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

Publisher Website

6 December 1982

journal article
research article
Published by American Physical Society (APS) in Physical Review Letters

Vol. 49 (23) , 1691-1694
https://doi.org/10.1103/physrevlett.49.1691

Abstract

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

increases through an integer

M

, the chemical potential and the highest occupied Kohn-Sham orbital energy both jump from

E_{M} - E_{M - 1}

to

E_{M + 1} - E_{M}

. The exchange-correlation potential

\frac{δ E_{xc}}{δ n (\vec{r})}

jumps by the same constant, and

\frac{\lim_{r \to \infty} δ E_{xc}}{δ n (\vec{r})} >~ 0

.

Keywords

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