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Local-density approximations are important in the construction of more sophisticated approximations to the exchange-correlation energy, such as [[generalized gradient approximation]]s (GGA) or [[hybrid functional]]s, as a desirable property of any approximate exchange-correlation functional is that it reproduce the exact results of the HEG for non-varying densities. As such, LDA's are often an explicit component of such functionals.
The local-density approximation was first introduced by [[Walter Kohn]] and [[Lu Jeu Sham]] in 1965.<ref name=":0" />
== Applications ==
Local density approximations, as with GGAs are employed extensively by [[solid-state physics|solid state physicists]] in ab-initio DFT studies to interpret electronic and magnetic interactions in semiconductor materials including semiconducting oxides and [[spintronics]]. The importance of these computational studies stems from the system complexities which bring about high sensitivity to synthesis parameters necessitating first-principles based analysis. The prediction of [[Fermi level]] and band structure in doped semiconducting oxides is often carried out using LDA incorporated into simulation packages such as CASTEP and DMol3.<ref>{{cite journal| last1=Segall| first1=M.D.| last2=Lindan| first2=P.J | title= First-principles simulation: ideas, illustrations and the CASTEP code | journal= Journal of Physics: Condensed Matter | year= 2002| volume=14| issue=11| pages=2717|bibcode = 2002JPCM...14.2717S |doi = 10.1088/0953-8984/14/11/301 | s2cid=250828366}}</ref> However an underestimation in [[Band gap]] values often associated with LDA and [[Density functional theory#Approximations (exchange–correlation functionals)|GGA]] approximations may lead to false predictions of impurity mediated conductivity and/or carrier mediated magnetism in such systems.<ref>{{cite journal| last1=Assadi| first1=M.H.N| title= Theoretical study on copper's energetics and magnetism in TiO<sub>2</sub> polymorphs| journal= Journal of Applied Physics | year=2013| volume=113| issue=23| pages= 233913–233913–5| doi=10.1063/1.4811539|arxiv = 1304.1854 |bibcode = 2013JAP...113w3913A | s2cid=94599250|display-authors=etal}}</ref> Starting in 1998, the application of the [[Rayleigh theorem for eigenvalues]] has led to mostly accurate, calculated band gaps of materials, using LDA potentials.<ref>{{Cite journal|last1=Zhao|first1=G. L.|last2=Bagayoko|first2=D.|last3=Williams|first3=T. D.|date=1999-07-15|title=Local-density-approximation prediction of electronic properties of GaN, Si, C, and RuO2|journal=Physical Review B|volume=60|issue=3|pages=1563–1572|doi=10.1103/physrevb.60.1563|bibcode=1999PhRvB..60.1563Z |issn=0163-1829}}</ref><ref name=":0">{{Cite journal|last=Bagayoko|first=Diola|date=December 2014|title=Understanding density functional theory (DFT) and completing it in practice|journal=AIP Advances|volume=4|issue=12|pages=127104|doi=10.1063/1.4903408|bibcode=2014AIPA....4l7104B |issn=2158-3226|doi-access=free}}</ref> A misunderstanding of the second theorem of DFT appears to explain most of the underestimation of band gap by LDA and GGA calculations, as explained in the description of [[density functional theory]], in connection with the statements of the two theorems of DFT.
== Homogeneous electron gas ==
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