Tilted-Plane Structure of the Energy of Finite Quantum Systems.

The piecewise linearity condition on the total energy with respect to the total magnetization of finite quantum systems is derived using the infinite-separation-limit technique. This generalizes the well-known constancy condition, related to static correlation error, in approximate density functional theory. The magnetic analog of Koopmans' theorem in density functional theory is also derived.

The convexity condition of density-functional theory.

It has long been postulated that within density-functional theory (DFT), the total energy of a finite electronic system is convex with respect to electron count so that 2Ev[N0] ≤ Ev[N0 - 1] + Ev[N0 + 1]. Using the infinite-separation-limit technique, this Communication proves the convexity condition for any formulation of DFT that is (1) exact for all v-representable densities, (2) size-consistent, and (3) translationally invariant. An analogous result is also proven for one-body reduced density matrix functional theory.