On the Chan-Das gauge for the calculation of molecular magnetizabilities

It is proven that the common origin gauge proposed by Chan and Das for the calculation of molecular magnetizabilities within the conventional approach using gaugeless basis sets, i.e., the center of electronic charge, does not minimize the van Vleck paramagnetic contribution to the diagonal tensor components, unless the Arrighini-Maestro-Moccia sum rules for gauge invariance, and charge conservation are satisfied. Additional quantum mechanical constraints for extremum values of formally diamagnetic and paramagnetic contributions have also been obtained for magnetizabilities calculated via procedures allowing for a continuous translation of the origin of the current density.