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Fractional electron loss in approximate DFT and Hartree-Fock theory

Peach, M.J.G.; Teale, A.M.; Helgaker, T.; Tozer, D.J.

Fractional electron loss in approximate DFT and Hartree-Fock theory Thumbnail


M.J.G. Peach

A.M. Teale

T. Helgaker


Plots of electronic energy vs electron number, determined using approximate density functional theory (DFT) and Hartree–Fock theory, are typically piecewise convex and piecewise concave, respectively. The curves also commonly exhibit a minimum and maximum, respectively, in the neutral → anion segment, which lead to positive DFT anion HOMO energies and positive Hartree–Fock neutral LUMO energies. These minima/maxima are a consequence of using basis sets that are local to the system, preventing fractional electron loss. Ground-state curves are presented that illustrate the idealized behavior that would occur if the basis set were to be modified to enable fractional electron loss without changing the description in the vicinity of the system. The key feature is that the energy cannot increase when the electron number increases, so the slope cannot be anywhere positive, meaning frontier orbital energies cannot be positive. For the convex (DFT) case, the idealized curve is flat beyond a critical electron number such that any additional fraction of an electron added to the system is unbound. The anion HOMO energy is zero. For the concave (Hartree–Fock) case, the idealized curve is flat up to some critical electron number, beyond which it curves down to the anion energy. A minimum fraction of an electron is required before any binding occurs, but beyond that, the full fraction abruptly binds. The neutral LUMO energy is zero. Approximate DFT and Hartree–Fock results are presented for the F → F– segment, and results approaching the idealized behavior are recovered for highly diffuse basis sets. It is noted that if a DFT calculation using a highly diffuse basis set yields a negative LUMO energy then a fraction of an electron must bind and the electron affinity must be positive, irrespective of whether an electron binds experimentally. This is illustrated by calculations on Ne → Ne–.

Journal Article Type Article
Acceptance Date Aug 21, 2015
Online Publication Date Oct 8, 2015
Publication Date Nov 10, 2015
Deposit Date Nov 19, 2015
Publicly Available Date Oct 2, 2016
Journal Journal of Chemical Theory and Computation
Print ISSN 1549-9618
Electronic ISSN 1549-9626
Publisher American Chemical Society
Peer Reviewed Peer Reviewed
Volume 11
Issue 11
Pages 5262-5268
Public URL


Accepted Journal Article (478 Kb)

Copyright Statement
This document is the Accepted Manuscript version of a Published Work that appeared in final form in Journal of Chemical Theory and Computation, copyright © American Chemical Society after peer review and technical editing by the publisher. To access the final edited and published work see

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