The influence of the zeolite framework type (FAU, CHA, MOR, MFI) and the crystallographic position on the acidity of zeolites is investigated. The most stable Bronsted acid sites of the high-silica frameworks are considered: O1-H(FAU), O1-H (CHA), A14-O2(H)-Si (MOR), and A17-O17(H)-Si4 (MFI, sinusoidal channel). The latter is compared with the less stable Al12-O24(H)-Si12 position (MFI, channel intersection). Both the heat of the deprotonation and the heat of ammonia adsorption are considered as measures of acid strength. A novel hybrid computational scheme is used that combines the quantum mechanical cluster description (QM) of the active site with interatomic potentials (Pot) for the periodic zeolite framework. Specifically, the Hartree-Fock method (QM) is combined with ab initio shell model potentials (Pot) for the zeolite framework and its interaction with ammonia and ammonium ions. Complete relaxation of the framework is possible within this scheme and long-range corrections to the reaction energies are obtained from the shell model potentials, The total QM-Pot reaction energies are remarkably stable with increasing cluster size. The calculated heats of deprotonation suggest the acidity sequence Y (1171 kJ/mol) > CHA (1190 kJ/mol) > MOR (1195 kJ/mol) > ZSM5 (1200 kJ/mol), which is neither explained by local structure effects nor by crystal potential effects alone. The calculated heats of NH3 adsorption suggest the sequence MOR > CHA approximate to Y > ZSM-5. The different order is caused by specific interactions of NH4+ with the negatively charged catalyst surface. The predicted heats of NH3 adsorption are -119, -114, -113, and -109 kJ/mol, respectively. Comparison is made with microcalorimetry and TPD data.