Relevance of the Slowly Varying Electron Gas to Atoms, Molecules, and Solids

We present a Thomas-Fermi-inspired density scaling under which electron densities of atomic, molecular, or condensed matter become both large and slowly varying, so that semiclassical approximations and second-order density gradient expansions are asymptotically exact for the kinetic and exchange energies. Thus, even for atoms and molecules, density-functional approximations should recover the universal second-order gradient expansions in this limit. We also explain why common generalized gradient approximations for exchange do not.

Figure 1

Scaled radial density of He atom.

Figure 2

Reduced density gradient for noble gas atoms.

Figure 3

Radial exchange energy density differences for Xe for different approximations (atomic units).

Figure 4

Scaled correlation energies for noble gas atoms (Hartree). The dashed lines correspond to the high-density limit of Eq. (5) for LDA (lower) and PBE (upper curve).