Langevin equation for diffusion of an adsorbed molecule

Starting from a microscopic classical mechanical model of adsorbed atoms, a set of coupled Langevin equations for the motion of the atoms can be derived [1]. For the situation where the adsorbed atoms form a stable molecule, we reduce this set of coupled equations to a one-dimensional Langevin equation for the molecule by confining the motion to the lowest energy paths between adsorption sites, thus reducing the multidimensionality of the problem. Comparing our results with previous calculations for a stiff dimer in one dimension, we find that our approach provides significant corrections to the diffusion coefficient prefactor. Finally, we extend the calculation to the case where the dimer can rotate in the direction perpendicular to the surface, allowing also for multiple diffusion paths.