Catalytic site ensembles: A context to reexamine the Langmuir-Hinshelwood kinetic description

The Langmuir-Hinshelwood formalism describes catalytic reactions of Langmuirian surface species under the assumption that all adsorbates are randomly-distributed – enabling adjacency of surface-bound intermediates to be determined solely by coverages of single-site occupants. We demonstrate herein that this approximation is inappropriate even for simple catalytic reactions (e.g. A + A → A₂) and manifestly neglects islanding of slowly-consumed species and partitioning of highly-reactive species inherently engendered by ≥ two-site elementary steps (e.g. A*–A* → A_2(g) + *–*). Rigorous description of kinetically-consequential islanding/partitioning phenomena requires explicit description of the coverage and chemical dynamics of all multi-site ensembles. Higher-order, ensemble-specific rate terms identify the particular microscopic events relevant to each ensemble, and, in doing so, reveal that each elementary step (e.g. A_(g) adsorption) describes not one event (e.g. A_(g) + * → A*), but a sum over all ensemble-specific paths (e.g. A_(g) + *–* → A*–* and A_(g) + A*–* → A*–A*). De-convoluting each elementary step into its constituent multi-site paths proffers kinetic detail otherwise inaccessible – enabling (i) identification of rate- and selectivity-determining site ensembles, (ii) calculation of rates and degrees of rate control of ensemble-specific elementary steps, (iii) incorporation of adsorbate surface diffusion, (iv) incorporation of lateral adsorbate interactions, and (v) quantitative description of catalysis of multi-site-occupying intermediates (e.g. *C_nH_m* species in hydrocarbon (de-)hydrogenation and C-C bond coupling/cleavage reactions) which we demonstrate is inaccessible to the Langmuir-Hinshelwood formalism even if adsorbate surface diffusion is infinitely-fast.