Current Density Functional Theory CDFT

6 Current Density Functional Theory (CDFT). - The Kohn-Sham density functional expression has to be modified when magnetic fields are present so that the density functional depends on the paramagnetic current density. A local exchange-correlation term then has the form 

The theory, known as eurrent density funetional theory (CDFT), has been developed by Vignale et al and applied by Handy and eo-workers.  

3 Review of Literature on Response of Molecules to Magnetic Fields June 

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Since the current density in the bulk measures the surface charges, the time-dependent current-density functional theory (CDFT) appears to be a way to investigate this problem. At least the results presented by de Boeij et al. [171] for the bulk susceptibility and by van Faassen et al. [172] for the polarizability of linear chains are encouraging, although this may not be the case for second-and third-order effects. 

Originally the fourth statement was considered to be as sound as the other three. However, it has become clear very recently, as a consequence of work of Eschrig and Pickett and of Capelle and Vignale, " that there are significant exceptions to it. In fact, the fourth substatement holds only when one formulates DFT exclusively in terms of the charge density, as we have done up to this point. It does not hold when one works with spin densities (spin-density-functional theory, SDFT) or current densities (current-density-functional theory, CDFT). (In Sect. VII we will discuss these formulations of DFT.) In these (and some other) cases the densities still determine the wave function, but they do not uniquely determine the corresponding potentials. This so-called nonuniqueness problem... 

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