We report high quality B3LYP Ab Initio studies of the electric dipole polarizability of three related series of molecules: para-XC6H4Y, XC6H4CH=CHC6H4Y and XC6H4N=NC6H4Y, where X and Y represent H together with the six various activating through deactivating groups NH2, OH, OCH3, CHO, CN and NO2. Molecules for which X is activating and Y deactivating all show an enhancement to the mean polarizability compared to the unsubstituted molecule, in accord with the order given above. A number of representative Ab Initio calculations at different levels of theory are discussed for azoarene; all subsequent Ab Initio polarizability calculations were done at the B3LYP/6-311G(2d,1p)//B3LYP/6-311++G(2d,1p) level of theory. We also consider semi-empirical polarizability and molecular volume calculations at the AM1 level of theory together with QSAR-quality empirical polarizability calculations using Miller's scheme. Least-squares correlations between the various sets of results show that these less costly procedures are reliable predictors of <α> for the first series of molecules, but less reliable for the larger molecules.