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A representation of the exchange energy functional as the product of a homogeneous gas functional and a rational function approximation in the density gradient is developed and shown to describe accurately both the total exchange energy and the local exchange energy density of atomic systems. For the atoms H through Kr, the error in the total exchange energy is generally 0.02 hartree except for Cr through Zn where it is 0.21 hartree.
DePristo et al. (Sun,) studied this question.