Stochastic model for surface diffusion of organic molecules
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A theoretical model for the diffusion of large molecules adsorbed on surfaces is developed. Starting from the classical equations of motion, a generalized non-Markovian Langevin equation for the center of mass diffusive motion of an adsorbed molecule is derived. In this model, the influence of the background on the molecule is separated into an adiabatic force, and a rapidly fluctuating stochastic force with a corresponding frictional damping term. The model accounts for energy exchange between the center of mass motion and vibrational degrees of freedom of the molecule, and expressions for the friction coefficient in terms of vibrational properties of the molecule and substrate are derived. This stochastic model is first applied to a harmonically bound dimer diffusing in one dimension. This simple model system allows for a systematic test of how the diffusive motion of a molecule is affected by its vibrational degrees of freedom, and specifically how important memory effects are in determining the diffusion coefficient. It is found that coupling to molecular vibrations leads to increased frictional damping and slower diffusion, and that memory effects are typically not important for small molecules, but could be significant in large molecules. The model is then used to study the diffusion of dithioanthracene on a Cu(111) surface. Density functional theory is employed to calculate the adiabatic force and vibrational properties, allowing for a first principles determination of all required quantities in the stochastic model. The diffusion coefficient is calculated and compared to scanning tunnelling microscopy measurements. Reasonable agreement with experiment is obtained, and it is seen that the stochastic model gives an estimate of the diffusion prefactor much closer to the measured value compared to standard transition state theory.