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m Make it clear that the electron density depends on the position |
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In general, for a spin-unpolarized system, a local-density approximation for the exchange-correlation energy is written as
:<math>E_{xc}^{\mathrm{LDA}}[\rho] = \int \rho(\mathbf{r})\epsilon_{xc}(\rho(\mathbf{r}))\ \mathrm{d}\mathbf{r}\ ,</math>
where ''ρ'' is the [[electronic density]] and ''ε''<sub>xc</sub> is the exchange-correlation energy per particle of a [[homogeneous electron gas]] of charge density ''ρ''. The exchange-correlation energy is decomposed into exchange and correlation terms linearly,
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