{"doi":"10.1103/physrevb.45.13244","title":"Accurate and simple analytic representation of the electron-gas correlation energy","abstract":"We propose a simple analytic representation of the correlation energy ${\\mathrm{\\ensuremath{\\varepsilon}}}_{\\mathit{c}}$ for a uniform electron gas, as a function of density parameter ${\\mathit{r}}_{\\mathit{s}}$ and relative spin polarization \\ensuremath{\\zeta}. Within the random-phase approximation (RPA), this representation allows for the ${\\mathit{r}}_{\\mathit{s}}^{\\mathrm{\\ensuremath{-}}3/4}$ behavior as ${\\mathit{r}}_{\\mathit{s}}$\\ensuremath{\\rightarrow}\\ensuremath{\\infty}. Close agreement with numerical RPA values for ${\\mathrm{\\ensuremath{\\varepsilon}}}_{\\mathit{c}}$(${\\mathit{r}}_{\\mathit{s}}$,0), ${\\mathrm{\\ensuremath{\\varepsilon}}}_{\\mathit{c}}$(${\\mathit{r}}_{\\mathit{s}}$,1), and the spin stiffness ${\\mathrm{\\ensuremath{\\alpha}}}_{\\mathit{c}}$(${\\mathit{r}}_{\\mathit{s}}$)=${\\mathrm{\\ensuremath{\\partial}}}^{2}$${\\mathrm{\\ensuremath{\\varepsilon}}}_{\\mathit{c}}$(${\\mathit{r}}_{\\mathit{s}}$, \\ensuremath{\\zeta}=0)/\\ensuremath{\\delta}${\\mathrm{\\ensuremath{\\zeta}}}^{2}$, and recovery of the correct ${\\mathit{r}}_{\\mathit{s}}$ln${\\mathit{r}}_{\\mathit{s}}$ term for ${\\mathit{r}}_{\\mathit{s}}$\\ensuremath{\\rightarrow}0, indicate the appropriateness of the chosen analytic form. Beyond RPA, different parameters for the same analytic form are found by fitting to the Green's-function Monte Carlo data of Ceperley and Alder [Phys. Rev. Lett. 45, 566 (1980)], taking into account data uncertainties that have been ignored in earlier fits by Vosko, Wilk, and Nusair (VWN) [Can. J. Phys. 58, 1200 (1980)] or by Perdew and Zunger (PZ) [Phys. Rev. B 23, 5048 (1981)]. While we confirm the practical accuracy of the VWN and PZ representations, we eliminate some minor problems with these forms. We study the \\ensuremath{\\zeta}-dependent coefficients in the high- and low-density expansions, and the ${\\mathit{r}}_{\\mathit{s}}$-dependent spin susceptibility. We also present a conjecture for the exact low-density limit. The correlation potential ${\\mathrm{\\ensuremath{\\mu}}}_{\\mathit{c}}^{\\mathrm{\\ensuremath{\\sigma}}}$(${\\mathit{r}}_{\\mathit{s}}$,\\ensuremath{\\zeta}) is evaluated for use in self-consistent density-functional calculations.","journal":"Physical Review B","year":1992,"id":4090,"datarank":22.758310177151454,"base_score":10.119364767858293,"endowment":10.119364767858293,"self_citation_contribution":1.5179047151787441,"citation_network_contribution":21.24040546197271,"self_endowment_contribution":1.5179047151787441,"citer_contribution":21.24040546197271,"corpus_percentile":99.1,"corpus_rank":179,"citation_count":24818,"citer_count":185,"citers_with_citation_signal":185,"citers_with_endowment":185,"datacite_reuse_total":0,"is_dataset":false,"is_oa":false,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":"1992-06-15","authors":[{"id":19081,"name":"Yue Wang","orcid":"0000-0002-0278-2347","position":1,"is_corresponding":false},{"id":5717,"name":"John P. Perdew","orcid":"0000-0003-4237-824X","position":0,"is_corresponding":true}],"reference_count":24,"raw_metadata":{"citation_network_status":"fetched"},"created_at":"2026-03-01T18:20:47.508186Z","pmid":null,"pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}