Conventional cluster models of strong and medium strength Lewis acid sites in alumina and zeolites, three-coordinate [Al(OH)(3)] and five-coordinate [Al(OH)(3)(OH2)(2)] respectively, are studied with the help of a density functional method. A constraint space orbital variation analysis reveals that the charge transfer from probe CO molecules adsorbed on cationic Al centre and the CO polarization comprise essential contributions to the adsorption energy D-e. An analysis of the adsorption-induced C-O frequency shift Delta omega(C-O) is also provided. Structural modifications of the Lewis acid sites are considered with respect to their influence on D-e and Delta omega(C-O). A comparison of the measured and calculated C-O frequency shifts supports a hypothesis on the existence of Lewis acid sites in oxides in the form of four-coordinate Al cations.