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Relativistic density-functional theory based on effective quantum electrodynamics

by Julien Toulouse

This Submission thread is now published as

Submission summary

Authors (as registered SciPost users): Julien Toulouse
Submission information
Preprint Link: scipost_202102_00027v2  (pdf)
Date accepted: 2021-05-06
Date submitted: 2021-04-29 21:38
Submitted by: Toulouse, Julien
Submitted to: SciPost Chemistry
Ontological classification
Academic field: Chemistry
  • Atomic, Molecular and Optical Physics - Theory
  • Theoretical and Computational Chemistry
Approach: Theoretical


A relativistic density-functional theory based on 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.

Author comments upon resubmission

Dear Editor,

I thank both referees for the reports and suggestions. I have revised the manuscript accordingly.
I hope that the revised manuscript is suitable for publication in SciPost Chemistry.
Julien Toulouse

List of changes

- The fact that the present theory is not Lorentz invariant has been added in Section 2.2.

- The explanation for using the opposite charge density has been added in Section 2.2.

- This explanation for why we consider only an external scalar potential has been added in Section 2.2.

- Some information about the Hartree-exchange-correlation potential has been added in Section 3.1 and 3.2.

- A discussion about the use of the absolute value of the charge density in the LDA functional has been added in Section 3.5.

- The fact that a practical implementation would require the development of regularization/renormalization procedures has been added in the Conclusions.

- Some language inconsistencies and typos have been corrected.

- In addition, a few very minor improvements have been done in various places of the manuscript.

Published as SciPost Chem. 1, 002 (2021)

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