The exchange-energy density of a HEG is known analytically. The LDA for exchange employs this expression under the approximation that the exchange-energy in a system where the density inis not homogeneous, is obtained by applying the HEG results pointwise, yielding the expression<ref name="parryang">{{cite book|last=Parr|first=Robert G|author2=Yang, Weitao |title=Density-Functional Theory of Atoms and Molecules|publisher=Oxford University Press|___location=Oxford |year=1994|isbn=978-0-19-509276-9}}</ref><ref>{{cite journal|last=Dirac|first=P. A. M.|year=1930|title=Note on exchange phenomena in the Thomas-Fermi atom|journal=Proc. Cambridge Phil. Roy. Soc.|volume=26|pages=376–385|doi=10.1017/S0305004100016108|issue=3|bibcode = 1930PCPS...26..376D }}</ref>
