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

Yuli Goshen, Eli Kraisler*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Description of many-electron systems with a fractional electron number (Ntot) and fractional spin (Mtot) 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 Ntot and Mtot, 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. We find a new derivative discontinuity, which manifests for spin variation at a constant Ntot, as a jump in the Kohn-Sham potential. We identify a previously unknown degeneracy of the ground state, such that the total energy and density are unique, but the spin-densities are not. Our findings serve as a basis for development of advanced approximations in density functional theory and other many-electron methods.

Original languageAmerican English
Pages (from-to)2337-2343
Number of pages7
JournalJournal of Physical Chemistry Letters
Volume15
DOIs
StatePublished - 2024

Bibliographical note

Publisher Copyright:
© 2024 The Authors. Published by American Chemical Society.

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