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Relativistic density-functional theory based on effective quantum electrodynamics

by Julien Toulouse

Submission summary

As Contributors: Julien Toulouse
Preprint link: scipost_202102_00027v1
Date submitted: 2021-02-18 22:23
Submitted by: Toulouse, Julien
Submitted to: SciPost Chemistry
Academic field: Chemistry
  • Atomic, Molecular and Optical Physics - Theory
  • Theoretical and Computational Chemistry
Approach: Theoretical


A relativistic density-functional theory based a Fock-space effective quantum-electrodynamics (QED) Hamiltonian using the Coulomb or Coulomb-Breit two-particle interaction is developed. This effective QED theory properly includes the effects of vacuum polarization through the creation of electron-positron pairs but does not include explicitly the photon degrees of freedom. It is thus a more tractable alternative to full QED for atomic and molecular calculations. Using the constrained-search formalism, a Kohn-Sham scheme is formulated in a quite similar way to non-relativistic density-functional theory, and some exact properties of the involved density functionals are studied, namely charge-conjugation symmetry and uniform coordinate scaling. The usual no-pair Kohn-Sham scheme is obtained as a well-defined approximation to this relativistic density-functional theory.

Current status:
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Submission scipost_202102_00027v1 on 18 February 2021

Reports on this Submission

Anonymous Report 1 on 2021-4-1 Invited Report


1 - I very much appreciate that the author in appendices A and B successively demonstrate that the effective QED Hamiltonian (7) possess the correct charge-conjugation symmetry and is equivalent to an alternative Hamiltonian that has been promoted in recent literature.
2 - Focus of the paper is on a relativistic formulation of density-functional theory, but foundations for wave function (or more correctly Fock space)-based theory is given as well.
3 - The DFT section provides foundations as well as important relations for relativistic DFT based on the effective QED Hamiltonian (7).
4 - The author points issues that need further study.
5 - The authors provides a rich bibliography and appears to me fair in his appreciation of these.


Some points need possibly further sharpening:
1 - First of all, this is not relativistic theory, in the sense of being Lorentz covariant, but rather adheres the pragmatic spirit in which relativistic molecular calculations are carried out presently. This could perhaps be stressed further.
2 - A practical realization of the present work will require the development for the practical realization of regularisation/renormalization procedures.
3 - The authors refers to (opposite) charge for several quantities. This could perhaps be discussed briefly.
4-This is a single author paper. The author adheres to the use of "we", following common practice, but on pages 2, 22 and 25 refers to "my knowledge". I advice being consisten.


This is an absolutely outstanding paper, a veritable treasure trove of important results, which should have very significant impact on the domain of relativistic molecular applications.

Requested changes

The paper can be published as it, but the author should consider the polish suggested above.

  • validity: top
  • significance: top
  • originality: top
  • clarity: top
  • formatting: excellent
  • grammar: excellent

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