The ground-state wave function of a strongly interacting electron system is strongly correlated, a situation far away from a wave function with single- particle orbitals (Slater determinant) which describes non-interacting electrons. In density functional theory, this strong-interaction limit is reached in a continuous series of ground-state wave functions $\Psi_\alpha[\rho]$ that are all associated with the same given particle density $\rho({\bf r})$, but where the Coulomb repulsion between the electrons is multiplied by a constant parameter $\alpha\ge0$. In the very limit $\alpha\to\infty$, this wave function describes a state of stricly correlated electrons (SCE). This SCE wave function may be viewed as the logical complement to the familiar concept of a Slater determinant. The SCE concept is illustrated here for one-dimensional (1D) $N$ electron systems as well as for 3D ones with spherical symmetry. The general relevance of this concept for electronic structure calculations of strongly correlated systems will be the subject of the subsequent talk. As a simple application, the SCE concept is used here to challenge the Lieb-Oxford bound.
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