The Exchange-Correlation Electric Field

For our purpose, the point is that the exchange-correlation electric field is another pathological aspect of the exact Kohn-Sham xc functional the 

If the ground-state were a triplet we should use the extension of KS-DFT to spin polarised systems, but in this case the pathology we are describing will not appear. 

In reciprocal space, Ghosez et al. [67] showed that the xc field corresponds to a 1/q divergence in the exchange-correlation kernel for small wavevectors q. This ultra-non-local density dependence is certainly missing from all density based approximations to the exact xc functional, potential or kernel. One possibility for approximating it within Kohn-Sham DFT has been explored recently by de Boeij et al. [68] by using a functional of the current rather than the density, in the low-frequency limit of time-dependent DFT. 

That is, mathematically non-local but with the range of the non-locality restricted to a few angstroms. 

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