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m Bot: Migrating 5 interwiki links, now provided by Wikidata on d:q898241 (Report Errors) |
m →Spin polarization: WP:CHECKWIKI errors fixed + general fixes using AWB (8961) |
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:<math>E_{xc}^{\mathrm{LSDA}}[\rho_{\alpha},\rho_{\beta}] = \int\mathrm{d}\mathbf{r}\ \rho(\mathbf{r})\epsilon_{xc}(\rho_{\alpha},\rho_{\beta})\ .</math>
For the exchange energy, the exact result (not just for local density approximations) is known in terms of the spin-unpolarized functional:<ref>{{cite journal|last=Oliver|first=G. L.|coauthors=Perdew, J. P. |year=1979|title=Spin-density gradient expansion for the kinetic energy|journal=Phys. Rev. A|volume=20|pages=397–403|doi=10.1103/PhysRevA.20.397|bibcode = 1979PhRvA..20..397O|issue=2 }}</ref>
:<math>E_{x}[\rho_{\alpha},\rho_{\beta}] = \frac{1}{2}\bigg( E_{x}[2\rho_{\alpha}] + E_{x}[2\rho_{\beta}] \bigg)\ .</math>
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