Gauge invariant calculation of magnetic properties from time-dependent current DFT*

We present a method to calculate magnetic properties from the current density that does not depend on the gauge choice for the vector potential when a finite basis set is used [1]. To obtain this we put paramagnetic and diamagnetic contributions to the current on equal footing by making use of a sum rule [1]. Our method is general. Here we use it to calculate static and dynamical magnetizabilities of molecules within Time-Dependent Current-Density-Functional Theory. \\[4pt] [1] N. Raimbault, P.L. de Boeij, P. Romaniello, and J.A. Berger, submitted