reaction (HER), and we systematically map its dependence on adsorption site and surface chemistry across all four systems. The trends are rationalized using a complementary set of electronic descriptors, including Bader charge analysis, spin-polarized projected density of states, d-band-centre shifts, and the exchange current density extracted from a volcano-plot benchmark. We find that pristine goldene binds hydrogen too weakly for the Volmer step to be favourable, that mono-vacancies bring vacancy-adjacent sites to near-thermoneutral ΔG_H (-0.075 eV), and that thiolate functionalization of mono-vacant goldene gives a uniformly moderate binding profile (ΔG_H ≈ -0.15 eV) across all sites. Both variants lie close to the apex of the volcano plot, and within the ±0.2 eV uncertainty of DFT-derived descriptors they cannot be ranked against each other. These results suggest undercoordinated sites and thiolate functionalization of vacancy-engineered goldene as a plausible route towards near-thermoneutral hydrogen adsorption on a 2D-metallic platform. We note that further calculations of reaction barriers, solvent effects and the effect of electrode potential, apart from experimental validation will supplement the hydrogen adsorption thermodynamics reported in this work.