Extended Hückel methods are known to be a useful tool in understanding surface phenomena. Important quantities about atoms and chemical bonds can be obtained from this computationally simple method, although caution must be exercised in interpreting the results. Application of Extended Hückel calculations to large metal clusters reveals the role of d orbitals in solids. Basic ideas of constructing model compounds have been developed. Several model systems for surface chemisorption processes are constructed in order to understand the surface catalyzed oxidative degradation of polyperfluoroethers. The activation of oxygen molecules can be explained. The Lewis acid character of the iron fluoride surface can be predicted. Based on these results, mechanisms of the degradation processes are discussed.