Enhanced Photocatalytic, Mechanical, and Optical Performance of Rare-Earth–Doped Mg₂Si: First-Principles Calculations and Machine Learning

Broadband light absorption, mechanical resilience, and efficient surface catalysis are all crucial for photocatalytic semiconductors, yet they are rarely improved together in one material. We combine first-principles calculations with machine-learning interpretability and Pearson correlation analyses to reveal that rare-earth (La, Er) doping of Mg₂Si can synergistically enhance its optoelectronic, mechanical, and hydrogen-evolution performance. La doping introduces conduction-band impurity states via La-5d/Si-3p orbital hybridization, boosting sub-bandgap (infrared) absorption by 60-fold (~0.6 × 10⁵ cm⁻¹) and extending the absorption edge into the near-infrared—translating to a solar-to-hydrogen conversion efficiency of up to 39.86%. It also percolates a metallic bond network that doubles the Poisson's ratio (0.23 → 0.46), transforming Mg₂Si from brittle to ductile. Er doping, in contrast, localizes 4f orbitals, yielding exciton-like absorption peaks (~10⁵ cm⁻¹) in the ultraviolet and inducing a distinct electronic and mechanical response. Both dopants push the Fermi level into the conduction band (degenerate n-type doping), fundamentally altering carrier characteristics. Catalytically, La doping generates delocalized sp³d² orbitals that give near-thermoneutral hydrogen adsorption (ΔG_H* ≈ −0.04 eV), outperforming noble-metal catalysts, whereas Er's extended electron density enhances H binding at the cost of slower H₂ desorption. SHAP (SHapley Additive exPlanations) analysis further identifies the key orbital and elastic descriptors governing these trends, providing a mechanistic blueprint.