The basicity of framework oxygen atoms in sodium-exchanged zeolites, in particular its dependence on the number and relative position of the aluminum atoms in four- and six-rings of faujasite, has been studied by a gradient-corrected density functional method using cluster models. The most basic oxygen atoms (determined by calculated proton affinities, PA) were found in a six-ring with two aluminum atoms in meta position (903 kJ/mol) and in a four-ring (897 kJ/mol), Exchange of Na+ by K+ increases the PA by about 25 kJ/mol, The PA is influenced primarily by the site potential as manifest by the orbital energies of the oxygen center probed. Similarly to the experimental relationship between the corresponding values for a series of oxygen containing molecules in the gas phase, the calculated PAs and O1s binding energy shifts correlate in a strictly linear fashion. For an increase of the O1s binding energy by 1 eV the PA increases by about 80 kJ/mol, From these findings, we suggest the O1s binding energy shift as a reliable measure of the basicity of oxygen centers, while we found calculated atomic charges to be of little value as basicity criterion, The oxygen position in the ring has a dominant influence on the O1s binding energy (resulting in shifts of up to 3 eV), while changes due to alterations of the Na+ position or the exchange of Na+ by K+ causes shifts of up to 0.4 eV only. The differences in the atomic charges of the oxygen atoms between the various cation positions are rationalized by the change of the external electrostatic potential generated by the cations,