  Collective diffusion coefficient in a one dimensional lattice gas adsorbate
is calculated using variational approach. Particles interact via either a
long-range, or a long range electron-gas-mediated (for a metallic substrate),
or a Lennard-Jones interaction. Diffusion coefficient as a function of the
adsorbate density strongly depends on the relationship between the substrate
lattice constant and the characteristic length of the inter--particle
interaction potential (which determines positions of the potential energy
minima). The diffusion coefficient at fixed density as a function of the
interaction characteristic length has an oscillating character due to the
interplay between the inter--particle distances allowed by the substrate
lattice structure and the average inter--particle distances which minimize the
total interaction energy.
