Abstract
Kohn-Sham density functional theory provides a usefully-accurate description for the ground-state electron density \({\text{n}}\left( {\mathop {\text{r}}\limits_ \sim } \right) \) and energy E of a many-electron system. The exchange-correlation energy has a hierarchy of density functional approximations for a system of slowly-varying electron density. The simplest, the local spin density (LSD) approximations, is reasonably good for real systems. However, the second-order gradient expansion (GEA) is typically worse, due to violation of exact properties which LSD respects. Real-space cutoff of the spurious long-range part of the GEA exchange-correlation hole, with cutoff radii chosen to restore those exact properties, leads to a nonempirlpal generalized gradient approximation (GGA) of the form EXC = ∫d3r f (n↑ n↓, ▽n↑, ▽n↓), which is almost as simple as LSD but usually more accurate. A possible rationale is presented for the successes and failures of GGA.
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Perdew, J.P. (1995). Density Gradient Expansion of the Electronic Exchange-Correlation Energy, and its Generalization. In: Gross, E.K.U., Dreizler, R.M. (eds) Density Functional Theory. NATO ASI Series, vol 337. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-9975-0_4
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