Some pointers towards a future orbital-free density functional theory of inhomogeneous electron liquids

Abstract

Recent work by Gál and March has been concerned with a model two-electron atom in which electron-nuclear Coulomb attraction is replaced by harmonic confinement. Furthermore, the interfermion interaction u(r 12) between electrons at separation r 12 is taken to be of inverse square form With these model simplifications, it then proves possible to obtain an exact analytical expression for the ground-state energy density functional. Turning to current usage of density functional theory of inhomogeneous Fermion liquids, in terms of a one-body potential V(r), the single-particle (s) kinetic energy functional T s[n] is next considered, for the experimentally interesting case of ultracold Fermion vapours which are magnetically trapped. This is again the case of harmonic confinement. Results for T s[n] for different dimensionalities have been obtained analytically for such systems and are summarized. The intimate relationship between this kinetic energy T s and the exchange energy E x is then exhibited, the off-diagonal density, or idempotent Dirac density matrix now being invoked. In turn this latter quantity can be related to the ground-state density n(r) via a partial differential equation. Finally, some brief discussion is given of the, as yet unsolved, problem of the electron–electron correlation energy.