A gradient expansion of the electronic current in the electron density is used to obtain expressions for the magnetic susceptibity and chemical shielding. The first term in the expansion is the Thomas Fermi expression. All succeeding terms diverge for both properties. A renormalized functional is used which removes the divergences and gives asymptotic diamagnetism. A single parameter which depends linearly on the number of electrons gives all heavy rare gas susceptibities to within 1% of exact calculation using the same electron density, Similar results are found for the chemical shielding. Susceptibility and shielding calculations for the helium dimer and the hydrogen molecule in singlet and triplet states are presented. The results are compared with other calculations over a full range of internuclear distances. (C) 1997 American Institute of Physics.