Lean NOx Trap (LNT) catalysts, a promising solution for reducing the noxious nitrogen oxide emissions from the lean burn and Diesel engines, are technologically limited by the presence of sulfur in the exhaust gas stream. Sulfur stemming from both fuels and lubricating oils is oxidized during the combustion event and mainly exists as SOx (SO2 and SO3) in the exhaust. Sulfur oxides interact strongly with the NOx trapping material of a LNT to form thermodynamically favored sulfate species, consequently leading to the blockage of NOx sorption sites and altering the catalyst operation. Molecular and kinetic modeling represent a valuable tool for predicting system behavior and evaluating catalytic performances. The present paper demonstrates how fundamental ab initio calculations can be used as a valuable source for designing kinetic models developed in the IFP Exhaust library, intended for vehicle simulations. The concrete example we chose to illustrate our approach was SO3 adsorption on the model NOx storage material, BaO. SO3 adsorption was described for various sites (terraces, surface steps and kinks and bulk) for a closer description of a real storage material. Additional rate and sensitivity analyses provided a deeper understanding of the poisoning phenomena.