Our previous first principles studies showed that both hopping and exchange processes need to be considered for a comprehensive description of the diffusion events for Li and Na surface systems. The analysis of the dimer interaction energies showed an attractive interaction of the nearest neighbours (NN) with the diffusing adatom but a negligible impact of the next-nearest neighbours. Here, we have adopted a lattice gas approach to describe the diffusion events within our in-house kMC implementation. Each grid point is defined by the translation vector T, following