Working-state descriptors for theory-guided CO₂ hydrogenation catalysis

Thermal CO₂ hydrogenation connects carbon-oxide recycling with low-carbon H₂ use and established product families, including CO, methanol, methane and C₂₊ hydrocarbons. The design problem is that the selective catalyst is often not the ideal surface used at the start of a calculation. H₂/CO₂/CO/H₂O feeds can redistribute phases, interfaces, adsorbates and promoter environments during measurement. First-principles descriptor maps and microkinetic models remain essential once candidate states are specified, but they cannot decide which states should enter the comparison. This Review asks how such states can be made analysable by linking operando and transient evidence, descriptor-based calculations, machine-learning interatomic potential (MLIP) sampling, kinetic identifiability analysis and reactor observables. Fe-based CO₂-to-hydrocarbon catalysis is used as the main case because oxide/carbide balance, promoter-rich interfaces, C/H/O chemistry, water survival, olefin readsorption and chain growth are coupled in one network. Working-state descriptors are therefore condition-bound variables or projections, such as phase-pool weighting, interface proximity, C/H/O balance, state-conditioned event weighting, readsorption probability and survival time, that become useful only when catalyst-state evidence, kinetic role and observable response remain connected.