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Accurate [[quantum Monte Carlo]] simulations for the energy of the HEG have been performed for several intermediate values of the density, in turn providing accurate values of the correlation energy density.<ref>{{cite journal | title = Ground State of the Electron Gas by a Stochastic Method | author = D. M. Ceperley and B. J. Alder | journal = Phys. Rev. Lett. | volume = 45 | pages = 566–569 | year = 1980 | doi = 10.1103/PhysRevLett.45.566 }}</ref> The most popular LDA's to the correlation energy density interpolate these accurate values obtained from simulation while reproducing the exactly known limiting behavior. Various approaches, using different analytic forms for ''ε''<sub>c</sub>, have generated several LDA's for the correlation functional, including
* Vosko-Wilk-Nusair (VWN) <ref name="vwn">{{cite journal | title = Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis | author = S. H. Vosko, L. Wilk and M. Nusair | journal = Can. J. Phys. | volume = 58 | pages = 1200 | year = 1980 | doi = 10.1139/p80-159 }}</ref>
* Perdew-Zunger (PZ81) <ref>{{cite journal | title = Self-interaction correction to density-functional approximations for many-electron systems | author = J. P. Perdew and A. Zunger | journal = Phys. Rev. B | volume = 23 | pages = 5048 | year = 1981 | doi = 10.1103/PhysRevB.23.5048 }}</ref>
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