Kinetic and standard Monte Carlo (kMC and sMC) simulation of the system, where a pair-interaction energy is an oscillatory function of interatomic distance, requires a very careful selection of a cutoff radius r(cut) of the pair-interactions. As an example, the homoepitaxy of Cu on Cu(111) is investigated. The surface-state mediated interaction between the Cu adatoms has a very long range and oscillates between attraction and repulsion as a function of the adatom-adatom distance. The simulations reveal that, at 15 K and 0.03 monolayer coverage, the Cu adatoms self-assemble into a dilute nanostructure with a weak local hexagonal order, where the average separation between adatoms equals 11.7 angstrom. The nanostructure consists of islands and chains of adatoms. The simulated structure of adlayer surprisingly strongly depends on the cutoff radius applied to the Monte Carlo model. The tendency to the dilute island formation strengthens and weakens with the same periodicity vs. r(cut) as the pair-interaction energy vs. interatomic distance. The submonolayer morphology stabilizes when r(cut) becomes longer than 50 angstrom. (C) 2008 Elsevier B.V. All rights reserved.