Density-Functional Theory for Fractional Particle Number: Derivative Discontinuities of the Energy

The Hohenberg-Kohn theorem is extended to fractional electron number $N$, for an isolated open system described by a statistical mixture. The curve of lowest average energy ${E}_{N}$ versus $N$ is found to be a series of straight line segments with slope discontinuities at integral $N$. As $N$ incre... View More