An exact approach for describing adsorption and catalysis of interacting species in lattice models

Lattice models provide a useful framework for studying the adsorption and catalysis of interacting species. For such systems, the mean-field and quasi-chemical approximations are widely used. At equilibrium, full enumeration of the grand-canonical partition function would allow for an exact solution to these problems. However, the combinatorial complexity confines this approach to small systems. In this work, we consider how large a lattice needs to be for full enumeration to yield a feasible solution for equilibrium systems. As representative applications, we consider adsorption isotherms and the rate of a catalytic bimolecular reaction for the case that the surface reaction is the rate-limiting step. In these applications, we show that full enumeration on appropriately chosen small lattices accurately reproduces the converged results of Monte Carlo simulations on much larger lattices. We find that the commonly employed mean-field approximation can be off by up to five orders of magnitude and the quasi-chemical approximation is also inaccurate, while results from full enumeration are exact and converged. Our results are promising for studies aiming to quantify surface phenomena from first principles. Moreover, the full enumeration approach can be extended to kinetics, making this approach feasible for both equilibrium and kinetic studies of surface phenomena.