Ensemble Ground State of a Many-Electron System with Fractional Electron Number and Spin: Piecewise-Linearity and Flat-Plane Condition Generalized.

Description of many-electron systems with a fractional electron number () and fractional spin () is of great importance in physical chemistry, solid-state physics, and materials science. In this Letter, we provide an exact description of the zero-temperature ensemble ground state of a general, finite, many-electron system and characterize the dependence of the energy and the spin-densities on both and , when the total spin is at its equilibrium value. We generalize the piecewise-linearity principle and the flat-plane condition and determine which pure states contribute to the ground-state ensemble.

Ionization potentials and fundamental gaps in atomic systems from the Ensemble-DFT approach.

Calculations in Kohn-Sham density functional theory crucially rely on high-quality approximations for the exchange-correlation (xc) functional. Standard local and semi-local approximations fail to predict the ionization potential (IP) and the fundamental gap, departing from the Kohn-Sham orbital energies, due to the deviation of the total energy from piecewise-linearity and the absence of the derivative discontinuity. The ensemble generalization procedure introduced in Phys.