Exchange-correlation energy limit

Uniform Density Limit of Exchange-Correlation Energy Functionals... 

In the low-density limit, the parallel-spin and anti-parallel-spin exchange-correlation energies are equal [57] because this is a classical limit in which spin... 

Figure 7 is a plot of Fxc in the LSD approximation. The curves are horizontal lines in this case, as the LSD approximation is independent of the local gradient. However, only in the high density limit, rs = 0, is Fxc = 1, because this is where exchange dominates. The increase in Fxc beyond 1 for finite values of rB represents the correlation contribution to the exchange-correlation energy. The LSD approximation obeys all the conditions of section 2 except Eqs. (39), (40), (44), (45), and (47), because it approximates the hole by a hole taken from another physical system. 

If ab initio is taken to mean that the method is based on theory, which in principle is able to produce the exact results, DFT methods are ab initio. The only caveat is that current methods cannot yield the exact results, even in the limit of a complete basis set, since the functional form of the exact exchange-correlation energy is not known. At present it is easier to systematically improve on a wave function description than adding corrections to the energy functional in DFT. Methods using reduced density matrices are still in their infancy, but promising results have been obtained in recent years. 

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