Scalar potential gauge freedom

Here Axe and are the exchange-correlation scalar and vector potentials of CDFT, respectively. Axe, in particular, is a gauge-invariant functional of the densities (r) and jp(r), written Axe[ , jp](r). By setting Axe = 0, one recovers from CDFT the equations of (S)DFT in an external vector potential A. If observables for Axe = 0, but B = V X A 0, are considered functionals of the external field B, one arrives at a formulation known as BDFT. " The novel feature of CDFT is that Axe accoimts for the orbital degrees of freedom in the single-particle equations, even in the absence of external fields, and allows calculation of orbital currents directly from a set of Kohn-Sham-type equations. 

---