Abstract
Expressions for the kinetic energy (and incidentally also for the exchange energy ) of a ground-state inhomogeneous electron gas as a functional of the electron density , and for as a functional of the one-electron potential , are readily generalized to the case of two unequal spin densities and . As an example the authors consider the expansions of up to fourth order in the gradients of , and of up to fourth order in the gradients of . These expansions are tested for the extreme case of one- and two-electron atoms. It is found that (i) The expansion contains serious pathologies, while the expansion leads to much more reasonable results when applied to either the exact density or to an obtained by minimization of the approximate total-energy functional . (ii) Good approximations to and in one-electron atoms are obtained only when the complete spin polarization of a single electron is taken into account via . (iii) Within a variational calculation, the inclusion of second- and fourth-order gradient corrections to the zeroth-order (Thomas-Fermi) approximation for leads to systematic improvements in the analytic behavior of near the nucleus. The authors also compare the local-exchange approximation with the local-exchange-correlation approximation in one- and two-electron atoms, and find that correlation should not be neglected.
- Received 31 October 1978
DOI:https://doi.org/10.1103/PhysRevA.20.397
©1979 American Physical Society