Structure–Activity Correlations in Low-Dimensional Heterogeneous Catalysts: Active-Site Geometry, Defects, Electronic Coupling, and Operando Validation

Low-dimensional heterogeneous catalysts are often discussed as though dimensionality itself were a catalytic descriptor. It is not. Shrinking a material to clusters, nanowires, or atomically thin sheets changes several quantities at once: coordination number, facet exposure, defect density, strain, charge transfer, transport, and the fraction of atoms located at an interface. The central problem is therefore causal rather than taxonomic: which structural variable controls the measured rate, selectivity, or deactivation behavior under reaction conditions? This review develops a practical framework for answering that question across thermal catalysis, electrocatalysis, and photocatalysis. We first separate geometric descriptors from defect and electronic descriptors, then examine representative 0 dimensional (0D), 1D, and 2D systems in which those variables have been experimentally constrained. Particular attention is paid to active-site counting, facet and edge effects, strain, vacancy chemistry, single-atom stabilization, metal–support interactions, and charge-transfer heterojunctions. Focused case studies on Mg-doped ZnO and 2D/1D graphene/Ag-Ag₂S are used to show how a nominal synthesis variable can simultaneously alter structure and electronic response. The review then turns to operando validation, because ex situ structures can be spectators once adsorption, redox cycling, potential, temperature, or solvent drives reconstruction. A dedicated section extends the same causal framework to heterogeneous organic synthesis, including immobilized metal complexes and supported molecular sites, where leaching and coordination-state evolution must be distinguished from genuinely surface-bound catalysis. We argue that the most useful structure–activity map is built from a quantified working-state descriptor, a defensible site-normalized kinetic metric, and an explicit test of competing explanations. Finally, we propose a minimum reporting set for cross-study comparison and identify where current evidence remains correlation rather than mechanism.