The calculation of diffusion coefficients for technical important molecules (e.g. linear and branched alkanes) under rare event conditions is still a great challenge. Other problems are the still unsolved question whether rigid or flexible walls have to be employed in calculations of diffusivities and multicomponent adsorption isotherms of zeolites and carbon nanotubes. In the first period of funding significant progress in respect of these problems could be made. The results were published or submitted for publication in several papers. An extension of the transition state theory was developed that is capable of computing quantitatively the diffusivity of adsorbed molecules in confined systems at nonzero loading. While molecular dynamic simulations are limited to relatively fast diffusion molecules or small rigid molecules, our approach extends the range of accessible time scales significantly beyond currently available methods. It is applicable to any system containing free energy barriers and to any type of guest molecules. A further investigation was directed towards the influence of flexible walls on self-diffusion in a single walled carbon nanotube. We could demonstrate that the flexibility has a crucial influence on self-diffusion at low loadings. We showed how this influence can be incorporated in a simulation of a rigid nanotube by using a Lowe-Andersen thermostat which works on interface-fluid collisions. This approach accelerated the simulations considerably.