Uniform Density Limit of Exchange-Correlation Energy Functionals

We present theoretical and practical reasons why a density functional for the exchange-correlation energy should be essentially exact in the uniform density limit. In this limit, the exchange energy is known exactly, and the correlation energy is known to within less than 1 millihartree in the range of valence-electron or lower densities. Some density functionals perform well in this limit, while others do not. Functionals with many parameters fitted to chemical data tend to fail in this limit, and also for real solids. The spin resolution of the correlation energy of the spin-unpolarized uniform electron gas seems simple but unlike that of the widely-used ansatz of Stoll et al., and its low-density limit brings a surprise: a positive parallel-spin contribution in the spin-unpolarized case.