Breakdown of the ionization potential theorem of density functional theory in mesoscopic systems

Vladimir U. Nazarov*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

The ionization potential (IP)-theorem of Kohn-Sham (KS) density functional theory (DFT) states that the energy of the highest occupied molecular orbital (HOMO) ϵHOMO equals the negative of the first IP, thus ascribing a physical meaning to one of the eigenvalues of the KS Hamiltonian. We scrutinize the fact that the validity of the IP-theorem relies critically on the electron density n(r), far from the system, to be determined by HOMO only, behaving as n(r)∼r→∞e-2-2ϵHOMOr. While this behavior always holds for finite systems, it does not hold for mesoscopic ones, such as quasi-two-dimensional (Q2D) electron gas or Q2D crystals. We show that this leads to the violation of the IP-theorem for the latter class of systems. This finding has a strong bearing on the role of the KS valence band with respect to the work-function problem in the mesoscopic case. Based on our results, we introduce a concept of the IP band structure as an observable alternative to its unphysical KS counterpart. A practical method of the determination of the IP band structure in terms of DFT quantities is provided.

Original languageAmerican English
Article number194105
JournalJournal of Chemical Physics
Volume155
Issue number19
DOIs
StatePublished - 21 Nov 2021
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2021 Author(s).

Fingerprint

Dive into the research topics of 'Breakdown of the ionization potential theorem of density functional theory in mesoscopic systems'. Together they form a unique fingerprint.

Cite this