Abstract
Although every stationary-state density (r→) of a many-particle system is not an extremum of the ground-state density functional [n], every extremum of [n] [i.e., every solution of the Euler equation δ/δn(r→)=λ] is a stationary-state density (r→). Always, []≤, where is the lowest stationary-state energy for density (r→); the equality holds if and only if (r→) is an extremum of [n]. The extrema lying above the absolute minimum are excited-state densities which fail to be pure-state v-representable. Surprisingly, infinitesimal number-conserving density variations δn(r→) about an extremum n(r→) do not lead to energy variations δ of order (δn when δn(r→)/(r→) fails to be square-integrable; in fact, variations δ of order ‖δn‖ about the ground state are exemplified by the recently discovered ‘‘derivative discontinuities of the energy.’’ This unconventional behavior of [n] may be traced in part to an asymptotic divergence of /δn(r→)δn(r→’). Conditions are presented under which a self-consistent solution of the Kohn-Sham single-particle problem represents an extremum of [n]. The multiplets of the ground-state orbital configuration of the carbon atom are examined. The local-density and Langreth-Mehl approximations are found to yield a remarkably accurate account of the degeneracy of the various ground-state densities for this system, but no estimate of the multiplet splitting is obtained. Finally, aspects of v-representability are discussed, with emphasis on the iron atom.
- Received 18 January 1985
DOI:https://doi.org/10.1103/PhysRevB.31.6264
©1985 American Physical Society