A coverage-corrected energetic span descriptor for comparing CO2 hydrogenation activity and selectivity on Cu–In surfaces

Abstract

Cu-In-based catalysts are promising for CO₂ hydrogenation to methanol, yet how alloy surface structure governs catalytic activity and selectivity has not been systematically resolved. A central challenge is reliably comparing catalytic activity across distinct surface terminations. While microkinetic modeling (MKM) rigorously links DFT energetics to reaction rates, its complexity limits rapid activity evaluation across multiple surfaces. As a cost-effective alternative, the energetic span model estimates catalytic activity from reaction profiles. However, in the Cu-In system, the conventional energetic span reproduces trends only within individual surfaces and can give misleading rankings across different surfaces due to coverage-dependent thermodynamic effects of key intermediates. Using DFT calculations and MKM, we investigate CO₂ hydrogenation on five Cu-In surfaces and reveal pronounced structure sensitivity: methanol turnover frequencies (TOFs) range from ~10^-2 s^-1 on Cu₇In₃(040)-a to ~10^-6 s^-1 on Cu₁₁In₉ surfaces, while Cu₂In(110) and Cu₇In₃(040)-b show similar TOFs (~10^-4 s^-1 ) yet contrasting selectivities, reflecting surface-dependent kinetic control. To address this discrepancy, we introduce a thermodynamic correction to the TOF-determining intermediate (TDI), based on the site requirement of the TOF-determining transition state (TDTS), restores agreement with MKM-predicted activity trends. Building on this, we reformulate surface-species energetics within a Gibbs formation-energy scheme and propose a compact descriptor, G_HL, requiring only a few key intermediate and transition-state energies, enabling rapid semi-quantitative comparison of catalytic activity across surfaces with well-defined mechanisms.