Exchange energy in Kohn-Sham density-functional theory

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Abstract
The development of a family of functionals of the electronic density and its first and second derivatives is described. These functionals contain correct contributions to the exchange energy from regions far from the nuclei of an atom or molecule, and simultaneously give rise to a Kohn-Sham potential that is asymptotically correct in these regions. However, numerical studies show that none of the functionals can give accurate exchange energies, and the reasons for this deficiency can be traced to an instability with respect to density fluctuations arising from the use of the Laplacian of the density.