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We investigate the coarse-graining of host-guest systems under theperspective of the local distribution of pore occupancies, along with thephysical meaning and actual computability of the coarse-interaction terms. Weshow that the widely accepted approach, in which the contributions to the freeenergy given by the molecules located in two neighboring pores are estimatedthrough Monte Carlo simulations where the two pores are kept separated from therest of the system, leads to inaccurate results at high sorbate densities. Inthe coarse-graining strategy that we propose, which is based on theBethe-Peierls approximation, density-independent interaction terms are insteadcomputed according to local effective potentials that take into account thecorrelations between the pore pair and its surroundings by means of mean-fieldcorrection terms, without the need of simulating the pore pair separately. Useof the interaction parameters obtained this way allows the coarse-grainedsystem to reproduce more closely the equilibrium properties of the originalone. Results are shown for lattice-gases where the local free energy can becomputed exactly, and for a system of Lennard-Jones particles under the effectof a static confining field.

Local free energy approximations for the coarse-graining of adsorption phenomena